Valuing Environmental Health Risk Reductions to Children a Workshop Sponsored by the US Environmental Protection Agency’s National Center for Environmental Economics (NCEE) National Center for Environmental Research (NCER) and Office of Children’s Health Protection; and the University of Central Florida October 20-21 2003


Valuing Environmental Health Risk Reductions to Children
OPENING REMARKS BY
MARIANNE L. HORINKO
ACTING ADMINISTRATOR OF THE U.S. ENVIRONMENTAL PROTECTION AGENCY
A WORKSHOP SPONSORED BY THE U.S. ENVIRONMENTAL PROTECTION AGENCY'S NATIONAL
CENTER FOR ENVIRONMENTAL ECONOMICS (NCEE), NATIONAL CENTER FOR ENVIRONMENTAL
RESEARCH (NCER), AND OFFICE OF CHILDREN'S HEALTH PROTECTION; AND THE UNIVERSITY OF
CENTRAL FLORIDA
October 20-21, 2003
Washington Plaza Hotel
Washington, DC
Prepared by Alpha-Gamma Technologies, Inc.
4700 Falls of Neuse Road, Suite 350, Raleigh, NC 27609

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ACKNOWLEDGEMENTS
This report has been prepared by Alpha-Gamma Technologies, Inc. with funding from the National Center for
Environmental Economics (NCEE). Alpha-Gamma wishes to thank NCEE's Kelly Maguire and Project Officer Nicole
Owens for their guidance and assistance throughout this project.
DISCLAIMER
These proceedings are being distributed in the interest of increasing public understanding and knowledge of the issues
discussed at the workshop and have been prepared independently of the workshop. Although the proceedings have been
funded in part by the United States Environmental Protection Agency under Contract No. 68-W-01-055 to Alpha-
Gamma Technologies, Inc., the contents of this document may not necessarily reflect the views of the Agency and no
official endorsement should be inferred.
2

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Remarks for Marianne L. Horinko
Acting Administrator of the U.S. Environmental Protection Agency
at the
Valuing Environmental Health Risk Reductions to Children Forum
Washington, D.C.
October 20, 2003
Thank you, Jessica (Furey), for that introduction. It is a pleasure to be here with you for
the 9th Economy and Environment workshop - again highlighting a great partnership between
EPA's Office of Policy, Economics and Innovation, Office of Research and Development, and
our co-sponsors, the Office of Children's Health Protection and the University of Central
Florida. For the second time, this series will focus on the importance of children's health
protection - a topic that we are taking very seriously at EPA, especially as we recognize
Children's Health Month during October. This month - and this forum - are excellent
opportunities for us to discuss how we can use economic analyses to improve our decision
making in the areas that affect children's health.
I'm not an economist, but those at EPA who are tell me that "environmental economists"
approach the problem of valuing health risk reductions differently than "public health
economists." I suspect that is true for children's risks as well, and it brings to mind what George
Bernard Shaw once said: "If all economists were laid end to end they would not reach a
conclusion." While they may not agree on a conclusion, economists provide vital information
that informs policy decisions throughout the agency.
At EPA we consider economics a science, just as biology, toxicology, and chemistry are
sciences. And, it is critical that we produce sound science that will help lead to quality
decisions. Part of the scientific process is to engage in debate and disagreement. That is how
progress is made, and it is why we are here. I encourage you to continue to engage on these
critical issues, even when serious disagreement exists among - and within - branches of
economics.
I will admit that I am frustrated when our economists say we lack the methods and
research necessary to value specific benefit categories. Often times we use proxies or no
valuation at all. We have to change that, and your work is crucial to gaining the information we
need to do so. Your research provides the underlying information needed to support sound
analyses and decision making. I am proud that our STAR grants program in the Office of
Research and Development provides support to some of you to help us fill these critical
knowledge gaps.
In the end, of course, there is far more agreement than disagreement. Indeed, the
underpinnings of benefit-cost analysis, discounting, willingness-to-pay, and other economic
3

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concepts are now fundamental principles in textbooks. So it seems clear to me that tackling the
problem of valuing health risk reductions to children is a situation where better communication
among the various fields of economics will lead us to the quality decisions we want and need for
our children. This conference will certainly get us closer to that goal. In fact, it is a goal that we
have already been working toward for several years at EPA.
Protecting children is an important part of EPA's mission, and finding ways to value risk
reductions for this vulnerable segment of society is critical to this work. As you may know, EPA
does not account for age differences when estimating benefits for policy-making. However, we
are committed to furthering our understanding of both the science and the valuation components
of our decisions - which is why in 2003, EPA spent $18.4 million on children's health risk
research.
We do know that children are not just little adults. As you know, their neurological,
immunological, and digestive systems are still developing. They eat more food, drink more
fluids, and breathe more air than adults in proportion to their body mass. And, children's
behavioral patterns - such as crawling and placing objects in their mouths - may result in greater
exposure to environmental contaminants. Because of these characteristics, children may not be
sufficiently protected by regulatory standards that are based on risks to adults.
That does not mean that we have not made real progress in protecting children. For
example, largely due to removing lead from gasoline, the median concentration of lead in blood
of children under the age of 5 dropped by 85 percent between 1976 and 2000. This is important
because lead exposure can result in lowered intelligence, impaired hearing, hyperactivity, and
other adverse health effects. Building on the progress made by removing lead from gasoline,
EPA spends $2.5 million annually on regulation development and public education to further
reduce children's exposure to lead. Clearly, all of our efforts over the last three decades are
working.
I hope that several years from now, the same will be said for our ongoing efforts to
reduce childhood asthma. Between 1980 and 1995 the percentage of children with asthma
doubled from 3.6 percent to 7.5 percent - today more than 6.3 million children under the age of
18 have this disease that forces them to miss 14 million days of school each year. The Clean
School Bus USA initiative - which EPA launched last spring - will help clean up emissions
from buses and reduce asthma symptoms by eliminating unnecessary idling, replacing older
buses with new ones, and equipping buses with advanced emission control technologies. This
program seeks to make sure that every public school bus on the road in all 50 states will be a
clean school bus by 2010. They will emit less pollution, contribute to cleaner air, and - most
importantly - keep our kids safe and healthy on the way to school.
Clean School Bus USA is the newest in a long line of EPA initiatives designed to
improve the lives of children suffering the health - and social - impacts of asthma. Tools for
Schools, Smoke Free Homes, and the President's Clear Skies Initiative - along with a request for
a $3 million increase in the President's FY 04 budget for children's health research - will
4

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continue to help us combat this epidemic.
The cases of lead and asthma show that when it comes to environmental health risks,
children need special attention. We have targeted children by focusing on things like school
buses, ventilation systems, and educational initiatives for families - but we must go further.
During my time as Acting Administrator - and in my former role as Assistant Administrator for
OSWER - I have seen that it is tremendously difficult to reflect children's issues in our
regulatory process - but I think we can all agree that we must continue to try.
As we work to develop better scientific data on how pollutants affect children, and better
regulatory analysis addressing children's risks, it is important to keep track of how well
children's health protection efforts are working. Earlier this year, EPA published the second
edition of America's Children and the Environment - a ground breaking report that shows trends
in children's environmental health. Today, I am pleased to announce the launch of the online
version of America's Children and the Environment which will house new information and data
as it becomes available and will be a valuable resource for researchers, concerned citizens, and
policymakers. I am also pleased to announce the release of the Children's Health Valuation
Handbook, which is a companion to EPA's Guidelines for Preparing Economic Analyses that
was released in 2002. The Handbook is a reference tool for those conducting economic analyses
of EPA policies that are expected to affect children's health, providing information on how we
might incorporate the unique risks to children into our analyses.
This is where you come in. Your research and the work you are presenting over the next
two days will be invaluable for our ability to further understand this process and ensure that we
develop policies that are protective of everyone - not just adults. It is a true measure of our
society how well we protect those who are the least able to protect themselves. I fully anticipate
that your presentations will challenge and inspire us to continue tackling these difficult issues in
an effort to improve public policy - and the lives of our children.
Thank you.
5

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Valuing Environmental Health Risk Reductions to Children
PROCEEDINGS OF
SESSION I: THE STATUS OF CHILDREN
A WORKSHOP SPONSORED BY THE U.S. ENVIRONMENTAL PROTECTION
AGENCY'S NATIONAL CENTER FOR ENVIRONMENTAL ECONOMICS (NCEE),
NATIONAL CENTER FOR ENVIRONMENTAL RESEARCH (NCER), AND OFFICE
OF CHILDREN'S HEALTH PROTECTION; AND THE UNIVERSITY OF CENTRAL
FLORIDA
October 20-21, 2003
Washington Plaza Hotel
Washington, DC
Prepared by Alpha-Gamma Technologies, Inc.
4700 Falls of Neuse Road, Suite 350, Raleigh, NC 27609

-------
ACKNOWLEDGEMENTS
This report has been prepared by Alpha-Gamma Technologies, Inc. with funding from
the National Center for Environmental Economics (NCEE). Alpha-Gamma wishes to
thank NCEE's Kelly Maguire and Project Officer Nicole Owens for their guidance and
assistance throughout this project.
DISCLAIMER
These proceedings are being distributed in the interest of increasing public understanding
and knowledge of the issues discussed at the workshop and have been prepared
independently of the workshop. Although the proceedings have been funded in part by
the United States Environmental Protection Agency under Contract No. 68-W-01-055 to
Alpha-Gamma Technologies, Inc., the contents of this document may not necessarily
reflect the views of the Agency and no official endorsement should be inferred.
11

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TABLE OF CONTENTS
Session I: The Status of Children
Changes in the Lives of U.S. Children: 1990-2000
Kristin Smith, U.S. Census Bureau	1
America's Children and the Environment: Measures of Contaminants,
Body Burdens, and Illnesses
Dan Axelrad, U.S. EPA, National Center for Environmental Economics	29
The National Children's Study
Peter Scheidt, NIH, National Institute of Child Health and Human
Development	53
Environmental Health Valuation for Children: Research in Europe
Nick Johnstone, Organisation for Economic Cooperation & Development	73
NOTE: Although Mr. Johnstone was unable to deliver this scheduled
presentation at the workshop, we are including his slide files in the
proceedings.
Summary of Q&A Discussion Following Session 1	87
in

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Changes in the Lives of U.S. Children:
1990-2000
Kristin Smith
Robert Kominski
Julia Overturf

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Introduction
M
ii
\a|C
¦ Once every ten years, the decennial census
provides the opportunity to generate snapshots of
the population for very small geographic units.
Much more than a complete count of the nation's
population, the census provides important social,
economic and housing detail about the population,
allowing policy-makers and planners to see how
characteristics have changed over time in cities,
towns and neighborhoods.

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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ffrfm

¦ Over the past decade there has been renewed
interest on the well-being of children.
Spearheaded by federal activities such as the
Federal Interagency Forum on Children and
Families, much of the focus has been on
identifying a variety of indicators of children's
well-being.

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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M
ii
¦ In this presentation, I present nine indicators of
child well-being from the 1990 and 2000
decennial Censuses. What is unique about this
presentation is that data for the items highlighted
here are shown for all fifty states and the District
of Columbia. Doing so allows one to see the
variability that exists across the Nation, as well as
providing details of change during the past decade.

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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Population and Family Characteristics

1
¦	Children living in married-couple families
¦	Children with difficulty speaking English
¦	Children who are foreign-born

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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Children Living in Married-Couple Families
1990-2000 Change
Percentage point change
~ Decrease of up to 4.2 (16)
Decrease of 4.2 to 5.6 (19)
Q Decrease of 5.6 or more (16)
National average: decrease of4.2
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses. Children in married-c
biological, adopted, and step sons and daughters of a married householder or a married subfamily reference person.
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Children Living in Married-Couple Families
In 2000, 68 percent of children under 18 years old lived in
married-couple families, down from 72 percent in 1990.
The decline in children living in married-couple families
occurred in all states in the nation, with several states
showing a decrease of about 7 percentage points. New
Jersey had a small decrease (1.7 percentage points) from
74 percent in 1990 to 72 percent in 2000.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Children With Difficulty Speaking English
1990-2000 Change
Percentage point change
| Increase of 1.4 or more (14)
~	Increase of up to 1.4 (31)
~	No significant change (6)
National average: increase of 1.4
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses. Children with difficulty speaking English
speak a language other than English at home and speak English less than 'very well.' This includes those who speak English 'well,' 'not very well,' or'not at all.'
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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Children With Difficulty Speaking English
Nationally, the proportion of children ages 5 to 17 with
difficulty speaking English increased from 5 percent in
1990 to 7 percent in 2000.
Most states experienced such an increase, with the largest
percentage point increase occurring in Nevada, where it
rose from 4 percent in 1990 to 9 percent in 2000.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Children Who Are Foreign-born
1990-2000 Change
F
Percentage point change
~	Increase of 1.1 or more (28)
| Increase of up to 1.1 (20)
~	No significiant change (2)
~	Decrease	(1)
National average: increase of 1.1
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses.
Foreign-born children were not born in the 50 states, the District of Columbia, U.S. outlying territories, or abroad to American parents.
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Children Who Are Foreign-born
In 2000, 4 percent of children living in the United States
were foreign-born, up from 3 percent in 1990.
Five states had increases of 2.5 percentage points or more
in the proportion of foreign-born children: Arizona,
Colorado, Nevada, Oregon and Washington - all of which
were also states that saw their percentages of children with
difficulty speaking English increase.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
11

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	RM
Children in families in poverty
Children in crowded housing
Children living with a full-time employed parent

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
12

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Percentage point change
~	Increase	(6)
~	No significant change (6)
~	Decrease of up to 1.7 (12)
~	Decrease of 1.7 or more (27)
National average: decrease of 1.7
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses. Child poverty includes
children living in households who are related to the householder and whose family income and family size put the child
below the poverty threshold. Poverty data collected in the 1990 and 2000 censuses refers to poverty in calendar year 1989 and 1999, respectively.
The average poverty threshold for a family of four was $12,674 in 1989 and $17,029 in 1999.
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
13

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	I'vii
\iljj
Child poverty decreased for the nation as a whole from 18
percent in 1990 to 16 percent in 2000.
Louisiana and Mississippi had large declines in child
poverty over the 1990s, even though they had the highest
levels among the states in 2000. Despite a decrease in
child poverty for the nation as a whole and for many
individual states, child poverty increased significantly over
the decade in five states and the District of Columbia.
|
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Percentage point change
|_J Increase of 2.8 or more (13)
I n c re a s e of u p to 2.8 (26)
|_| No significant change (4)
~ Decrease	(8)
National average: increase of 2
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses.
Children living in crowded housing live in a house where the number of persons per room is greater than 1.
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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In 2000, 19 percent of children lived in crowded housing,
up from 16 percent a decade earlier.
¦	In Nevada, a rapidly-growing state, the proportion of
children living in crowded housing increased 7.6
percentage points over the decade, from 19.7 percent in
1990 to 27.3 percent in 2000, the largest increase in the
nation.
¦	However, the largest decrease was found in Texas, where
the rate decreased from 25 percent in 1990 to 15 percent in
2000.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Percentage point change
¦ Increase of 7.0 or more (9)
~	Increase of 5.7 to 7.0 (17)
O Increase of up to 5.7 (24)
~	Decrease	(1)
National average: increase of 5.7
NOTE: Includes children under 18 in households who are not householders, subfamily reference persons or their spouses. Children living with an employed parent areth
never-married biological, adopted, and stepsons and stepdaughters of a householder or a subfamily reference person, living with one or two parents who are employed
and working at least 35 hours per week.
SOURCE: U.S. Census Bureau, 1990 and 2000 Censuses.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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In 2000, 83 percent of children lived in families with at
least one parent employed full time, up from 77 percent in
1990.
The largest gain in parental employment was found in
Michigan where the rate of children living in families with
an employed parent rose from 73 percent in 1990 to 84
percent in 2000.
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Education

	I'vii
3- to 5-year olds enrolled in school

18- to 24-year olds who have completed high
school

16- to 19-year olds not working nor enrolled in
school

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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3- to 5-Year Olds Enrolled in School
1990-2000 Change
Percentage point change
| Increase of 22.0 ormor^10)
¦ Increase of 19.4 to 22.0(18)
| Increase of up to 19.4 (23)
National average: increase of 19.4

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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3- to 5-Year Olds Enrolled in School

	I'vii
\iljj
Nationally, the proportion of children ages 3 to 5 enrolled
in early education rose from 42 percent in 1990 to 61
percent in 2000, representing an increase of 19 percentage
points.
The figure clearly shows the geographic variation in early
education among children ages 3 to 5, with most of the
smaller increases clustered among the Western states.
Georgia, a Southern state, had the largest increase from 41
percent in 1990 to 67 percent in 2000.

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
21

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18- to 24-Year Olds Who Have Completed
High School
1990-2000 Change
Percentage point change
¦ Increase	(13)
~	No significant change (5)
~	Decrease of up to 1.2 (8)
~	Decrease of 1.2 or more (25)
National average: decrease of 1.2 I
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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18- to 24-Year Olds Who Have Completed
High School
Nationally, the percentage of people ages 18 to 24 who had
completed high school dropped from 84 percent in 1990 to
82 percent in 2000. Part of this decrease was related to
changes in the demographic composition of this age group,
particularly with respect to the Hispanic population.
Declines occurred in many states where the proportion of
young Hispanics in the population increased, such as in
Arizona, Colorado, Nevada, and North Carolina.
Twelve states and the District of Columbia experienced
increases in high school completion rates. The rates in
California and West Virginia increased about 3 percentage
points from 1990 to 2000.	
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
23

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16- to 19-Year Olds Not Working Nor Enrolled
in School
1990-2000 Change
Percent point change
| Increase	(6)
~ No significant change (14)
H Decrease of up to 0.9 (10)
Q Decrease of 0.9 or more (21)
National average: decrease of 0.9
USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
24

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16- to 19-Year Olds Not Working Nor Enrolled
in School

	 —l!(ii
In 2000, 9 percent of youth ages 16 to 19 neither worked
nor attended school, representing a decrease from 10
percent in 1990.

Several states experienced decreases of around 2
percentage points. In contrast, the rate significantly
increased in only six states (Colorado, Delaware, Hawaii,
North Carolina, South Carolina, and South Dakota).

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002

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Additional Data
M
ii
¦	Future U.S. Census Bureau reports on child well-being will
build upon the data presented here today and incorporate
other data to more fully portray changes in the lives of
U.S. children.
¦	Census report to be published by end of 2003,
"Children and the Households They Live In: 2000"
using Census 2000 data.
¦	Census report to be published in 2004 comparing 1990
and 2000 Census data on more indicators.
¦	Many more indicators of child well-being are available for
analysis at many geographic levels (Nation, State, MSA,
county, tract, etc.).

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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Other available data
Hispanic origin
Foreign language spoken at home
Recent immigrant
Citizenship
Metropolitan residence
Home ownership
Labor force status of parents
Household utilities (incomplete plumbing or kitchen, no
telephone or vehicle)
Teen marital status
Family structure and living arrangements
USCENSUSBUREAU
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Other available data
M
ii
¦	Receipt of government assistance
¦	Multi-generational household
¦	Foreign-born parent
¦	Parent's educational status
¦	Living with a parent who is disabled
¦	Parent is a recent immigrant
¦	Living with a parent who speaks English less than very
well

USCENSUSBUREAU
Helping You Make Informed Decisions • 1902-2002
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America's Children and the Environment:
Measures of Contaminants,
Body Burdens, and Illnesses
US Environmental Protection Agency
Office of Policy, Economics and Innovation
Daniel A. Axelrad
29

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America's Children and the
Environment	
•	First edition - December 2000
•	Second edition - February 2003
•	Goals:
-	Identify environmental conditions and health
outcomes of greatest relevance for children
-	Identify best available data
-	Develop most informative measures
-	Identify limitations, data needs, future
directions

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Topics Addressed
•	Environmental Contaminants
•	Body Burdens
•	Childhood Illnesses

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Environmental Contaminants
•	Outdoor Air Pollutants
•	Indoor Air Pollutants
•	Drinking Water Contaminants
•	Pesticide Residues
•	Land Contaminants

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Criteria Air Pollutants - Exceedance of Standards
Measure E1
Percentage of children living in counties in which
air quality standards were exceeded

•		 Ozon\ /
eight-hour standard /
Ozone
one-hour standard

PM-2.5
Carbon
monoxide «


IrVl |
ArM-1 U
f 1- '	
SOURCE: U.S. Environmental Protection Agency, Office of Air and Radiation, Aerometric Information
Retrieval System
33

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Criteria Air Pollutants - Daily Air Quality Index
Measure E2
Percentage of children s days with good, moderate, or
unhealthy air quality
Good
No Monitoring Data
Moderate
Unhealthy
SOURCE: U.S. Environmental Protection Agency, Office of Air and Radiation, Aerometric
Information Retrieval System
34

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Criteria Air Pollutants - Long Term
Measure E3a
Long-term trends in annual average concentrations
of criteria pollutants
70%
PM-10, percent
of annual standard
Nitrogen dioxide,
percent of
annual standard
Sulfur dioxide,
percent of a
annual standard
SOURCE: U .S. Environmental Protection Agency, Office of Air and Radiation, Aerometric Information
Retrieval System
35

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Drinking Water
Measure E6
Percentage of children living in areas served by public water systems
that exceeded a drinking water standard or violated treatment requirements
Any health-based violations
Microbial "^-Treatment and filtration
contamin
Chemical and radiati
Lead and copper
Nitrate/nitri
SOURCE: U.S. Environmental Protection Agency, Office of Water, Safe Drinking Water Information System
(Percentages are estimated)
36

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Body Burdens
•	Concentrations of Lead in Blood
-	in children age 5 and under
•	Concentrations of Mercury in Blood
-	women of childbearing age
•	Concentrations of Cotinine in Blood
-	marker for exposure to Environmental
Tobacco Smoke
-	in children under age 18

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90th percentile
Median
1976-1980
1988-1991 1992-1994
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics,
National Health and Nutrition Examination Survey
1999-2000
38

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Lead Body Burdens
Measure B2
Median concentrations of lead in blood of children ages 1-5, by race/ethnicity
and family income, 1999-2000
Hispanic
Black
non-
Hispanic
White
non-
Hispanic
All
Races/
Ethnicities
0	1	2	3	4	5
Median concentrations of lead in blood (ng/dL)
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics,
National Health and Nutrition Examination Survey
> 200% of Poverty Lev
100-200% of Poverty L«
< Poverty Level
All Incomes
>200% of Poverty Leve
100-200% of Poverty L
< Poverty Level
All Incomes
> 200% of Poverty Level
100-200% Poverty Le*
< Poverty Level
All Incomes
> 200% of Poverty L^
100-200% of Poverty
< Poverty Level
All Incomes
Ivel
level
39

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Mercury Body Burdens
Measure B4
Distribution of concentrations of mercury in blood of women of
childbearing age, 1999-2000
Concentration of mercury in blood (parts per billion)
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics, National Health
and Nutrition Examination Survey
Note: EPA's reference dose (RfD) for methylmercury is 0.1 micrograms per kilogram body weight per day.
This is approximately equivalent to a concentration of 5.8 parts per billion mercury in blood.
40

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Cotinine Body Burdens - marker for ETS exposure
Measure B5
Concentrations of cotinine in blood of children
90th percentile
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics
National Health and Nutrition Examination Survey
41

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Childhood Illnesses
Scope:
Important childhood diseases and disorders that
may be influenced by exposure to
environmental contaminants
•Respiratory Diseases
•Childhood Cancer
•Neurodevelopmental Disorders
•Birth Defects (CA data only)

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Asthma Prevalence
	Measure D1
Percentage of children with asthma
14%
Children ever
diagnosed
with asthma
Children with asthma
in the past 12 months
Children ever
diagnosed
with asthma
and having an
asthma attack
in the past
43
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics, National
Health Interview Survey
Note: The survey questions for asthma changed in 1997; data before 1997 cannot be directly compared to data in 1997 and later.

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Asthma Prevalence
Measure D2
Percentage of children having an asthma attack in the previous 12 months,
by race/ethnicity and family income, 1997-2000
> 200% of Poverty Levi si
100-200% of Poverty L ivel
< Poverty Level
All Incomes
> 200% of Poverty Levi
ll


100-200% of Poverty L
ivel


< Poverty Level
All Incomes



> 200% of Poverty Levi
si

100-200% of Poverty L
ivel

< Poverty Level


All Incomes


> 200% of Poverty Levi si
100-200% of Poverty L svel
< Poverty Level
All Incomes
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics,
National Health Interview Survey
44

-------
ER Visits for Respiratory Effects
	Measure D3
Children's emergency room visits for asthma and other
respiratory causes
500
All asthma and
other respiratory causes
Acute upper respiratory
infections
1992	1993	1994	1995	1996	1997
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics
National Hospital Ambulatory Medical Care Survey
45

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All asthma and other respiratory causes
Acute bronchitL
Acute upper respiratory infections
46

-------
Incidence
Mortality
Cancer incidence and mortality for children under 20
SOURCE: Incidence data from National Cancer Institute, Surveillance, Epidemiology and End Results Program;
mortality data from Centers for Disease Control and Prevention, National Center for Health Statistics,
National Vital Statistics System
Childhood Cancer Incidence and Mortality
Measure D5
47

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Mental Retardation
	Measure D7
Children reported to have mental retardation, by race/ethnicity
and family income, 1997-2000
14
White Black
non- non-
Hispanic Hispanic
< Poverty 100-200% >200%
Level of Poverty of Poverty
Level Level
SOURCE: Centers for Disease Control and Prevention, National Center for Health Statistics,
National Health Interview Survey

-------
Birth Defects in California
Measure S5
Number of birth defects in California per 1,000 live births and
fetal deaths
Heart Defects Oral Cleft Defects Down Syndrome Intestinal Defects Limb Defects
SOURCE: California Birth Defects Monitoring Program
49

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Conclusions
•	Areas of improvement, including:
-	reduced blood lead levels and exposure to
secondhand smoke
-	modest decreases in exposure to air
pollutants and drinking water contaminants
•	Areas of concern, including:
-	prenatal mercury exposure
-	rising prevalence of asthma
•	Much remains to be learned about how
pollutants affect children's health

-------
Acknowledgments
•	Authors:
-	Tracey J. Woodruff, US EPA
-	Daniel A. Axelrad, US EPA
-	Amy D. Kyle, UC Berkeley
-	Onyemaechi Nweke, US EPA
-	Gregory G. Miller, US EPA
•	Thank you!!! to:
-	EPA Office of Children's Health Protection
-	CDC National Center for Health Statistics

-------
AMERICA'S CHILDREN
and THE ENVIRONMENT
Measures of Contaminants, Body Burdens, and Illnesses
'My* A
•-.•v ,v ;
http://www.epa.gov/envirohealth/children

-------
THE NATIONAL
CHILDREN'S
STUDY
Peter Scheidt
Program Office and Interagency Coordinating Committee
U.S. Department of Health and Human Services
NICHD, CDC, NIEHS
U.S. Environmental Protection Agency
53

-------
Children have increased
vulnerability to environmental exposures
-> Critical windows of vulnerability during
development
-> Immature mechanisms for detoxification and
protection
-> Differences in metabolism and behavior that
may yield higher exposure in the same
environments
c

-------
55

-------
v^. Rationale for the
^J\ National Children's Study
From The President's Task Force on Health Risks and
Safety Risks to Children, 2000
-> Compared to adults, children are especially vulnerable to
environmental exposures - metabolism, behavior
-> Exposures to some agents demonstrate potential for serious
developmental effects - lead, prenatal alcohol
-> Current known exposures of high frequency - pesticides, violence,
media
-> Numerous high burden conditions with suspected environmental
contribution - learning disabilities, autism, diabetes, asthma, birth
defects, premature birth
-> Existing research too limited in size & scope to answer the
questions
-> Life-course (longitudinal) design needed to correctly link with
multiple exposures and multiple outcomes
Why Now?
Since the 1950s, many environmental factors have been
introduced (chemicals in air, food, water, and soil) to
increase the effects of the environment and its interaction
with the genetic constitution of the developing fetus and
the child. Others (DDT) have been decreased, at least in
the U.S.
Since the 1950s, many technological advances have been
made (identifying biomarkers, mapping the human
genome, computerization, etc.) that would contribute to
the ability to identify environmental risks
56

-------
ijp PL 106-310
Children's Health Act of 2000
(a)	PURPOSE- ... to authorize NICHD to conduct a national longitudinal
study of environmental influences (including physical, chemical,
biological, and psychosocial) on children's health and development.
(b)	IN GENERAL- The Director of NICHD shall establish a consortium of
representatives from appropriate Federal agencies (including the CDC
and EPA) to-
(1)	plan, develop, and implement a prospective cohort study, from birth to
adulthood, to evaluate the effects of both chronic and intermittent
exposures on child health and human development; and
(2)	investigate basic mechanisms of developmental disorders and environmental
factors, both risk and protective, that influence health and developmental
processes.
(e) AUTHORIZATION OF APPROPRIATIONS- There are authorized to be
appropriated to carry out this section $18,000,000 for fiscal year 2001,
and such sums as may be necessary for each the fiscal years 2002
through 2005.
57

-------
•f[\ Study Concepts
-> Longitudinal study of children, their families and
their environment
-> National in scope
-> Environment defined broadly (chemical, physical,
behavioral, social, cultural)
-> Study common range of "environmental"
exposures and less common outcomes
(n~ 100,000)
-> Environment & genetic expression

-------
•f[\ Study Concepts (con't)
-> State-of-the-art technology -
tracking, measurement, data
management
-^Consortium of multiple agencies
-> Extensive public-private
partnerships
-> National resource for future studies

-------
Study Population - Issues
->Generalizability to U.S. population
-> Additional study populations, e.g.
^Specific high-risk populations
^Agricultural
^Industrial
-> Economically disadvantaged
->Women of child-bearing age - possible
effects on fertility & pregnancy

-------
Criteria for Core Hypotheses
-> No single hypothesis
-> Hypothesis required for costly elements
-> Important for child health & development
(prevalence, severity, morbidity, mortality, disability,
cost, public health significance)
-> Reasonable scientific rationale
-> Require the large sample size (~100,000)
-> Measurable with study of this size
-> Requires longitudinal follow-up

-------
Jdr" Priority Outcome Areas
"fC (and example hypotheses)
-> Undesirable outcomes of pregnancy (infection and
mediators of Inflammation during pregnancy are major factors
associated with pre-term birth)
-> Neurobehavioral development (proposed -
environmentally induced biochemical and physiological
conditions of birth and infancy, including maternal
hypothyroidism, neonatal hyperbilirubinemia, and others, are
associated with learning and cogitative disabilities,.
Injury (Repeated head trauma w/o anatomic damage -
cumulative adverse effects on neurocognitive development)

-------
Jdr" Priority Outcome Areas
"fC (and example hypotheses)
-> Asthma (maternal stress during pregnancy is
associated with the prevalence and severity of asthma
in offspring)
-> Obesity and physical development
(Obesity and insulin resistance is associated with
impaired glucose metabolism in pregnancy and
interacting factors in the physical and social
environment)

-------
Associations and Interactions in
the National Children's Study
Asthma
Chemical
Expos.
Infection
Gene
expression
Social
Environ
Physical
Environ
Health
Care
Medicine &
Pharm
Birth
Defects
Development
& Behavior
Growth
Fertility &
Pregnancy
64

-------
jjp Measures Anticipated -
Exposures
-> Environmental Samples: air, water, dust
-> Bio-markers for chemicals: blood, breast milk,
hair, tissue, etc.
-> Interview and history
-> Serology and medical data
-> Housing & living characteristics
-> Family and social experiences
-> Neighborhood and community characteristics

-------
Anticipated -
-> Fetal growth and outcome of pregnancy
-> Birth defects and newborn exam
-> Growth, nutrition and physical development
-> Medical condition and history: illness (e.g.
asthma), conditions, & injuries
-> Cognitive and emotional development
-> Mental, developmental and behavioral
conditions
t<\ Outcomes
66

-------
€ Projected Time Line
2000-2004	Pilot study/methods development work
2001-2002	Form advisory committee and working groups
Periodically: Meetings, peer reviews, consultations
Mid 2003 Finalize specific hypotheses, develop study design
Mid 2005 Select initial centers or alternatives and pilot test core
protocol
Late 2005 Begin full study with vanguard centers
2005-2007 Enroll additional centers
2008-2009 First preliminary results available from pregnancy
2007-2030 Analyze data as collection continues, publish results
throughout:
67

-------
^ Potential Benefits of the NCS
for Prevention of Diseases

Condition
Potential
Reduction
Potential
Annual Benefit
Pre-term Birth
10%
$0.6 Billion
Asthma
25 %
$3.2 Billion
Obesity & Diabetes
12.5 %
$14.5 Billion
Juvenile Diabetes
15 %
$15 Billion
Injuries
10%
$39 Billion
Schizophrenia
33 %
$3.1 Billion
Learning problems
One cause comparable to lead
8%
$100 Billion

-------
c NCS - Funding Status
-> FY '02 - $6 M
FY '03 - $10 M Proposed
-> FY '04 - $26 M Estimated need
-> Funding for FY '05 & beyond to
NIH/HHS-EPA/OMB
-> Congressional appropriation uncertain

-------
c The NCS will provide
-> The answer to concerns about known exposures
during childhood to potential toxicants
-> The power to determine absence of effects or benefit
of exposures to various products important for our economy
-> Causal factors for a number of diseases and conditions
of children with suspected environmental causes
-> How multiple causes interact to result in multiple
outcomes
-> Large sample size required to apply knowledge of the
human genome to understand multifactoral genetic
conditions
-> Identification of early life factors that contribute to
many adult conditions
-> A national resource to answer future questions by
using stored biological and environmental samples and the
extensive data for decades to come

-------
Contact information
Check the Web site:
httD://NationalChildrensStudv.aov
Join the listserv for news and
communication
Contact us at ncs@mail.nih.gov

-------
It
THE NATIONAL^
CHILDREN'S
STUDY
The End
72

-------
Environmental Health Valuation


for Children:


Research in Europe

Pascale Scapecchi & Nick Johnstone


National Policies Division


OECD


OECD (( 1) OCDE

-------
Context
Much fewer studies in Europe than in the United
States
However, recent growth in interest in European
countries
OECD project on the valuation of environmental
health risks to children
OECD «# o<

-------

European studies

Very few economic European studies
valuation of children's health
on the
•
Greater emphasis on epidemiological work

•
Most European valuation studies estimate
related quality of life (HRQOL) measures
Health-
•
Only one study which estimates WTP to
children's health
protect

OECD ({(3) OCDE

-------
Valuation of Air Pollution in Europe
Navrud (2001) estimates parental WTP to avoid ill-
health episodes for their children.
Health impacts considered: asthma attacks and
coughing.
Sample: parents of children under 17 years of age.
Possibility of comparing parents' WTP for their own
health with parents' WTP for their children's health.
Mortality risk reduction is valued higher than
morbidity risk reduction.
Results show that WTP to prevent the child from
illness is higher than WTP to prevent an adult from
illness.
OECD (( 4) OCDE
76

-------
16 D Questionnaire
•	Apajasalo et al. (1996a) —- health-related quality of life (HRQOL)
measure of adolescent aged 12-15.
•	16 multiple choice questions representing one health-related
dimension (e.g. mobility, vision, hearing, breathing, etc)
•	Sample: "normal" and affected children (children waiting for organ
transplantation, children with genetic skeletal dysplasias, and
children with epilepsy).
•	New approach: adolescents fill in the questionnaire by themselves,
& questionnaire sent to their parents for comparison.
•	Main Results:
-	The profiles differ significantly according to the diagnosis.
-	The measures obtained from the children and the parents differ
-	Differences between boys and girls.
•	Conclusion: Reliable HRQOL measures of adolescents' health
should be based on data collected from the adolescents
themselves.
OECD «# OCDE

-------
17 D Questionnaire
Apajasalo et al. (1996b) -- HRQOL measure for
children aged 8-11 years.
Based on the 16D questionnaire, they construct a
measure consisting of 17 dimensions.
Sample: affected and non-affected children.
The children completed the questionnaire with the
help of an interviewer.
Similar results to the 16D study: the profiles vary
according to the diagnosis.
Reliable estimates of the HRQOL of children can be
obtained when children fill in the questionnaire by
themselves.
However, recognition that limited cognitive capacities
of young children.	oecd^Hocde
78

-------

Children's QoL Assessment
•
Manificat and Dazord (2002) assess quality of life

(QoL) among 4 to 12 year old children.
• The questionnaire covers 27 items covering the main

paediatric QoL domains, e.g. family life, social life,

children's activities and health.
•
Sample: ill and non-ill children.
•
Children have to fill in the questionnaire by

themselves.
•
Results show differences across ages, health status

and living condtions.

OECD 7>OCI)K
79

-------
Ongoing Work Programmes
The Pan-European Programme assesses the evaluation of
transport-related health impacts, with a particular emphasis on
children. Countries involved: Austria, Switzerland, France,
Malta, The Netherlands, and Sweden + WHO.
•	Children's Environment and Health Action Plan for Europe
(CEHAPE) undertaken by WHO, to tackle the environmental
risk factors that most affect European children's health and
providing concrete tools to address them. Countries involved:
Member countries.
•	The RANCH Project addresses the effects of noise on
children's cognition and health. Countries involved: the
Netherlands, Spain, Sweden and the UK.
•	Work in Norway : projects referenced in the Norwegian
Research Database (http://dbh.nsd.uib.no/nfi/english/)
OECD «# OCDE

-------
OECD Workshop
Objectives:
•	Review the state of knowledge;
•	Assess the different valuation approaches; and,
•	Highlight the needs for further research and political
action.
Structure: 4 sessions:
•	general overview of differences;
•	conceptual and methodological issues;
•	comparison of methodologies; and,
•	policy perspectives.
Key issues:
•	Unique challenges;
•	Availability of data;
•	Valuation methodology; and,
•	Benefit transfer
OECD «# 0(

-------
Findings (1)
Overview of the differences between adults and
children
-	Risk differences
•	Children are not little adults
•	Heterogeneity between children
•	Great number of uncertainties
-	Valuation differences
•	4 potential sources of valuation differences: age, risk
preferences, context of valuation, and perspective.
•	Affect estimates
•	Estimated VSL of a child > Estimated VSL of an adult
OECD (( 1(| (X

-------

Findings (2)
Conceptual and methodological issues
-
Formulation of children's preferences:

• Parental perspective most appropriate

• Application of intra-household allocation model (unitary vs. pluralistic)

• Est'd WTP to reduce risk for children > Est'd WTP to reduce risk for adults.
-
Transfer of adults' values

• Risk of under-estimation

• Adjust adults' values with relevant marginal rate of substitution between

adults' and children's health values.

Discountinq children's health

• Scarcity of relevant examples

• Time-varying discount rate may be appropriate

• Long term benefits accounted with care

Economic uncertainties

• Key sources of uncertainty: risk context, time, irreversibility, formulation of

children's preferences, valuation context and altruism.

• Children's health value included in parent's health value.

• Methodological concerns of greater importance. OECD (( 11 OCDE
83

-------
Findings (3)
Comparison of methodologies
-	Stated vs. Revealed preferences techniques
•	Stated-preferences techniques more appropriate.
•	Revealed-preferences more demanding and difficult to implement, in
particular in that context of valuation.
-	WTPvs. QALYs
•	WTP impose less restrictions on the structure of individual preferences
but are more sensitive to the respondent thinking.
•	Any standard chosen is arbitrary
•	The choice will depend upon the setting
-	Health outcome measures
•	Studies conclude that perspective of children is preferred
•	Multi-attribute utility instruments provide reliable results
•	But what is the validity of the value obtained?
OECD 0(

-------
Findings (4)
Policy perspectives
-	Children are highly vulnerable to environmental
degradation
-	Children are not little adults
-	Morbidity and mortality risks reduction greatly differ
-	Research on the valuation of children's health should
be encouraged and supported
-	More comparative studies in different countries
-	Better risk and economic assessments are required
OECD ««3 OCDE

-------
Conclusions
Misallocation of resources devoted toward children (and
between children and adults)
•	Linked to allocation (misallocation) of resources between
morbidity and mortality
•	Leads to wrong priorities being set across different
impacts and wrong standards within individual impacts
•	Much more information and research data are necessary
to provide reliable policy advice
OECD(( 14 ocde
86

-------
Summary of Q&A Discussion Following Session I
Matt Clark (EPA/NCER) asked Dr. Scheidt whether there were any economists doing
willingness-to-pay studies in association with the National Children's Study. When Dr.
Scheidt responded "No," Dr. Clark suggested that a "wealth of data that would be very
useful for policy matters" could be acquired for very little incremental cost, and he stated
that similar joint efforts have been successful in the past. He strongly urged Dr. Scheidt
to have economists participate and develop some survey materials that could augment the
patient study.
Dr. Scheidt responded that the Study group was "very open to that kind of thing" and, in
fact, has an economist/sociologist (Bob Michaels from the University of Chicago)
involved on the advisory committee, although they've "not engaged in that level of
economic study." He invited any interested economists to contact the Study group
directly.
Glenn Harrison (University of Central Florida) asked two questions of Dr. Scheidt. He
first stated that health economists can easily find studies that relate to the number of
children who have hospital stays and diagnosis codes, etc., but they often can't find links
to cost measures. Acknowledging that the costs are difficult to measure, he asked
whether the Study was going to link to existing surveys that can actually give information
on the costs of delivering healthcare. His second question concerned the issue that
"surveys of children's health . . . very often start too late"—that is, they don't provide
information on fetal deaths and infant deaths. The resultant "sample selection bias" can
make a dramatic difference to the inferences one draws.
Dr. Scheidt responded that they definitely anticipate merging and linking to appropriate
existing data sets (e.g., from the Census Bureau), and he stated that there is a white paper
and workshop in the planning phase designed to examine all identifiable data sets
relevant to the study which are candidates for linking. He said that this search is wide
open, ranging "from social data to atmospheric air pollution" data being measured
through satellite technology at NASA.
Dr. Scheidt acknowledged the concern with the question on fetal deaths and particularly
with health risk issues from the critical period of early in the first trimester onward.
Citing the logistical and economic difficulties of following the entire sample of those of
child-bearing age from pre-pregnancy on, he stated that they at least hoped to track
women whose children are enrolled in the study and who subsequently become pregnant.
Kerry Smith (North Carolina State University) commented on the difficulty, partly due to
confidentiality reasons, in linking spatial data (i.e., latitude and longitude) to the
households involved in the surveys, and he asked Dr. Scheidt to pay attention to getting
economists access to that information, if possible. When, Dr. Scheidt asked for clues
about how that might be accomplished, Dr. Smith clarified that what is needed is "a
87

-------
convenient way in which researchers can ask for the matching to take place by a third
party." He acknowledged that certain for-profit entities allow linking to their databases,
but this introduces the issue of cost.
Dr. Smith then asked whether in doing the design work there is "a provision to actually
talk to household members about how they think about these choices" (i.e., the
precautions parents take with their children). He suggested focus groups, cognitive
interviews, etc. as means of ensuring that the right questions are being asked "as opposed
to just itemizing what we think we'd like to know without talking to them."
Dr. Scheidt responded, "Yes, unequivocally," and mentioned that an extensive set of
focus group discussions had begun and would be expanded as the protocol becomes
clearer.
Dr. Smith asked whether the results of those discussions would be reported before the
survey goes out, and Dr. Scheidt responded that information is posted on the website.
Rachel Nugent (NIH Fogarty International Center) called attention to the fact that both
people and environmental contaminants move across borders and that "there are a lot of
particularly vulnerable populations of children in the U.S. who may have foreign
backgrounds or otherwise be influenced by other country backgrounds." She asked Dr.
Scheidt to speak to the issue of coordinating the study with other countries.
Dr. Scheidt cited the Tri-National Commission's efforts in addressing the environmental
impact of NAFTA and in urging Canada and Mexico to carry out "coordinated an parallel
studies that would be quite an advantage to us to provide ranges of exposures that we
would not otherwise have and potential sample size reductions." Dr. Scheidt
acknowledged the potential problem of including participants from other countries who
may migrate. In the study, they clearly anticipate including Spanish-speaking subjects
and not excluding systematically any potential migrants, and they plan to provide long-
term follow-up of anyone who does migrate. He stated that although the details of that
had not yet been determined, they would do as much as is feasible.
Bryan Hubbell (EPA/OAQPS) brought up the issue of the limited network of monitors
for many environmental contaminants. He wondered how the study was ensuring that
"certain populations that don't happen to live where a monitor is" are not excluded and
asked whether they planned to do additional monitoring.
Dr. Scheidt reiterated that the data from numerous sources (e.g., NASA) were being
merged. He also stated that the study anticipated supplementing available data with "an
extensive degree of monitoring" itself and was exploring the range of technologies
available for doing this economically and efficiently. The study working groups and pilot
studies are considering these issues.
88

-------
J.R. DeShazo (UCLA School of Public Policy) stated that the household's totality of
response to a perceived risk is important to factor into an evaluation of how households
are economically responding to risk. He emphasized that remedial actions taken once a
health outcome is expressed, and not just defensive mitigating actions, involve dedicating
time and money resources by household members. He asked whether that consideration
"was coming front and center in the survey instrument."
Dr. Scheidt asked for a clarification and Dr. DeShazo replied that "the fundamental issue
is how parents evaluate the portfolio of health risks their children could face—the level of
risk they perceive and what they do to defend and mitigate the risk of exposure to the
child, and then once the child shows symptoms what kind of remedial behavior they
undertake to reduce their level of risk . . " in other words, the intra-household process of
identifying and dealing with risks to children.
Dr. Scheidt responded that it was an "interesting question" and, saying that they had not
focused on the decision-making dynamic in families, he wondered how they might go
about doing that. He acknowledged that study participants, as a consequence of
participating in the study, would learn a lot about health risks that their children face, or
don't face, and that they are a bit concerned about the potential impact this will have on
the long-term outcomes of the study. He closed by restating that they had not studied
how parents process that information.
Ed Chu, the session moderator, closed the session by urging everyone to look at the study
website, and he commented that one of the primary reasons for having Dr. Scheidt speak
at the workshop was to stimulate economists' interest and involvement in the study.
89

-------
Valuing Environmental Health Risk Reductions to Children
PROCEEDINGS OF
SESSION II: HOUSEHOLD DECISION MAKING
A WORKSHOP SPONSORED BY THE U.S. ENVIRONMENTAL PROTECTION AGENCY'S
NATIONAL CENTER FOR ENVIRONMENTAL ECONOMICS (NCEE), NATIONAL CENTER FOR
ENVIRONMENTAL RESEARCH (NCER), AND OFFICE OF CHILDREN'S HEALTH PROTECTION;
AND THE UNIVERSITY OF CENTRAL FLORIDA
October 20-21, 2003
Washington Plaza Hotel
Washington, DC
Prepared by Alpha-Gamma Technologies, Inc.
4700 Falls of Neuse Road, Suite 350, Raleigh, NC 27609

-------
ACKNOWLEDGEMENTS
This report has been prepared by Alpha-Gamma Technologies, Inc. with funding from the National Center
for Environmental Economics (NCEE). Alpha-Gamma wishes to thank NCEE's Kelly Maguire and
Project Officer Nicole Owens for their guidance and assistance throughout this project.
DISCLAIMER
These proceedings are being distributed in the interest of increasing public understanding and knowledge of
the issues discussed at the workshop and have been prepared independently of the workshop. Although the
proceedings have been funded in part by the United States Environmental Protection Agency under
Contract No. 68-W-01-055 to Alpha-Gamma Technologies, Inc., the contents of this document may not
necessarily reflect the views of the Agency and no official endorsement should be inferred.
11

-------
TABLE OF CONTENTS
Session II: Household Decision Making
Commissioned Paper: Benefit Cost Analysis and the Entanglements of Love
Ted Bergstrom, University of California, Santa Barbara	1
Weak Substitution, Environmental Vulnerability, and Choice
Mary Evans, University of Tennessee 	25
Abstract of Preliminary Research on Family Decision Making and the Value of
Preventing Childhood Development Impairment
Sandra Hoffman, Resources for the Future	55
Discussant
Robin Jenkins, U.S. EPA, National Center for Environmental Economics 	56
Discussant
Mark Agee, Pennsylvania State University 	62
Summary of Q&A Discussion Following Session II	69
ill

-------
Benefit Cost Analysis and
the Entanglements of Love
Theodore C. Bergstrom *
November 1, 2003
1 Introduction
Suppose that after careful thought, a parent reports that she is willing to pay
up to $100 to save her child from one day of cold symptoms.1 How can we use
her answer and those of other parents to analyze the benefit of public projects
that affect child health? Would it make sense to calculate the expected number
of child days of cold symptoms that a project would prevent and to multiply
this number by the average willingness to pay of a sample of parents?
But if a child has two parents, maybe we should value the child's health at
the sum of the two parents' willingness to pay. Or, if the two parents' answers
differ, perhaps we should use the maximum or perhaps the minimum of their
two answers. And what of the child's own valuation on improved health? Why
shouldn't we count that as well? To answer questions like these, we need to
* Aaron and Cherie Raznick Professor of Economics, University of California, Santa Bar-
bara. This paper was prepared for a conference on Valuing Environmental Health Risk Reduc-
tions to Children, sponsored by the US EPA's National Center for Environmental Economics,
the National Center for Environmental Research, and the University of Central Florida. I am
grateful for helpful suggestions from Robin Jenkins of the EPA and Mark Agee of Penn State
University.
1A series of carefully conducted studies have asked questions similar to this. Viscusi, Magat
and Huber [25] interviewed individual parents who were asked their willingness to pay for
hypothetical "safer" insecticides and toilet cleaners that would reduce health hazards for their
children by specific amounts. Liu et al [16] found that a sample of Taiwanese mothers were
willing to pay an average of about US $57 to avoid a cold for one of their children and about
$37 to avoid a cold for themselves. (An earlier study by Alberini et al [1] asking Taiwanese
adults about their willingness to pay to avoid colds for themselves found very similar values.)
Dickie and Ulery [11] asked parents about their willingness to pay for the reduction of cold
symptoms for a single child and for themselves. Dickie and Gerking [10] surveyed individual
parents, asking their willingness to pay for a hypothetical sunscreen that reduced risk of skin
cancer by a specified amount.
1

-------
step back and examine the logic of benefit-cost analysis as applied to families
in which some individuals care about the well-being of others.
2 What Can Benefit-Cost Analysis Do?
Without explicit instructions about how to compare one person's benefits with
those of another, we can not expect benefit-cost analysis to tell us whether a
public project should or should not be adopted. The best we can hope for
from benefit-cost analysis is to learn whether a project is potentially Pareto
improving. To see why this is so, it is useful to revisit a device found in Paul
Samuelson's beautiful 1950 paper, "Evaluation of the Real National Income [23].
Samuelson introduces what he calls "the crucially important utility possibility
function" to help us understand the logic of benefit cost analysis.
Consider a community with two people. A possible project would produce a
public good valued by both persons. In order to produce it, community members
will have to reduce their total consumption of private goods. If the project
is not implemented, then alternative divisions of the total quantity of private
goods will determine different utility distributions. These possible distributions
generate a "utility possibility frontier" as described by the curve UP in Figure
1.
Figure 1: Utility Possibilities and Benefit Cost
UP-
UP'-
If the project is implemented there will be less private goods to be distributed
between the two people, but each will enjoy a higher level of public goods. This
will generate a new utility possibility frontier UP'. Because the curves UP'
and UP are not "nested" there is not an obvious way to determine which is the
better situation. Some utility distributions are attainable only if the project is
not implemented and others are attainable only if the project is implemented.
2

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Suppose that we know that we know that if the project is not implemented,
then the utility allocation will be the point A in the graph. We see from the
figure that the curve UP' contains points above and to the right of A. This
implies that it is possible to produce the public good and to divide its costs in
such a way that both individuals are better off than they were at A. When this
is the case, we say that the project is potentially Pareto improving. Stating this
formally:
Definition 1 A public project is potentially Pareto improving if it is possible
to implement the project and to distribute its costs in such a way that in the
resulting allocation some community member(s) are made better off and none
are made worse off.
In a suitably simple economy, benefit-cost analysis can determine unambigu-
ously whether a project is potentially Pareto improving. One such "suitably
simple economy" is the following: A possible public project produces a public
good that benefits several individuals and harms none.2 The economy has a
single pure private good.3 Implementing the project requires the input of a
known amount of private goods.
If individuals are selfish, the logic of benefit-cost analysis in this economy is
very simple. An individual's "willingness-to-pay" for the project is defined to
be the maximum amount of private good that she would be willing to sacrifice
in order to enjoy the benefits of the public goods provided by the project. The
benefit-cost test compares the sum of all individuals' willingnesses-to-pay for
the project to its cost. It is quite easy to see that for this simple economy,
the sum of individual willingnesses-to-pay exceeds total cost if and only if the
project is potentially Pareto improving.4
The relation between benefit cost analysis and potential Pareto improvement
becomes more complex when some of the beneficiaries are children who are loved
and supported by parents, and even more complex if the parents care about
each others' happiness. In this paper, we try to untangle the logic of these
attachments a few strings at at time.
2	It is not hard to extend these principles to an economy where some individuals benefit
and others are harmed. But this simpler model suffices to illustrate the principles.
3	The single-good assumption is appropriate in a multi-good economy if adopting and paying
for the project does not result in changes in the relative prices of the private goods.
4If the sum of willingnesses to pay exceeds total cost, then it is possible to pay for the
project while assessing no individual a share of the cost smaller than her willingness to pay.
Implementing the project and paying for it with any such assessment constitutes a Pareto
improvement. Conversely, if the project is potentially Pareto improving, there is a way to
assess the costs of the project so that nobody is worse off after the project is implemented.
Each individual's assessment would, by definition be smaller than his willingness-to-pay. Since
these assessments add to the cost of the project it follows that the project would pass the
benefit-cost test.
3

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In order to extend the principles of benefit-cost analysis to a family, we need
to specify and apply a theory of household decision-making for that family. Of
course the world is filled with a great variety of family structures, which differ
in membership and in the distribution of decision-making authority. As we will
see, the prescriptions for benefit-cost analysis can vary significantly with the
family type.
As we extend benefit-cost analysis to multi-person households, we face the
question of how to reinterpret the criterion of potential Pareto improvement.
This paper takes the position that the government is not able to intervene in
the distribution of private goods within the households. Thus we consider a
project to be potentially Pareto improving if and only if there is a way to assign
the costs to families so that given the household decision structure in each family,
no individual is made worse off and at least one is made better off.
3 A Single-Parent Household
Suppose that an economy is made up of households consisting of a single parent
and a dependant child. Assume that each parent cares about her own consump-
tion and her child's health and consumption and is selfish with respect to those
outside her household. Assume also that children care only about their own con-
sumption and health. Consider a government project that uses private goods as
inputs and produces a public good which increases the health of children. How
can we determine whether or not the project is potentially Pareto improving?
Let each parent's utility function take the form:
U (x, v(k, h)) (1)
where x and k are the amounts of private goods consumed by the parent and
the child respectively and h is a measure of the child's health. The child has no
income and receives consumption goods only from its parent. The parent has
an after-tax income, to which she allocates between her own consumption and
that of her child.5 Then, contingent on the child's health being h, the highest
utility that a parent can achieve with after-tax income to is
U*(m,h)= max U(x,v(k,h)). (2)
x-\-k
-------
Definition 2 If the sum of all parents' willingness-to-pay for a project exceeds
the cost of the project, it is said to pass the benefit-cost test for parents.
We can show that if a project fails the benefit-cost test for parents, then it
is not potentially Pareto improving. To say this in another way:
Remark 1 In an economy with single-parent households, if a project is poten-
tially Pareto improving, then it must pass the benefit-cost test for parents.
The proof is simple, but instructive. If the project is potentially Pareto
improving, it must be possible to implement the project and to assign its costs
it in some way so that no parent is worse off and at least one is better off than
if the project is not implemented. Suppose that a project fails the benefit-cost
test. Then in order for the project to be funded, some parent must be assessed
a cost greater than her willingness to pay. Since the parents have complete
control of their family incomes, this means that the parent who is forced to pay
more than her willingness to pay for the project will be worse off if the project
is implemented. Therefore the project cannot be potentially Pareto improving.
From Remark (1), we see that even though the Pareto criterion accounts for
the well-being of children, it would be misguided to measure benefits by adding
the value that children place on their own health to the values that their parents
place on it. Adding children's valuations to those of their parents would lead
to acceptance of projects that do not pass the benefit-cost test for parents and
which are therefore not potentially Pareto improving.
The converse of Remark (1) is not in general true. That is, there may be
projects that pass the benefit-cost criterion for parental preferences, but which
do not allow a Pareto-improving reallocation in which the well-being of children
as well as parents is (weakly) improved. This is not very surprising, especially
since it has not been assumed that parents agree with their children about what
is good for them. But, more remarkably, the converse fails to be true, even if
parents and children share the same preferences over alternative combinations
of child consumption and child health.
Parent's preferences are said to be benevolent if the parent's preferences over
the child's consumptions coincide with child's.6 Stated more formally, we say
that
Definition 3 A parent's preferences are benevolent if the parent's utility func-
tion is Ui {xi,Vi(ki,hi)) where Vi represents the child's preferences.
Even if parents have benevolent preferences, it is possible that some projects
that pass the benefit-cost test parental preferences will lead to outcomes that
''Though this usage is common in welfare economics, those who have been parents and those
who have been children will recognize that parents who are "benevolent" by this definition
would not always act in the best long-run interests of their children.
5
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are worse for some children. This can happen because the child's health may
be such a strong substitute for the child's income that with a healthier, the
parent will reduce the amount of consumption goods transferred to the child by
so much that the child is actually worse off after the transfer than before.
Figure 2: Parent's Consumption and Child's Utility
x
UP'
UP
v
This effect is illustrated in Figure 3. The curves labeled UP and UP' shows
combinations of parents' consumption and child's utility that are possible be-
fore and after a project is implemented. The point A on UP represents the
preferred point of the parent if the project is not implemented and the point B
on UP' represents the point preferred if the project is implemented. With the
indifference curves that we have drawn, the parent will prefer B to A despite
the fact that the child has a lower utility at B than at A. Notice that in Figure
3, the indifference curves drawn are consistent with parental benevolence, since
the parents always prefer higher v to lower. One could imagine, for example,
that for an impoverished family, an improvement in the child's health would
induce the parents to require the child to earn its own food. Under these cir-
cumstances, despite their benevolence toward the child, the parents might favor
an improvement in child health that is accompanied by such a large reduction
in income transfers to the child that the child is worse off. Section 8.1 of the
appendix, presents an algebraic example of preferences for which this is the case.
4 Lovebirds without Kids
Archie and Bess are a couple. They care about their own consumption of private
goods and their own health. They also care about each other's happiness. Archie
and Bess spend a good deal of time together and so each has become a good
judge of the other's happiness, though this information arrives with a brief lag.
6
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Let XA(t) and Xfi(t) be expenditures on consumption, and let h,A(t) and hB(t)
be measures of health for Archie and Bess respectively at time t.
Archie's happiness at time t is determined by the function
UA(t) = vA (xA(t),hA(t)) + aUB(t - 1) (4)
and Bess's happiness is determined by the function
UB(t) = vB + bUA(t - 1). (5)
Elsewhere [4] and [6], I show that this dynamical system is stable under
plausible dynamics if and only if ab < 1. As these earlier papers explain,
this stability condition limits the mutual intensity of their care for each other's
happiness.
The government is considering a women's health project that will improve
Bess's health by a known amount A. Archie and Bess are separately interviewed
about their willingness to pay for this improvement. Bess realizes that if her
health improves, this will have a direct effect on her happiness, which Archie
will observe and enjoy, which in turn will make Bess herself happier, and so
on ad infinitum. Can either Bess or Archie extract a reasonable answer to
the interviewer's question from the blur of reflected happiness in this hall of
mirrors?7
Equations (4) and (5) can be "inverted" to determine more conventional
utility functions that depend only on the consumption and health of Archie and
Bess. If consumptions and health levels are constant over time, equations (4)
and (5) determine a time path of utilities for Archie and Bess that converges to
equilibrium values. To find these equilibrium values, we set U^(t) = UA(t — 1),
UB(t) = UB(t — 1) in Equations (4) and (5) and solve. Then U^(xa, xB,h,A,hB)
and UB(xA,xB,hA,hB) are the equilibrium utilities that result from the con-
stant outcome (xA,xB,hA,hB). These utility functions are as follows:
U*A{xA,xB,hA,hB) = 1 (vA(xA,hA) + avB(xB,hB)) (6)
1 — ab
and
UB(xA,xB,hA,hB) = (vB(xB,hB) +bvA(xA,hA)) (7)
1 — ab
Let us call va(-) and vB(-) the private utility functions of Archie and Bess
respectively and let us call U\(-) and U\j(-) their social utility functions. We
assume that Archie and Bess are able to untangle their affections so as to find
private and social utility functions as in Equations (6) and (7). There remain
some tricky questions to answer. If know that their social utility functions
7Miles Kimball [15] suggested the hall-of-mirrors metaphor.
7
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take this form, how can we use Archie's and Bess's reported valuations for im-
provements in Bess's health in a benefit-cost analysis? To answer this question,
we need some assumptions about the way that Archie and Bess make family
decisions.
4.1 Archie the Dictator
Gary Becker's famous "Rotten Kid Theorem" [2] operates on the assumption
that family decisions are determined according to the preferences of a single
benevolent household member.8 Although this assumption is politically incor-
rect and, I believe, descriptively inaccurate for modern Western households, it
remains worth studying for at least two reasons. First, the simplicity of this
model makes it an instructive place to develop intuition and understanding that
can be extended to other environments. Indeed since almost all economists in-
terested in the economics of the family have cut their teeth on Gary Becker's
patriarchal family [2], this model has become a benchmark against which alter-
native theories need to be tested. More importantly, not all of the households
that interest us are modern and Western. Some of the most important appli-
cations of benefit cost analysis to public health programs are likely to concern
traditional societies and highly patriarchal societies.
Assume that Archie has no direct control over his own health or that of
Bess, but he is able to determine the amount of consumption expenditure that
each receives, subject to a budget constraint. Then he chooses xA and xB to
maximize his social utility function
UA{xA,XB,hA, hB) = vA(xA,hA) + avB(xB,hB) (8)
subject to the budget constraint xA + xB = M, where M is the family income.
For given health levels and family income, the possible distributions of the
private utilities, vA and vB are points lying on or below the curved line in
Figure 4.1. Archie's indifference curves over these possible distributions will
be straight lines with a slope of —1/a and his preferred distribution of private
utilities will be at the point marked A*
Suppose that benefit-cost analysts interview Bess and ask her the following
questions.
B.l What is the largest amount of your personal consumption that you would
be willing to give up in order to improve your health by A units?
8In Becker's treatment, although Archie is benevolent, Bess is selfish. I think he chose to
do this not out of misogyny, but because he wanted to avoid the hall-of-mirrors complications
of mutual affection.
8
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Figure 3: Utility Possibilities
B.2 Given the way that Archie allocates income in your family what is the
largest amount of family income that you would want to give up in order
to improve your health by A units?
Let us also suppose that they interview Archie and ask him:
A.l What is the largest amount of family income that you would be willing to
give up in order to improve Bess's health by A units?
When will the answers to these questions be different and when will they be
the same? And how should we use the answers in benefit-cost analysis?
A Harmonious Case
Let us assume that Archie and Bess both have positive but diminishing marginal
utility9 for their own consumption of private goods and that Bess's private utility
function is of the special form,
i'B (xb ,hs) = fb (xb + khB) (9)
9We have assumed that utility functions are additively separable between Archie's and
Bess's private utilities. In the additive form, the v functions are unique up to positive afRne
transformations. The property of diminishing marginal utility for private consumption there-
fore has operational content in that it is preserved under all positive afRne transformations.
9
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where fc is a constant and where the function fs{ ) displays positive but dimin-
ishing marginal utility. In this case Archie and Bess will be in perfect agreement
about the value of an improvement in Bess's health. Bess's answer to question
B.l be will be the same as her answer to B.2 and also be the same as Archie's
answer to question A.l.10 In order to determine whether the health project is
Pareto improving, a benefit-cost analyst could use this answer to represent the
whole family's willingness to pay.
Remark 2 If Archie and Bess both have diminishing marginal utility for pri-
vate goods, if Bess's utility function is of the form h) = fsi^B + khg)
and, Archie chooses the distribution of family income between private goods for
himself and for Bess, then all three questions, B.l, B.2, and A.l have the same
answer, which is kA. If the health project is implemented and Archie and Bess
pay any amount less than kA, both will be better off if the plan is implemented.
If they must pay more than kA,then if it is implemented,, at least one of them
will be worse off.
It is easy to see that Bess's answer to question B.l must be fcA. If she gives
up p < fcA of her own consumption and her health increases by A, the net effect
is to increase her private utility and if she gives up exactly p = kA her private
utility remains unchanged.
If the family spends p to improve Bess's health by A, Archie will allocate
private consumption between himself and Bess by choosing xa and xg to maxi-
mize his utility, va(xa, hA) + afB(xB + khB + kA), subject to the constraint that
xa+xb = M—p. If we define ys = xs + hs + kA, then we can restate this max-
imization problem as the equivalent problem: Maximize va(xa, hjC) + afs(yB)
subject to xb + Vb = M + kh + (kA — p). If the project is implemented and
the family pays p, the net effect is seen to be the same as that of increasing
Archie's budget by fcA — p. Thus Archie would be willing to pay any amount
p up to fcA for the project. Therefore Archie's answer to Question A.l is fcA,
which is the same as Bess's answer to B.l. Since we have assumed that both
spouses have diminishing marginal utility of private consumption, it also true
that an increase (decrease) in Archie's budget results in an increase (decrease)
in both xa and ys and hence in Bess's private utility. Therefore Bess's answer
to Question B.2 is also fcA.
Generous Archie?
With the utility function described in the previous section, Archie will agree
to spend family funds on Bess's health if and only if she would be willing to
pay for the increase entirely out of her own consumption. But if Bess's private
10This will be true for any positive a, that is, even if Archie is very selfish, so long as he
cares a little about Bess's well-being.
10
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utility function takes the additively separable form, vb(xb, hg) = fB(xB) + khs
where Archie and Bess have diminishing marginal utility of private consumption,
Archie will be willing to "share the cost" of an improvement in Bess's health.
In this case, Archie's answer to Question A.l is greater than Bess's answer to
Question B.l and equal to Bess's answer to B.2.
More generally consider the case where Archie considers Bess's health and
her consumption to be complements, where complementarity is defined as fol-
lows.
Definition 4 Person A regards the health and consumption of Person B as
complements if for any distribution of consumption between A and B, an in-
crease in Person B's health does not reduce A's marginal rate of substitution
between B's consumption and A's consumption.
A proof of the following result can be found in the Appendix.
Remark 3 If Archie and Bess both have diminishing marginal utility for private
goods and if Archie regards Bess's health and consumption as complements, then
Archie's willingness to pay for an improvement in Bess's health exceeds the
amount that she would be willing to pay for this improvement out of her own
consumption.
In the example discussed in Remark 2, Bess's health and consumption are
not complements but substitutes. In this case, if Bess's health improves, Archie
reduces the amount of consumption goods that she receives so as to leave her
private utility unchanged. It is possible however, even where Archie is benev-
olent, that an improvement in Bess's health would induce him to reduce her
allocation of consumption goods by so much that she is left worse off than he
would choose her to be if she were less healthy. This is a case where he regards
her health and her consumption as very strong substitutes. The example that
we discussed in Section 3, where an improvement in child health led the benevo-
lent parent to choose an outcome that is worse for the child can be reinterpreted
to illustrate this case, with Archie cast in the role of parent and Bess in the role
of child.
5 Non-dictatorial Outcomes
In modern Western societies, we do not expect either adult member of an ordi-
nary household to have dictatorial power over the allocation of private goods.
We consider two alternate theories of household allocation. One of these is
a bargaining model in which the Nash cooperative bargaining solution to the
household environment. The other is a model in which Archie and Bess reach
unanimous agreement on outcomes based on a shared notion of fairness.
11
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5.1 Fairness Norms and a Household Welfare Function
Suppose that in the course of their relationship, Archie and Bess build a mu-
tually agreed notion of "household fairness" which governs their decisions. As
Samuelson [24] suggests, this consensus might be expressed by means of a house-
hold "social welfare function which takes into account the deservingness or eth-
ical worths of the consumption levels of each of its members." We could reason-
ably assume that this social welfare function would be an increasing function
of each member's social utility as defined in Equations (6) and (7). Thus the
household welfare function would be of the form
An appealing case can also be made that the household welfare function should
be linear in its two arguments, so that we have
for some a between 0 and 1.
A social welfare function with linear weights on individual social prefer-
ences would be implied if the couple formed their ethical preferences by "veil-
of-ignorance" reasoning of the sort: "How would you want to divide household
resources if there were an equal chance that I were you and you were me?"
Although this kind of ethical reasoning can establish the existence of a social
welfare function of the form of Equation (11), it is not sufficient to determine
the parameter a that weights Archie's UA relative to Bess's UB. For example,
our argument so far gives one no special reason to think that a = 1/2 is more
"fair" than any other a between 0 and 1. The scaling of the functions v a and
vB is arbitrary and if these function are rescaled, then in order to preserve the
same household preferences, the weight a would have to be altered.11 As they
cooperate with each other, Archie and Bess would need to develop a household
consensus that determines the weight a that both regard as "fair". As Bin-
more [8] suggests, in the long run we might expect these weights to be close to
the weights that would sustain a Nash cooperative bargaining solution for the
household, since if there were a significant and persistent difference, the partner
who could do much better with bargaining and threatening might defect from
the social consensus expressed by the household social welfare function.
Recall from Equations (6) and (7) that the social utility functions are them-
selves linear combinations of the private utility functions, va(xa, ^a) and vb(xb, hB).
In particular, we have
1:lAbram Bergson [3] introduced the notion of a social welfare function for an entire society.
Harsanyi [14] proposed ethical foundations for such a function. Binmore [8] suggested that
small, tightly-woven groups like families, may evolve a concept of group fairness that is well
described by a household social welfare function.
W(UX(xA,xB,hA, hB),UB(xA, XB, hA, hB)).
(10)
W(U*A,U*B)=aU*A + (l-a)U*B
(11)
12
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W(U*a,U*b) = +«^(-)) +Y^b(M-) + bvA(-)) (12)
Since preferences determine utility functions only up to an increasing trans-
formation, and since by assumption ab < 1, we have an equivalent household
welfare function if we multiply the expression (12) by 1 — ab. Doing this and
combining terms, we have
W = (a + 6(1 — a)) va(xa, hA) + (1 — a + aa)vB(xB, fig). (13)
If Archie and Bess share a household social welfare function, then the in-
terpretation of their answers to benefit-cost questions is really easy. If money
is taken from household income to help pay for a public project that improves
Bess's health, they both agree about how the cost will be shared in terms of
their private consumption. Thus each of them would give the same answer to
the question "How much would you be willing to pay for an increase of A in
Bess's health?" The appropriate number for benefit-cost analysts to use is the
number given by either of them. It would be a mistake to use the sum of their
answers, since they both would agree that the sum as twice as much as they
would want to pay.
5.2 Bargaining Equilibrium
The pioneering work on models of household bargaining was done by Marilyn
Manser and Murray Brown [19] and Marjorie McElroy and Mary Horney [20],
who proposed to model household decision making with the Nash cooperative
bargaining model. In these papers, a marriage is modelled as a static bilateral
monopoly. A married couple can either remain married or they can divorce
and live singly. There is a convex utility possibility set S containing all utility
distributions (C/i, C/2) that could possibly be achieved if they remain married.
The utility of person i if he or she divorces and lives singly is given by V^. It
is assumed that there are potential gains to marriage, which means that the
there are utility distributions (C/i, C/2) in S that strictly dominate the utility
distribution (Vi,!^)- These papers propose that the outcome in a marriage
will be the symmetric Nash bargaining solution where the "threat point" is
dissolution of the marriage with both persons choosing to live singly. According
to the Nash bargaining theory, the outcome in this household will be the utility
distribution (U^U^) that maximizes (Ui — Vi)(U2 — V2) on the utility possibility
set S*.12 In this theory the outcome in a marriage is completely determined by
12This expression is sometimes known as the Nash product. John Nash [21] proposed a set
of axioms for resolution of static two-person bargaining games such that the only outcomes
that satisfy the axioms maximize the Nash product on the utility possibility set.
13
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the utility possibility set and by the position of the threat point, (Vi, V2). This
theory has the interesting prediction that social changes that affect the utility
of being single will affect the distribution of utility within the household and
hence may change household spending patterns, even if they have no effect
on the budget of the household, while changes in the apparent distribution of
earned income within the household will have no effect on the distribution of
utility in the household if they do not change the threat point from being single.
Shelly Lundberg and Robert Pollak [18], [17] propose an alternative Nash
bargaining model. They suggest that for many marriages the relevant threat
point for the Nash bargaining solution should be not divorce, but an "uncoop-
erative marriage" in which spouses would revert a "division of labor based on
socially recognized and sanctioned gender roles." The Lundberg-Pollak model
makes predictions that differ significantly from the divorce-threat model. For
example, in the Lundberg-Pollak model, if government child-allowances are paid
to mothers rather than to fathers, the threat point shifts in favor of the moth-
ers. Accordingly, the outcomes of cooperative bargaining within households
are likely to be more favorable to women. By contrast, in the divorce-threat
model, changing the nominal recipient of welfare payments when the couple is
together will have no effect on the household outcomes if there is no change in
the beneficiary in the event of a divorce.
To many married persons it seems unlikely that couples would resolve dis-
agreements about ordinary household matters by negotiating under the threat of
divorce. If one spouse rejects the other's proposed resolution to a household dis-
pute, the expected outcome is not a divorce. More likely, there would be harsh
words and burnt toast until another offer or counteroffer is made. It might even
be that if the couple were to persist forever in inflicting small punishments upon
each other, it would be worse both of them than a divorce. Nevertheless, the
divorce threat may not be credible because divorce imposes large irrevocable
costs on both parties, while a bargaining impasse need last only as long as the
time between a rejected offer and acceptance of a counteroffer.
Nash's axiomatic approach to cooperative bargaining gives us no direct guid-
ance about the appropriate threat points for bargaining in a marriage. But use-
ful insight can be gained from Ariel Rubinstein's [22] model of noncooperative
bargaining with alternating offers. Ken Binmore [7] extended the Rubinstein
model to the case where each bargaining agent has access to an "outside op-
tion". Binmore's model is like the Rubinstein model, except that each person
has the option of breaking off negotiations at any time and receiving a payoff of
the value of an outside option.
The Rubinstein-Binmore model, as applied to marriage lends formal support
to the Lundberg-Pollak notion of bargaining. The non-cooperative bargaining
model predicts that household outcome will either be the Nash bargaining so-
14
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lution in which the threat point is delayed agreement and burnt toast so long
as this Nash solution is better for both than divorce. Thus the divorce threat
will influence the outcome only if the bargaining solution reached under the
threat of burnt toast is worse than divorce for one of the partners. In case the
divorce threat is relevant, one partner enjoys all of the surplus and the other is
maintained at a point of indifference between being divorced and being single.
In our example with Archie and Bess, suppose that health levels are deter-
mined by public policy while the allocation of private goods is determined by
bargaining. Suppose that the utility that each would obtain in the absence of
agreement depends on total household income and on the health of each. Where
x is total household income, let us represent these "threat point utilities" by the
functions Ta(xJia) and Tb(xJib) The Nash bargaining theory predicts that
the outcome of household bargaining will be an allocation of private goods that
maximizes the Nash product
subject to the constraint that xa + %b = x
For fixed levels of health, the Nash product in Expression (14) works like a
utility function a household utility function in the sense that private goods are
allocated in such a way as to maximize this function. If a public health project
is implemented and their household is taxed, the utility possibility frontier for
Archie and Bess will be altered and so will their threat points. The household
bargaining theory predicts a new allocation of utility. Neither Archie nor Bess
cares directly about the value of the Nash product, but only about his or her
own utility in the solution to the bargaining problem. Therefore they will in
general not agree on their willingnesses to pay for a specific change in health.
(UX-Ta)(U*b-Tb).
(14)
Figure 4: Health and Bargaining
UP
UP
15
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In a bargaining environment, not only is it possible that Archie and Bess
have differing willingness to pay for a public project. It may even be impossible
to get them to agree to fund a project that strictly increases the set of possible
utility allocations.13 This can happen because the project may shift bargaining
power and/or the shape of the utility possibility frontier in such a way that the
bargaining outcome is worse for one of them, even though the project shifts the
utility possibility frontier strictly outward. This effect is is illustrated fairly in
Figure 5.2. The initial utility possibility frontier is shown by the curve UP and
the initial threat point is located at T. The point that maximizes the Nash
product (14) is labelled E. Now suppose that a public health project is intro-
duced and a fixed amount of tax is collected from the Archie-Bess household.
One result of the project and the tax is to shift the utility possibility frontier
outward from UP to UP'. A second result is to move the threat point from T
to T'. Then the Nash bargaining theory predicts that the equilibrium outcome
for the family moves from E to E'.
We see that a curious thing has happened. The health project and asso-
ciated tax seems to be an unambiguous boon for Archie and Bess, since their
utility possibility frontier moves everywhere outward. But if the project is im-
plemented, the actual outcome in the household must be the corresponding
bargaining solution E' and as we see in the diagram, E' assigns a smaller utility
to Archie than his utility in the initial equilibrium E. Therefore Archie would
oppose this change.
Thus if we continue to use the benefit-cost test to ask whether a public health
project is potentially Pareto improving, we would have to use the minimum, of
Archie's and Bess's valuations to evaluate the benefits to this household.
6 Couples with Kids
After all this foreplay, it is time to bring a child into the Archie-Bess household
and contemplate how to apply benefit-cost analysis to projects that improve
children's health. A natural starting point for this theory is to think of the
child's health as a "public good" that is valued by both Archie and Bess. Let
us assume that Archie and Bess care about each others' happiness, as well as
the health and well-being of their child and about their own consumptions of
private goods.
Suppose that they have social utility functions of the form
U*A(xA,xB,xc,hc) = vA(xA,vc(xc,hc)) + avB(xB ,vc{xc ,hc)) (15)
13Lundberg and Pollak [17] apply similar reasoning to suggest that in the absence of binding
contracts, married couples may not be able to make efficient household decisions about matters
that affect relative bargaining power.
16
-------
UB(xA,xB,xc,hc) = vB(xB,vc(xc,hc)) + bvA(xA,vc(xchc)) (16)
where xc is the child's consumption, he is the child's health and where vc (xc, he)
measures the child's well-being.
6.1 Father Archie Calls the Shots
Let us begin by considering the Beckerian assumption that Archie is dictator
of the allocation of private goods. Then given the level of child health he and
family income x, Charlie chooses the consumption levels xA, xB, and xc so as to
maximize Expression 15 subject to the family budget constraint, xA+xB+xc =
x. Archie's willingness to pay for a small improvement A in the health of the
child is approximately A times his marginal rate of substitution between child
health and his own consumption. Assuming that he chooses to spend a positive
amount of the household income on the consumption goods for Beth and for
the child, Archie's marginal utility of consumption for the child is equal to
his marginal utility of consumption for himself and also equal to his marginal
utility of consumption for Bess. Therefore, Archie's marginal rate of substitution
between child health and his own consumption is equal to his marginal rate of
substitution between the child's health and the child's own consumption. But
this marginal rate of substitution is seen to be simply the ratio of the two partial
derivatives of the function vc(xc,hc) that measures the child's health. Thus
Archie's willingness to pay for a small increase A in the health of the child is
approximately
Thus Expression (17) is Archie's answer to the question "How much money
would you be willing to pay for an increase of A in the health of your child?"
Suppose that the child has the same perception of its welfare as do its par-
ents and its preferences are represented by the same function vc(xc,hc) that
appears as an argument in the parents' utilities. If the child is questioned about
the amount of consumption that it would be willing to forego for an increase
of A in its health, its answer would be A times its marginal rate of substitu-
tion between health and consumption. We see from Equation (17) that this is
precisely the same as Archie's marginal rate of substitution between the child's
health and family income. It follows that the child's answer would be the same
as Archie's.
We seem to have a kind of "Rotten Kid Theorem" here, but does it extend
to Bess? Given that Archie dictates the household allocation of consumption
goods, how will Bess answer the question "How much of the household income
would you be willing to surrender to pay for an increase of A in the health of your
child?" Bess realizes that if family funds are paid to support child health, the
dhc
(17)
17
-------
resulting changes in private consumption by family members will be determined
according to Archie's preferences. Given that Bess realizes this, the amount she
would be willing to have the family spend to pay for an improvement of A in
the child's health can be shown to be
w°=H'< (S+S~B) ¦
-------
6.3 Allocation with Divorced Couples
Suppose that after producing a child, Archie and Bess get a divorce. After the
divorce, they have little affection for each other, but both care about the child's
well-being. Bess has custody of the child and they set up separate household
accounts, with each of them having a separate income. The only way that
Archie can contribute consumption goods to the child is by giving money to
Bess, who can allocate it as she chooses between herself and the child. Suppose
that Archie makes no voluntary payments to Bess because only a fraction of the
money that he gives her would be spent on the child's consumption.
In this situation, the appropriate measure for benefit cost purposes would
be the sum of their two answers. If Archie is willing to pay an amount Wa
and Beth an amount Wb for an improvement of A in the child's health, then
both would benefit from implementing the project if amounts Pa < Wa and
Pb < Wb are collected from the two parents. Thus their total willingness to
pay is Pa + Pb- In this case, a benefit cost study that measured benefits of a
child health project as the sum of the willingnesses to pay of a single parent for
each child would underestimate the value of the project.
6.4 What About Grandparents and Aunts and Uncles?
A child's parents are not the only people who care strongly about its health
and well being. Across almost all known societies, other close relatives besides
parents are intensely concerned about the well-being of a child.
The theory of evolutionary biology gives us strong reason to expect that this
must be true. The chances that our ancestors survived to reproduce successfully
depended not only on the behavior of their own parents, but on the amount of
help they got from their grandparents, uncles and aunts. If behavior toward
one's near relatives is inherited, then the fact that we are products of successful
evolution implies that humans can be expected to display significant willing-
ness to care for their near relatives. In 1964, the great evolutionary biologist,
William D. Hamilton [13] developed a theory that offers a systematic quantita-
tive prediction of the extent to which individuals, on average, will care about
their relatives. This prediction has come to be known as Hamilton's Rule.
Biologists define the "coefficient of relatedness" between two animals of the
same species to be the probability that a rare "gene" found in one of these
animals will also appear in the other. For sexual diploids if mating is between
unrelated individuals, the coefficient of relatedness between two full siblings is
1/2, that between half-siblings is 1/4, that between an individual and a full
sibling's child is 1/4, that between full cousins is 1/8, that between parent and
offspring is 1/2, that between grandparent and grandchild is 1/4, and so on.
Hamilton proposes that natural selection would produce individuals who try to
19
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maximize inclusive fitness where inclusive fitness is defined to be a weighted
sum of one's own reproductive success and that of one's siblings, half-siblings,
and cousins of various types, where the weights are coefficients of relatedness.14
(Of course some care has to be taken to avoid double-counting of say, one's
children's fitness and that of one's grandchildren.)
Hamilton stated his rule as follow:
The social behaviour of a species evolves in such a way that in
each behaviour-evoking situation the individual will seem to value
his neighbor's fitness against his own according to the coefficient of
relatedness appropriate to the situation.
Hamilton's rule implies that when faced with the option of sacrificing c units
of its own reproductive success in order to increase the success of a relative whose
coefficient of relatedness is k, by b units, the decision maker should make the
sacrifice if it passes the benefit-cost test kb > c.
Should we add the willingness to pay of a child's grandparents and other
relatives to that of its parents? Or does this amount to double-counting as
we found to be the case if we added the willingness to pay of its two parents
in an intact family? To answer this question in a really satisfactory way, we
would need a theory of decisions for extended families. In extended families
where transfers occur or are expected to occur between the grandparents and
the parents of a child, it might be argued that the family operates under a single
budget and that a parent's answers to questions about her willingness to pay for
improvements in the child's health incorporate her understanding of the psychic
benefits this improvement will confer on the grandchildren and her beliefs about
how the costs of this improvement would be shared under family transfers.
On the other hand, it seems likely that in most Western families, adult sib-
lings have independent family budgets with no significant sidepayments between
families. In this case it is appropriate for benefit cost analysis to add the will-
ingness to pay of a child's other relatives to that of its parents. As we argued
in the case of a divorced couple, if changes in a child's health and in the tax
burdens of its relatives do not otherwise affect the pattern of transfers between
relatives, then a public project that improves a child's health and costs its rel-
atives less than the sum of their willingnesses to pay allows a potential Pareto
improvement.
14More recent theoretical work [9] [12] [5] has shown that Hamilton's rule is strictly correct
only where the benefits and costs from interaction between relatives take a linear form.
20
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7 Conclusion
We have tried to untangle some of the strings of familial affection in order to
give practical guidance for benefit cost analysis. Some of these strings untie
relatively easily. For example, the members of a single-parent household will
not enjoy a Pareto improvement if the household is assessed a cost greater than
the parent's willingness to pay. Thus adding willingness to pay of children to
that of their parents would lead a benefit cost analysis to accept projects that
are not potentially Pareto improving.
We showed that with reasonable restrictions, the reflected happiness between
loving couples can be resolved into a well-defined household welfare function
over allocations. If the household acts to maximize such a function, then the
willingness to pay stated by either parent is an appropriate measure of the
benefits to the entire household. If there are relatives outside of the household
who also have significant willingness to pay, then a proper accounting of benefits
from child health should include the valuations of these relatives.
For households with bargained outcomes or for divorced households, inter-
pretation of parents' responses to questions about their valuation of a child's
health can, in principle be more complex. We have shown that married couples
who allocate private goods by bargaining may differ in the amount of household
funds that they would be willing to spend on the child's health. In these cases,
strict adherence to the principle of identifying potentially Pareto improving
projects suggests using the smaller of the answers proposed by the two parents.
The recommendation is quite different for divorced couples so estranged that the
noncustodial parent makes no voluntary contributions to the custodial parent's
household. In this case, benefit cost analysis should add the willingness to pay
of the noncustodial parent to that of the custodial parent.
8 Appendix
8.1 An Example
Each parent i has an income m > 1 and a utility function of the form f/j =
Xi + 2vi(ki, hi)1/2, where the function Vi(ki, hi) is a utility function representing
child i's preferences. There are two possible values for hi. These are hi = 0
and hi = 1. where initially hi = 0, and the public project is adopted, hi = 1,
and where Vi(k, 0) = k and Vi(k, 1) = k/2 + 4/9. The total cost of the project
is N/6, where N is the number of parents. Each parent allocates her income
Xi and ki so as to maximize her utility. When hi = 0, this occurs where k = 1
and Xi = rtii — 1. Thus if the project is not adopted, each parent i has utility
TOj + 2 — 1 = TOj + 1 and each child has utility 1. If the project is adopted,
then the parent the parent optimizes by choosing ki = 0 and = m;. In
21
-------
this case the utility of child i is Vi = A = A/9 and the utility of the parent is
rrii + 2 A1'2 = rrii +4/3. Each parent has a willingness to pay of 1/3 for the
project to be implemented and so the sum of willingnesses to pay is N/3. Since
the cost of the project is N/6, it passes the parental benefit-cost test. But, as
we have seen, if the project is implemented, each child's utility will be reduced
from 1 to 4/9.
Moreover, if the project is implemented, in order for children to be as well
off as before the project, each child must receive at least k = 10/9. Any transfer
scheme in which each child receives at least 10/9 and where parents pay a total
of N/6 for the project must be worse than the outcome without the project for
at least some of the parents.
8.2 Proof of Remark 3
Let xa and xg be the consumptions that Archie would choose for himself and
Bess if the the health project is not implemented. Let pt, be the maximum
amount that Bess would be willing to sacrifice out of her own consumption
in order to improve her health by A. Then it must be that Bess is indifferent
between her initial situation and the allocation in which her health is hg + A and
her consumption is reduced to xg — Pb- If the family budget is reduced by ps
and Bess's health is improved by A, then since Beth has diminishing marginal
utility of private consumption and since Archie views Beth's consumption and
her health are complements, it must be that Archie's preferred allocation of
private goods out of the new budget is one in which Bess's consumption is
reduced by less than ps ¦
22
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References
[1] A. Alberini, M. Cropper, T. Fu, A. Krupnick, D. Shaw, and W. Harrington.
Valuing health effects of air pollution in developing countries: The case of
Taiwan. Journal of Environmental Economics and, Management, 34:107-
126, 1997.
[2] Gary Becker. A Treatise on the Family. Harvard University Press, Cam-
bridge, Ma, 1981.
[3] Abram Bergson. A reformulation of certain aspects of welfare economics.
Quarterly Journal of Economics, 51:310-334, 1938.
[4] Theodore Bergstrom. Love and spaghetti, the opportunity cost of virtue.
Journal of Economic Perspectives, 3(2):165-173, Spring 1989.
[5] Theodore Bergstrom. On the evolution of altruistic ethical rules for siblings.
American Economic Review, 85(1):58—81, March 1995.
[6] Theodore Bergstrom. Systems of benevolent utility functions. Journal of
Public Economic Theory, 1(2):71-100, 1999.
[7] Ken Binmore. Bargaining and coalitions. In Alvin Roth, editor, Game The-
oretic Models of Bargaining, pages 259-304. Cambridge University Press,
Cambridge, 1985.
[8] Ken Binmore. Just Playing. MIT Press, Cambridge, MA, 1998.
[9] L. Cavalli-Sforza, Luigi and Marcus W. Feldman. Darwinian selection and
"altruism". Theoretical Population Biology, 14:268-280, 1978.
[10] Mark Dickie and Shelby Gerking. Valuing children's health: parental per-
spectives. Technical report, University of Central Florida, Dept of Eco-
nomics, UCF, Orlando F1 32826, 2003.
[11] Mark Dickie and Victoria Ulery. Parental altruism and the value of avoid-
ing acute illness: Are kids worth more than parents. Technical report,
University of Central Florida, Dept of Economics, UCF, Orlando F1 32826,
2002.
[12] Alan Grafen. The hawk-dove game played between relatives. Animal Be-
haviour, 27(3):905-907, 1979.
[13] William D. Hamilton. The genetical evolution of social behavior, i and ii.
Journal of Theoretical Biology, 7(1):1—52, July 1964.
[14] John Harsanyi. Cardinal welfare, individualistic ethics, and the interper-
sonal comparison of utility. Journal of Political Economy, 63:309-321, 1955.
23
-------
[15] Miles Kimball. Making sense of two-sided altruism. Journal of Monetary
Economics, 20:301-326, 1987.
[16] Jin-Tan Liu, James M. Hammitt, Jung-Der Wang, and Jin-Long Liu.
Mother's willingness to pay for her own and her child's health: A con-
tingent valuation study in Taiwan. Health Economics, 9:319-326, 2000.
[17] Shelley Lundberg and Robert Pollak. Bargaining in families. Technical
Report 8642, NBER, 2001.
[18] Shelly Lundberg and Robert Pollak. Separate spheres bargaining and the
marriage market. Journal of Political Economy, 101(6):998-1011, Decem-
ber 1993.
[19] Marilyn Manser and Murray Brown. Marriage and household decision
theory-a bargaining analysis. International Economic Review, 21(1):21—
34, February 1980.
[20] Marjorie McElroy and Mary Horney. Nash-bargained decisions: Towarda
generalization of the theory of demand. International Economic Review,
22:333-349, 1981.
[21] John Nash. The bargaining problem. Econometrica, 18(1):155-162, Jan-
uary 1950.
[22] Ariel Rubinstein. Perfect equilibrium in a bargaining model. Econometrica,
50(1):97-109, January 1982.
[23] Paul Samuelson. Evaluation of real national income. Oxford Economic
Papers, 2(1) :1—29, January 1950.
[24] Paul Samuelson. Social indifference curves. Quarterly Journal of Eco-
nomics, 70(l):l-22, February 1956.
[25] W. Kip Viscusi, Wesley A. Magat, and Joel Huber. An investigation of the
rationality of consumer valuations of multiple health risks. RAND Journal
of Economics, 18(4):465-479, Winter 1987.
24
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Preliminary research: Please do not cite
Weak Substitution, Environmental Vulnerability, and Choice
10/6/03
V. Kerry Smith, Mary F. Evans, H. Spencer Banzhaf, and Christine Poulos*
I. Introduction
Feenberg and Mills' [1980] concept of weak substitution provides the basis for
expanding the role of revealed preference methods in measuring individual willingness to
pay to reduce pollution-related health effects. To support this argument we outline a
graphical analysis of how weak substitution can enhance our use of models based on
averting and mitigating behaviors. Moreover, the proposed structure offers an economic
framework for describing why different groups might be considered more or less
vulnerable to the health effects of pollution. Our discussion begins by summarizing
Smith and Banzhaf s [2003] proposed approach to describe how weak complementarity
and the Willig condition contribute to the estimation of the economic value for reducing
pollution's impact on environmental amenities.
Discussions of the preference restrictions used to recover information about
consumers' values for non-market goods largely ignore weak substitution. For example,
after reviewing the concept in some detail in his 1992 book, Freeman [2003] reflected the
apparent professional consensus and excluded weak substitution from his revised edition.
He maintains that an assumption of less than perfect substitution is not especially
* Paper prepared for presentation at EPA/UCF Workshop: Valuing Environmental Health Risk Reductions
to Children, October 20-21, 2003. University Distinguished Professor, CEnREP, North Carolina State
University and University Fellow Resources for the Future, Assistant Professor, University of Tennessee,
Knoxville, Fellow, Resources for the Future, and Assistant Professor, University of Missouri, Columbia,
respectively. Smith's research was partially supported by U.S. Environmental Protection Agency (Grant
#R-82950801). Thanks are due to Dan Phaneuf for comments on aspects of this research and to Susan
Hinton for help in preparing this paper.
25
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informative without including a more detailed preference specification. Following Bartik
[1988], Freeman argues that, at best, substitution offers upper and lower bounds for
Hicksian welfare measures.1 By contrast, our analysis suggests weak substitution may be
comparable to weak complementarity in its ability to enhance the insights derived from
revealed preference analysis of individual choice.
This paper provides a short primer on the logic underlying our arguments. We
rely on graphical analysis and some simple analytical arguments but stop short of
attempting to develop an empirical example. Section two outlines the first building block
for understanding the link between weak substitution and choice. Our focus parallels
Willig's [1978] use of weak complementarity. That is, we treat changes in environmental
services as analogous to quality changes in private goods. This strategy redirects attention
to selecting the private good whose price offers the most informative index of how a
quality change affects consumer choice. Section three defines weak substitution and
illustrates how a graphical analysis informs the structuring of economic models to
recover preference information for the non-market resource with this restriction. By
considering the price index capturing the effects of changes in environmental services,
we isolate the private demands most likely to isolate an individual's non-market/market
tradeoffs. Section four introduces a role for separability and with it a framework that
demonstrates how an individual or household's economic circumstances, together with
their physical (or health) conditions, contribute to a definition of their vulnerability to
pollution. The last section describes how our logic relates to two past applications and
1 Neill [1988] also discusses the prospects for substitution and complementarity relationships for groups of
private commodities serving as bounds for willingness to pay measures.
26
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how the framework might be used in new revealed preference (RP) or combined RP and
stated preference research.
II. Analysis of Consumer Surplus with Indifference Curves
Following conventional discussions of Hicksian consumer surplus, we begin with
the analysis of price changes. In analytical terms using indirect utility (V(-)) or the
expenditure function (
-------
functions- a conditional expenditure function that acknowledges the level of q can
influence expenditures onX, labeled e (•), and an expenditure function which includes
expenditures on q, labeled
-------
price for the good used to represent the environmental service. However, the choice
process is described in a format that prevents her from actually choosing the amount
desired at the available price.
As a rule, prices do not exist for environmental services. Thus, a comparison of
Ae and Ae* diverts attention from an issue that seems more relevant in models destined
for empirical analysis. This issue concerns the selection of a private good (and hence a
price) that provides the greatest insight into the importance of changes in q for an
individual's observable choices. To develop this argument we need to consider a
different way of describing the WTP for a change in q. This alternative entails selecting
a single commodity and defining the price change that is equivalent to the change in q.
We define this equivalence by specifying the changes in q and the selected good's price
that require the same compensation (or payment) to restore the original utility level.
Thirty-five years ago, Fisher and Shell [1968] proposed a similar strategy in
considering the issues associated with adjusting prices for quality changes. They
demonstrate two results that seem underappreciated in the literature on non-market
valuation.4 The first of their results on price indexes relates to a quality change in a
private good equivalent to augmenting the quantity of that good. This formulation of
how quality influences preferences is the only one that allows the definition of a quality
adjusted price (for the good experiencing the quality change) independent of the amounts
of all other commodities being purchased. The second of their key theorems concerns
another aspect of preference restrictions and focuses on conditions, other than simple
repackaging (or equivalently quantity augmentation), that allow quality adjustment to the
29
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price of one or more goods other than the one experiencing the quality change.5 Their
examples for this type of preference restriction implicitly recognize a role for weak
complementarity6:
"... suppose there is a quality change in refrigerators. If this
change simply makes one new refrigerator deliver the services of
some larger number of older ones, then the simplest price
adjustment in the cost-of-living index is indeed an adjustment in
the price of refrigerators. On the other hand, if that quality change
also increases the enjoyment obtained from a quart of ice cream,
then an adjustment in refrigerator price will not suffice; an
adjustment in the price of ice cream is also called for. Indeed, if
the only effect of a refrigerator quality change is to augment
the enjoyment attained from ice cream, then the simplest
adjustment is one made only in the price of ice cream, even
though the quality change takes place in refrigerators. In this
case, an adjustment in the price of refrigerators can be made to
suffice; the magnitude of that adjustment, however, will depend on
the quantities demanded of all goods. An adjustment in the price
of ice cream will also suffice; the magnitude of that adjustment,
however, will only depend on the quantity of ice cream and the
quantity of refrigerators" (p. 123, bold highlights added).
The conditions that assure the quality change can be reflected in a subset of
private goods' prices parallel the conditions required to recover estimates of the role of
non-market services (quality) from consumers' choices of private goods. This link is
consistent with our proposal to consider the equivalence relation between quality changes
and price changes as a guide to revealed preference modeling.7
To develop this logic we reconsider the measurement of consumer surplus for a
price change, first in Marshallian terms. Consider one of the private goods, X, and a
4 Banzhaf [2001] makes this point in discussing the adjustment of cost of living indexes for non-market
environmental services.
5 Hanemann [1984] addresses cases similar to this general idea in his evaluation of cross product
repackaging for quality.
6 This concept had not been defined at the time they developed their reasoning.
7 As we noted, this argument is similar to Neill's [1988] use of substitution and complementarity
restrictions for sets of private goods in relation to a non-marketed good to establish bounds for WTP.
30
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change in the price of Xfrom /, to P0 (with Pl > P0 ). I'{)TSRI\ represents the change
Marshallian consumer surplus (MCS) for an ordinary demand curve in panel a of Figure
3. Our argument is outlined for the linear case, but holds as an approximation for other
cases. Equation (4) provides an algebraic description of P0TSRPl.
MCS^-P^X.+^-PjX^-X,) (4)
Rearranging terms, we have equation (5):
MCS^fc-P^X i+jr0) (5)
Panel b of Figure 3 provides an alternative representation of this relationship. Assume
the interior budget constraint corresponds to a price of Xat P} and the exterior to P0. The
tangency at D corresponds to X1 and at B to X0 . Marshallian consumer surplus for this
linear case is exactly equal to the average of CD+BA. This is established directly once
we recognize that, with numeraire good priced at unity, the following relations hold:
m0L = PlXl
m0N = P0X i
m0M = P0X0
(6)
o
m0J = PlX0
As a result, CD =m0L-m0N and AB=m0J-mjVL . Substituting from equation (6) yields
the relationship given in equation (7).
-Pa )Xt +(P, )x, ]
MCS = \{Pl -P0 )(X, +X0 )=\{CD+AB)
To use this logic to illustrate the connection between changes in q and equivalent
(in welfare terms) price changes, we assume weak complementarity. Let Xand q be
weak complements. The indifference curves for a given utility level with different levels
31
-------
of q will intersect at R on the vertical axis (i.e. at zero consumption level for X) as in
Figure 4, panel a. This feature follows from weak complementarity. That is, when there
is no consumption of X the non-market good has no value to the consumer. We assume
that qi>q0 . Quality improvements imply an inward fanning of indifference curves
because the levels of the weak complement (X) and the numeraire (z) required to maintain
the same level of utility decrease as q increases.
Now consider the definition of price change for X equivalent to the quality change
in q. For the income level defined by the vertical intercept T in the figure, the budget
constraints tangent to indifference curves labeled V(q0)and V(q1) at B and C,
respectively, provide the equivalent price change. Moreover, the average of CD and AB
in this case corresponds to the Hicksian willingness to pay for this price reduction (e.g.
from the budget constraint tangent to V(q1) to the one tangent to V(q0)) or equivalently
the WTP for the increase in environmental services from q0 to ql. This conclusion
follows because the utility level associated with these indifference curves is the same by
construction (i.e. V(q0)=V(q])). As in our earlier discussion of price changes, the
argument holds exactly for the case of a linear Hicksian demand function and
approximately with nonlinear demands.
Panel b of Figure 4 introduces a third indifference curve, l/(q]), corresponding to
a quality level of ql but a different utility level. Comparisons of V(ql) and V(cj])
isolate the individual's choices holding income constant. We examine the case where
prices correspond to the outer budget constraint. Therefore, j(CD+EF) corresponds to
32
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the Marshallian consumer surplus for the Hicksian equivalent price change and thus for
the change in environmental services as well.
Smith and Banzhaf [2003] use this relationship (i.e. between AB+CD) and
¦y(CD+EF)) to illustrate how weak complementarity and the Willig [1978] condition can
be combined to recover Hicksian consumer surplus measures for the amenity values
provided by enhanced quality. Here we argue that Willig's focus on the relationship
between the Marshallian consumer surplus for a quality change relative to the level of
consumption of a private good (that is a weak complement to quality) and the price
adjustment for that good with respect to quality is another way of suggesting that the
conditions required for quality adjusted price indexes parallel those needed to define
welfare measures for changes in quality.
III. Weak Substitution
Feenberg and Mills [1980] define weak substitution as another form of demand
interdependency that arises for private goods and environmental services when the
relative prices of those interdependent private goods are "high". In the case of weak
complementarity, the choke price of the private good is crucial to isolating the marginal
value of an increase in the related non-market environmental service (see Smith and
Banzhaf [2003] for details). In the case of weak substitution, the level of consumption of
a private good is defined, but the interaction between the private good and quality (or
non-market services) implied by this definition is different. That is, we assume there
exists a level of consumption for the private good (the weak substitute) above which
improvements in the non-market environmental service have no value. For price levels
33
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of the weak substitute above the level corresponding to this threshold, consumption of the
weak substitute is below the threshold and quality improvements are valuable. Formally,
if Pa defines the price that induces the threshold consumption level, Xa, as in equation (8),
then the condition for weak substitution is given in equation (9).8
Vp_
Vm
= Xa (8)
dV_
dq
, =0 \/P
-------
AB = 4r(Pz(^)-Pz(Vo)}zo (10a)
Pr
CD=y{Pz{^)~PzM)-^ (10b)
a
UaB+CD)=H-i-W (9l )-P; (?„ )>(z, +z„) (10c)
2
P
y1 a J
When Pa is normalized to unity, this relationship reduces to one that is comparable to our
earlier description of the measurement of the Hicksian willingness to pay for a quality
change. In this case however, we use the price of the numeraire and not the price for the
private good serving as the weak substitute.
As in the case of our discussion of weak complementarity, introducing a third
indifference curve, here at the level corresponding to a quality level of qi (labeled V (<;/,)
in Figure 6b), also yields the Marshallian measure of the quality change (or price change
in z) as ~Pa "CAB+FG) in the figure.
In some respects, our simple interpretation in Figure 6b may be misleading. The
relative prices of X and z determine consumption levels of both goods. As we noted,
Figure 6b assures that when z=0, consumption of X equals Xa, the threshold beyond
which q no longer has value. The pivoting of the budget constraints at this point are
intended to illustrate increases in the relative price of z in comparison to X, with the price
for X remaining at Pa9 To some degree this representation is artificial because the
diagram illustrates relative prices for a given income. Thus, Pa could be represented for a
9 The actual slope of the budget constraint is _f /'-y/ ']. Increases in the price of z relative to Pa forXpivot
the budget constraint inward.
35
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different income level without pivoting atXa. Figure 7 recasts the diagram starting the
budget constraint at a position where P
-------
not important) or weak complementarity is associated with larger amounts of
consumption that might be associated with specialty desserts (e.g. ice cream cakes that
must be refrigerated for some period time).
These examples have been quite simple. As a result, we relegated all other goods
to the background without really explaining how this outcome was accomplished. In
short, z was implicitly a composite of all other goods. Our graphical strategy sought to
focus on the properties of each of the two goods' prices as candidates for the quality
adjustment. In the process we implicitly assumed that one of them was an index for
everything else.10 One way to take account of other goods' prices in developing
restrictions that use weak substitution imposes separability. This next step is discussed
below.
IV. Separability and Environmental Vulnerability
To limit our attention to the relationships between z, X, and q and allow a more
explicit treatment of the remaining private goods, we introduce a new argument in the
preference function, r, which designates a composite of all other goods. Pr represents its
price (or price index).11 Separability of z, X, and q from r implies we can write the
indirect utility function as in equation (11).
V = V(v(P,Pz,q,mv), |i(Pr,m-mv)) (11)
Separability also assures that consumption choices can be described as if they were
undertaken as part of a process that decomposes the budget into components for each set
10 This was not what Fisher and Shell intended in their discussion of the problem.
11 r can be a vector of goods and Pr a vector of prices. We do not need to be more specific here because our
objective is to illustrate how separability allows the role of Pr to be limited to its influence on income
effects.
37
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of separable goods. Thus, we can specify mv as the expenditures on Xand z, given levels
of q. mv will be a function of all goods' prices (P ,PZ, and Pr) as well as q and m.n This
strategy "focuses" the patterns of influence. That is, separability allows us to distinguish
the roles of the prices of goods in the sub-function, P and Pz, from all other goods'
prices, Pr. All prices continue to affect the conditional demand for X and z. However,
those outside the sub-function enter through reallocation of income about separable sets
of goods. With this specification, the influence of both Pr and m are observed through
the income effect. Perhaps more importantly the effects of q on the demands for other
goods are observed exclusively through the reallocation of income (e.g. m-mv) and their
income effects. There are no separate substitution effects attributable to q with other
private goods.
Consider now the definition of conditional weak substitution given in equations
(12a) and (12b). Equation (12a) defines the conditional demand for X, given the budget
allocation between X and z and all other goods implied by mv.
vP
dv
dq
= Xa (12a)
p=pn
= 0 V P
-------
Hanemann and Morey [1992]). {Pz (ql )-Pz (q0 ))z0 evaluates initial consumption of z at
the old and the new prices with Pz(lo)' zo representing initial expenditures and Pz(
-------
economic and demographic (or other) factors. Because the two considerations influence
observed responses, efforts to isolate sensitive groups and measure their responses must
resolve a difficult identification problem. The analysis must take account of the
economic consequences of the threshold defining vulnerability.
Interpreting the separability restriction as a means of introducing household
models illustrates an alternative use of the framework. For example, Chiappori's [1988]
collective household model imposes budget decomposition on the allocation of income in
the household through his structuring of the household decision process. Combining this
preference assumption with a further restriction that different members of the household
consume different goods, we extend the use of weak separability to develop some
specific insights into the use of averting or mitigating behavior models within a
household setting. To illustrate this point, consider a two-person household where
changes in q only affect individual one. Each household member consumes an exclusive
private good, represented by X1 and X2 respectively. In addition, assume that, for
individual one, the exclusive consumption good, X1, serves as a weak substitute for q.
Chiappori's efficient household model yields budget decomposition similar to what we
described in equation (12). However, the interpretation of the decomposition in the
household setting is different.14 In Chiappori's model, the expenditure groups represent
consumption by different people in the household, rather than simply different groups of
goods consumed by the same person as in our equation (12). Equation (13) clarifies the
distinction. Let f1 (•) designate the first individual's indirect utility function viewed as
environmental quality across individuals and use these physical or technical distinctions along with
differences due to economic circumstances (since X=0 for all cases).
14 See Smith and Van Houtven [2003] for a discussion of some of the welfare implications of the model.
40
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the solution to Chiappori's efficient household. ^1(-) is a function of all goods' prices,
income, and q. The left-hand side of equation (13) simply indicates that the indirect
utility realized by individual one depends upon the prices for all the goods consumed by
the household, q, and income. The right-hand side recognizes the exclusive goods
consumed by each of the household members. As given here, individual one consumes
the first good but not the second.
t(Pl,P2,q,m) = Vl(Pl,q,s(Pl,P2,q,m)) (13)
s(-) represents the income available to individual one. The remainder, m-s(•), is the
portion of household income available to individual two.
Equation (13) suggests two possibilities for defining the threshold level of
commodity one implied by weak substitution, either in terms of V1^) or «'(•) The
central issue is whether the definition for Xla implies that the income allocation is held
constant. Equation (14a) uses Roy's identity for the Marshallian demand to define the
price function for P1 (e.g. labeled here as Pla) that yields Xla in terms of V1^).
K
= XIa (14a)
1 a
h=ha
vls
Equation (14b) defines weak substitution holding individual one's available income (,s(-))
constant.
i';
= 0 \/ Pt
-------
t=Vl+Vlsq (15)
Substituting from (14b) for Px < Pla we have equation (16) for prices that satisfy this
inequality.
£lq=® + Vs 'Sq (16)
In other words, the model suggests that the tradeoffs we observe associated with
individual one's choices in response to a change in q reveal any reallocation of income
due to the change in q. This result holds provided we assume his (or her) income is held
constant in defining Pla.
In contrast, if we define weak substitution in terms of /' (•), the model suggests
that, for Pla defined in this way, the incremental value of changes in q is counterbalanced
by budget reallocation within the household. Equations (17a) or (17b) illustrate the
result.
l\=0=Vg1+Vs1sq (17a)
V1
-------
choices, and the responses of other household members to changes in some element of
environmental quality or services. In the next section we discuss how the framework
presented above relates to a few recent papers that sought to use household responses and
specific sensitive populations to estimate individual willingness to pay for improvements
in q.
V. Implications for Empirical Models
Weak complementarity has been the dominant restriction used in revealed
preference approaches to measure the economic values for changes in non-market
environmental services. More generally, complementarities between goods and services
are important to the processes through which new goods (or services) generate
improvements in individual well being. Bresnahan and Gordon [1997] developed this
important insight in the introduction to their volume on incorporating new goods in cost
of living measures. They used the example of artificial light to introduce their argument,
noting that over the past century:
"A series of new goods, such as whale oil for lamps, gaslight, and
then the electric light bulb, rapidly lowered the costs of using artificial
light, a commodity which is complementary to a wide variety of
household and workplace activities. Thus, as artificial light grew
cheaper, activities which had been economic only for short parts of the
day spread to evening, activities confined to summer became year-
round, and jobs became easier to perform" (p.3)
These types of complementarities have cascading effects - with cheap artificial
light transforming the allocation of individual time throughout the day and creating a new
mix of demands for goods and services - both new and old.
43
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An important dimension of these effects is a set of discontinuities which was not
emphasized by Bresnahan and Gordon and is central to Smith and Banzhaf s [2003]
generalization ot weak complementarities. Relationships between goods and services
may change substantially at different levels of consumption. Recognizing and using this
information should be regarded as a preference restriction. Weak complementarity at a
point and weak substitution are restrictions that provide a conceptual basis for developing
these restrictions in ways that can be used in understanding individual choice.15 That is,
weak substitution's definition requires that we identify a point of discontinuity in the role
for quality (or environmental services). As a result, it is adding more information than
alternative specifications of substitution patterns (as might be associated with classes of
preference functions, such as a constant elasticity specification).
To our knowledge, none of the empirical analyses of the costs of mitigating or
averting behavior has imposed weak substitution. Moreover, while several papers have
offered recommendations for future empirical analyses that follow the implications drawn
from our combined models with separability and weak substitution, these studies do not
suggest how the additional data would be used in estimation.16 By specifying a formal
structure, we believe the empirical implementation may be clearer. To illustrate this
point we selected two applications that consider environmental impacts on family
members - Agee and Crocker [1994] and Mansfield et al. [2002],
(a) Agee and Crocker [1994. 1996]
15 We owe this observation to Dan Phaneuf who commented on the Smith-Banzhaf argument for weak
complementarity by noting it created discontinuities and with them more information for revealed
preference models.
16 Shogren [2001] listed as his top two recommendations in a paper on valuing effects of environmental
hazards on children's health: (a) "pay more attention to how decisions of intrahousehold resource allocation
and distribution are made by caregivers; and (b) begin efforts to construct a systematic framework to help
44
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Both Agee and Crocker papers investigate parental willingness to pay for risk
information and therapy for children with differing confirmed levels of body lead. The
focus of their analysis is on the decision to undertake chelation treatment given
information about health risks, parental background (including education and labor
market status), body lead levels, and household income. The authors are careful to
include time costs in their estimates for the full costs of treatment (e.g. blood chelation).
They consider average estimates for parental time commitment but do not have specific
information on time allocations to the chelation activity or other activities for each
family. The income, employment status, wage rates, family composition, and education
levels are specific to each group.
Agee and Crocker find the chelation decision was related to parental education,
family status (e.g. father present), lead levels, and measures of the full price. The results
suggest more educated mothers and traditional families are less likely to choose the
therapy. The authors suggest this outcome could imply a substitution of caregiving time
for the therapy. Our framework would suggest that this behavioral response is exactly
where one should expect to recover information about the economic value of reducing
lead in the environment based on its impact on children. However, the information
available to these authors provides no specific details on time allocation choices of
parents, children's health status (that might serve as the threshold for a weak substitution
effect), or reallocation of resources within the household. The authors correctly
conjecture these issues are likely to be important but are unable to estimate a structural
model without these details.
organize how we think about the interaction of environmental threats and the behavioral choices of society,
caregiver and children..." (highlights of author's summary, pp.7-8).
45
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(b) Mansfield et al. T20021
Mansfield et al. [2002] propose an ambitious diary study of families with
asthmatic children to investigate parental responses to high ozone warnings. The authors
hypothesize that changing the mix of activities undertaken by children offers a behavioral
response to changes in air pollution. They use a national sample including asthmatics
and non-asthmatics during times when high ozone might be expected so it seems
reasonable to anticipate observed responses. The authors' preliminary results focus on
total hours spent outdoors and the fraction of the day spent outside. Specifically, for each
activity in which the child participated parents were asked to whether the activity was
undertaken "totally indoors", "mostly indoors", "half indoors and half outdoors", "mostly
outdoors", or "totally outdoors". Based on the time diaries, the authors calculated the
total number of hours spent in each of these categories. The results do not adhere to
one's a priori expectations. On average, parents of asthmatic children indicated that their
children spent more time mostly outdoors more often than parents of non-asthmatics. Of
parents who reported their child's time was spent "totally outdoors", the average hours
were higher among parents of non-asthmatic children. However, as in the "mostly
outdoors" category, the differences across the two groups were not large and did not
appear to be significantly different. Multivariate analysis confirms the simple analysis -
ozone warnings did not have a differential effect for the two groups.
The weak substitution framework suggests a potential explanation for this finding:
the need to separate the sample with children distinguished by a health threshold. This
partition might reflect parental judgments about when high levels of ozone are likely to
be problematic in ways that are comparable to our weak substitution relationship. Our
46
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model also suggests that the household's capacity to reallocate resources among its
members should affect the recoverability of the air quality effect. Our comparison of
weak substitution defined as £l =0 versus V]q =0 illustrated the importance of resource
allocation. While our model focused on reallocation in terms of income, a reformulation
to reflect time reallocation is a straightforward extension. The lesson for this analysis is,
as Shogren suggested, greater attention to caregivers' time and monetary reallocations.
Overall, these two examples suggest that behaviors consistent with the weak
substitution framework seem quite likely. What appears to be missing are data that
include not only responses concerning the weak substitute, but other goods or services (or
in the case of the household, the person) that a weak substitution model suggests is the
best source for choice information.
47
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z
A
B
X
C D
Figure 1: Conventional Description of Willingness to Pay - Price Reduction
m = income
WTP = willingness to pay for a
change in the rationed good
from qotoqi
Aq = q}- q0
r = price of rationed good
A XoB = Ae*
B to C = r • Aq
m to R = r ¦ q0
Legend for Figure 2
m-WTP
T
Figure 2: Freeman's Description of Lankford Model - Change in Rationed Goods
48
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Price
Quantity (X)
Panel a
Figure 3: Marshallian Consumer Surplus for a Price Change
m
o
N
M
L
J
X
X
Panel b
49
-------
R
T
Panel a
Figure 4: Illustrating Quality Change
z
V(q )
R
T
X
Panel b
50
-------
z
X
Xa
Figure 5: Weak Substitution
X
Panel a Panel b
Figure 6: Weak Substitution and Hicksian Demand
51
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Figure 7: Weak Substitution with Alternative Relative Prices
-------
References
Agee, Mark D. and Thomas D. Crocker, 1996, "Parental Altruism and Child Lead
Exposure: Inferences from the Demand for Chelation Therapy," The Journal of Human
Resources 31 (3): 677-691.
Agee, MarkD. and Thomas D. Crocker, 1994, "Parental and Social Valuations of Child
Health Information," Journal of Public Economics 55 (September): 89-106.
Banzhaf, Spencer H., 2001, "Quality-Adjusted Prices: Theory, History, and Application
to Air Quality," Ph.D. Dissertation, Department of Economics, Duke University.
Bartik, Timothy J, 1988, "Evaluating the Benefits of Non-marginal Reductions in
Pollution Using Information on Defensive Expenditures," Journal of Environmental
Economics and Management 15: 111-127.
Blackorby, Charles, Daniel Primont, and R. Robert Russell, 1978, Duality, Separability
and Functional Structure: Theory and Economic Applications (New York: New
Holland).
Blundell, Richard and Jean-Marc Robin, 2000, "Latent Separability: Grouping Goods
without Weak Separability," Econometrica 68: 53-84.
Bockstael, Nancy E. and Kenneth E. McConnell, 1993, "Public Goods as Characteristics
of Non-Market Commodities." Economic Journal 103 (September): 1244-1257.
Bradford, David F. and Gregory G. Hildebrandt, 1977, "Observable Preferences for
Public Goods," Journal of Public Economics 8 (October): 111-132.
Bresnahan, Timothy J. and Robert J. Gordon, 1997, "Introduction," The Economics of
New Goods, edited by T.J. Bresnahan and R.J. Gordon (Chicago: University of Chicago
Press for NBER).
Chiappori, Pierre-Andre, 1988, "Rational Household Labor Supply," Econometrica 56
(January): 63-89.
Feenberg, Daniel and Edwin S. Mills, 1980, Measuring the Benefits of Water Pollution
Abatement (New York: Academic Press).
Fisher, F.M., and K. Shell, 1968, "Taste and Quality Change in the Pure Theory of the
True Cost-of-Living Index," in J.N. Wolfe, editor, Value, Capital and Growth: Papers in
Honor of Sir John Hicks (Chicago: Aldine Publishing Co.): 97-140.
Freeman, A. Myrick III, 2003, The Measurement of Environmental and Resource Values:
Theory and Methods, Second Edition (Washington, DC: Resources for the Future).
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Hanemann, W. Michael, 1984, "Discrete/Continuous Models of Consumer Demand,"
Econometrica 52 (May): 541-562.
Hanemann, W. Michael and Edward Morey, 1992, "Separability, Partial Demand
Systems, and Consumer's Surplus Measures," Journal of Environmental Economics and
Management 22: 241-258.
Maler, Karl G., 1974, Environmental Economics: A Theoretical Inquiry (Baltimore: John
Hopkins University Press for Resources for the Future).
Mansfield, Carol, George Van Houtven, F. Reed Johnson, Zachary Pekar, Jui Chen Yang,
Timothy Gibson, and Douglas Crawford Brown, 2002, "Behavioral Reactions to Ozone
Alerts: Study Design for Assessing Parents' Values for Protecting Their Children's
Health," Presented at the Southern Economic Association Meetings, November 24-26,
2002.
Neill, Jon R., 1988, "Another Theorem on Using Market Demands to Determine
Willingness to Pay for Non-traded Goods," Journal of Environmental Economics and
Management 15 (2): 224-232.
Shogren, Jason F., 2001, "Children and the Environment: Valuing Indirect Effects on a
Child's Life Chances," Contemporary Economic Policy 19 (October): 382-396.
Smith, V. Kerry and H. Spencer Banzhaf, 2003, "A Diagrammatic Exposition of Weak
Complementarity and the Willig Condition," American Journal of Agricultural
Economics (forthcoming).
Smith, V. Kerry and George Van Houtven, 2003, "Recovering Hicksian Consumer
Surplus within a Collective Model: Hausman's Method for the Household,"
Environmental and Resource Economics (forthcoming).
Willig, Robert D., 1978, "Incremental Consumer's Surplus and Hedonic Price
Adjustment," Journal of Economic Theory 17 (February): 227-53.
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ABSTRACT
Family Decision Making and the Value of Preventing Childhood Developmental Impairment
Alan Krupnick1, Wiktor Adamowicz,2 Ann Bostrom3 and Sandra Hoffmann1
Resources for the Future, 2U. of Alberta, 3Georgia Institute of Technology
Objectives. This multi-disciplinary study has three objectives: (1) to provide more comprehensive
valuation of reducing risk of childhood developmental impairment neurotoxins by estimating parental
willingness to pay (WTP) to reduce lead-paint hazards; (2) to develop more accurate methods of
eliciting parental WTP to protect children's health by testing the impacts of using intra-household
resource allocation models rather than unitary household models; and (3) to develop more systematic
approaches to designing non-market survey instruments by using mental models research to better
understand the underlying decision processes.
Experimental Approach. Current research on parental WTP to protect children's health from
environmental hazards models household choice as an action by a single decision-maker with a unitary
utility function and a pooled budget. A large body of literature in economics and sociology of the
family and in cognitive psychology suggests that these assumptions are flawed, and may lead to
incorrect measures of parental WTP to protect children's health from environmental hazards. The study
proposed here tests these assumptions.
Environmental neurotoxins can have permanent effects on children's intelligence, motor development,
and attention. New research suggests that environmental exposure may be a larger contributor to
developmental impairment than previously thought. Lead paint exposure will be used as the representa-
tive neurotoxin hazard. Lead paint abatement options provide an excellent vehicle for testing unitary
versus bargained household models in estimating parental WTP to protect children's health. EPA cur-
rently relies on more limited cost-of-illness and human capital estimates of the benefits of protecting
children from lead and other neurotoxin hazards.
This study has two phases. The first phase will elicit "mental maps" of parents' risk perceptions and
decision making about reducing their children's health risks from lead paint. Thirty couples will be
interviewed individually and as a couple about their risk perceptions, definitions of the decision problem
and choice set, and roles in family decision making. Results from phase one will guide development in
phase two of a attributed-based/conjoint contingent behavior survey of 250 couples to assess the
influence of individual and shared parental risk perceptions and preferences on household choice of
lead-paint abatement to protect children.
Expected Results. This research will produce estimates of individual and household willingness to pay
for reduced risk of developmental impairment in children. It will also generate measures of the degree to
which estimates from bargained and unitary household models differ. Insights into household decision
making on environmental health risk issues from the valuation and mental model results will help guide
future valuation efforts as well as neurotoxin risk communication programs.
55
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Robin Jenkins's Policy Discussion of
"Benefit Cost Analysis and the Entanglements of Love"
Theodore C. Bergstrom, In progress, October, 2003 and
"Weak Substitution, Environmental Vulnerability, and Choice"
V. Kerry Smith, Mary F. Evans, H. Spencer Banzhaf, and Christine Poulos, October 6, 2003
I will discuss Prof. Bergstrom's paper, the Smith et al paper, and end with connections
between the two.
Prof. Bergstrom's paper has two broad objectives. The first is to try to figure out how
introducing an important aspect of real life into economic models will affect our interpretation of
benefit-cost analysis (BCA). The important aspect is family relationships. How will accounting
for the interdependencies of families affect how we conduct and interpret economic analysis?
Prof. Bergstrom's second objective is to simultaneously figure out whose willingness to
pay (WTP) is valid when conducting BCA for families. (Should one examine the mother's, the
father's or the child's WTP? Some combination thereof?)
Both of these objectives are important to policy-makers. EO 13045, issued by the
Clinton administration in the late 1990s, directed policy makers to consider health risks to
children. This introduced a new need for policy analysts to try to look separately at the impact
of government policies on children. It turns out that this task is virtually impossible if one relies
on the traditional tools of economics in which individuals maximize utility for themselves
subject to a budget constraint. Children are not rational beings, they don't have access to the
family budget and they don't operate as individuals. Children are inherently connected to family.
Thus, a new question arose - how do we manipulate the tools of economics to find out whether
we've improved the welfare of children? Prof. Bergstrom's paper is taking a stab at the answer.
He's really asking how we use the traditional tools of economics (utility theory and BCA) in
new, perhaps somewhat unconventional ways, in order to get at valid measures of the effect of
policy on child and family welfare.
Prof. Bergstrom starts by reminding us what exactly we get from BCA, anyway. BCA
tells us whether a project leads to a potential Pareto improvement (PPI), a situation where the
winners could potentially compensate the losers. In the simplest model of an economy, to check
for a potential Pareto improvement, one would just examine whether the sum of individuals'
WTP exceeds the cost of the project.
Prof. Bergstrom suggests, however, that the relationship between BCA and potential
Pareto improvements gets more complicated when you move away from the individual and try to
model family relationships in which people care about one another's well-being. To understand
the effect of family relationships he shows that we need a theory of household decision-making.
He proceeds to examine households of different compositions and with different decision
structures:
56
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Household Compositions, Decision-Making and WTP
Household Composition
Decision-Making Structure
Whose WTP for BCA?
Single parent
Dictator
Parental WTP
Child-free Couple
One is dictator
Dictator's WTP

Unanimity
WTPm=WTPf

Bargaining solution
Minimum WTP
Married couple with child
One is dictator
Dictator's WTP

Unanimity
WTPm=WTPf

Bargaining solution
Minimum WTP
Divorced couple with child
(independent budget)
Separate dictators
WTPm + WTPf
Extended family
(independent budget)
Separate dictators
Follow rule for nuclear
family + WTP ext fam
Prof. Bergstrom offers a new criterion for passing BCA when family decisions are being
accounted for: The sum of parents' WTP must exceed project costs to pass the BC test for
parents. As he has worded it, the criterion clearly reveals whose perspective counts: parents.
We don't add a child's WTP to parents or we'd end up accepting projects that don't meet this
new criterion.
For each household construct, what he considers to get the third column, is a hypothetical
government project that improves the health of children for the families with kids, or that
improves the health of the female member for the families without kids. As the third column
shows, to assess this criterion, depending on the composition and decision-making structure of
the family, the policy analyst would collect WTP from different people. The following rule
seems to fall out:
Rule for appropriate WTP:
"Interview all families who care about the child and operate with independent budgets. For each
of those families,
a) if there is not unanimity between the adults, then count the WTP of the head (dictator) or, if
there is not a head, count the WTP that is the lower of the two adults' WTP;
b) if there is unanimity, count the WTP from either individual."
This suggestion has immediate practical implications. For analysts relying on parental data, one
must now acknowledge that parental WTP might overestimate if the un-interviewed spouse has a
lower WTP, or for divorced couples, it might underestimate since really we should be adding in
57
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the WTP of the ex-husband/wife too.
In addition, if there are segments of the population that are more or less likely to be
characterized by one or another of the family compositions or the decision-structures then those
sub-populations might be systematically mis-represented. One can see how this is likely to be a
real problem since culture is an important determinant of the prevailing power structure within
the family. For example, the head-of-household model is probably more common among
Hispanic families than non-Hispanic. In addition, certain family compositions are more likely
among certain sub-populations - single parent families among inner-city African Americans.
Thus the mis-representation of certain sub-cultures might follow from neglecting to model one or
another of the possibilities in the table.
Prof. Bergstrom points out that in most of these models, a project could pass the BC test
for parents, and children could experience a decline in utility. This is because of substitutability
between the child's health and consumption. The parent might reduce the child's consumption
by enough to offset an improvement in the child's health, so that the child's utility actually
declines. Prof. Bergstrom offers a practical example of an impoverished family that requires a
child to go to work once his health is restored. This is a disturbing possibility — that by relying
on parental WTP, policy makers might choose projects that ultimately lead to reductions in the
direct utility and consumption of children.
This is a disturbing possibility and one to be aware of but, as Prof. Bergstrom himself
points out, at least for western cultures, it seems like a remote one. In response to the child's
improved health, the parent would have to reduce the child's consumption by an amount big
enough to offset the improved health. I would assert that in Western families, health might be
more realistically modeled as complimentary to consumption, since healthy kids probably eat
more, are more concerned about social pressures regarding dress and play, and probably recreate
and travel more too. In other words, improving children's health is not likely to decrease their
direct utility for families in the U.S. at least not as a consequence of parents considering child
health to be a substitute for child consumption of goods.
An interesting question is that as this paper develops, will there be more examples in
which direct child utility declines even though a project passes the parental BC test — examples
more applicable to western cultures. Are there certain cases or circumstances where we should
be concerned about this outcome? Clearly there are outlier parents - drug addicts, for example —
for whom we should be reluctant to rely on parental WTP to represent the well-being of children.
But are there also broader cases or situations for which we should exercise caution when relying
on parental WTP?
A final comment about the importance of Prof. Bergstrom's work. It goes beyond
implications for the interaction of policy and child health. In fact, just as children are inherently
family members, so too are most adults. In the final section of his paper, Prof. Bergstrom
suggests adding together the WTP of divorced couples and adding to the WTP of a nuclear
family, the WTP of extended family members with independent budgets. These suggestions
58
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imply that for adults we should also collect WTP for adult health from family members operating
in households with independent budgets. For cultures like ours and most Western ones, where
household budgets are fairly independent but there is a great deal of concern for extended family
member's health, Prof. Bergstrom's work suggests that individual WTP probably understates
society's valuation of health.
Turning to the Smith, Evans, Banzhaf and Poulos paper . . .
The major thrust of this paper is to propose a new framework for revealed preference
research. As a policy analyst, after reading the first few paragraphs of this paper, I was excited
about the significance of what they suggest. Clearly, analysts would find very useful yet another
set of conditions under which we could tease out values of non-market goods or more
specifically, for the EPA, environmental goods. The paper sets out to show that when certain
conditions hold regarding the interrelationship between a private market good and a substitute
environmental good, economists can study the demand for the private good and tease out
valuation of the environmental one.
We are accustomed to thinking this way about complimentary goods - for years
economists have been learning about the value of natural areas by examining recreation demand;
e.g., the demand for fishing or for beach house rentals. As the authors of this paper highlight,
Rick Freeman's much-cited text on Measuring Environmental and Resource Values covers the
conditions surrounding weak complementarity. His latest version of the text, however, has all
but eliminated discussion of weak substitutability. The authors intend, with this paper, to correct
this oversight and to encourage economists to study, or at least be more aware of, this neglected
category of market products - that is, substitutes for difficult-to-value non-market goods.
For weak complementarity, two conditions must be met. Together they suggest that
when the price of the complementary market good is at or above its choke price (so that
consumption is zero), changes in the environmental good have no welfare significance. Weak
substitutability also requires that two conditions hold. Together they suggest that there exists a
level of consumption for the private good (the weak substitute) above which improvements in
the non-market environmental service have no value. In other words, if the price of the weak
substitute is high enough, consumption of the market good is low and increases in the
environmental good are valuable.
One can easily see how positing the conditions for weak substitutability might offend
environmentalists. The hypothetical is that there is a market good that is a substitute for some
set of environmental services. If the price of that market good drops low enough, then people no
longer have a need for the non-market environmental services. Years ago when I taught an
undergraduate environmental economics course, following Tom Teitenburg's textbook, I would
start the semester by exposing students to ideas of the "optimists" and the "pessimists." The
citations to these schools of thought go back at least to the 1960s. The pessimists believed the
world's population was growing at a rate that would outstrip resources and lead to a collapse
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with starvation and misery. The environmentalists in the classroom were sympathetic to these
ideas. The optimists believed that advances in technology would outpace resource depletion and
eventually replace the need for the natural world. Generally speaking, the optimists viewpoint
was disliked by the environmentalists.
Drawing a connection to the paper, in general, studying goods that are complementary to
nature, suggests that we have a continuing need for the natural world. These products
complement or enhance our experience of the natural world. However, studying goods that
substitute for nature, the very notion that goods can completely replace the demand for
environmental goods, is in concert with the ideas of the optimists. The weak substitutability
condition that there are prices of the market good below which changes in the quality of the
environment are no longer valued might be more offensive to some people than the choke price
assumption behind weak complementarity.
This leads to a practical question: Is the weak substitutability condition more restrictive
or less representative of practical experience as well? I think not as long as one carefully
characterizes the case under study. The private market good substitutes for a specific subset of
services derived from an environmental good, and generally not for the entire set of services.
The paper would do well to emphasize this caveat.
This point is illustrated by the examples identified by Smith et al in which weak
substitutability might lend insight. Both are drawn from the existing literature and in both, the
substitute goods are medical care and certain aspects of a cleaner environment. In other words,
the consumer is substituting an averting or mitigating behavior for a cleaner environment, in
both examples for their children. Agee and Crocker look at chelation therapy as a substitute for
removing lead from a child's environment; Mansfield et al study removing children from the
out-of-doors as a substitute for cleaning the air of pollutants that exacerbate asthma.
Certainly, if analysis of weak substitution can be as illuminating for environmental
valuation as weak complementarity has, as the authors suggest, then the examination of averting
and mitigating behaviors takes on a new importance. A simple application that comes to mind
might be to examine purchases of bottled water as the route to valuing cleaner water.
I wanted to draw attention to an important connection between the two papers. In the
final section of the Smith et al. paper, the authors highlight that in order to impose weak
substitution in analyses of the costs of mitigating or averting behavior, analysts need more
information about decision-making within the household . Clearly, Bergstrom's paper is a step
in the right direction to fulfilling that need.
To close, both papers advance the state of knowledge regarding non-market valuation
which ultimately is useful to policy-makers as an input into BCA; for analysts at the EPA for
BCA of environmental policy. The Bergstrom paper gives insight into family decision-making
and into the appropriate willingness-to-pay measures for children's health. The Smith, et al
paper suggests a new approach to valuing environmental services, and in the examples they
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offer, the value stems from protecting human health. These papers make clear contributions to
advancing policy-makers understanding of the benefits of human health protection.
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Mark Agee's Comments on: "Weak Substitution, Environmental Vulnerability, and Choice,"
by V. Kerry Smith, Mary F. Evans, H. Spencer Banzhaf, and Christine Poulos.
This paper examines usefulness of identifying a threshold demarcating
consumption and non-consumption of substitutes linked to an environmental amenity to
assess Hicksian welfare changes associated with amenity improvements.
The paper provides an interesting and seeming applicable framework for use of
revealed preference data to valuing environmental amenities. A highly desirable aspect
of this framework is its focus on observable goods demands (i.e., does not necessitate
specification/estimation of the consumers' underlying home production technologies) and
the consumers' observed tradeoffs between these demands.
The first part of the paper lays out a detailed graphical portrayal of the concept of
welfare measurement using weak substitution as another form of demand
interdependency that arises for private goods and environmental services. I found the
approach very interesting, and most of my comments/questions focus on my thoughts as
to how the approach might be put in to practice.
Application-related questions/comments:
On page 14, z is referred to (from this point on) as a "mitigating good." Given
this characterization, are we saying (or can we say) in effect that the separability notion is
one of partitioning the classes of goods (averting and/or mitigating) that identify as
substitutes in the individual's choice set—of which are then linked to the individual's
utility and environmental amenity through perceived health, or risk to health, etc.? If so,
then it seems that a binary choice model might be useful in identifying and estimating
key thresholds of interest (you refer to these thresholds as points of discontinuity in the
role for q) as well as identify the conditional demand for z?
• e.g., suppose Xa represents a substitute (averting) good such that, at a threshold, z
(a mitigating good) is no longer demanded. A binary choice model similar to
Agee and Crocker (1996) and Dickie and Gerking (1991) could be used to
identify either positive or zero consumption levels of z by estimating:
• v(P, Pz,Pr, q, y, m) + error,
or
• y[Pz, P, q, r, ™v (P, P„Pr, q, y, m)\ + error,
where v(-) is an econometric specification of a conditional indirect utility function for z,
and y accounts for personal characteristics.
Estimation of the probability of "positive" consumption would also provide
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• an estimate of P*,
the price of Xa that reduces z to zero (or the individual's estimated choice index below
the threshold), and
• an estimate of (the Marshallian) z as a function of prices, income and personal
characteristics: z(Pz,P,Pr,q,m,y) = - dvO/dPz ^ase(j on anaiySis 0f the
dv(-)/dm
threshold of no consumption.
The paper also mentions the importance of demographic and physical traits that
contribute to characterizing individuals who are differentially vulnerable to the
environmental hazard in question. If the model can be estimated as a threshold of zero
consumption, it seems that the level of q is also important in identifying key aspects of
the price P* since the relationship between goods linked to q can change as q changes:
• e.g., with reference to child lead exposure—there are burdens of body lead such
that mitigation is not even considered; burdens such that mitigation together with
exposure reduction are absolutely necessary (complementary goods); and burdens
(likely close to the threshold) such that exposure reduction can suffice for
chelation therapy (substitute goods).
• This of course would change the sign of the coefficient for P* (i.e., only used,
used with chelation, used as a substitute to chelation) in the estimated v(-)
expression.
In these cases, it seems that a set of interactions between P* and q (and between P* and
some of the personal characteristics) would be necessary to identify any critical
thresholds for potential sign-changes of the P* coefficient, as well as to correctly identify
(calibrate) measures of z0, zi, and P* for estimation of WTP.
Another estimation issue is encountered if X is multidimensional. If X is a vector, is
it in general necessary to identify the entire vector of X in order to correctly specify z?
• e.g., z might denote (one-dimensional) medical care consumption that mitigates
air pollution respiratory ailments; and X denotes exposure reducing activities that,
at a point, may render mitigation either very improbable or unnecessary..
Can the problem of multidimensionality of P in z be dealt with adequately by
estimating a specification of v[-] (e.g., like the second v[-] specification mentioned
above) that includes each individual's observed fraction, mv, of their budget allocated
towards z and a single selected element of P (such as the price of air purifiers)? If so,
since mv is a function of all prices, q, income, and personal characteristics, it seems that
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one might want to account for possible correlation between mv and the error term to
avoid potential bias of the P and other coefficients in the binary choice regression (see
e.g., Rivers and Vuong (1988) or Wooldridge (2002), p. 472 for cross section data; or
Jones and Landwehr (1988) for panel data).
—or—
Might it be possible to construct a one-dimensional averting activities index (like
intensity of use from a limited set of "most used" averting activities) with an
accompanying averting cost index that condenses P to a single measure for estimation?
Sources:
Agee, Mark, and Thomas Crocker. 1996. "Parental Altruism and Child Lead Exposure:
Inferences from the Demand for Chelation Therapy," Journal of Human
Resources 31: 677-691.
Dickie, Mark, and Shelby Gerking. 1991. "Willingness to Pay for Ozone Control:
Inferences from the Demand for Medical Care," Journal of Environmental
Economics and Management 21:1-16.
Jones, J. Morgan and Jane T. Landwehr. 1988. "Removing Heterogeneity Bias from
Logit Model Estimation," Marketing Science 7(1): 41-59.
Rivers, D., and Q.H. Vuong. 1988. "Limited Information Estimators and Exogeneity Tests
For Simultaneous Probit Models." Journal of Econometrics 39: 347-66.
Wooldridge, Jeffrey M. 2002. Econometric Analysis of Cross Section and Panel Data
Cambridge, Mass.: MIT Press.
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Suppose X9 represents a substitute [averting] good such
that—at a threshold—z [a mitigating good] is no longer
demanded. A binary choice framework can identify
either positive or zero consumption levels of z using:
• + error
--or--
. v[Pz,P,q,r,mv(P,Pz,Pr,q,y,m)] + error
where
K~) = specification of a conditional indirect utility
function for z
Y = personal characteristics
Estimation of the probability of "positive" consumption
provides
• an estimate of
P
*
a
• the price of X3 that reduces z to zero (the
individual's estimated choice index below the
threshold)
• an estimate of (the Marshallian) z :
dv(.)/dPz
z(Pz,P,Pr,q,m,y)
dv(-)/dm
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Mark Agee's Comments on: "Benefit Cost Analysis and Entanglements of Love,"
by Theodore C. Bergstrom
This paper develops a creative approach to addressing some important questions
about aggregation of willingness to pay (WTP) when WTP has altruistic connections
between individuals within a family. Four specific questions are addressed:
• When considering a public project that increases children's health, would it make
sense to calculate the aggregate value of that project by summing the average
parent's WTP by the total number of parents; or
• if parents (within the same household) reveal WTP differences for the project,
should the maximum or minimum of these values be used (exclusively) to
represent the entire household's value; and
• should children's own values be accounted for and included; and
• should values of family members outside the immediate family be counted.
These questions are addressed within the frame of a specific criterion: is the project
Pareto improving? That is:
• is it possible to implement the project and assign project costs to families in such
a way that, given the household decision structure, no family member is made
worse off and at least one member is made better off?
The initial part of the paper rearticulates this criterion by demonstrating that, if
parents have complete control of their family incomes, if one parent is forced to pay more
than his/her WTP for a project (implying project costs exceed the sum of parental WTP),
then the project is not Pareto improving—and thus the benefit-cost test for parents
provides a clear-cut gauge of satisfaction of the Pareto criterion.
The benefit-cost test is then applied to a variety of family structures involving one or
two parents with and without a single child, and a variety of family preference and
distribution structures common to the household decisionmaking literature. The paper
acknowledges that the preference and distribution assumptions of some of the models do
not accurately portray modern U.S. households. However, a few of these models had
structural assumptions that came (somewhat) close to the frameworks found in the
limited number of literature studies examining parental valuations of specific child health
attributes. Specifically:
• A parent decisionmaker who allocates after-tax income between own utility-
enhancing consumption and child utility-enhancing consumption;
• A parental utility function that derives utility from parental perceptions of child
utility; and
• An exogenous index of child health that enhances parent utility through child
utility.
Although the basic structure of these examples (within the context of the above
assumptions) preclude the possibility of endogeneity of parental decisions regarding child
health and child numbers, the paper demonstrates a result similar to prior studies:
• that parental WTP for a child's health improvement equals the health
improvement times that adult's MRS between own consumption and child health,
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but it also finds that
• the parent not charged with income allocation may reveal a different WTP for the
same child's health improvement—if this parent's marginal utility of child
consumption exceeds her marginal utility her own income allocation,
in which case it is appropriate to
• use only the lowest of the two parents' WTPs to represent the family's WTP for
the child's health improvement.
If a general household welfare function is used to link all family members' utilities, then:
• only one parent's WTP (which equals the other parent's and child's WTP) should
represent the entire household's maximum WTP for the child health
improvement.
However, if family utilities are disconnected (e.g., because of divorce or independent
budget arrangements) then
• the sum of adults' WTP for the child health improvement satisfies the benefit-cost
test.
These results suggest that aggregate WTP estimates of children's health
improvements may inaccurately reflect true WTP if calculated simply as the "average" of
parent's WTP multiplied by the number of U.S. parents. The paper highlights the
importance of how specification of family allocation processes and the structure of family
preferences can potentially impact aggregate WTP estimates. The question of whether to
aggregate by U.S. family numbers, number of U.S. parents, or by U.S. parents
categorized by their degree of "control" over household resources provides a good start to
better understanding how aggregate WTP for children's health improvements can most
justifiably be approximated. Listed below are some questions/comments that came to my
mind upon several readings of the paper:
First, I'm not entirely convinced of the plausibility of the argument on page 4
regarding strong substitutability between parental income and child health and the
potential for children being made worse off by their parents. The argument in the
household utility function that seems to be missing here is parental own health, which has
an intergenerational link (heritability) to child health. Would healthier parents (who
likely have healthier children) necessarily behave in this fashion? The question closely
parallels the discussion of parent and child endowments and parental investments in child
human capital found in Becker and Tomes (J. of Labor Economics., 1986, 4:S1-S39).
Although children with better endowments are much more productive/efficient utilizers
of human capital investments, better endowed parents still discount investments in their
(better endowed) children at lower rates and invest more resources in them.
Second, does the current preference structure impose that parents treat their children
as a "collective child" with an expressed, single willingness to pay for their improved
health? An important question in my mind is—if we randomly select one child in a
family would the parent's willingness to pay for that child's health improvement,
multiplied by child numbers be the correct sum? For example, suppose expressions (10)
and (11) in the paper incorporate a summation over n (predetermined) family members
thus creating a household welfare function that varies also by n. With this (seemingly)
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minor change, would the appropriate number for benefit-cost analysts likewise be a
single number representative of either parent or a single child—or would summing either
parent's response across child numbers overstate aggregate WTP by a factor of n-21
As an additional thought, the current preference structure has child utility nested in
parental utility reflecting the concern each parent has for their child, i.e., the parental
marginal utility of child utility. Perhaps child numbers could enter as in Becker, Murphy,
and Tamura (J. of Political Economy, 1990, p.S12-S37) who assume that, with diminishing
marginal utility of children, parental altruism is negatively related to child numbers (they
also refer to parental altruism as an intergenerational discount rate applied by parents to the
per capita consumption of their children). With this modification, how might diminishing
marginal utility of children relate to the parents' determination of WTP for child health
improvements, and does it provide any insights as to whether parental WTP is for 1 In or
some other fraction of child numbers?
Finally, another question might be posed with reference to the role of child health
in the determination of family utility. Certainly, the current exogeneity of child health in
child utility enables ease of mathematical tractability; however, if child utility is modified
such that parental allocations of child consumption goods also influence child health,
would endogeneity of child health bring about any changes in your results?
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Summary of Q&A Discussion Following Session II
Ronnie Leven (EPA, Region 1) stated that in addition to complications in the theory,
there are complications in the cases being used, specifically the lead abatement studies.
She went on to assert that "chelation therapy is not all good"and actually leads to a spike
in blood lead levels and a correlating spike in brain lead levels. She also noted the spike
in exposure after certain types of abatement that release lead paint dust into the air to be
inhaled, and she listed encapsulation, replacement, delay, improved maintenance, and
temporary removal as alternatives to immediate abatement. She ended by saying that the
studies on purchasing bicycle helmets also had some complicating health issues.
Scott Grosse (Centers for Disease Control and Prevention) suggested this extension for
Professor Bergstrom: Consider willingness to pay for health as a public good and not just
as a private good. Dr. Grosse stated that "if we treat health as a private good, then you
can't include the willingness to pay for the extended family members who also have
children of their own."
Professor Bergstrom responded by saying that he was thinking about how a particular
questionnaire related to a specific project should be framed ("it might be a local
community project, it might be a national whole airshed, or it might be a national
project"). To him it seems reasonable to ask someone, "How would you feel about an
improvement in the health of your child?" or, in fact, "How would you feel about an
improvement in the health of each of your seven children?" and then on to, "How would
you feel about an improvement in the health of your nephew?" Professor Bergstrom said
that he would propose evaluating that project then by building up from these micro-
answers.
Grosse: "But, it may be that people are not willing to spend "n" times as much to help
"n" children."
Professor Bergstrom reiterated that you would ask a sequence of questions-regarding the
valuation of the health of one's own children, and then on to a relative's children, and
even on to a stranger's children-as the building blocks to constructing a policy.
Ellen Post (Abt Associates, Inc.) told Professor Bergstrom that she was bothered by the
fact that assigning the willingness to pay value entirely to the dictator parent in a
dictatorial household model (and thereby ignoring the other parent because that person,
though possibly willing, has nothing to pay with) basically incorporates ////ra-household
politics into the policy assessment. She further stated that the belief "if one person
controls the budget then only that person's willingness to pay should be counted" would
be true for all similar situations of valuing non-market goods.
Professor Bergstrom replied, "Yes, we'll be a little careful about the "should," of course,
but essentially if you believe that your policy will not change the structure of household
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decisions, then it seems to me a realistic assessment of policy is the consequences of the
policy given the household structure." He also provided the reminder that, at least in
theory, this is "a benevolent dictator who buys the flavor of ice cream that his children
want, and so on," and clarified that "whether that theory is an accurate theory is yet
another question."
Post: "I guess I was just saying that the idea of saying that there are different kinds of
families with different intra-family politics which determine people's budgets-that has a
lot wider implications than, say, just children's health risks.
Bergstrom: "Indeed, I agree."
Laurie Chestnut (Stratus Consulting, Inc.): stated that she was "alarmed" at the
suggestion that we should be seeking to determine various relatives' willingness to pay
for a particular child's health. Citing a paper concerning altruism from a few years ago
by Jones Lee, she said it was her understanding that "if what people care about is other
people's utility, then the optimal allocation is just adding up everyone's willingness to
pay for their own utility change, and that takes care of everybody." She further stated that
it's only in the case where one cares about another's consumption of a specific thing that
the willingness to pay issue gets more complicated. She closed by saying, "what we care
about is each other's happiness, which I think is the primary model of families caring
about each other."
Professor Bergstrom responded that it's a bit tricky with a divorced family, where the
money transferred from the non-custodial parent to the custodial parent does not go
directly to the child-but, a health benefit does. He stated that if a divorced parent
voluntarily transfers money to the custodial parent, then one can presume that they had
come to an agreement about where marginal money should go.
Chestnut: "So, health might be a special case in some circumstances . . ."
Professor Bergstrom replied that he had put a lot of thought into the relatives issue and
concluded that if you're not willing to give your brother some money and say "go buy
your child some medicine," maybe that suggests that you find no extra valuation in that.
"On the other hand, it may be that institutions aren't well set up."
Don Kenkel (Cornell University) asked this of Robin Jenkins, referring to her discussant
presentation of Ted Bergstrom's paper: "Is the potential Pareto improvement criterion
really consistent with the Executive Order?-sort of plucking out children and saying,
"This deserves special attention."" Is this suggesting that even if the social welfare
function doesn't pass the sufficiency test, we should still worry about children's
welfare?"
Robin Jenkins: "In other words, do we want transfers to children?
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Kenkel: "Even if the parents don't want them."
Spencer Banzhaf (Resources for the Future) followed with a comment that he said is
actually very similar, and he pointed out that toward the end of Ted Bergstrom's
presentation, wasn't it ironic that there was clearly a potential for Pareto improvement,
but "the husband was made worse off because of the reallocation in the family?" He
concluded that "that irony raises this doubt about the usefulness of potential Pareto
criteria when the agency in charge of the policy does not actually have the power to
reallocate wealth . .
Kerry Smith (North Carolina State University) said that he had a different take: "If we
take the way Ted characterized the household model and different views of it and look at
what he's doing ... In environmental economics we have sort of two ways we've
approached looking at environmental policy: One way has been to present people with
programs, and we've said, "Here's a program to do this-or do something else, on a
national level." So the commodity that was actually in preferences was however they
conceived of the program, and there were all sorts of questions raised with respect to
"Well how should people have preferences about programs?" He's actually proposing to
commoditize programs, and so he's basically saying, "We're going to introduce a
program that has these kinds of consequences and let's be very, very specific about what
those consequences are-it would improve the health of child #1 this much, child #2, the
wife, and so forth. . . . But the challenge then becomes converting programs into what
commodities would change, so that now we have, if we get very, very specific, with
individuals-my nephew's health is going to improve; my niece is going to go down the
rathole or something-I then have to think about exactly how is that going to be
accomplished with the policy or with the program. So, we don't get around the challenge
of connecting policy to commodity outcomes-we simply do a better job of identifying the
features and preferences that we can recover from behavior and what we can't recover
from behavior, whether it's stated or revealed."
Professor Bergstrom responded that if people are asked how they feel about a policy that
they don't understand very well (which is typical), "their answer will be of some interest
to politicians, of course, but to welfare economists of less interest I suppose. The point
is, it always seems to me a useful thing to map policies to consequences as well as
possible."
Glenn Harrison (University of Central Florida) directed his comment at Professor
Bergstrom but said it was motivated by Robin's "paternalistic"comment that kids are not
rational. He said he was disappointed that Professor Bergstrom didn't address the issue
of how kids form preferences, and he lamented that all of the discussion so far in the
workshop totally ignored the kids preferences and went straight to the parents. "Now, I
understand the simplicity of doing that-I understand the logistic ease of doing that, but
it's a pretty sloppy way of thinking about the social welfare function. Just because kids
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are vertically challenged, we disenfranchise them." He summarized Robin's viewpoint
as being that kids don't have well-formed preferences so we can't rely on them, and then
he posed the question: "Shouldn't we be thinking about kids' preferences as state-
dependent, broadly defined, where the state is the information they have and at a certain
age and with a certain information load, they act more consistently over time? And the
question, then, is what implications does that have when you start thinking about social
willingness to pay as distinct from aggregating up from an individual willingness to pay?
And indeed, arguably we're interested in social willingness to pay."
Professor Bergstrom replied that it was "a lovely question" that he was reluctant to tackle
at the time due to the upcoming lunch break. He offered to speak to Dr. Harrison on the
subject later.
J.R. DeShazo (UCLA) commented, "Ted's presentation, I think, illustrates that when we
elicit values from parents what we're really eliciting are household preferences for
investments in children's health and the benefits that accrue to children as perceived by
the households, so that households can express the schedule of values for the children as
a function of the number of children they have, as a function of the governance structure
within the household. I simply want to point out that this approach misses the
fundamental theoretical construct that we're trying to recover, which are the net benefits
to the child of the policy. I think we should just recognize the disconnect between what
we can measure and theoretically what we optimally would like to know in order to set
the optimal policy."
Professor Bergstrom replied, "That is a technical issue that in a sense I did address. The
question is to what extent do the parents' evaluations of the child help represent the
child's interests. . . If there's complementarity between the child's health and the child's
conception, then definitely the parent will always be acting in the child's interest, and if
there's not, there are cases where indeed the parent will not, despite the fact that the
parent cares about the child's interests. I can't give you magical answers, you know."
Sandra Hoffman (Resources for the Future) said, "It seems to me that there is a logical
inconsistency in the discussion we're having here, because on the one hand we're saying
that children do not have well-formed preferences-they haven't developed the judgment
that's able really to express preferences-and yet when we look at parents' preferences,
we're looking at the child's utility entering the parent's utility function. So there's a
transformation going on there. We're not directly measuring the child's benefits, and
maybe we don't want to. So it seems to me that J.R.'s point still stands-we're at best
getting at a transformation, and perhaps . . ."
Professor Bergstrom clarified that this is not such a difficult issue-the parent's and the
child's notions of what's good for the child "needn't be identical-it's as simple as that."
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Glenn Harrison said, "But no one here has assumed that the child does not have well-
formed preferences."
Professor Bergstrom responded, "I've never made such an assumption. I think it's a very
interesting issue, but again, I don't want to spend our lunchtime here."
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Valuing Environmental Health Risk Reductions to Children
PROCEEDINGS OF
SESSION III: VALUING FETAL AND INFANT HEALTH EFFECTS
A WORKSHOP SPONSORED BY THE U.S. ENVIRONMENTAL PROTECTION AGENCY'S
NATIONAL CENTER FOR ENVIRONMENTAL ECONOMICS (NCEE), NATIONAL CENTER FOR
ENVIRONMENTAL RESEARCH (NCER), AND OFFICE OF CHILDREN'S HEALTH PROTECTION;
AND THE UNIVERSITY OF CENTRAL FLORIDA
October 20-21, 2003
Washington Plaza Hotel
Washington, DC
Prepared by Alpha-Gamma Technologies, Inc.
4700 Falls of Neuse Road, Suite 350, Raleigh, NC 27609
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ACKNOWLEDGEMENTS
This report has been prepared by Alpha-Gamma Technologies, Inc. with funding from the National Center
for Environmental Economics (NCEE). Alpha-Gamma wishes to thank NCEE's Kelly Maguire and
Project Officer Nicole Owens for their guidance and assistance throughout this project.
DISCLAIMER
These proceedings are being distributed in the interest of increasing public understanding and knowledge of
the issues discussed at the workshop and have been prepared independently of the workshop. Although the
proceedings have been funded in part by the United States Environmental Protection Agency under
Contract No. 68-W-01-055 to Alpha-Gamma Technologies, Inc., the contents of this document may not
necessarily reflect the views of the Agency and no official endorsement should be inferred.
11
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TABLE OF CONTENTS
Session III: Valuing Fetal and Infant Health Effects
Preliminary Research: Combining Psychological Economic Methods To Improve
Understanding of Factors Determining Adults' Valuation of Children's Health
Cheryl Asmus, Colorado State University 1
Pregnant Mother's Valuation of Own and of Child Health
Thomas Crocker, University of Wyoming 16
Commissioned Paper: Valuing Fetal and Infant Health: What Can Be Learned
From Empirical Health Economics Literature?
Don Kenkel, Cornell University 56
Discussant
Trish Hall, U.S. EPA, Office of Ground Water and Drinking Water 95
NOTE: Dr. V. Kerry Smith of North Carolina State University also presented discussant
comments, but his remarks are not included in these proceedings.
Summary of Q&A Discussion Following Session III 108
ill
-------
Of- -" A ¦.>' '"<>. OF' >-*' ^ ' *•.% ¦.>' .*• ' *;\ ..>'
Combining Psychological and Economic
Methods to Improve Understanding of
Factors Determining Adults' Valuation
of Children's Health
. ->¦ . ->¦ . >¦ m
Cheryl Asmus, Paul Bell, John Loom is, and
Helen Cooney
Colorado State University
/
:fc&'3m;
-------
.'W^fe'
4* uF- " ' '*;, uf- JF- ' ' •*;., '"" '''i; <*• •" "•*... •.-¦•'
Research Question
i f "f V f s ''^TV. ? ~ '$
• What are the factors that influence adults'
willingness-to-pay to avert risks to children's
health?
• Stressor -> Nitrate (N03) contaminated drinking
water
• Model -> Theory of Planned Behavior
• Method -> Survey and choice task
2
-------
Attitudes
Subjective
Norms
Behavioral
Intentions
Knowledge
Beliefs
Perceived
Control
Actual
Behavior
3
-------
gLv ¦W>^'''vi
•jf '^. wf •;• .;.•' -jf ^S. ¦ >' -jf \:; _-
Participants
5 "'^^. / "¦ ,; '"¦'$ ^ '-' '1§ f '-¦ " J? f f %.
• 520 participants
• 90 from Fort Collins (control group)
• 215 from the Eastern Plains of Colorado (experimental)
• 115 in consequential choice treatment
• 215 from the San Luis Valley of Colorado (experimental)
• 115 in consequential choice treatment
• The survey/methodology will be piloted on a
sample of 30 participants (10 from each of the
geographical areas listed above)
-------
Procedure
yf \\ *5? V ' V ']{ \\ "3? Y'
Survey will assess various components of TPB
with respect to the stressor and the various
behavior options
Respondents will be presented with a
contingent valuation task
• '3? v -S V '5 V ¦' - ¦$ v
5
-------
Contingent Valuation Task
Do Nothing
_ ± " V'JC ¦
Purchase
Bottled Water
Risk of Severe
Health Effects
Risk of Moderate
Health Effects
6
-------
Procedure (cont.)
3^ *, ,•
M-
¦3 iL
Half of the respondents in the two
experimental conditions will be instructed
that one of the decisions they make in the
contingent valuation task will be binding
v V '•? V 'yf v ¦ v '''S V -
7
-------
Current Status
Vfti
A '->?¦ " - <#" ' -'A
Expert Advisory Groups
i, > i, *, t3s'
• Survey development
contingent valuation task

¦M,.J' *
1 V .
f •' . • fifc
5g; V '3? V '}f V '"3? V '"3? V
• •**».%£/. • .-r: v£ • ** • r £T wsi^p- ~~ wff- <*'¦ ¦
mSk »: - rj$. "!fi/%
8
-------
yf- if'- ',S^S. yf. yf- ' ' uT ' uf >-*'
Nitrate Advisory Group
.•V ' '"9? V ¦ ^ V V '-y( V V V
• Survey should assess knowledge of
different potential sources of nitrate
contamination
• Survey should assess knowledge of how
responsibilities differ for public and private
water supplies
• Items regarding source reduction strategies
should be broad
9
-------
uT '^:, >••' uF' ' ' $., >-*' uF' ' -N, >-*' «#'• " '•V.i ->' ur V' 'S
Nitrate Advisory Group
V ¦ !? V- j/ V )/ V *$ V
• Survey wording should avoid "test-like"
quality
• Providing some participants with a reverse
osmosis filter would be problematic
.•V' '"5 V '® V ''•)/ V '*® V : V'
10
-------
••if'''?1'
~ '-r'i'. ef- -,>'.vS, >?• ' :• . «#'• ',"!'A >: df'- '"".'A v? • ' '' ;% ¦',/
Health Advisory Group
' '"S; )t' '¦'• '5 V *3? V '"5? V *$ V
• Should determine if the communities under
investigation have had cases of blue baby
syndrome
• Determine if each community has problems
with contaminants other than nitrate
• Survey should include items pertaining to
pre-natal exposure
11
-------
Health Advisory Group
V. V V 'V- V yf V
respondents' own infants and infants in the
community
12
-------
5k,"'jS;,;','V V: > V, •».; JL •».;
Methodology Advisory Group
• Choice task should be simplified
• The different behavior options should be
more compatible
• A practice round would be helpful in the
consequential choice treatment
• Survey should provide information
acknowledging that the options may be
beneficial for other reasons
13
-------
Methodology Advisory Group
v; "s. v ¦ - 5 v j v j v ¦ -
• Costs for the different options should be
constructed to be credible and to ensure that
some participants will actually purchase the
option
' j? V S? V "' S? V ' )? V ¦$ V
14
-------
Next Steps
'"i V ¦} V;'. f-, '- s " ••• V;'. '' s
Complete survey development
Translate survey into Spanish
Collect pilot data
'' 'jS. uF 'jS »* ^ ' itf"
/.J "' >*>. "' >.
?V '. '? V '? V '? V '•? i;
*¦- • ' -r: v£. ^(fr-%j£?*
- 'Y; ' •
15
-------
September 2003
Pregnant Mother's Valuation of Own and of Child Health*
by
Stefanos A. Nastis
and
Thomas D. Crocker
Department of Economics and Finance
University of Wyoming
Laramie, WY 82071-3985
JEL Classification: Dl; Q2
Keywords: Benefit transfers; birthweight productivity.
*A paper prepared for the USEPA Workshop on Valuing Environmental Health Risks to
Children, Washington, DC, October 20-21, 2003.
Although the U.S. Environmental Protection Agency provided financial support through Grant
#R2871601, the research has not been subjected to the Agency's required peer and policy review
and therefore does not necessarily reflect the views of the Agency.
16
-------
Table of Contents
Abstract 19
I. Introduction 20
Figure 1. A Causal Chain 22
II. The Endogeneity of Maternal Health 25
III. Model and Econometric Procedures 27
A. Model 27
B. Econometric Procedures 30
IV. Data Description 33
IV. Results 35
VI. Summary and Conclusions 41
References 43
Appendix 52
17
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List of Tables
Table 1. Summary Statistics 46
Table 2. Demand Estimates 48
Table 3. Mother's Period 2 Health (Weight Gain) 49
Table 4. Child's Period 2 Health (Birthweight) 50
Table 5. Mother's Value of Own Relative to Child Health 51
18
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ABSTRACT
The value an adult attaches to own health relative to child health is estimated when adult
health inputs are choice variables and adult health is an input to child health. Mothers' weight
gains during pregnancy and children's birthweights respectively measure adult and child health.
Estimates suggest mothers value child health about six times more than own health, and that this
relative value declines with number of siblings, increases with family income, and varies with
maternal consumption patterns.
19
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I. INTRODUCTION
This paper uses a pregnant woman's own - consumption in its various commodity -
specific forms to estimate the value she attaches to own - health relative to the health of the fetus
she carries. The current U.S. federal agency practice of transferring widely available adult health
benefit measures unadjusted to children's health gives the issue policy relevance.1 Also, except
insofar as it reduces household resources available to a child, the "child development" influence
of the commodity - specific particulars of a parent's own - consumption have been little studied
in economics. Yet parents engage in many activities which directly or indirectly give them
utility while simultaneously producing consequences for their children. Thus, for example, a
parent may drink alcohol excessively and subsequently abuse or neglect her child, or a pregnant
woman may indulge a diet which adversely affects the health of her fetus.
Because adults do not resemble children either biologically or economically, the current
U.S. federal agency practice of using unadjusted adult health economic benefit measures to
assess the benefits of improving children's health is suspect. Differences between the biological
responses of adults and children to many identical environmental stressors are widely
acknowledged. And children live with adults whose internal household allocation and
investment behaviors can amplify or temper these biological responses. The degree of
amplification or tempering many differ between adult and child because of differences in the
choices adults make for themselves and for their children. For example, the scope of the
activities adults choose for themselves is commonly less restricted than those they choose for
their child. Also, adult investments in children's health can be riskier and thus the return to
human capital investments less than equivalent own - health investments, given that children
1 See, for example, the health benefit transfer procedures propounded in Kuchler and Golan (1999), and in U.S.
Environmental Protection Agency (2000).
20
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have no performance records indicative of potential investment payoffs. Markets to insure
against this risk are more incomplete for children than for adults. But children have longer
expected life spans than do adults, which allows them to accumulate more human capital than an
adult whose capital stock is already largely built. Given the concavity of health investments
(Grossman, 1972) in producing human capital, the marginal productivity of investments in
children will exceed that of genetically similar adults. In general, the value to adults of own
relative to children's health improvements is an empirical question influenced by the relative
prices and the properties of the not always identical health hazard risk - reduction technologies
applied to adults and to children. Thus a similar health hazard exposure may induce quite
different marginal benefits and marginal costs for adult and for child health — physical,
intellectual, and emotional.
To estimate the relative value adults attach to own health relative to child health we focus
on the intrauterine environment a pregnant woman provides her fetus. The impact of the
intrauterine environment upon child health and development and ultimately upon that child's
adult well-being is a recent concern in economics that has a very large literature in other
disciplines. This noneconomic literature suggests the health of a fetus and its adult well-being
are connected through the causal chain depicted in Figure 1 involving both adult caretaker
behaviors and biological processes. The starting point is maternal health endowments and
behaviors. Maternal endowments and behaviors are linked to the intrauterine environment and
fetal growth, and to contemporaneous maternal health. The intrauterine environment and the
mother's contemporanceous health positively affect birthweight, which is positively linked to the
child's post-natal health (Institute of Medicine, 1990). Post-natal health is a significant positive
21
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Figure 1. A Causal Chain
Birthweight
Intrauterine
environment
Mother's
health
Post-natal health
Maternal endowments and behaviors
I
Adult production and consumption
determinant of the child's ultimate adult production and consumption and of its societal
contribution (Becker and Murphy, 1992).
For two reasons, our attention here is limited to the first three levels of Figure 1. First, as
Figure 1 suggests, there is evidence that the effects of lower birthweight are long-term, even
intergenerational (e.g. Hack et al., 1995; Barker, 1998; Currie and Hyson, 1999; Henriksen,
1999; Agee and Crocker, 2002). Lower birthweight children are less healthy than their peers,
and they do less well in school. Increasing birthweight increases adult earnings and schooling
(Behrman and Rosenzweig, 2001). Given that birthweight drives post-natal child health, it is
plausible that an adults' relative valuation of own to post-natal child health reflects the in utero
22
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investment the pregnant mother made. If so, an estimate of the own/fetus health valuation will
be predictive of the evolution of her own/child health valuation.
Second, maternal health has positive and negative impacts on post-natal child health. In
the post-natal setting, increased parental consumption or investments in own health impact the
household budget constraint, implying that child health and parent health are substitutes. Better
parent health or more consumption then implies lesser child health. But better parent health
frequently means the parent can provide the child a better quality of care, resulting in enhanced
child physical, intellectual, and emotional health. For the young child the net effect of an
increase in parental consumption or health investment depends on the sign of the sum of these
two factors. This sign is an empirical question dependent upon the mix of phenotypes of
individual household members and upon the determinants of intrahousehold resource allocations
to these members. Grasping the complexities of the mix and the determinants can be a daunting
analytical and empirical task, especially if adult and child behaviors are jointly determined or if
household public goods are present. In contrast, the sign of the connection between maternal
health and fetal child health is unambiguous: it is positive and unidirectional from mother to
2 3
fetus. This positive and unidirectional linkage is widely recognized in the medical literature.
A mother's morbidity and poor health habits result in growth retardation in utero, and,
consequently, a
2 See, however, The Economist (2003) which reviews literature suggesting that the fetus, when stressed, allocates a
greater share of available resources to brain development. No evidence exists that this reallocation fully
compensates for poor maternal health or health practices in all dimensions of post-natal child health.
3 ACC/SCN (2000) provides a thorough review. Other reviews are to be found in Battaglia and Simmons (1979)
and in Kramer (1987). This same literature presents evidence consistent with the marginal products of many post-
natal inputs for lower birthweight children being less than those for normal birthweight children. Thus the
disadvantage of lower birthweight may become progressively greater with age.
23
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reduced birthweight for her child.4 The health of the fetus defined in terms of its realized
birthweight for a given gestation period is the result only of its genotype and the
contemporaneous health behaviors and health state of its mother. No other intervening or
mediating influences enter.
Both the biomedical health and the health economics literatures report the results of
extensive research on the determinants of birthweight.5 The economics literature can be
distinguished from the biomedical literature by the emphasis of the former on the endogeneity of
many health inputs, unobserved heterogeneity, and selectivity of women who become pregnant
and who produce live births. This paper extends the previous economics literature in two ways.
First, while continuing to account for input endogeneity and selectivity, it treats the pregnant
mother's health as endogenous. Second, this treatment of the health of the pregnant mother as
endogenous permits derivation of the value this mother attaches to own health relative to the
health of her fetus. We find the contemporaneous, endogenous health of the pregnant mother to
be a significant determinant of the health of her fetus, where fetus health is defined as its live
birthweight. Our representative mother values the health of her fetal child about six times more
than she values her own health.
The next section discusses the implications of the endogeneity of contemporaneous
maternal health for estimates of birthweight production functions. A third section develops a
model of birthweight production which provides restrictions for an econometric specification.
The data used to estimate the birthweight production function are described in a fourth section
4 The medical literature defines low birthweight (LBW) as a weight at birth less than 2500 grams, about 5.5 pounds.
LBW results from premature birth and intrauterine growth retardation. This purportedly universal threshold fails to
consider variations in genetically determined normal birthweights.
5 Economic interest in the issue appears to have first appeared with Rosenzweig and Schultz (1982). Representative
subsequent treatments in the economics literature include Grossman and Joyce (1990), Rosenzweig and Wolpin
(1991), Levinson and Ullman (1998), Warner (1998), Evans and Ringel (1999), Joyce (1999), and Abevaya (2001).
24
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and estimation results take up the fifth section. A summary of and caveats about results
conclude.
II. THF FNDOGENEITY OF MATKRYAI HI AI TII
Epidemiological research (e.g., Kirchengast and Hartman, 1998; Shapiro et al., 2000)
unequivocally concludes that a mother's weight gain during her pregnancy has a strong positive
influence on her child's birthweight. This weight gain is a function of her preconception health
endowment and her nutritional and morbidity state while pregnant (Institute of Medicine, 1990).
Her nutritional and morbidity state while pregnant is influenced by her contemporaneous health
input behavior (Osami and Sen, 2003). That is, the pregnant mother's health as measured by her
contemporaneous weight gain is an endogenous input to her child's birthweight. Physicians
recognize this as they recommend behaviors for individual mothers which they think will result
in a weight gain for her conforming to guidelines recommended by the American College of
Obstetrics and Gynecology (1998).
Although development economists (e.g., Strauss, 1986; Devlalikar, 1988) frequently treat
weight as an endogenous variable in studies of labor productivity, none of the economics
literature dealing with birthweight takes account of the possible endogeneity of the pregnant
mother's health as measured by her pregnancy weight gain.6 To see the consequences of this
neglect for acquiring accurate insights into the determinants of birthweight, let the pregnant
mother's health (her pregnancy weight gain), hm, be determined by
hm=hm(z,y,vm) (1)
6 Nor does it even account for the mother's anthropometry. Warner (1998) is an exception but he treats the mother's
weight gain as exogenous.
25
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where vm is the mother's phenotype (her genetic and social inheritances), y represents the health
infrastructure (predetermined or exogenous social, environmental, and economic factors such as
her marital status, employment, income, education, and access to health services), and z is a
vector of endogenous inputs such as prenatal care.
The health technology of the child (its birthweight) h° is described by
hc=hc(hm,z,y,vc), (2)
where vc is the child's genotype. The relationship between the mother's and the child's health is
made explicit in (2) by including the mother's health, hm, as an argument in the child's health
n
technology. This same relation between parent and child health also holds for a young child,
but it is most vivid for a fetus.
The effect of a marginal improvement of the exogenous health infrastructure, y, and of
the endogenous health inputs, z, on the child's health is:
d^_djf_ dhc dhm
dy dy dhm dy ^
dhc dhc dhc dhm
dz " dz + dhm dz (4)
The differences between reduced forms that ignore the endogeneity of maternal health in the
child's health technology and a structural system which accounts for endogeneity are the second
terms in expressions (3) and (4). That is, the marginal products of changes in y and in z depend
upon their direct biological effects, the Sh7dy and the dh7dz, and the indirect effects, the
(<9h7<9hm)( <9hmA9y) and the (<9h7<9hm)( <9hm/<9z), representing the mediating influence of the
mother's health. To neglect these indirect effects is to presume that parents ignore the effect of
7 For example, an ill parent can engage in fewer activities with her child. She is able to do less with and for her
child.
26
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own-health on child health. If the presumption is incorrect, then, for example, the negative effect
of a decline in exogenous health infrastructure or in positive endogenous health inputs on child
health will be understated. The decline directly reduces maternal health as well child health and
the decline indirectly reduces child health via its effect on maternal health. Similarly, the
presumption will understate the effectiveness of an infrastructure or chosen input increase since
an improvement in the mother's health improves the child's health.
III. MODEL AND ECONOMETRIC PROCEDURES
A. Model
Let a cooperative equilibrium exist between parents such that household preferences can
be described by a single preference function. Consider a two-period model, j = 1,2, where in the
first period the resolution (abort, carry) of the pregnancy is determined. In the second period the
fetus is carried to birth. The mother chooses the quantity of health inputs, Zj, to allocate to own
and to child health in each period. She also chooses own consumption of a composite good, Xj.
Her maximal expected two-period utility is then:
V= maxU(%(h1m(-\z1,yyi\x1) +
8{e{K)v\zi )+ (i- eiKW\4)\
(5)
where
V1 = max U(h£ {h% (z\,y, v™ ),z\,y,vc2), x\)
z2 ,x2
(6)
V2 = maxU(0,xl),
(7)
and
WM o,i]
(8)
27
-------
7 /'• -v • /',-••
(9)
Ij is income in period j, 8 is the mother's fixed discount rate, and 6(hf) is the probability that the
child is born alive. It is assumed that the mother does not die with the birth of the child. The
superscripts on z and x are 1 for a live birth of the child and 2 otherwise. 9 (hf) is a
monotonically increasing continuous function of the child's first-period health. The mother's
health is a pure investment commodity in that she values own health only as an input into her
child's health (Grossman, 1972). While pregnant, the mother makes first-period allocations of
health inputs based on her expectations of the child's survival, the health endowments, vcand vc,
health input prices, pz, social, environmental, and economic factors, y, and income, I, in both
periods. In the second period, the child is born or not, uncertainty is resolved, and the allocation
problem is static. The maximal expected utility for the live birth state is V1{z\ , x\ ), and
V2{xl ) otherwise. If the fetus is not born, its health is normalized to zero in the second period
and the optimum is = 1 . First-order conditions are derived in the Appendix.
Given a live birth, the mother's valuation of her child's health can be derived from the
dual of her second-period allocation problem. Presuming that the expenditure function
associated with this dual is continuous, strictly increasing, and unbounded above in U, as well as
nondecreasing, homogenous of degree one, concave, and differentiable in prices, this problem
can be written as
min pjx\\pjz\ (10)
z\ .x\ X2 22
subject to:
(11)
28
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where U\ is the mothers maximal utility in the second period, given a live birth. Efficiency
requires
u\-u\ = 0
p j + X U1l = 0
4. 3du*
p71 + ^
r)K r)K dh™
r)K \ dz\ dtt? dz\
= o.
(12)
(13)
(14)
where X is the Lagrange multiplier.
With a live birth, solution of the problem in (10) and (11) yields parental demand
functions for consumption, x\, and the health inputs, which, when substituted into the
budget constraint, yield the expenditure function for the second period

(15)
By the envelope theorem, the mother's valuation of a change in the health infrastructure is:
de2(-) ,dU\ (•)
&
A-
A
dU\ c)K dU\ C)K C)K

(16)
dh^ dy dh^ dh!£ dy
Substituting for X from expression (14):
de20
dy
r)ti2 c)h'l dh
dy dh% dy
~d% dhfdh?'
1 1 ^ "|j ffl 1 m
dz2 dn-, dz2
(17)
which says that, given a live birth, a mother's marginal valuation of an exogenous improvement
in health infrastructure is her monetized marginal rate of substitution between y and z.
29
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A mother's marginal valuation of her child's health is:
3e,(;) dU\ 3%
~^r=x
m dvc2
-p,
r)l% r)ti2 ()h"2
y dz\ dh% dz\ j
dK
(18)
\dv2j
that is, a mother's marginal valuation of an improvement in her child's health is defined as the
tradeoff between family income and the marginal improvement. Similarly, a mother's valuation
of own health is:
de2(-) xdU\dK
dvZ
dv"2
-p,
f)l% dh2 dh2
dz\ dh% dz\
dhc2 dh™
(19)
dtt? dv.
2 J
A mother's value of own health relative to her value of child health is then
den
dK (dh?/dvZ)
d%~dh" (d%/dvZ)'
dvc
(20)
which is the marginal improvement of own health relative to the marginal improvement in child
health.
B. Econometric Procedures
In contrast to the great bulk of the biomedical literature, the economic literature on the
household production of health emphasizes that technical processes together with prices and
income condition a person's or a family's health input choices. Thus simple correlations
between inputs and health outcomes cannot be used to determine causality. Specifically,
30
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unbiased estimates of technical family health relationships such as those derived above must be
obtained from a behavioral framework in which health inputs are endogenous. To account for
heterogeneity in the production of mother's and of child's (fetus') health, we propose the
following four equation system: 1) the child's health production to determine survival selection
through the first period; 2) the mother's health in the second period for children who survive the
first period; 3) the surviving child's health in the second period; and 4) the mother's demands for
health inputs in both periods.
Given the mother's utility maximizing quantities of health inputs, a linear representation
of the child's period one health production is
K = (y,Pi,P2)'A)'a2 + mc«3 + (21)
where jJ + e{ - v,. jJ is the child's observable endowment, and ecx is that facit of the
endowment known to the mother but unobservable to anyone else. The (y,pi, P2)' and (Ii, I2)'
vectors determine the mother's utility-maximizing equilibrium quantities of the z\. Second
period prices and income appear in (21) because the child's first period survival depends on the
mother's expected second period behaviors. For hcx < 0, the mother expects the child will not
survive or a spontaneous abortion occurs. With hcx > 0 the mother carries the child to birth. The
child's first period health is therefore an indicator variable taking a zero if the child is not born
and one if it is born. Failure to account for selection in the resolution of pregnancies will bias
estimates of the consequences of the mother's second period decisions (Grossman and Joyce,
1990). Unacknowledged adverse selection, where women who make relatively small
investments in health care are more likely to give birth, will bias downward the estimated
productivity of health investments. Favorable selection, which refers to women who are more
31
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likely to give birth when they make large investments, will, when unacknowledged, impart an
upward bias.
The mother's second period health is
h~ = z2pi + yp2 + iim P3 + eZ, (22)
and the surviving child's second period health is
/22c = z21^4 + ^5 + 4^6 + M% + <. (23)
Given that the child survives the first period, the estimating equation of the mother's second
period decision rule for the z2 is
A = + Guc„0'72 + m + 02, (24)
where 2 = «,<).
Our empirical strategy proceeds by obtaining first-stage estimates of the z. and then
applying the fitted values of these quantities to estimate the hc. and the h™. First period health
for the mother is considered to be predetermined. This is reasonable given that this first period
corresponds to the three months immediately after conception. The four equation system is
expressions (21) through (24) applies to our entire sample of pregnant women but expressions
(22) and (23) are observed only for women for whom > 0. Moreover, some health inputs
such as prenatal care visits will be influenced by whether or not h° > 0. These truncations imply
that the error terms among expressions (21), (23), and (24) will be correlated since some of the
32
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same health input factors that influence first period child survival also influence second period
child health. We correct for this problem by assuming that the joint distributions of (e[,ec2) and
of (e[,§2) have bivariate normal densities which allows application of Heckman's (1979) two-
stop selection correction procedure. Following Grossman and Joyce (1990), we implement the
procedure by estimating expression (21) as a bivariate probit function, compute the inverse of the
Mills ratio, and then insert this inverse as a regressor into expressions (22), (23), and (24).
IV. DATA DESCRIPTION
Our data come from the 1988 National Maternal and Infant Health Survey (NMIHS), a
data set specifically designed to acquire information on pregnancy outcomes for American
women. After eliminating 13,479 observations with incomplete data, and data referring to
adolescent mothers, mothers more than 35 years old, gestations less than 20 and more than 45
weeks, and birthweights less than 400 and more than 6,000 grams, our full sample of 12,876
o
mother/child observations remained with 10,644 live singleton births. The NMIHS data was
augmented with physician visit costs and with cigarette price per pack for each of 48 states
(Montana and South Dakota refused to participate in the NMIHS).9 About 25 percent of the
sample mothers are homemakers exclusively. Their reservation wages were calculated using the
1983 estimated reservation wage equation of Hofler and Murphy (1994) inflated to 1988 by the
U.S. Consumer Price Index. The wages variable thus represents observed wages for working
mothers and calculated reservation wages for homemakers.
8 Grossman and Joyce (1990) and Werner (1998) employ similar elimination criteria.
9 Physician visit costs are calculated from the 2000 Medicare Physician Fee Schedule as the Nonfacility Fee Amount
deflated to 1988 by the U.S. Bureau of Labor Statistics' Consumer Price Index. Cigarette prices include all
applicable state taxes for 1988, as cited in the Tobacco Institute (1997).
33
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Table 1 provides summary statistics and descriptions of the data we employ. A Durbin-
Wu-Hausman test (Greene, 2000) suggested endogeneity for the mother's number of prenatal
care visits while pregnant and the number of weeks she delayed her initial visit after her last
menstrual period. If no care was sought, a delay of 45 weeks was assumed. This delay variable
is thus a negative correlate of the quantity and quality of care and should thus have a negative
coefficient in the probability of survival and birhtweight production function estimates. In
addition to the mother's health, other variables the test proposed as potentially endogenous in
one or more estimated expressions are the order of birth (parity) and smoking during the
pregnancy.
A long list of variables finally treated as exogenous appears in one or more estimated
expressions. Included among them are distance in minutes to a prenatal care facility and the
days not engaged in paid work while pregnant as measures of the time sacrifices the mother
made. The days the mother took off from work are thus treated as a medical necessity. Price
measures include the mother's wages and the cost of a pack of cigarettes. Her anthropometric
and sociodemographic features are represented by the mother's race, age, marital status, number
of household children, number of household smokers, prior smoking habits, number of prior
induced and spontaneous abortions, and prepregnancy body mass index (weight in kilograms
divided by height squared in meters), and the child's gender. Attributes of the mother's
pregnancy include the number of nights she was hospitalized while pregnant, gestation, and
dichotomous variables to indicate whether or not general pregnancy problems/complications
existed and whether efforts had to be made to prevent a premature delivery. The mother's
education, household income, WIC support, Medicaid or insurance coverage, drug use, residence
in a metropolitan area, mental health (CES Total Scale) while pregnant, and whether or not the
34
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pregnancy was wanted are included to reflect the mother's health knowledge, stress and
attitudes, and her propensity to seek medical care.
Our objective is to estimate expression (20), the marginal contribution of mother's health
to her child's health. Expression (20) says that this is simply the utility-maximizing marginal
product of a one unit change in mother's health upon child health. Thus, a meaningful
comparison of a change in mother's health (weight gain) relative to an improvement in child
health (birthweight) induced by a common source requires a common measure. This is
accomplished via a linear monotonic transformation of the distribution of mother's weight gain
and child's birthweight such that these distributions have identical means and variances. The
two transformations are:
birthweight in grams ^
! standard deviation of birthweight ^ ^
weight gain in grams
1 s tan dard deviation of weight gain
f (26)
/— weight gain in grams \
+ {h - mean( — )).
standard deviation of weight gain
The i subscript refers to a sample child or mother and hc is the sample arithmetic mean for
expression (25).
V. RESULTS
The potential selectivity bias in a straightforward estimate of the birthweight expression
in (23) is quite strong since almost 18 percent of the pregnancies in our sample were aborted. If
the mother's second period utility is positively correlated with the child's birthweight, then
35
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abortions, which cause birthweight to be observed only for live births, push the observed
distribution of the mother's utility to the right. Following Heckman (1979), we correct this bias
by estimating expression (21) in linear form for the full sample, using two-stage probit (Lee et
al., 1980) while assuming a bivariate normal form. We then computed a correction factor, the
inverse Mills ratio, for each of the sample women who gave birth. This ratio, which had an
arithmetic mean of 0.3079, and a standard deviation of 0.0963, was then inserted as a regressor
in expression (22), (23), and (24). As a regressor, this selection correction factor can be
interpreted as proportional to the inverse of the probability that a pregnancy is terminated.
Because epidemiological evidence suggests that almost none of the mother's weight gain
occurs in the first trimester (Kramer et al., 1992), mother's first period health is treated as
exogenous in the birth probability equation and is measured by her anthropometric and
sociodemographic endowments. A Durbin-Wu-Hausman test (Greene, 2000) suggested
endogeneity of smoking, parity, the number of prenatal care visits, and delay of the first such
visit in the birth probability equation. Reduced form demand functions for these variables were
estimated by OLS for the full sample of 12,876 mother/child observations. All of the previously
mentioned exogenous variables were treated as regressors except for all of the variables
describing the mother's pregnancy attributes, prior abortions, drug use, and mother's body-mass-
index (BMI) immediately before her current pregnancy. The fitted values for these four
endogenous variables were then entered as regressors in the birth probability equation along with
mother's age, mother's wantedness attitude, and the immediately aforementioned exogenous
variables that were excepted from the demand estimates. Fitted versions of the number of
prenatal care visits, delay of the first such visit, and parity were statistically significant positive
correlates of birth probability and smoking was a statistically significant negative correlate. Of
36
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the exogenous variables entered in the birth probability equation, only the coefficients for
mother's age and for her BMI were significant at less than 5 percent. Both exhibited negative
signs.
Table 2 presents OLS estimates for the endogenous regressors in period 2. Since birth
selection for the current pregnancy cannot affect parity and is presumed not to affect period 2
smoking behavior, the demand expressions for these two variables do not include the Mills
correction and thus apply to both periods 1 and 2. Among the more notable of the results for the
smoking expression is the positive impact of prior smoking or smoking while pregnant and the
statistical insignificance of the impact of cigarette price upon smoking while pregnant. These
results are consistent with an addiction to smoking.10 The elasticity of the mother's smoking
while pregnant with respect to prior smoking is 0.967. Her education has an elasticity of -.379,
implying that she chooses to consume about 8 fewer daily cigarettes while she is pregnant when
she has an additional year of education.
Consistent with Rosenzweig and Schultz (1983), more educated women who earn higher
wages experience fewer pregnancies and have them later in life. However, the Table 2 finding
that women living in urban environments have higher fertility is contrary to Rosenzweig and
Schultz (1983). Black mothers and mothers who are depressed get pregnant less frequently, all
else equal.
10 Another source of addiction is alcohol intake. Rosenzweig and Wolpin (1991) and Warner (1995) find that
alcohol use is not a significant influence upon birth weight. Our preliminary birthweight regressions confirmed this
result, perhaps because more than 90 percent of the pregnant mothers in our full sample drank less than one
alcoholic beverage per month. Some 83 percent of the full sample were nondrinkers while pregnant and only 1.1
percent drank more than one drink daily. Our NMIHS full sample is likely not rich enough to capture any
birthweight effect from alcohol.
37
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The estimated demand equations for the number of prenatal care visits (xvisit) and the
delay in the initial visit (visit) exhibit favorable selection, contrary to Joyce (2001). Most other
results are consistent with those obtained by Grossman and Joyce (1990). However, the Table 2
result that married women who are pregnant have lesser delays for their initial prenatal care visit
contradicts Grossman and Joyce (1990). The Table 2 finding that an unwantedness attitude and a
depressed state of mind reduce and delay prenatal care suggest that convincing pregnant women
to seek medical help is more than a matter of simply manipulating economic and easily observed
sociodemographic factors.
Table 3 presents 2SLS estimates for the mother's period 2 health (mother's weight gain,
transformed). Only visit-hat is endogenous. It thus represents fitted values from the visits
equation in Table 2. The Mills correction for selection is statistically insignificant. Most Table 3
explanatory variables, including visit-hat, are also insignificant but weight gain is positively
responsive to black mothers and to women who were big before becoming pregnant, and
negative with respect to mother's age. The positive and statistically significant result for wages
is consistent with numerous biomedical and economic results (e.g., Grossman, 1972) indicating a
positive association between health and wealth. The positive signs attached to the statistically
significant coefficients for depression (ces-total) and drug use defy ready explanation.
Table 4 presents birthweight equations estimated by TSLS. Each column of Table 4
represents a combination of the endogeneity or the exogeneity of weight gain for mothers who
gave live births, h%, and a correction or lack of such for selection via the termination of a
pregnancy. When a selection correction is made as in Columns (1) and (2), because the inverse
Mills ratio is a non-linear function of the variables included in the first-stage probit model, the
38
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second-stage model is identified even if the regressors in the first and second stage models are
identical. Nevertheless, as an extra identification precaution, two exclusion restrictions were
imposed. First, there is at least one covariate in the first-stage not in the second-stage; second,
there is at least one variable in the instruments for each endogenous variable that does not appear
in the second-stage. Basically, enabling variables such as income, insurance, etc., were assumed
to affect birthweight only indirectly through the mother's weight gain.
A version of Sargan's (1976) test, known as the Pagan-Hall (1983) test, for
misspecification in models with instrumental variables failed to reject at the 1 percent level the
hypothesis of no misspecification for our complete set of instruments.11 However, a Breusch-
Pagan (1979) test revealed heteroskedasticity between the error terms in the mother's weight
gain and the child's birthweight equations. Consequently, three-stage least squares estimates
were obtained. These 3SLS estimates caused the Mills selection correction variable to become
insignificant in the birthweight equation and reduced the magnitude of the coefficient for the
number of prenatal care visits without altering its statistical significance. Coefficient estimates
and levels of statistical significance for the other covariates in Table 4, including especially the
endogenous and the exogenous versions of the variables for mother's health, were essentially
12
unchanged. Given the focus of the paper upon the mother's value of own relative to child
health, the following discussion centers upon Table 4 and its value implications.
All columns of Table 4 indicate that mother's pregnancy weight-gain is a positive and
statistically significant influence upon the child's health. More importantly, by treating the
11 See Godfrey (1988, pp. 174-176) for a succinct exposition of these tests.
12 For example, the 2SLS estimate for - hat with selection is .160 with a standard error of .014; for the 3SLS
estimate it is . 170 with a standard error of .019.
39
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mother's weight gain as endogenous, one increases this positive influence by a factor of three.
Failure to take into account the indirect effect of the mother's health upon the child's health
greatly underestimates the importance of the mother's health behaviors to the child's health.
Apart from mother's health, there are only very minor differences across columns in the
coefficients for the Table 4 regressors. However, there are substantial differences for the
selection and no selection results for the case of mother's health endogeneity as well as that for
exogeneity. The effect of the number of prenatal care visits is two times higher with than
without selection, as is the effect of parity. An accounting of selection has little effect upon the
birthweight influence of drugs, smoking, gestation, or gender.
Expression (20) implies that the coefficient on h% - hat in Table 4 measures the mother's
value of own relative to her child's health. For the case of no selection, - hat has a value of
.170, implying that the representative mother values her child's health about six times more than
her own health. Thus four conclusions emerge from Table 4: 1) pregnant mothers value child
health more than own health; 2) mother's health and child health are complements; 3) the
indirect effect of maternal behaviors increases the estimated contribution mother's health makes
to child health; and 4) selection due to pregnancy termination does not affect the estimated
contribution of maternal health to child health.
The contribution of maternal health to child health and thus the mother's value of own to
child health was also estimated for subsamples of the NMIHS women who gave live births.
Table 5 gives the results. The most striking difference emerges for nulliparous women (this
pregnancy is their first child) and women who already have at least one child. If mother's health
40
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is endogenous, nulliparous women value their child's health relative to their own health more
than twice as much as do other women who have had children. This result is consistent with the
tradeoff between the quantity and the "quality" of children emphasized by Becker and Lewis
(1973). Nonsmoking mothers appear to value their children more highly than do smokers. More
income, as reflected in the income, medicaid/no medicaid, and married/not married subsamples
seems to increase the relative value of child health. Education also increases this relative value,
perhaps because of the opportunity costs of the time a mother expects she will subsequently have
to devote to a born child.
VI. SUMMARY AND CONCLUSIONS
We have presented a framework suitable for estimating the value an adult attaches to own
health relative to child health when health inputs are endogenous and adult health is an input to
child health. Heretofore, no research has specifically examined the impact of adult behaviors on
own health and thence upon child health. Though our focus is upon pregnant woman and the
child they carry, the framework could, likely at considerable cost in analytical and empirical
complexity, be extended to the care adults provide post-natal children. A parent's discretionary
behaviors affect her contemporaneous health and this health impacts what she can do with and
for her child. What she does with and for her child influences its health. By aiding her own
health, the mother helps her child's health.
When the maternal health input to child health is treated as endogenous our empirical
results indicate that, on average, pregnant mothers value the prospective health of their as yet
unborn children about six times more than they value own health. Treatment of the maternal
health input as exogenous will reduce the estimated impact of this input upon child health
41
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relative to the impact when it is treated as endogenous. Consequently, for a given observed child
health improvement, part of the contribution of maternal health to this improvement will be
attributed to other health inputs, thus reducing the estimated value of maternal health relative to
child health.
Our empirical results also suggest that the mother's relative valuation of own and of child
health is sensitive to her personal and family characteristics and behaviors such as number of
siblings for the child, family income, and maternal consumption patterns (e.g., smoking).
The result that pregnant mothers value own health considerably less than they value child
health promotes skepticism about the one-to-one transfer of adult health benefits measures to
children. Whatever the average relative valuation employed, they also promote caution about
use of a one-size-fits-all constant for these transfers.
42
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References
Abrevaya, J. (2001), "The Effects of Demographics and Maternal Behavior on the Distribution
of Birth Outcomes," Empirical Economics 26:247-257.
ACC/SCN (Administrative Committee on Coordination/Sub-Committee on Nutrition) (2000), J.
Podja and L. Kelley, eds., Low Birth weight. Nutrition Paper #18, Geneva, Switzerland:
World Health Organization.
Agee, M.D., and T.D. Crocker (2002), "Parents' Discount Rate and the Intergenerational
Transmission of Cognitive Skills," Economica 69:143-154.
American College of Obstetrics and Gynecology (1998), Guidelines for Perinatal Care.
Washington, DC: American Academy of Pediatrics.
Barker, D.J.P. (1998), Mothers. Babies and Diseases in Later Life. London, U.K.: Churchill
Livingston.
Battaglia, F. C., and M.A. Simmons (1979), "The Low-Birth-Weight Infant," in F. Falkner and
J.M. Tanner, eds. Human Growth. Vol. 1, New York, NY: Plemum Press.
Becker, G.S., and H.G. Lewis (1973), "On the Interaction between the Quantity and Quality of
Children," Journal of Political Economy 8:S279-S288.
Becker, G.S., and K.M. Murphy (1992), "The Division of Labor, Coordination Costs, and
Knowledge." Quarterly Journal of Economics 107:1137-1160.
Behrman, J.R., and M.R. Rosenzweig (2001), The Returns to Increasing Body Weight. Working
paper, Department of Economics, University of Pennsylvania.
Breusch, T.S., and A.R. Pagan (1979), "A Simple Test for Heterosckedasticity and Random
Coefficient Variation," Econometrica 47:1287-1294.
Currie, J., and R. Hyson (1999), "Is the Impact of Health Shocks Cushioned by Socioeconomic
Status?" The American Economic Review 89:245-250.
Deolalikar, A.B. (1988), "Nutrition and Labor Productivity in Agriculture, "The Review of
Economics and Statistics 70:406-413.
Evans, W.N., and J.S. Ringel (1999), "Can Higher Cigarette Taxes Improve Birth Outcomes?"
Journal of Public Economics 72:135-154.
Godfrey, L.G. (1988), Misspecification Tests in Econometrics: The Lagrange Multiplier
Principal and Other Approaches. Cambridge, U.K.: Cambridge University Press.
Greene, W.H. (2000) Econometric Analysis. 4th ed., Princeton, NJ: Prentice Hall.
43
-------
Grossman, M. (1972), "On the Concept of Health Capital and the Demand for Health," Journal
of Political Economy 98:983-1007.
Grossman, M., and T.J. Joyce (1990), "Unobservables, Pregnancy Resolutions, and Birth Weight
Production Functions in New York City," Journal of Political Economy 98:983-1007.
Hack, M., N.K. Klein, and G. Taylor (1995), "Long-term Developmental Outcomes of Low
Birth Weight Infants," The Future of Children 5:19-34.
Heckman, J.J. (1979), "Sample Selection Bias as a Specification Error," Econometrica 47:153-
161.
Henriksen, T. (1999), "Fetal Nutrition, Fetal Growth Restriction and Health Later in Life," Acta
Paediatrica 429s :4-8.
Hofler, R.A., and K.J. Murphy (1994), "Estimating Reservation Wages of Employed Workers
Using a Stochastic Frontier," Southern Economic Journal 60:961-976.
Institute of Medicine (1990), Subcommittee on Nutritional Status and Weight Gain During
Pregnancy, in Nutrition During Pregnancy. Washington, DC: National Academy of
Sciences.
Joyce, T. (1999), "Impact of Augmented Prenatal Care on Birth Outcomes of Medicaid
Recipients in New York City," Journal of Health Economics 18:31-67.
Joyce, T. (2001), "Self-Selection, Prenatal Care, and Birthweight among Black, Whites, and
Hispanics in New York City," Journal of Human Resources 29:762-794.
Kirchengast, S., and B. Hartman (1998), "Maternal Prepregnancy Weight Status and Pregnancy
Weight Gain as Major Determinants for Newborn Weight and Size," Annals of Human
Biology 25:17-28.
Kramer, M. (1987), "Determinants of Low Birth Weight: Methodological Assessment and Meta-
Analysis," Bulletin of the World Health Organization 65:663-737.
Kramer, M., F. McLean, E. Eason, and R. Usher (1992), "Maternal Nutrition and Spontaneous
Preterm Birth," American Journal of Epidemiology 136:574-583.
Kuchler, F., and E. Golan (1999), Assigning Values to Life: Comparing Methods for Valuing
Health. Agriculture Economics Report No. 784, Food and Rural Economics Division,
Economic Research Service, U.S. Department of Agriculture, Washington, DC.
Lee, L., G.S. Maddala, and P.R. Trost (1980), "Asymptotic Covariance Matrices of Two-Stage
Probit and Two-Stage Tobit Methods for Simultaneous Equations with Selectivity,"
Econometrica 48:491-503.
Levinson, A., and F. Ullman (1998), "Medicaid Managed Care and Infant Health," Journal of
Health Economics 17:351-368.
44
-------
Osami, S., and A. Sen (2003), "The Hidden Penalties of Gender Inequality: Fetal Origins of Ill-
Health," Economics and Human Biology 1:105-121.
Pagan, A.R., and A.D. Hall (1983), "Diagnostic Tests as Residual Analysis," Econometric
Reviews 2:159-218.
Rosenzweig, M.R., and T.P. Schultz (1982), "The Behavior of Mothers as Inputs to Child
Health: The Determinants of Birth Weights, Gestation, and Rate of Fetal Growth," in
V.R. Fuchs, ed., in Economic Aspects of Health. Chicago, IL: University of Chicago
Press.
Rosenzweig, M.R., and T.P. Schultz (1983), "Estimating a Household Production Function:
Heterogeneity, the Demand for Health Inputs, and Their Effects on Birth Weight,"
Journal of Political Economy 9:723-746.
Rosenzweig, M.R., and K.I. Wolpin (1991), "Inequality at Birth: The Scope for Policy
Intervention," Journal of Econometrics 50:205-228.
Sargan, J.D. (1976), Testing for Misspecification after Estimating Using Instrumental Variables.
Unpublished paper, London, U.K.: London School of Economics.
Shapiro, C., V.G. Sutija, and J. Bush (2000), "Effect of Maternal Weight Gain on Infant Birth
Weight," Journal of Perinatal Medicine 28:428-431.
Strauss, J. (1986), "Does Better Nutrition Raise Farm Productivity?" Journal of Political
Economy 94:297-320.
The Economist (June 14, 2003), "The Child is Father to the Patient," :78-79.
Tobacco Institute (1997), "Historical Compilation," The Tax Burden on Tobacco, vol. 32.
U.S. Environmental Protection Agency (2000), Guidelines for Preparing Economic Analyses.
EPA 240-R-00-003, Washington, DC.
Warner, G.L. (1995), "Prenatal Care Demand and Birthweight Production of Black Mothers,"
The American Economic Review 85:132-137.
Warner, G.L. (1998), "Birthweight Productivity of Prenatal Care," Southern Economic Journal
65:42-63.
45
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Table 1. Summary statistics, n=12,876
Variable
Mean
Std. Dev.
Description of variables
abortions
.4344517
.9231301
Number of previous abortions, induced and spontaneous
alive
.8265219
.3786747
Dichotomous: 1 if child was born alive
attitude
.4558356
.498065
Dichotomous: 1 if pregnancy was not wanted
bweight
2579.276
1111.054
Baby's birth weight in grams
ces_total
13.99845
12.10674
CES Depression scale for pregnant mother
children
1.180147
1.384186
Number of children in the household
cigprice
130.9913
9.75674
Price of one packet of cigarettes, including all taxes in cents (1988 US
dollars)
distance
20.40993
16.35411
Distance in minutes to prenatal care provider
drugs
.0755332
.2642599
Dichotomous: 1 if mother used drugs in the 12 months before delivery
gender
.4740597
.499346
Dichotomous: Baby's gender 1 if female
gestation
35.97053
5.837431
Length of gestation in weeks
health_child
2.321469
1
Child's health index, transformation of child's birth weight
health_mother
2.321469
1
Mother's health index, transformation of mother's weight gain
income
25672.04
21067.1
Total annual household income, whole dollars (1988 US dollars)
insurance
.6350523
.4814341
Dichotomous: 1 if mother had health insurance at delivery time
mage
26.57325
4.242554
Mother's age in years
marital
.6201629
.485365
Dichotomous: 1 if married
mbmibefore
28.04287
5.512001
Mother's Body Mass Index before pregnancy
medicaid
.3010469
.4587308
Dichotomous: 1 if covered by Medicaid
meduc
12.59558
2.318349
Mother's education in years
metro
.777027
.4162565
Dichotomous: 1 if family lives in metropolitan area
nights
7.8185
13.80952
Number of nights hospitalized during pregnancy (excluding delivery)
parity
.8675456
1.428883
Number of previous pregnancies
premature
.3535259
.4780827
Dichotomous: 1 if action was taken to prevent premature delivery
prenatalcost
361.44
27.406
Cost of prenatal care visit, whole dollars (1988 US dollars)
46
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Table 1. Summary statistics (cont.)
priorsmoke
5.077975
9.224811
Number of cigarettes smoked by the mother prior to pregnancy, per day
problems
.8952314
.3062669
Dichotomous: 1 if complications with pregnancy
race
.528425
.499921
Dichotomous: 1 if mother is black
smokers
.480817
.8589116
Number of smokers in the household
smoking
3.065995
6.889637
Number of cigarettes smoked by the mother during pregnancy, per day
totaldays
66.40775
110.6519
Total days the mother did not work
visit
10.41171
8.45774
Weeks since pregnancy started before first prenatal care visit
wages
37043.31
23570.97
Mother's wages annually, whole dollars (1988 US dollars)
wgain
9586.068
9881.782
Mother's weight gain during pregnancy, in grams, after birth
wic
.3422257
.4744731
Dichotomous: 1 if WIC food aid provided during pregnancy
xvisits
11.23893
6.130369
Number of prenatal care visits
Note: The mother's and the child's health index transformation is explained in the text. The WAGES variable also includes
reservation wages for homemakers, as explained in the text.
47
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Table 2. Demand Estimates
visit xvisit smoking parity

Coefficient
t
Coefficient
t
Coefficient
t
Coefficient
t
distance
-.085
-18.12
.027
7.64
-.005
-2.14
-.003
-3.98
attitude
3.202
14.27
-1.381
-8.09
.189
2.37
.054
2.27
children
.535
8.38
-.273
-5.64
.231
8.00
.368
42.46
wic
-2.185
-9.95
1.440
8.63
-.121
-1.30
-.054
-1.94
insurance
-1.482
-7.01
.653
4.06
-.190
-2.09
-.318
-11.63
marital
-1.386
-6.92
.872
5.73
-.309
-3.23
-.010
-0.35
mage
-.123
-5.78
.046
2.84
.034
3.75
.034
11.71
race
-2.978
-9.20
2.463
10.00
-.068
-0.78
-.288
-11.14
meduc
-.227
-5.87
.208
7.07
-.092
-5.01
-.073
-13.19
wages
-,103e-04
-2.70
,688e-07
2.37
,476e-07
2.83
-,336e-07
-6.65
income
,266e-04
-5.36
,128e-04
3.39
-,930e-07
-3.96
,299e-08
0.42
medicaid
.929
4.01
-.460
-2.61
.084
0.81
.120
3.84
total days
,225e-04
0.03
.002
2.96
-.001
-1.98
,162e-07
0.02
metro
-.485
-2.46
.247
1.65
.063
0.68
.142
5.12
cigprice
.011
1.28
-.014
-2.17
-.002
-0.49
-,047e-03
-0.04
cestotal
-.073
-4.70
.060
5.06
.006
1.97
-.005
-5.09
prenatal cost
-.004
-1.33
.005
1.95
.001
0.50
.002
4.36
priorsmoke
.045
5.23
-.007
-1.13
.584
142.20
.012
10.12
mills
22.689
8.37
-17.234
-8.36
—
—
—
—
Constant
15.350
9.80
9.028
7.58
.349
0.50
.153
0.73
Observations 10,644 10,644 12,876 12,876
F-statistic 102.42 48.30 1293.63 247.29
R* .1548 .0795 .6443 .2572
Note: All estimates were obtained by ordinary-least-squares.
48
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Table 3. Mother's Period 2 Health (Weight Gain)
K
Coefficient
t
distance
-.001
-0.51
attitude
-.003
-0.08
children
.008
0.97
wic
-.074
-1.50
insurance
-.058
-1.50
marital
.002
0.05
mage
-.014
-5.58
race
.010
4.29
meduc
.005
0.84
wages
,126e-07
3.14
income
,123e-07
1.78
medicaid
-.003
-0.11
total days
,146e-03
-1.69
metro
-.032
-1.32
cigprice
-,458e-03
-0.48
cestotal
.004
4.35
prenatal cost
.001
1.67
priorsmoke
-,848e-04
-0.08
mbmibefore
.074
45.11
gestation
.003
2.08
drugs
.111
3.17
visit-hat
-.008
-0.56
mills
.161
0.76
Constant
.208
0.63
Observations
10,644

F-statistic
99.45

R2
.1708

Note: Estimated by two-stage-least-squares. Variables denoted with a "-hat" are endogenous.
49
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Table 4. Child's Period 2 Health (Birthweight)
(1) Endogenous/ (2) Exogenous/ (3) Endogenous/ (4) Exogenous/No
Selection Selection No Selection Selection
K
Coefficient
t
Coefficient
t
Coefficient
t
Coefficient
t
visit-hat
.018
1.49
.019
1.74
.008
1.70
.007
1.51
xvisits-hat
.051
5.07
.055
5.47
.029
3.20
.028
3.09
parity-hat
.039
3.96
.040
4.05
.020
2.18
.016
1.77
smoking-hat
-.012
-9.98
-.012
-10.29
-.010
-8.95
-.010
-8.95
drugs
-.071
-3.28
-.066
-3.03
-.068
-3.13
-.062
-2.83
h™ ~hat
.160
11.51
—
—
.170
12.32
—
—
K
—
—
.055
9.76
—
—
.057
10.11
mills
.346
4.88
.423
6.00
—
—
—
—
gestation
.134
144.49
.136
147.20
.134
144.20
.136
147.00
gender
-.104
-9.45
-.104
-9.45
-.106
-9.60
-.106
-9.63
Constant
-3.639
-20.34
-3.530
-19.75
-3.185
-20.82
-2.956
-19.55
Observations
10,644

10,644

F-statistic
2546.65

2533.73

2855.86

2836.60

R2
.6831

.6820

.6824

.6809

Notes: All estimates were obtained by two-stage-least-squares. Variables denoted with a "-hat" are endogenous. The columns
denote whether or not h™ was treated as endogenous, and whether or not a selection correction was made.
50
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Table 5. Mother's Value of Own Relative to Child Health.
With endogeneity Without endogeneity
Subsample
Observations
Coefficient
z
R2
Coefficient
z
R2
Whites
5234
.1546
5.19
.5189
.0552
6.25
.5558
Blacks
5410
.1789
6.38
.7000
.0527
7.14
.7165
No other children
3967
.1005
3.08
.6622
.0524
5.72
.6777
One or more children
6677
.2254
8.52
.6261
.0601
8.16
.6524
Pregnancy wanted
5628
.1621
5.42
.6562
.0531
6.78
.6688
Pregnancy not wanted
5016
.1810
6.45
.6211
.0604
6.82
.6319
Not insured
3922
.1717
5.32
.6125
.0658
5.97
.6200
Insured
6722
.1700
6.60
.6759
.0489
7.17
.6936
Unmarried
4158
.1902
6.40
.5650
.0712
6.88
.5925
Married
6486
.1561
5.05
.6842
.0458
6.52
.6971
Not on Medicaid
7344
.1589
5.95
.6863
.0535
8.05
.6940
On Medicaid
3300
.2065
6.01
.4565
.0663
5.83
.4897
Live outside
metropolitan area
2312
.1955
3.29
.6234
.0813
6.30
.6279
Live inside
metropolitan area
8332
.1673
7.83
.6038
.0509
7.84
.6134
Nonsmoker
7808
.1440
5.99
.6703
.0475
7.20
.6823
Smoker
2836
.2381
5.26
.4572
.0811
6.80
.4632
Education<=12 years
6458
.1864
6.85
.6240
.0614
7.62
.6388
Education >12 years
4186
.1391
4.58
.7044
.0472
5.37
.7132
Homemaker
4014
.1833
5.97
.5411
.0591
5.84
.5688
Employed
6630
.1718
6.41
.6939
.0563
8.13
.7060
Income< 10000
3250
.1960
4.61
.4428
.0724
5.19
.4801
Income <=50000
6925
.1640
6.68
.6610
.0563
8.07
.6729
Income >50000
1059
.1497
3.74
.6747
.0196
1.21
.6852
The results are based on two-stage least squares without selection.
51
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Appendix
52
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Appendix
The problem of the parent is to maximize her expected "lifetime" utility. Her maximal
expected "lifetime" utility in the first period is:
V= maxE{U(%[h?(.\z1,yyilx1) + (A.l)
Zl,*l
si8wv\4,4)H i-
V'= ma*u(h;(h?(4,yX),4,y,vl),xl) (A.2)
zl ,x2
V2 = maxt/(0,jc22) (A.3)
x22
WM0,1] (A.4)
I j = PxXj + PZjPj (A.5)
where Xj is period j parental consumption, Ij is period j income, 8 is the parent's discount rate and
9 is the probability of a "normal" pregnancy. We assume that each period's income is
predetermined (labor supply decisions for the mother are exogenously determined), the parent's
discount rate 8 is fixed and the probability of the child born alive 9 is a monotonically increasing
continuous function of the child's health in the first period. Superscripts on x and z in equation
(A.5) are omitted for notational simplicity. The mother chooses X21 and z2' at the beginning of
period one.
Substituting the budget constraint (A.5) into equations (A.l), (A.2) and (A.3), the system
becomes:
V = maxE{U(h;(h?(Zl,y,vm),zj,vf \Iy- pxzx) +
(A. 6)
)+ (i-emK^y,<)^yy,\W\zl)]}
V = max U(hc2(h™(z\,y,v™),z\yy2),I2 - p2z\) (A.7)
z2
53
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V2 = max£7(0,12 - p2z22) (A.8)
z2
The optimal 7.2 is the solution to equation (A.6). Efficiency requires that:
rl3Udh£ dU dhc2 dh2 dU
V ' <)K dz\ + <)K dh™ dz\ ~ Pl dcx (A'9)
The first term in equation (A.9) is direct effect on utility of a change in z on the
child's health, as would be predicted if only the "reduced-form" effect was considered,
and the second period, given that the child does not survive, the mother does not consume
any health inputs for the child, therefore:
V2:x2 = — (A. 10)
o
Equation (A.8) states the familiar result of consumer theory that in order to
maximize utility, the parent must allocate resources so as to make the ratios of marginal
utilities equal to the ratios of prices.
Efficiency for equation (A.6) requires that:
dEU r)h; dEU r)h; dh" dEU dCl e r)d . r)d 2 ,
()h'\ dzl + r)h; dhT dzl ~ dc, dz,Pl+ [dz,V ~ dZlV ]~° (A11)
where
dd dd dh: dtt Sh™
(A'12)
54
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Equation (A. 11) is the marginal change in the probability of survival in the second period
from a change in z. The solution of the problem comes from solving the first-order
condition (A.8), and then (A. 10).
55
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Valuing Fetal and Infant Health:
What Can Be Learned from Empirical Health Economics Research?
Don Kenkel, PhD
Department of Policy Analysis & Management
Cornell University
Currently, Academic Visitor
Department of Economics & Related Studies
University of York
Heslington York
United Kingdom
dsklO@cornell.edu
dkl6@york.ac.uk
October 2003
Preliminary draft prepared for presentation at "Valuing Environmental Health Risk Reductions to
Children," October 20 - 21, 2003, Washington DC. Comments welcome.
56
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I. Introduction
Despite many encouraging trends in environmental quality, serious environmental health
threats to fetal, infant, and child health remain. For example, some research suggests that
particulate matter air pollutants may be associated with higher infant mortality.1 In 2001
approximately 25 percent of children lived in counties that exceeded the annual standard for
particulate matter (US EPA 2003). This suggests a similarly large fraction of all pregnant
women may be exposed to unhealthy levels of particulates The importance of fetal and infant
health is underscored by the inclusion of data on birth defects in California as a Special Feature
in the most recent EPA (2003) report on America's Children and the Environment. As the EPA
notes, "birth defects are leading cause of infant death in the first year of life, accounting for about
20 percent of infant deaths in 1999." Although some birth defects are inherited, environmental
and public health policies may be able to reduce nongenetic risk factors for birth defects, and
improve fetal and infant health more generally.
Benefit-cost analysis of policies to improve fetal, infant and child health requires
valuation of those health improvements. A number of studies extend market and non-market
approaches to estimate willingness to pay for child health. Because children are not in the labor
market and do not make independent consumption decisions, the studies focus on parents'
decisions that affect the health and safety of their children. Analysis of parents' child safety seat
use, automobile purchases, and bicycle helmet purchases provides estimates of willingness to pay
1 In addition to the references in US EPA (2003), Chay and Greenstone (1999, 2001)
analyze data on infant mortality, birthweight, and air quality improvements in the early
1970s and the early 1980s. Their findings suggest a strong relationship between air
quality as measured by total suspended particulates and infant mortality rates, and a
somewhat weaker relationship between air quality and birthweight.
57
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for child mortality risks , summarized as the value of a statistical life for a child (Carlin and
Sandy 1991; Mount etal. 2000; and Jenkins, Owens and Wiggens 2001). Other child health
effects valued include: child lead exposure (Agee and Crocker 1996); colds (Liu etal. 2000);
risks of non-melanoma skin cancer (Dickie and Gerking 2001); lifetime cancer risks (Maguire,
Owens and Simon 2001); and child health effects related to secondhand smoke exposure (Agee
and Crocker 2001). However, there seem to be few if any existing estimates specific to the
value of fetal and infant health.
The goal of this paper is to examine the implications of empirical health economics
research for the valuation of fetal and infant health. Section II sets the stage by reviewing
illustrative empirical evidence on the various ways parents invest in prenatal health, including
market purchases such as medical care, and lifestyle changes such as smoking cessation. Section
III presents a simple version of the standard household health production model, to serve as the
theoretical framework for the valuation expressions and the empirical research to be reviewed.
Section IV reviews health economics research that estimates infant health production functions.
Combining the estimates of the marginal product of prenatal care with estimates of the full price
paid yields estimates of parental marginal willingness to pay for infant health. Section V reviews
studies of maternal demand for cigarettes and alcohol during the pre-natal period, and discuss the
implications for fetal and infant health valuation. Section VI discusses health economics studies
2
In the recent review by Neumann and Greenword (2002), all of the studies of effects
associated with prenatal exposure use the cost-of-illness approach. The review includes
estimates of willingness to pay to reduce infants' mortality risks, based on Dickie and
Nestor's (1999) analysis of the results of Joyce, Grossman and Goldman (1989).
58
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that estimate the impacts of public policies on fetal and infant health, and explores whether these
can be used to shed light on the health valuation question.
At the outset, limitations of the scope of this paper should be noted. The emphasis of the
paper is on lessons from health economics, so the environmental economics research literature is
not reviewed in depth. The valuation approach is to infer parents' willingness to pay for fetal
and infant health based on their preferences as revealed in the markets for medical care,
cigarettes, and so on. The paper does not review studies from three other approaches that shed
light on health valuation: the cost-of-illness approach; the contingent valuation or stated
preference approach; or the quality-adjusted life year approach used in cost-effectiveness
analysis. To date, most evaluation studies relevant to fetal and infant health follow the cost-of-
illness approach; for summaries of these studies see Neumann and Greenwood (2002). Cost-of-
illness estimates provide a lower bound to willingness to pay (Berger et al. 1987, Kenkel 1994),
so these estimates are a way to check the plausibility of willingness to pay estimates from other
approaches. Two contingent valuation studies estimate willingness to pay related to infertility
risks (Neumann and Johanneson 1994, Smith and Van Houten 1998), but the implications for the
value of fetal and infant health are not clear. Finally, in principle it should be possible to follow
the common approach in cost-effectiveness analysis and estimate the number of quality-adjusted
life years lost from fetal and infant poor health and death. For example, the Harvard Catalogue
of Preference Scores includes weights to calculate the quality-adjusted life years for children with
a range of neurologic disabilities. However, in all of the cases the preference scores were
measured based on author or clinical judgement, and so may not reflect either parental or societal
preferences over these health states.
59
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II. Parental Investments in Prenatal Health: An Overview
Table 1 provides an overview of maternal investments in prenatal health. The data are
from the National Maternal and Infant Health Survey (NIMHS) 1988, conducted by the National
Center for Health Statistics. The 1988 NMIHS consists of three independent national files of live
births, fetal deaths and infant deaths. The full sample consists of 18,594 mothers who had a live
birth, fetal death or infant death in 1988. Of these 18,594 mothers, 9,953 women had live births,
"3
3,309 had late fetal deaths and 5,332 had infant deaths. Table 1 presents the patterns of prenatal
investments for the full sample and for each of the sub-samples.
As can be seen in Table 1, during the prenatal period women invest both money and time
to improve fetal health. Virtually all (98 percent) of pregnant women in the U.S. receive prenatal
medical care, and on average make almost 13 prenatal visits. Additional data from the NMIHS
(not reported in Table 1) indicate that about a third of the women report paying for the prenatal
care out of their own income. In addition, some of those whose care was covered by private
insurance or Medicaid still incurred out-of-pocked costs due to copayments or coinsurance,
although data on this was not collected in the NMIHS. Women also incurred time costs to travel
to and receive prenatal care; the average travel time to prenatal care for NMIHS respondents was
about 21 minutes.
3 In 1988, there were 3,898,922 live births to women between 15 and 49 years of age, 15,259
fetal deaths of 28 weeks or more gestation, and 38,917 infant deaths to United States residents.
The overall probability of the 1988 NMIHS selection was about 1 of every 354 live births, 1 of
every 4 fetal deaths and 1 of every 6 infant deaths. The overall response rate for the national file
of 18,594 mothers is 71%; it is 74% for live birth mothers, 69% for fetal death mothers, and 65%
for infant death mothers.
60
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In the full sample, 38 percent of pregnant women also attend prenatal childbirth class, but
fewer women in the fetal death and infant death samples attend such classes. About 80 percent
of pregnant women take multivitamins and/or minerals at least three days a week after they found
out they were pregnant, up from about 25 percent of women who took vitamins before they found
out they were pregnant.
Women also commonly make lifestyle changes after they find out they are pregnant. In
the 1988 NIMHS, pregnancy is associated with a drop in the prevalence of smoking from 30
percent to 22 percent. Even those women who continue to smoke while pregnant still on average
report that they decreased the amount, from about 16 cigarettes per day to 12 cigarettes per day.
Pregnancy is also associated with a drop in the prevalence of drinking alcohol, from 45 percent to
21 percent. And those women who continue to drink while pregnant on average report that they
decreased the amount, from 9 drinks per month to about 3 and a half drinks per month. The
only exception to these patterns is that is somewhat more common for women to quit exercising
after they discover that they are pregnant than it is for women to start exercising.
The data in Table 1 are presented to make the broad point that during the prenatal period
women make substantial investments in fetal health. Table 1 neglects some investments, such as
changes in maternal diet and illicit drug use, as well as all paternal investments in fetal health.
On the other hand, because the data are self-reported, the changes in maternal behavior may be
over-stated. It also should be noted that while women invest in fetal health, in many cases their
choices are not optimal from the public health viewpoint, i.e. their choices do not maximize fetal
health. For example, public health goals call for increasing the proportion of women who
receive early and adequate prenatal care from its 1998 level of 74 percent to a 2010 target level
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of 90 percent (USDHSS 2000). Nevertheless, it is clear that many women are willing to
sacrifice money, time, and cigarette and alcohol consumption to improve the health of their
unborn children. The next section outlines the standard economic approach to modeling this
behavior.
III. Conceptual Framework
This section considers a highly simplified one-period version of Grossman's (1972)
household production model of the demand for health and health-related goods. Assume the
mother receives utility from consuming a numeraire good X, her infant's health IH, and from
smoking cigarettes S: U = U(X, IH,S). The mother may purchase in the market prenatal medical
care (M), which does not provide utility directly, but is used to produce the commodity infant
health according to a household production functions. Infant health is also assumed to depend on
maternal smoking, and exogenous influences such as environmental quality, E: IH = IH (M, S,
E).
The mother chooses X, S, and M to maximize her utility subject to a standard budget
constraint and the household production function. The first order conditions for this
maximization problem implicitly define goods demand functions for X, S, and M as functions of
market prices, income, and the parameters that describe preferences (U (.)) and the technology of
household production (IH (.) ). Formally, the model also includes a commodity demand function
for infant health, which is conceptually distinct from the infant health production function.
Before discussing empirical applications, some brief comments on this theoretical model
are in order. Grossman's (1972) seminal model contains two key features: first, that health is a
commodity produced in the household; and second, that health is a form of human capital. The
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focus here is on behavior during the prenatal period and the production of fetal and infant health,
so the model is simplified to one period and abstracts from the dynamics of health capital over
the life cycle. Grossman (2000) provides a comprehensive review of theoretical and empirical
work based on his human capital model of health, while Currie (2000) contains an intertemporal
model of parents' investments in child health. By focusing on the mother's utility function, the
model also abstracts from the more complex problem of decision-making within the family. This
extension is discussed in a series of recent health economics papers (Jacobson 2000, Case and
Paxson 2001, Bolin, Jacobson and Lindgren 2001, 2002), as well as by Bergstrom (2003).
The general structure of the household production model of health provides the
conceptual framework for a great deal of empirical research in health economics. One approach
is to estimate a structural health production function as a function of endogenous health inputs
and exogenous factors. Section IV of this paper reviews research on the household production
of infant health in the U.S. , but the approach has also been commonly used in the context of
low-income countries (e.g., Barrera 1990, the Cebu Study Team 1992).
The Grossman model also provides the explicit or implicit framework for empirical
studies of the demand for various health-related goods. Section V of this paper reviews some
recent research on the demand for cigarettes and alcohol by pregnant women. These papers are
extensions of an extensive empirical literature reviewed in several chapters of the Handbook of
Health Economics: Chaloupka and Warner (2000) review empirical studies of the demand for
cigarettes; Cook and Moore (2000) review empirical studies of the demand for alcohol; and
Kenkel (2000) reviews empirical work on the demand for prevention broadly defined. As
Kenkel (2000, p. 1685) points out, while some empirical studies have tight links between the
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structure of the theoretical model and the empirical specification, more commonly the theoretical
model only provides general guidance for the empirical investigations, for example in terms of
the explanatory variables to be included in a demand model.
A number of recent studies take one step further away from structural models, and focus
on reduced-form estimates of the impacts of public policies on health, including the impact of so-
called "natural policy experiments." This approach can be used to study the impact of policy
changes on health outcomes and on the use of health inputs. For example, Currie and Gruber
(1996) examine the impact of Medicaid expansions on infant mortality; Currie and Grogger
(2002) examine the combined impact of Medicaid expansions and welfare reform on both the use
of prenatal care and fetal deaths. However, it is not in general appropriate to interpret the
estimated equations as either structural production functions or demand functions. As
Rosenzweig and Schultz (1983) demonstrate, the estimated coefficients from such hybrid
equations will generally be mixtures of preference and technology parameters. Section VI
discusses some examples from this body of research.
IV. Health Production Function Estimates and the Value of Infant Health
Willingness to Pay Expression
The health production function approach is a well-established method in environmental
economics research on the valuation of health as a non-market commodity (Freeman 1993, pp.
344-360). It is a revealed preference approach to valuation, where consumers' demand for a
health input reveals the value they place on the health output. The model in section III can be
used to derive the standard expression for marginal willingness to pay (MWTPe) for a health-
improving change in environmental quality (E). To complete the model sketched above, assume
64
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a simple goods budget constraint: Y = X + pm M + ps S; where Y is income and pm and ps are
the money prices of medical care and cigarettes. (Recall that X is the numeraire good so its price
is normalized to one.) To find the MWTPe, set the total derivative of the utility function equal to
zero and substitute in the first order conditions. After some manipulations, the change in income
necessary to hold utility constant after a change in environmental quality can be expressed as a
ratio of the technological parameters of the production function, which can be interpreted as the
marginal rate of technical substitution between E and M in producing infant health:
MWTPe = d Y/ d E = (IHE/ Mm ) Pm
As Freeman (1993, p. 349) stresses, one of the advantage of this expression is that on the
right hand side "all of the measures are functions of observable variables that can be calculated
given knowledge of the production function." Strictly speaking, the valuation expression
involves the individual's perceptions of the parameters of the health production function. It is
therefore typically assumed that, at least on average, individual perceptions are correct, so
econometric knowledge of the production function translates into knowledge of consumers'
perceptions of the production function. Unless extra data are collected on individual perceptions,
this type of assumption is common in the revealed preference approach. For example, many
studies of the value of a statistical life make comparable assumptions about the risks associated
with labor market and consumption decisions (e.g. Viscusi 1992a, Jenkins, Owens, and Wiggins
2001).
The household health production approach has been used to estimate marginal
willingness to pay for air quality-related health improvements for adults (Gerking and Stanley
1986) and infants (Joyce, Grossman and Goldman 1987). Dickie and Gerking (1991) extend the
65
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analysis to consider multiple symptoms, i.e. multiple health outputs. If the number of health
inputs exceeds the number of symptoms to be valued, it is still possible to express the marginal
willingness to pay for each symptom as a ratio of the technological parameters of the household
health (symptom) production function. Agee and Crocker (2001) provide a recent example of
the approach with multiple health outcomes, namely child and adult health. They use cross-
sectional data on parents who are smokers from a 1991 follow-up of the 1988 National Maternal
and Infant Health Survey (NMIHS). Each household in the sample has a three-year-old child.
Agee and Crocker use these data to estimate a structural household production model of parents'
smoking behavior, adult health, child secondhand smoke exposure, and child health.
The expression for MWTPe relies on the assumption that prenatal care is only demanded
as an input into infant health production. In many cases, important health inputs either provide
utility directly, such as cigarette smoking in the model sketched above, or enter some other
household production function.4 When an input like S is jointly demanded for several reasons,
the MWTPe can not be expressed as the marginal rate of technical substitution between E and S.
Instead, unobservable utility terms remain in the expression. Section V below discusses an
approach to health valuation in this situation.
The approach in previous environmental economics studies is to estimate directly the
necessary parameters of the health production function, including the marginal product of
environmental quality on health (IHe). As is noted elsewhere (Freeman 1993, p. 349, Dickie
1999), implementing this approach is thus very demanding of the data. Of particular relevance to
4More accurately, cigarette smoking jointly enters the infant health production function,
enters the mother's utility function directly, and enters the health production function of
the mother. This extension is sketched below in section V.
66
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the current literature review, health economics data sets often lack the necessary measures of
environmental quality. However, marginal willingness to pay for an improvement in fetal and
infant health (MWTPm), i.e. the marginal rate of substitution in consumption between X and IH,
is not as demanding. It can be shown that:
MWTPih = Um / Ux
= (d Y/ d E ) / IHe
= pm / Mm
The MWTPih thus requires only an estimate of IHm from health economics research on
infant health production functions, and a corresponding measure of the price of prenatal care.
The MWTPe can be thought of as the value of a standardized improvement in environmental
quality or any other exogenous change that yields a marginal change in infant health. It can be
used to value any public policy change that improves infant health at the margin, assuming, of
course, that the policy analyst has an outside estimate of the infant health improvement (i.e., a
term analogous to IHe).
Empirical Estimates of Infant Health Production Functions
Table 2 lists eleven studies that estimate the marginal product of prenatal care in
improving infant health. Seven of the studies use microdata and measure infant health by
birthweight in grams. Three studies use county- or state-level aggregate data and measure infant
health by the percentage of infants born at a low birthweight (below 2500 grams); one study uses
county-level data on neonatal mortality rates. The use of prenatal care is usually measured in
terms of whether it was initiated in the first trimester of pregnancy or delayed. In addition to
67
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measures of prenatal care, all of the studies include endogenous health inputs such as maternal
smoking and other variables such as maternal age and schooling.
The research on infant functions addresses a number of specification issues. The
functions are generally specified to be linear, although Rosenzweig and Schultz (1983, 1988)
also estimate Cobb-Douglas specifications, and Warner (1988) also estimates linear with
interaction terms, quadratic, and square root specifications.5 As might be expected,
specifications have evolved over time to address new research questions. Several of the studies
suggest that the parameters of the infant health production function vary significantly by race. In
another extension, Warner (1998) emphasizes the importance of maternal anthropometric
measures such as height and weight. Warner (1995, 1998) also explores whether subsequent
more frequent prenatal visits substitute for delaying pre-natal care after the first trimester.
The research on infant health production also addresses a number of econometric issues.
Following Rosenzweig and Schultz (1983), a central concern has been the endogeneity of the
health inputs. Rosenzweig and Schultz show that with individual heterogeneity that is known to
the mother but unobservable to the econometrician, ordinary least squares (OLS) yields biased
estimates of the parameters of the health production function. Their empirical results suggest
that women with health problems may seek prenatal care earlier to compensate, causing OLS to
underestimate the productivity of prenatal care. Rosenzweig and Schultz and most subsequent
studies use two stage least squares or a related instrumental variables technique to treat prenatal
care and other health inputs as endogenous. This approach generates a research debate across the
5Rosenzweig and Schultz (1983) also consider the translog specification, but it is
rejected in favor of the Cobb-Douglas.
68
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studies about the validity of the identifying exclusion restrictions and the explanatory power of
the instrumental variables as predictors of input demand.
Grossman and Joyce (1990) argue that in addition to treating health inputs as endogenous,
it is important to control for self-selection in the resolution of pregnancies as live births or
induced abortions. The selectivity bias could be in either direction. They find strong selection
effects for blacks but not whites, with the results suggesting that among blacks the unobserved
factors that increase the probability of a live birth are correlated with unobserved factors that
increase use of prenatal care and increase birthweight. Subsequent studies that use vital statistics
data also control for selectivity bias (Joyce 1994, Liu 1998). However, other recent studies such
as Warner (1998) that use data from surveys of mothers can not, because the data necessary to
estimate the selection equation are lacking.
Because of the variety of specifications, econometric methods, and data sets used, it is
difficult or impossible to determine a single 'best' estimate of the marginal product of prenatal
care in improving health. There is a strong consensus in the research that prenatal care is
productive, but the precise magnitude varies. A few examples illustrate typical results. After
controlling for the endogenous choice of health inputs, Rosenzweig and Schultz (1983) results
imply that prenatal care delay decreases birthweight by approximately 50 grams. Warner (1995)
estimates a monthly delay productivity of between 25 and 30 grams for black mothers. After
controlling for both endogeneity and selectivity bias, Liu (1998) estimates that each month of
prenatal care delay decreases birthweight by 76 grams. To consider a different health outcome
measure, Corman, Joyce and Grossman (1987) estimate that prenatal care reduces black mortality
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by 1.82 deaths per 1000 live births, but reduces white mortality by only 0.30 deaths per 1000 live
births.
Illustrative Calculations of Willingness to Pay for Infant Health
Marginal willingness to pay for infant health can be calculated by combining an estimate
of the marginal productivity of prenatal care in improving infant health with an estimate of the
price of prenatal care. Ideally, the price should be specific to the sample used to estimate the
infant health production function, in terms of both geographic area and time period. In addition,
although the simple model presented above abstracted from these complications, price should be
measured as the out-of-pocket cost paid by the mother after insurance, plus additional travel and
time costs incurred to receive the care. In practice, developing such a price measure is
challenging, so the following calculations should be viewed as illustrative.
Suppose the full price (out-of-pocked monetary costs plus travel and time costs) of
reducing one month of prenatal care delay is $300. From the studies reviewed above, this
reduction in delay might increase birthweight by 25 to 76 grams. Assuming the increase is 50
grams, the implication is that maternal marginal willingness to pay is about $6 per extra gram of
birthweight.
As another illustrative calculation, combining the cost of prenatal care with the estimate
from Joyce, Grossman and Goldman (1989) of the marginal product of prenatal care in reducing
neonatal mortality yields the willingness to pay for a small reduction in neonatal mortality risks.
As is conventional, this can be conveniently summarized as the value of a statistical life. Dickie
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and Nestor (1998) conduct the needed calculations to derive the per birth value of $43,000 to
$750,000 for whites and $59,00 to $1,450,000 for blacks.
V. Demand Function Estimates and the Value of Infant Health
Willingness to Pay Expression
The model sketched in section III can be extended to focus on mothers' consumption
choices that affect both their own health and fetal health. Suppose now that the parent receives
utility from consuming S, X, and her own health H, and additional utility from her child's health
IH. Assume the parent's utility is a separable function of consumption utility (U) and utility (W)
from child health: utility = U (X, S, H) + W (IH). Parent health and child health are produced
according to household production functions: H = H(S) and IH = IH (S). (This abstracts from the
use of prenatal care, to simplify the presentation). A smoking parent chooses S and X to
maximize her utility subject to a standard budget constraint and the household production
functions; call these optimizing choices S* and X *, with the corresponding parental and child
health consequences H* and IH*. For the parent who finds it optimal to quit smoking, call her
optimizing choices of consumption S** = 0 and X**, with the corresponding parental and child
health consequences H** and IH**. The net benefits of quitting smoking are therefore given by:
(1) NB = {U [ 0, X **, H**)] + W [IH**]} - {U [S*, X *, H*] + W [IH*]}
Equation (1) can be seen as the motivation for the empirical research on smoking during
pregnancy discussed below. If NB > 0, the individual is observed to quit smoking; otherwise the
individual remains a smoker. Equation (1) provides the basis for comparative static predictions
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about the determinants of smoking cessation. Pregnancy increases the net benefits of smoking
cessation through the W[ ] terms in equation (1). Standard arguments suggest that cigarette
prices, income, and various demographic characteristics and life cycle events also enter as
possible determinants of NB.
To derive the implications of maternal smoking decisions for valuing infant health,
consider a smoker who quits because of pregnancy or a new child. Before children her optimal
choice was to smoke, so the parent's direct utility from consumption is lower when she quits to
improve child health:
(2) ? U = U ( 0, X **, H**) - U (S*, X *, H*) < 0
Measured in utility units, ? U is the net consumption utility foregone in order to invest in
infant health. But for the smoker who finds it optimal to quit, NB > 0, which implies:
(3) ?U
-------
psO , pxO and income Y°, define the indirect sub-utility from consumption before child health
concerns with choices S*, X* and H* as v* = v(psO, pxO, Y°). Given the same prices and
income, but rationing the consumer to S** = 0, let her indirect sub-utility be given by v** =
v(ps0, pxO, Y°; s** = 0). A dollar-valued measure of the utility from goods consumption
foregone to invest in health is the compensating variation (CV) in income implicitly defined by:
(4) v(ps0, pxO, Y°) = v(ps0, pxO, Y° + CV; S** = 0)
This compensating variation is the amount the consumer would have to be paid after she
has quit smoking to give her just as much consumption utility as she received when she was a
smoker. Because the parent quit smoking due to infant health concerns, CV will be the operable
definition of the parent's willingness to pay for infant health.
The CV can be approximated using standard methods from applied welfare economics
(Deaton and Muellbauer 1980, Varian 1978). In that approach, the CV implicitly defined by
equation (4) can be related to an area of consumer's surplus measured to the left of a
compensated (utility-held-constant or Hicksian) demand curve for cigarettes. The appropriate
area is measured with reference to a "virtual price" of cigarettes, psl that would convince the
consumer to quit smoking even before child health concerns (see Neary and Roberts 1980, and a
similar application by Kenkel 2002). The empirical estimates reviewed below provide measures
of the effect of pregnancy, a new child, and cigarette prices on the decision to quit smoking. The
estimated effects can be used to calculate the virtual price increase that has the same effect as a
pregnancy or new child. Consumers' surplus can then be calculated using estimates of the price
elasticity of smoking. Although the price elasticity estimates will correspond to an ordinary
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demand curve, the area CV measured with an ordinary demand curve approximates the exact
measure of compensating variation (Willig 1976).
The simple model used to derive parents' willingness to pay for infant health abstracts
from addiction, a potentially important aspect of decisions about cigarette and alcohol
consumption. Consumers' surplus needs to be carefully interpreted in the context of an addictive
good. Most smokers report a desire to quit, but this does not invalidate economic models of
smoking (Viscusi 1992b). The fact that they continue to smoke despite a stated desire to quit
means that quitting is costly; addiction may mean that this cost is better interpreted as the pain of
quitting rather than the foregone pleasure of smoking. Regardless how this cost is interpreted,
estimates of the costs smokers incur to quit smoking when pregnant reveal their willingness to
pay for child health.
Another concern is that estimates of smokers' or drinkers' willingness to pay for infant
health underestimate the average parents' willingness to pay. Research suggests that smokers
have different risk preferences from nonsmokers (Hersch and Pickton 1995, Viscusi and Hersch
2001). Assuming their willingness to pay for child health shows the same patterns, the estimates
of average smokers' willingness to pay will be a lower bound to average parents' willingness to
pay for child health. A related issue is that smokers appear to process risk information
differently (Viscusi, Magat, and Huber 1999). Smokers may have placed a low weight on
reports linking secondhand smoke to child health. In this case, smokers may be relatively
unwilling to change their behavior partly because they are using low risk assessments. These
limitations should be kept in mind.
Empirical Estimates of Maternal Demand for Cigarettes and Alcohol During Pregnancy
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Table 3 lists six empirical studies of the demand for cigarettes and alcohol during
pregnancy. Four of the studies explore the determinants of pregnant women's smoking
participation, i.e. whether or not they are regular smokers. One study explores the determinants
of both smoking participation and the daily consumption of cigarettes conditional on being a
current smoker; another study explores the determinants of drinking participation and the
monthly consumption of alcohol conditional on being a drinker. Three of the studies of smoking
participation use data from the national natality files, which starting in 1989 include an indicator
of whether the mother smoked during pregnancy. The first such study by Evans and Ringel
(1999) uses a sample of over 10 million births between 1989 and 1992, and the subsequent
studies by Ringel and Evans (2001) and Gruber and Koszegi (2001) increase the sample size
further by extending the sample period. Colman, Grossman and Joyce (2003) use an alternative
data set overseen by the CDC, and by pooling together data from 10 states over the years 1993 -
1999 obtain a sample of 115,000 women. The remaining two studies - Bradford's (2002) study
of smoking and Kenkel and Lin's (2003) study of drinking - use a sample of about 6,000 women
from the 1988 NMIHS, and its 1991 Followup. Although it is a smaller sample over a limited
time period, the NMIHS provides much more detailed information about smoking and drinking
behavior and the women's circumstances.
The main focus of research on the demand for cigarettes and alcohol during pregnancy is
to estimate the price-elasticity of demand, to explore whether higher taxes might be effective to
change these prenatal behaviors and thus improve health. For example, Ringel and Evans (2001)
estimate a price elasticity of -0.7, which suggests that cigarette taxes may be a powerful tool to
reduce smoking during pregnancy. However, as Corman, Grossman and Joyce (2003) point out,
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their estimate may be too optimistic: real cigarette prices have risen 60 percent since 1997, but
smoking during pregnancy dropped by only 7.6 percent, not the 42 percent drop implied by a
price elasticity of -0.7.
Bradford (2002) uses data from the 1988 NMIHS and its 1991 Followup to conduct a
more in-depth study of smoking behavior during pregnancy. Kenkel and Lin (2003) also use the
NMIHS data to conduct a similar study of drinking behavior during pregnancy. The NMIHS is a
sample of women who were pregnant in 1988, and some but not all of these women were again
pregnant when they were re-surveyed in the 1991 Followup. As a result, these studies are able
to estimate the impact of both pregnancy and prices on maternal behaviors. For example,
Bradford finds that during pregnancy light smokers reduce consumption by 1.6 cigarettes per day,
moderate smokers reduce their consumption by 3.4 cigarettes per day, and heavy smokers reduce
their consumption by 5.7 cigarettes per day. Analogously, Kenkel and Lin estimate that during
pregnancy, a drinking mother reduces her alcohol consumption by 4.5 drinks per month, and
again there are differences in the response of light and heavy drinkers. Because they also
estimate the price elasticity of cigarette and alcohol demand by pregnant women, the studies by
Bradford (2002) and Kenkel and Lin (2003) can be used to implement the valuation approach
based on consumers' surplus calculations.
Illustrative Calculations of Willingness to Pay for Infant Health
To illustrate the approach to infant health valuation, this section presents back-of-the-
envelope calculations of the values that are revealed by smoking and alcohol consumption
decisions. Bradford (2002) estimates that light smokers voluntarily forego from $610 to $800 in
consumers' surplus in response to pregnancy, while heavy smokers having their first child forego
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over $2,800 in surplus during pregnancy. According to information from the USDHSS (2001),
smoking during pregnancy increases the rate of perinatal mortality (still births and neonatal
deaths) from about 8 per 1,000 births to about 10 per 1,000 births. A heavy smoker who quits
while pregnant therefore gives up $2,800 to reduce perinatal mortality risks by 0.002. Together
these numbers imply that the value of a statistical life for an infant is $1.4 million. While many
caveats obviously apply, this back-of-the-envelope estimate compares reasonably well to other
estimates of the value of life of adults and older children.
Analogously, Kenkel and Lin (2003) calculate the consumers' surplus drinking mothers
give up during pregnancy. On average, during the entire pregnancy, the forgone consumer
surplus for an average drinking mother is about $37.8.6 However, this average obscures
important differences between three groups of drinking mothers: light drinkers, moderate
drinkers, and heavy drinkers. It is useful to explore the surrendered consumer surplus for sub-
populations since studies have shown that heavy drinking mothers impose higher risks on their
n
unborn children than moderate and light drinking mothers do. A drinking mother with less than
31 drinks monthly is defined as a light drinker; one with 31 to 59 drinks monthly is defined as a
moderate drinker, one with at least 60 drinks monthly is defined as a heavy drinker. This
definition is the same as that in most alcohol studies. On average, a heavy drinking mother
surrenders $451.3 in consumer surplus; a moderate drinking mother surrenders $ 247.9 and a
6 For those drinking mothers who choose to quit during pregnancy, the surplus foregone can only
be viewed as a lower bound of their perceived value to invest in their unborn child's health.
7 In Quelette et al. (1977), babies born to heavy drinkers had twice the risk of abnormality over
those born to abstainers or moderate drinkers. They find that 32% of infants born to heavy
drinkers demonstrated congenital anomalies; as compared to 14% in the moderate group and 9%
in the abstinent group.
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light drinking mother surrenders $24.2. Heavy drinkers, compared to moderate and light ones,
give up much more in consumer surplus since they perceive a larger benefit from reducing
alcohol consumption during pregnancy. A conservative incidence rate is that among heavier
o
drinking women the incidence of Fetal Alcohol Syndrome (FAS) is 1 in every 1000 live births.
Because an average heavy drinking mother reveals her willingness to pay to reduce probability of
FAS by 1/1000 is $451.3, this implies the value of a statistical case of FAS is $451, 300. By way
of comparison, the cost of illness estimates of Harwood and Napolitano (1985) value a case of
FAS at about $347,000 (in 1990$).
VI. Impact of Public Policies on Infant Health and Implications for Valuation
Willingness to Pay Expression
There are at least two challenges to estimating willingness to pay from empirical studies
of the impact of public policies on infant health. First, it may not be possible to recover the
necessary structural parameters from the reduced form equations estimated. Second, in many
cases a change in public policy represents a non-marginal change. The first point is similar to
Rosenzweig and Schultz's (1983) criticism of what they term "hybrid" health equations. In a so-
called hybrid equation, one input, for example prenatal care, and variables like income and prices
that are the determinants of the other inputs, are regressed against a measure of health. The
results are often interpreted as the causal effect or marginal product of prenatal care. However,
Rosenzweig and Schultz (1983) argue that this interpretation is invalid: they show that the
8 Estimates of FAS prevalence vary from 0.5 to 3 per 1000 live births in most populations.
However, the prevalence rate in some American Indian communities is as high as 9 per 1000
births.
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estimated effect of prenatal care on health from such an equation embodies both technology
parameters of the health production function and preference parameters of the utility function.
Even compared to a hybrid health equation, the approach of many empirical health
economics studies is further away from structural estimation of the household health production
function. For example, Currie and Gruber (1996) estimate the impact of Medicaid expansions on
infant mortality. In essence, Medicaid as a determinant of the use of prenatal care has been
substituted into the hybrid equation. The resulting reduced-form equation may be a desirable
approach to estimate the impact of the specific policy change. But the estimated effect of
Medicaid now combines the impact of Medicaid on the use of prenatal care (a demand effect)
and the impact of the use of prenatal care on infant health (a production function effect). It might
be possible to use additional information or assumptions about some of the structural demand
parameters to disentangle the effects. If the policy change can be treated as a marginal change, it
would be then be possible to derive estimates of the marginal product of prenatal care in
producing infant health. Such an estimate could be used in the expression derived above for the
marginal willingness to pay for infant health.
However, as has been already noted, in many cases discrete policy changes represent non-
marginal changes. Bockstael and McConnell (1983) suggest that it may be possible to value
such changes with reference to the areas behind appropriate marginal value and marginal cost
curves. Bockstael and McConnell provide a general discussion of welfare measurement in the
household production framework, emphasizing the distinction between a commodity such as
infant health and the market goods that are used as inputs to produce the commodity. They show
how the welfare effect of a change in the level of a public good can be measured either in the
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hypothetical 'market' for the commodity (output) or in an actual market for a good (input). The
welfare measure in the goods market is empirically implementable, and corresponds to the
change in the area behind a compensated demand curve for an input that is caused by a change in
the level of a public good. Dickie and Gerking (1991) use this approach to infer willingness to
pay for ozone control from the demand for medical care.
Some empirical studies estimate the impact of a policy on both the commodity infant
health and its impact on the use of a health input like prenatal care. This raises the hope that the
results are informative about the change in the area behind the demand curve for prenatal that
results from the policy change. As in the similar example of Dickie and Gerking (1991), it is
probably reasonable to assume that prenatal care satisfies the assumptions needed for the
Bockstael and McConnell (1983) approach to be valid. And although privately and publicly
insured consumers may pay little or no out-of-pocket monetary costs for prenatal care, a demand
curve can be still derived with respect to travel and time costs incurred. With estimates of the
demand curve and how the policy changes the demand curve, in principle it should be possible to
implement the welfare measurement derived by Bockstael and McConnell (1983). However, the
problem of recovering structural parameters from reduced-form equations re-appears. In this
case, the problem is to recover a demand function from a reduced-form equation showing the
impact of a policy change on input usage. For example, it may not be clear if the estimated effect
of the policy is on the demand side through changes in consumers incentives or the supply side
through changes in providers' incentives. It may again require extra information or assumptions
to identify the parameters of the demand function needed to implement the Bockstael and
McConnell (1983) welfare measure.
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Empirical Estimates of the Impact of Public Policies on Infant Health
Table 4 lists 10 studies of the impact of public policies on infant health. In all but one
study, the focus is on public policies such as Medicaid that are targeted at low-income and
disadvantaged populations. All of the studies examine the impact of a policy on some measure
of infant birthweight, with the focus often being on low birthweight and very low birthweight as
the most serious adverse outcomes. At least four of the studies also estimate the impact of the
policy under study on the use of prenatal care. At least some of the remaining studies measure
prenatal care, but it may not be used as an outcome variable. For example, Currie and Cole
(1993) include prenatal care use as an explanatory variable to estimate the impact of AFDC
participation on infant birthweight, controlling for differences in prenatal care use. Currie and
Cole (1993) do not provide a structural interpretation of the estimated impact of AFDC
participation, but note that it may combine an income effect with an additional effect due to
improved access to a range of other services from the welfare system.
Illustrative Calculations of Willingness to Pay for Infant Health
Existing research on the impact of natural policy experiments on infant health inputs and
outcomes does not support calculations of willingness to pay for infant health. As discussed
above, such calculations require additional information or assumptions to: (a) recover structural
parameters from the estimation results; and (b) implement the appropriate welfare measure for a
marginal or non-marginal change. Alternatively, an avenue for future work might be to re-
analyze these data sets to estimate the value of infant health.
VII. Discussion
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The review of empirical health economics research suggests a potential vein to be mined
for information on the value of fetal and infant health. As discussed in section III, it is probably
most straight-forward to derive estimates of maternal marginal willingness to pay for infant
birthweight. Because birthweight is associated with infant mortality and a range of subsequent
outcomes, it is a useful summary of infant health. Similarly, estimates of the value of
birthweight are potentially useful for the benefit-cost analysis of a variety of environmental and
public health policies. For example, food safety regulations to prevent exposure to Toxoplasma
gondii reduce risks for infants (Roberts and Frenkel 1990). Previous analyses that value reduced
infant mortality risks based on the discounted present value of lifetime earnings may substantially
underestimate willingness to pay.
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References
Agee, Mark and Thomas D. Crocker (1996). "Parental Altruism and Child Lead Exposure:
Inferences from the Demand for Chelation Therapy." Journal of Human Resources 31: 677-691.
Agee, Mark and Thomas D. Crocker (2001). "Smoking Parents' Valuations of Own and
Children's Health." Working Paper, Department of Economics, Pennsylvania State University -
Altoona.
Barrera, Albino (1990). "The Role of Maternal Schooling and Its Interactions with Public Health
Programs in Child Health Production." Journal of Development Economics 32: 69-91.
Berger, Mark, Glenn Blomquist, Don Kenkel and George Tolley (1987). "Valuing Changes in
Health Risks: A Comparison of Alternative Approaches," Southern Economic Journal 4: .
Bergstrom, Ted. (2003). "Benefit Cost Analysis and the Entanglements of Love." Presentation
at "Valuing Environmental Health Risk Reductions to Children," October 20 - 21, 2003,
Washington DC.
Bockstael, Nancy and R. McConnell (1983). "Welfare Measurement in the Household
Production Framework." American Economic Review 73: 806-814.
Bolin, Kristian, Lena Jacobson, and Bjorn Lindgren (2001). "The Family as the Health Producer
- When Spouses are Nash-bargainers." Journal of Health Economics 20: 349-362.
Bolin, Kristian, Lena Jacobson, and Bjorn Lindgren (2001). "The Family as the Health Producer
- When Spouses Act Strategically." Journal of Health Economics 21: 475 - 495..
Bradford, W. David (2001). "Pregnancy and the Demand for Cigarettes." Working Paper,
Department of Health Administration and Policy, Medical University of South Carolina.
Bresnahan, Brian W. and Mark Dickie (1995). "Averting Behavior and Policy Evaluation."
Journal of Environmental Economics and Management 29: 378-392.
Carlin, P. And R. Sandy (1991). "Estimating the Implicit Value of a Young Child's Life,"
Southern Economic Journal 58 (1): 186-202.
Case, Anne and Christina Paxson (2001). "Mothers and Others: Who Invests in Children's
Health?" Journal of Health Economics 20: 301-328.
Cebu Study Team (1992). "A Child Health Production Estimated from Longitudinal Data."
Journal of Development Economics 38: 323-351.
83
-------
Chaloupka, Frank J. and Kenneth Warner (2000). "The Economics of Smoking." Handbook of
Health Economics, Joseph Newhouse and Anthony Culyer, Editors (North-Holland).
Chay, Kenneth Y. and Michael Greenstone (1999). "The Impact of Air Pollution on Infant
Mortality: Evidence from Geographic Variation in Pollution Shocks Induced by a Recession."
NBER Working Paper No. 7442.
Chay, Kenneth Y. and Michael Greenstone (2001). "Air Quality, Infant Mortality, and the Clean
Air Act of 1970." Working Paper, Department of Economics, University of Chicago.
Colman, Greg, Michael Grossman and Ted Joyce (2003). "The Effect of Cigarette Excise Taxes
on Smoking Before, During and After Pregnancy," Journal of Health Economics forthcoming.
Corman, Hope, Theodore Joyce, and Michael Grossman (1987). "Birth Outcome Production
Function in the United States." Journal of Human Resources 22 (3): 339 - 360.
Currie, Janet (2000). "Child Health in Developed Countries." Handbook of Health Economics,
Joseph Newhouse and Anthony Culyer, Editors (North-Holland). 1053 - 1090.
Currie, Janet and Nancy Cole (1993). "Welfare and Child Health: The Link Between AFDC
Participation and Birth Weight." American Economic Review 83 (4): 971-985.
Currie, Janet and Jonathan Gruber (1996). "Saving Babies: The Efficacy and Cost of Recent
Expansions of Medicaid." Journal of Political Economy.
Currie, Janet and Jeffrey Grogger (2002). "Medicaid Expansions and Welfare Contractions:
Offsetting Effects on Prenatal Care and Infant Health?" Journal of Health Economics 21: 313-
353.
Currie, Janet, L. Nixon, and N. Cole (////) "Restrictions on Medicaid Funding of Abortion -
Effects on Birthweight and Pregnancy Resolutions." Journal of Human Resources 31 (1): 159-
188.
Deaton, Angus and John Muellbauer (1980). Economics and Consumer Behavior. Cambridge:
Cambridge University Press.
Devaney, Barbara, Linda Bilheimer, and Jennifer Schore (1992). "Medicaid Costs and Birth
Outcomes: The Effects of Prenatal WIC Participation and the Use of Prenatal Care." Journal of
Policy Analysis and Management 11 (4): 573-92.
Dickie, Mark (1999). "Willingness to Pay for Children's Health: A Household Production
Approach." In Valuing Health for Environmental Policy With Special Emphasis on Children's
Health Protection. Proceedings of the Second Workshop in the Environmental Policy and
84
-------
Economics Workshop Series, March 24 - 25, 1999. Edited by Shi-Ling Hsu, Environmental Law
Institute, Washington DC.
Dickie, Mark and Shelby Gerking (1991)."Valuing Reduced Morbidity: A Household Production
Approach," Southern Economic Journal 53: 967-983.
Dickie, Mark and Shelby Gerking (1991). "Willingness to Pay for Ozone Control: Inferences
from the Demand for Medical Care." Journal of Environmental Economics and Management 21:
1 - 16.
Dickie, Mark D. and Shelby Gerking (2001). "Parents' Valuation of Latent Health Risks to the
Children." " In Economic Valuation of Mortality Risk Reduction: Assessing the State of the Art
for Policy Applications, Proceedings, November 7, 2001. Edited by Abt Associates, Inc.
Dickie, Mark and Deborah V. Nestor (1999). "Valuation of Environmental Health Effects in
Children: A Survey." Working Paper.
Dubay, Lisa, Robert Kaestner, and Timothy Waidman (2001). "Medical Malpractice Liability
and Its Effect on Prenatal Care Utilization and Infant Health." Journal of Health Economics 20:
591-611.
Evans, William N., and J.S. Ringel (1999). "Can Higher Cigarette Taxes Improve Birth
Outcomes?" Journal of Public Economics 72: 135-154.
Frank, Richard G., Donna M. Strobino, David S. Salkever, and Catherine A. Jackson (1992).
"Updated Estimates of the Impact of Prenatal Care on Birthweight Outcomes by Race." Journal
of Human Resources :629-642.
Freeman, A. Myrick (1993). The Measurement of Environmental and Resource Values: Theory
and Methods. (Washington DC: Resources for the Future)
Gray, Bradley (2001). "Do Mediciad Physician Fees for Prenatal Services Affect Birth
Outcomes?" Journal of Health Economics 20: 571-590.
Grossman, Michael (1972). "On the Concept of Health Capital and the Demand for Health."
Journal of Political Economy 80 ( 2). March/April.
Grossman, Michael (2000). "The Human Capital Model." Handbook of Health Economics,
Joseph Newhouse and Anthony Culyer, Editors (North-Holland).
Grossman, Michael and Theodore J. Joyce (1990). "Unobservables, Pregnancy Resolutions, and
Birth Weight Production Functions in New York City." Journal of Political Economy 98 (5, part
1): 983 - 1007.
85
-------
Gruber, Jonathan and B. Koszegi (2001). "Is Addiction 'Rational'? Theory and Evidence,"
Quarterly Journal of Economics 116 (4): 1261-1305.
Hersch, Joni and Todd S. Pickton (1995). "Risk-Taking Activities and Heterogeneity of Job-
Risk Tradeoffs." Journal of Risk and Uncertainty 11 (3): 205-17.
Ippolito, Pauline M. and Richard A. Ippolito (1984). "Measuring the Value of Life Saving from
Consumer Reactions to New Information," Journal of Public Economics 25: 53-81.
Jacobson, Lena (2000). "The Family as Producer of Health - An Extended Grossman Model."
Journal of Health Economics 19: 611-637.
Jenkins, Robin, Nicole Owens, and Lanelle Wiggins (2001). "Valuing Reduced Risks to
Children: The Case of Bicycle Safety Helmets," Contemporary Economic Policy, 19: 397-408.
Johansson, Per-Olov (1993). Cost-Benefit Analysis of Environmental Change (Cambridge
University Press).
Jones, Andrew (1990). "An Econometric Investigation of Low Birth Weight in the United
States" Journal of Health Economics 10: 81-99.
Joyce, Theodore (1994). "Self-Selection, Prenatal Care, and Birthweight among Blacks, Whites,
and Hispanics in New York City." Journal of Human Resources 29(3): 762-94.
Joyce, Theodore (1999). "Impact of Augmented Prenatal Care on Birth Outcomes of Medicaid
Recipients in New York City." Journal of Health Economics 18: 31-67.
Joyce, Theodore J., Michael Grossman, and Fred Goldman (1989). "An Assessment of the
Benefits of Air Pollution Control: The Case of Infant Health." Journal of Urban Economics 25:
32-51.
Kenkel, Donald (1994). "The Cost of Illness Approach," in George Tolley, Donald Kenkel and
Robert Fabian, editors, Valuing Health for Policy: An Economic Approach (Chicago: University
of Chicago Press).
Kenkel, Donald (2000). "Prevention," in the Handbook of Health Economics, A.J. Cuyler and
J.P. Newhouse, editors. North-Holland, 2000, pp. 1675-1720.
Kenkel, Donald (2001). "Using Estimates of the Value of a Statistical Life in Evaluating
Consumer Policy Regulations." Manuscript prepared for a conference on Valuing the Health
Benefits of Food Safety, sponsored by the FDA, USD A, CDC, EPA, and others, September 13 -
15, 2000, College Park Maryland (invited speaker).
86
-------
Kenkel, Donald (2002a). "Approaches to Valuing Health for Policy: Common Ground and
Disputed Territor." Manuscript prepared for the "Health Valuation Workshop," University of
Central Florida, Orlando, March 18 - 19, 2002.
Kenkel, Donald (2002b). "Investments in Prevention: Health Economics and Healthy People. "
In Lindgren, B (ed) Individual Decisions for Health. London: Routledge. Forthcoming.
Kenkel, Donald and Tsui-Fang Lin (2003). "The Impact of Pregnancy and Taxes on Women's
Alcohol Use." Prepared for presentation at the Workshop on the Social Cost of Alcohol,
Neuchatel Switzerland, October 24-25 2003.
Levinson, Arik and Frank Ullman (1998). "Medicaid Managed Care and Infant Health." Journal
of Health Economics 17: 351-368.
Liu, Gordon G. (1998). "Birth Outcomes and the Effectiveness of Prenatal Care," Health
Services Research 32 (6): 805 - 823.
Liu, Jin-Tan, James K. Hammitt, Jung-Der Wang, and Jin-Long Liu (2000). "Mother's
Willingness to Pay for her own and her Child's Health: A Contingent Valuation Study in
Taiwan." Health Economics 9 (4): 319-326.
Maguire, Kelly B., Nicole Owens and Nathalie Simon (2001). "What Do Organic Baby Food
Purchases Tell Us About Parental Value for Reductions in Risks to Children's Health." In
Economic Valuation of Mortality Risk Reduction: Assessing the State of the Art for Policy
Applications, Proceedings, November 7, 2001. Edited by Abt Associates, Inc.
Mansfield, Carol (2001). "Discussion of Section V: Comments on 'Smoking Parents' Valuations
of Own and Children's Health' by Agee and Crocker." " In Economic Valuation of Mortality
Risk Reduction: Assessing the State of the Art for Policy Applications, Proceedings, November 7,
2001. Edited by Abt Associates, Inc.
Mount, Timothy, W Weng, and William Schulze (2000). "Automobile Safety and the Value of
Statistical Life in the Family: Valuing Reduced Risk for Children, Adults, and the Elderly."
Working Paper, Department of Applied Economics and Management, Cornell University.
Neary, J.P. and K.W.S. Roberts (1980). "The Theory of Household Behavior Under Rationing,"
European Economic Review 13: 25-42.
Neumann, J. and H. Greenwood (2002). "Existing Literature and Recommended Strategies for
Valuation of Children's Health Effects." National Center for Environmental Economics
Working Paper.
Neumann, P. and M. Johannesson (1994). "Willingness to Pay for In Vitro Fertilization: A Pilot
Test Using Contingent Valuation," Medical Care 32 (7): 686-699.
87
-------
Reichman, Nancy and Maryanne Florio (1996). "The Effects of Enriched Prenatal Care Services
on Medicaid Birth Outcomes in New Jersey." Journal of Health Economics 15 (4): 455-476.
Ringel, J. and William Evans (2001). "Cigarette Taxes and Smoking During Pregnancy,"
American Journal of Public Health 91: 1851-1856.
Roberts, Tanya and J. K. Frenkel (1990). "Estimating Income Losses and Other Preventable
Costs Caused by Congenital Toxoplasmosis in People in the United States." JAVMA 196 (2):
249 - 256.
Rosenzweig, Mark R., and T. Paul Schultz (1983). "Estimating a Household Production
Function: Heterogeneity, the Demand for Health Inputs, and Their Effects on Birth Weight."
Journal of Political Economy 91 (5): 723-746.
Rosenzweig, Mark R., and T. Paul Schultz (1988). "The Stability of Household Production: A
Replication." Journal of Human Resources 23 (4): 535-549.
Rosenzweig, Mark R., and T. Paul Schultz (1991). "Who Receives Medical Care - Income,
Implicit Prices, and the Distribution of Medical Services Among Pregnant Women in the United
States." Journal of Human Resources 26 (3): 473-508.
Tolley, George, Donald Kenkel and Robert Fabian (1994). Valuing Health for Policy: An
Economic Approach (Chicago: University of Chicago Press).
U.S. Department of Health and Human Services [USDHHS] (2000). Healthy People 2010:
Objectives for Improving Health.
U.S. Environmental Protection Agency [EPA] (2003). America's Children and the Environment:
Measures of Contaminants, Body Burdens, and Illnesses.
Varian, Hal R. (1978). Microeconomic Analysis. New York: W. W. Norton & Co. Inc.
Viscusi, W. Kip (1992a). Fatal Tradeoffs: Public and Private Responsibilities for Risk (New
York: Oxford University Press).
Viscusi, W. Kip (1992b). Smoking: Making the Risky Decision (New York: Oxford University
Press).
Viscusi, W. Kip. (1996). Economic foundations of the current regulatory reform efforts. Journal
of Economic Perspectives 10: 119-134.
Viscusi, W. Kip and Joni Hirsch (2001). "Cigarette Smokers as Job Risk Takers," Review of
Economics and Statistics 83: 269-280.
88
-------
Viscusi, W. Kip, Wesley A. Magat, and Joel Huber (1999). "Smoking Status and Public
Responses to Ambiguous Scientific Risk Evidence." Southern Economic Journal 66 (2): 250-
270.
Warner, Geoffrey (1995). "Prenatal Care Demand and Birthweight Production of Black
Mothers," American Economic Review 85: 132-137.
Warner, Geoffrey (1998). "Birthweight Productivity of Prenatal Care," Southern Economic
Journal 65 (1): 42-63.
Willig, R. (1976). Consumer Surplus without Apology. American Economic Review 66: 589-
597.
89
-------