NCEE Working Paper Do Discrete Choice Approaches to Valuing Urban Amenities Yield Different Results Than Hedonic Models?


NCEE Working Paper

Do Discrete Choice Approaches to
Valuing Urban Amenities Yield
Different Results Than Hedonic
Models?

Paramita Sinha, Martha Caulkins, and Maureen
Cropper

Working Paper 18-04
May, 2018

U.S. Environmental Protection Agency	|k|f*CC iff

National Center for Environmental Economics	hw

https://www.epa.aov/environmental-economics	e n v' r o n m e n ta^econ o m i cs

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Do Discrete Choice Approaches to Valuing Urban Amenities Yield Different Results

Than Hedonic Models?

Paramita Sinha, Martha Caulkins, and Maureen Cropper

Abstract: Amenities that vary across cities are typically valued using either a hedonic model, in
which amenities are capitalized into wages and housing prices, or a discrete model of household
location choice. In this paper, we use the 2000 Public Use Microdata Sample (PUMS) to value
climate amenities using both methods. We compare estimates of marginal willingness to pay
(MWTP), first assuming homogeneous tastes for climate amenities and then allowing
preferences for climate amenities to vary by location. We find that mean MWTP for warmer
winters is about four times larger using the discrete choice approach than with the hedonic
approach; mean MWTP for cooler summers is twice as large. The two approaches also differ in
their estimates of taste sorting. The discrete choice model implies that households with the
highest MWTP for warmer winters locate in cities with the mildest winters, while the hedonic
model does not. Differences in estimates are due to three factors: (1) the discrete choice model
incorporates the psychological costs of moving from one's birthplace, which the hedonic models
do not; (2) the discrete choice model allows for city-specific labor and housing markets, rather
than assuming a national market; (3) the discrete choice model uses information on market
shares (i.e., population) in estimating parameters, which the hedonic model does not.

Key words: amenity valuation, location choice, hedonic models, value of climate
JEL codes: Q51; Q54

DISCLAIMER

The views expressed in this paper are those of the author(s) and do not necessarily represent those of the
U.S. Environmental Protection Agency (EPA). In addition, although the research described in this paper
may have been funded entirely or in part by the U.S EPA, it has not been subjected to the Agency's required
peer and policy review. No official Agency endorsement should be inferred.

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Do Discrete Choice Approaches to Valuing Urban Amenities Yield Different Results

Than Hedonic Models?*

Paramita Sinha, RTI International; Martha Caulkins, University of Maryland; and
Maureen Cropper, University of Maryland and RFF

1. Introduction

To value amenities that vary across cities, researchers have typically followed one of two
approaches, they have used either hedonic models of wages and housing prices (Roback 1982;
Blomquist et al. 1988; Albouy et al. 2016) or discrete models of location choice (Cragg and
Kahn 1997; Bayer et al. 2009; Fan et al. 2016; Sinha et al. 2016). The former approach infers
willingness to pay for amenities by estimating hedonic price functions for wages and housing
costs as a function of location-specific attributes; the second, by estimating the probability that
consumers choose a city in which to live as a function of wages, housing prices, and location-
specific attributes.

Cragg and Kahn (1997), Bayer et al. (2009), and Sinha et al. (2016) note that the discrete
choice approach typically produces estimates of amenity values that are very different from
estimates produced by the continuous hedonic approach. In a discrete choice model where
households choose the US state in which to reside, Cragg and Kahn (1997) find the marginal
willingness to pay for July and February temperatures exceeds the marginal prices implied by
hedonic price functions. Bayer et al. (2009) estimate marginal willingness to pay (MWTP) to
reduce air pollution using a discrete choice approach and find MWTP is three times greater than
values capitalized into per capita incomes and property values. Sinha et al.'s (2016) discrete
choice model estimates higher damages associated with projected climate changes in US cities
under the A2 scenario in the Special Report on Emissions Scenarios than comparable estimates
from Albouy et al.'s (2016) hedonic model.

While previous research has compared the hedonic and discrete choice approaches in the
context of a single housing market (Bayer et al. 2007; Klaiber and Phaneuf 2009), valuing
amenities that vary across cities introduces different issues. Hedonic estimates of the value of
city-specific amenities involve the capitalization of amenities in both the labor and housing

* We thank the US Environmental Protection Agency, RTI International, and Resources for the Future for funding.
This paper would not have been possible without GIS support from RTI. We thank Christopher Timmins, Nicolai
Kuminoff, David Albouy, and Charles Griffiths for their valuable comments. Any errors are ours.

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markets. An important question is whether these markets should be treated as national markets or
city-specific markets. Moving costs across cities are one reason to question the assumption of
national labor and housing markets. And moving costs may prevent city-specific amenities from
being fully capitalized in wages and housing prices. Hedonic models typically assume perfect
mobility, while moving costs are more easily incorporated into discrete choice models.

In this paper, we use the same dataset to value climate amenities using hedonic and
discrete choice methods. We compare estimates from each approach, first assuming
homogeneous tastes for climate amenities and then allowing preferences for climate amenities to
vary by location. Similar to Albouy (2012), our hedonic models regress the weighted sum of
wage and housing price indices on climate amenities and various city characteristics using
metropolitan statistical areas (MSAs) as the geographic unit. Wage and housing price indices are
estimated, following Albouy et al. (2016), assuming national labor and housing markets. We
construct a weighted sum of wage and housing price indices for each MSA using the same
weights as in Albouy et al. (2016) and, alternately, using a traditional set of weights (Roback
1982). We capture preference heterogeneity by allowing the marginal price of climate amenities
to vary by city using local linear regressions (Bajari and Benkard 2005; Bajari and Kahn 2005).

In discrete location choice models, consumers choose among MSAs based on predicted
wages and housing costs, moving costs from birthplace, and the same set of location-specific
amenities as used in the hedonic models. To capture heterogeneity in preferences, we estimate
random parameter logit models and calculate the distribution of each household's tastes for
climate conditional on the city in which they live. This allows us to estimate mean MWTP for
climate amenities by city.

We focus on prime-aged households when comparing the two approaches. Because the
hedonic approach assumes that amenities are capitalized into wages, and because a significant
fraction of older households have no wage income, Albouy et al. (2016) focus on workers aged
25-55. We estimate discrete location choice models for various age groups and find that
preferences for climate amenities vary by the age of the household head; however, we focus on
households with heads between 25 and 55 when comparing discrete choice with hedonic
estimates.

We find that the two approaches produce different estimates of MWTP for climate
amenities when tastes are assumed to be homogeneous and different sorting patterns when we
allow preferences to be heterogeneous. Although both approaches find that households have
positive MWTP for warmer winters and cooler summers, mean estimates produced by the
discrete choice approach are two to three times larger than estimates produced by the hedonic

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approach. Moreover, the taste sorting patterns produced by the two approaches are very different.
The discrete choice model finds that households sort across locations based on their preferences
for winter temperature: there is a strong positive correlation between winter temperature and
MWTP for warmer winters. The hedonic model with traditional weights finds a negative
correlation between MWTP for warmer winters and winter temperature. The discrete choice
model thus projects that under most climate scenarios, the parts of the country that will benefit
from warmer winters value this less than the average US household. The hedonic model with
traditional weights projects the opposite. When adjusted (Albouy) weights are used to estimate
the hedonic model, the sorting pattern is closer to that of the discrete choice model but differs for
some parts of the country.

We also explore why estimates produced by the two approaches vary. One reason is that
the hedonic and discrete choice models differ in their underlying assumptions about consumer
mobility. The hedonic approach assumes perfect mobility, whereas moving costs are more easily
incorporated in discrete models of location choice. As Bayer et al. (2009) note, moving costs—
both psychological and out-of-pocket—may prevent amenities from being fully capitalized into
wages and housing values. When we estimate the discrete choice model without moving costs,
the value of climate amenities falls significantly. It is also the case that moving costs, which vary
by household and city, help identify sorting patterns in the discrete choice model (Berry and
Haile 2010). When they are removed, sorting patterns are (incorrectly) reversed.

A related reason for differences in the two sets of estimates is the way in which data on
wages and housing prices are used. The hedonic model assumes a single national labor market
and a single housing market. The data are used to estimate price indices for each MSA, assuming
that the returns to human capital and marginal prices of housing characteristics are the same
everywhere. The discrete choice model assumes that each MSA constitutes a separate labor and a
separate housing market. It is the variation in wage income and housing costs across MS As, as
well as the variation in moving costs across MSAs, that identifies household preferences in the
discrete choice model. This suggests that differences in how the two models use information on
housing and labor markets account in part for the difference in estimates.

The paper is organized as follows. Section 2 describes the hedonic model of amenity
valuation as originally developed by Roback (1982) and modified by Albouy (2012) and Albouy
et al. (2016). We present the discrete location choice model that we estimate in section 3 and
describe our data and empirical specifications in section 4. Section 5 presents the results of both
modeling approaches. This includes estimates of MWTP for climate amenities assuming
homogeneous tastes and the implications of both models for taste sorting. Section 6 concludes.

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2. Hedonic Models of Amenity Valuation

2.1. The Roback and Albouy Models

The hedonic approach to valuing location-specific amenities dates from Jennifer
Roback's (1982) seminal article "Wages, Rents, and the Quality of Life," which built on Rosen's
(1974) model of product differentiation and implicit prices. Roback posited that in a world of
perfectly mobile individuals, wages and land prices would adjust to equalize utility in all
locations. Consider a world of homogeneous individuals who receive utility from housing, H, a
traded good, C, and a location-specific amenity, a.1 In each location, j, the individual selects C
and Hto maximize utility subject to a budget constraint,

max U(Cj, Hj; aj) s.t.Wj + I = rjHj + Cj

CpHj	^ '

where /', is the rental price of housing; W, is wage income; / is nonwage income, which is

2

independent of location; and the price of the traded good, C, has been normalized to 1. This
yields an indirect utility function, V(Wj, rj} aj). If individuals are perfectly mobile, locational
equilibrium requires that utility be everywhere equal,

V{Wj,rj,aj) = k	(2)

implying that housing prices and wages will adjust to equalize utility. Roback shows that the

value to consumers of a small change in aj is given by

¦	Va ,rdr dW jMWTPa Va 1 d logr d\ogW	m

MWTPa = —— = H—	—and——— = —— = SH—			

Vw da da	W VwW	da da

where sh is the share of the consumer's budget spent on housing.

The literature following Roback (1982) has inferred MWTP for local amenities by
estimating hedonic wage and property value equations. For example, Blomquist et al. (1988) use
census data on individuals residing in different counties to estimate hourly wage (w) and housing
expenditure (P) equations. A common econometric specification in the literature (Gyourko and
Tracy 1991) is the semilog3

In wm) = y" + X%tr™ + AjrA'° +	(4)

1	Roback's model deals with land, not housing. In the subsequent literature, r is treated as the rental rate on housing.

2	It is assumed that each individual offers a single unit of labor in each location.

3	Blomquist et al. (1988) use Box-Cox transformations of wages and housing prices, i.e., (wx-l)/X and (P'-1)//.. They
estimate a value of 1 = 0.2 for the housing price equation and 1 = 0.1 for the wage equation, in contrast to a
logarithmic specification (X = 0).

4

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In Ptj = <5° + X^x'° + Aj4a-° + 77°.	(5)

where wmj is the hourly wage earned by worker m in location /; X^j is a vector measuring the

education, experience, demographic characteristics, industry, and occupation of worker m; Py is
housing expenditure by household i in location j\ and is a vector of dwelling characteristics.

Aj is a vector of attributes characterizing location j. In using equations (4) and (5) to infer the
value of location-specific amenities, Blomquist et al. (1988) multiply the hourly wage by the
average number of workers per household and the average number of hours worked per week
and weeks worked per year, and monthly housing expenditure by 12. The two are added together
to determine the impact of amenities; thus, implicitly, wage differentials across counties are
weighted approximately three times as much as housing price differentials.

Albouy (2012) makes significant modifications to Roback's approach. He argues that the
weight placed on wage income is too high, relative to the cost of nontraded goods, and he
suggests an alternate approach to estimating the value of local amenities. Nontraded goods, as
Albouy points out, include more than housing and hence occupy a larger fraction of the
household's budget. At the same time, it is after-tax income that matters. This raises the weight
placed on nontraded goods (proxied by housing) relative to wages. Second, Albouy estimates
wage and housing price indices for each geographic area and combines them into a quality of life
(QOL) index, using his adjusted weights. The QOL index is then regressed on site-specific
amenities to estimate marginal amenity values.

To elaborate, consider the utility maximization problem faced by households, where
indirect utility depends on income (both wage and nonwage), the prices of nontraded goods,
taxes, and the location-specific amenities in each location. The MWTP for amenity a as a
percentage of average total income (fn) can be shown to be equal to the derivative of a QOL
index, as described by equation (6),

MWTPa dQOLj	d\n(pjH)	dln(wy)

-m- = ^- = {s>l + rs°)—	(1-I)S»-5T"	(S)

where sH is the share of income spent on housing, s0 is the share of income spent on other
nontraded goods, sw is the share of income that comes from wages, and r is the marginal tax
rate, y is the ratio of the housing price to the price of nontraded goods. The QOL index
corresponding to (6) can be viewed as the consumption a household is willing to forgo to live in
city j compared with living in the average city. The weights in the QOL, however, differ from

5

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those in Roback. The weight on housing prices now includes the share of income spent on all

4

local goods, and the weight on wage income has been reduced by taxes.

To estimate QOL indices, Albouy et al. (2016) estimate national wage and housing price
equations similar to (4) and (5) in two stages. Including location-specific fixed effects in the
hourly wage and housing rent equations in the first stage yields wage and housing price indices,
AJ and Aj 5

In wm)=XZlrx'1+Ay+vil	(4')

\nP,j=XfJAx-1+Af +n}j	(5')

These indices are then used to construct the QOL index in equation (6), where AJ and Aj
from equations (4') and (5') replace d\n(pjH) and dln(wy). Based on Albouy (2012),

(sH + yso) = 0-33, r = 0.32 and sw = 0.75. This yields the QOL index on the left-hand side of
equation (7), which is then regressed on location-specific amenities.

QOLj = 0.33A] - 0.51AJ = AjO + ^	(7)

Albouy and coauthors (2016) apply this approach to Public Use Microdata Area (PUMA)
level data from the 2000 census to estimate the value of changes in temperature in the United
States. They use flexible functional forms to relate binned temperature data to the QOL index,
while controlling for other amenities. To allow for taste sorting, they apply a variant of Bajari
and Benkard's (2005) local linear regression to estimate separate temperature coefficients for
each PUMA.

2.2. Hedonic Models That We Estimate

We estimate two sets of hedonic models, one using traditional weights on the wage and
housing price indices generated by equations (41) and (51) (i.e., the weights in equation 3) and the
other applying the weights proposed by Albouy to the same wage and housing price indices (i.e.,
the adjusted weights in equation 7). The national wage and property value equations we estimate
use the same set of explanatory variables as the wage and housing cost hedonic equations that
underpin the discrete choice model described below and are estimated using the same samples of
workers and houses.

4

To relate this to Roback's MWTP formulation, if we assume that housing is the only local nontraded good (s0 =
0), that all income comes from wages (sw = 1), and that there are no income taxes (r = 0), this reduces to Roback's
MWTP expression in equation (3).

5	This is similar to the approach followed by Bieri et al. (2013), who argue that estimation in two stages ensures that
the implicit price of the amenity is not conflated with the implicit price of unobserved worker and housing attributes.

6

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We regress each set of QOL indices (traditional and adjusted) on the same set of amenity
variables used in estimating the discrete choice model. Our estimates of equations (41) and (51)
yield price indices for 284 MSAs; hence, we have 284 observations for our QOL regressions.6
To allow the coefficients on temperature variables to vary by MSA, we use a modified local
linear regression, in the spirit of Bajari and Benkard (2005) and Bajari and Kahn (2005).
Specifically, we regress the QOL index on all amenities except for climate amenities, and then
use the residuals (ey) from this equation in a local linear regression with kernel weights, as
described in equation (8), where T denotes a matrix of climate amenities, N{) denotes the normal
distribution, b is bandwidth, and az is the sample standard deviation of characteristic z. This
approach yields coefficients for each MSA for climate amenities, where the notation j* in
equation (8) emphasizes this.

0j* = argmin(e — T0)'W(e — T0)	/g\

0	^ '

i=[et] W=[diag(K„(Tj-Tj.))]

k(z)=y\n^zj - zi-y^)

all z

Kb(Z) = K(b)/b

3. A Discrete Choice Approach to Valuing Climate Amenities

The discrete choice approach to amenity valuation, like the hedonic approach, assumes
that households choose among geographic locations based on the utility they receive from each
location, which depends on wages, housing costs, and location-specific amenities. Variation in
wages, housing costs, and amenities across locations permits identification of the parameters of
the household's indirect utility function.

One advantage of the discrete choice approach is that it allows the researcher to more
easily incorporate market frictions, including the psychological and informational costs of
moving. The hedonic approach assumes that consumers are perfectly mobile and, hence, that the
weighted sum of wage and housing price gradients will equal the consumer's MWTP for an
amenity (equation 3). Bayer et al. (2009) demonstrate that this equality fails to hold in the

6 We estimate these models using ordinary least squares (OLS) and compute robust standard errors. Albouy et al.
(2016) indicate that they weight observations by population in their QOL models. We believe that using population
weights in the estimation of equation (7) is inappropriate, since population is endogenous in an urban location
model; however, we do present population-weighted estimates in the appendix for completeness.

7

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presence of moving costs, and they incorporate the psychological and informational costs of
leaving one's birthplace into an equilibrium model of household location choice. Barriers to
mobility also imply that the assumption of national labor and housing markets, which underlies
the hedonic approach, may not accurately capture wage and housing costs in different cities
(Cragg and Kahn 1997).

3.1. The Discrete Choice Model

Our discrete choice model builds on the work of Bayer et al. (2009) and Cragg and Kahn
(1997). We model household location assuming that each household selected its preferred MSA
from the set of MS As in the United States in 2000. Household utility depends on consumption of
a numeraire good (the Hicksian bundle), a vector of housing characteristics and amenities, and
the psychological costs of leaving the household head's birthplace. Formally, household z's
utility from location j is given by

Uij =	(9)

where Q is consumption of the numeraire good, A7'is a vector of housing characteristics, A, is a
vector of amenities observed by the researcher, and c, is an amenity not observed by the
researcher. MCij represents the psychological cost of moving to city / from the head of
household's birthplace, sy captures unobserved heterogeneity in preferences. Equation (9) is
maximized subject to the household's budget constraint,

r„ = c„ +	do)

where Yy is the sum of household z's nonwage income, /,, which is assumed not to vary by city,
and the wages of all family members, Wy. Pj(Xp) is the hedonic price function in city j.

Following Sinha et al. (2016), we assume that households consume the same bundle of housing
characteristics in all cities and thus use Py = Pj(X[0) to represent the expenditure of household z
on housing in city j, where Xf0 represents household z's observed housing bundle. Substituting
equation (10) into (9) yields the household's indirect utility function, which we assume takes the
form

Vij ~ a(Xij ~ ^ij) AjPi + MCij	£ij-	(11)

To capture preference heterogeneity, we allow the coefficients on moving costs and

7

amenities to vary across households. To predict the earnings of household workers and housing

7 In Sinha et al. (2016), we allow the coefficient on ) „ - to vary across households. We also allow Yy - to
enter the utility function in quadratic form.

8

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expenditure in locations not chosen, we estimate hedonic wage and housing price equations for
each MSA, as described below.

In equation (11), Y,, represents income before taxes. We also estimate versions of (11)
with income measured after taxes. Following Albouy et al. (2016), we use an average tax rate of
32 percent. We acknowledge that this is a very simple way of modeling taxes; however, we
adopt it to make our results comparable to Albouy et al. (2016). Ideally, we would like to
incorporate tax rates that are MSA-specific, although this is complicated by the fact that some
MSAs cross state boundaries.

Moving costs capture the psychological, search, and out-of-pocket costs of leaving the
household head's place of origin. Seventy-five percent of households in our prime-aged sample
(see Table 1) live in the census region in which the head was born; 69 percent live in the same
census division. Although households have been moving to warmer weather since the Second
World War (Rappaport 2007), family ties and informational constraints may have prevented this
from occurring more completely. As shown in section 5.2, failure to account for these costs
significantly alters the value attached to climate amenities.

Following Bayer et al. (2009), we represent moving costs as a series of dummy variables
that reflect whether city j lies outside of the state, census division, or census region in which
household V s head was born. Formally,

MCij = n0dfjate + + tz2d™gion (12)

where d,/u"e denotes a dummy variable that equals 1 if j is in a state that is different from the one
in which household head i was born, diPlvlslon = 1 if MSA j is outside of the census division in
which the household head was born, and dijReglon = 1 if MSA j lies outside of the census region in
which the household head was born.8

3.2. Estimation of the Discrete Choice Model

Estimating the location choice model requires information on the wages that a household
would earn and on the cost of housing in all MSAs. Because wages are observed only in the
household's chosen location, we estimate a hedonic wage equation for each MSA and use it to
predict Wy. The hedonic wage equation for MSA j regresses the logarithm of the hourly wage

8 Allowing moving costs to vary by marital status or by presence of children makes little difference to our results
(see Sinha et al. 2016).

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rate for worker m in MSAj on variables (X^j), measuring the demographic characteristics—
education, experience, and industry, and occupation—of worker m.

In wmj = yf + X™jrf2 + v2nj Vj = 1,... ,J (13)

Equation (13) is identical to equation (4) above but allows the coefficients on X" to vary
by MSA. It is estimated using data on full-time workers in the PUMS.9 The coefficients of (13)
are used to calculate the earnings of each worker in the sample used to estimate the discrete
choice model, under the assumption that individuals work the same number of hours and weeks
in all locations. Summing earnings over all individuals in each household, we obtain predicted
household wages for household i in location j (Wv ).

The cost of housing in each location is estimated based on hedonic property value
equations for each MSA,

InPij = Sf + XfjA*'2 + rfinj V) = 1,...,/ (14)

Pij is the annual cost of owning house i in city j, computed as the sum of the monthly mortgage
payment or rent and the costs of utilities, property taxes, and property insurance. Xfy contains a
dummy variable indicating whether the house was owned or rented, as well as a vector of
dwelling characteristics. Utility costs are added both to the costs of owning a home and to rents
because heating and cooling requirements vary with climate. We wish to separate these costs
from climate amenities. Equation (14) is estimated separately for each MSA in our dataset. We
predict housing expenditures for household i in city j assuming that the household purchases the
same bundle of housing characteristics in city j as it purchases in its chosen city.

This is clearly a strong assumption. To test its validity, we examine the mean value of
key housing characteristics (number of bedrooms and number of rooms) and their standard
deviation across MSAs for different household groups, characterized by income group and
household size. The coefficient of variation for number of bedrooms and number of rooms
within income and household size groups averages only 0.07-0.08, suggesting that households of
similar size and income tend to live in dwellings of similar characteristics, thus supporting our
methodology for predicting housing expenditures.

9 We have also estimated equation (13) allowing for nonrandom sorting (Dahl 2002). Specifically, we compute the
probability of moving from each birthplace to current location (in terms of census divisions) conditional on each
education group listed in Table 1 by taking the appropriate cell counts in our sample of workers (close to 3 million
individuals). Including this probability correction term (in quadratic form) in equation (13) has minimal impact on
our wage regression results, possibly due to the inclusion of industry and occupation indicators in the equation.

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As a sensitivity analysis, we estimate a location choice model that uses a housing price
index, following Bayer et al. (2009), rather than predicting housing expenditures in each MSA.
In Bayer et al. (2009), utility is assumed to be of the Cobb Douglas form (9'), which is
maximized subject to (10'). H is housing consumption, and pj is the housing price index in city j
This implies that indirect utility (11') is a function of a housing price index pj that varies across
cities, not households.10

10 The housing price index for each MSA is the estimated MSA fixed effect in the national hedonic housing price
equation, equation (5').

11

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Utj = C^cH^HeMClJeAJPle^eeiJ	(9-)

Qj + PjHij = Ytj	(10')

InVij = a0 + aylnYij + MCi} - aHlnpj + Ajfii + 

11	In the case of the Cobb Douglas utility function,

In Vij = a0 + aY\nYLj + MCi} + 8- + ey ,

where

S'j = —aH\npj + AjP + Sj .

12	In estimating the mixed logit model, the means of amenity coefficients are constrained to be zero. They are
estimated in the second stage of the model (equation 16).

12

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The parameters of equation (17) are estimated via simulated maximum likelihood techniques,
using a choice set equal to the household's chosen alterative and a sample of 59 alternatives from
the set of 284 MS As.13

To examine how taste heterogeneity varies by location, we compute the distribution of fk
for each household, conditioning on where the household has chosen to locate. Specifically, we
use Bayes' rule (Revelt and Train 1999) to derive the distribution of fh conditional on chosen
location, household attributes, and the population distribution of p,

Using this conditional distribution yields an expression for mean taste parameters, pLu for
households of type XL:

These household-level parameters are estimated via simulation. Taking the average over all
households in each MSA and dividing by the coefficient on the Hicksian bundle yields average
MWTP for all households in a given MSA. A similar method can be used to derive the
conditional variance-covariance matrix 11.

4. Data and Empirical Specifications

The data used to estimate our discrete choice and hedonic models come from the 5
percent PUMS of the 2000 census as well as other publicly available data sources.

4.1. Data Used to Estimate Hedonic Price Functions

The variables that we include in the hedonic wage and housing price equations (equations
4', 5', 13, and 14) are listed in Appendix Tables A.l and A.2, together with coefficient estimates.
The hedonic wage equation is estimated using all persons in the 2000 PUMS who live in an
MSA for which we have complete amenity data and work at least 40 weeks per year and between

13 The validity of the McFadden sampling procedure (McFadden 1978) hinges on the independence of irrelevant
alternatives, which does not hold in the mixed logit model. Nerella and Bhat (2004) use simulated data to examine
the effect of sampling on the empirical accuracy of parameter estimates in a mixed logit model. They suggest using
at least one-quarter of the universal choice set in estimating a mixed logit model. We do, however, face
computational trade-offs in estimating the mixed logit model using more than one-quarter of the universal choice set
and a sample large enough to estimate 284 fixed effects with precision. Experiments with the size of the choice set
indicate that increasing the size of the choice set beyond 60 MS As does not significantly alter parameter estimates.

h(P\choicei,Xi,fi,I) =

PrjchoiceilXj,/])

?r(choicei\X[, [i, I)

(18)

,, = = j ft hWckoice.X^.WP

(19)

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14

30 and 60 hours per week. Persons who are self-employed, in the military, or in farming,
fishing, or forestry are excluded from the sample. The housing equations are estimated using data
on all households living in one of the 284 MSAs for which we have complete amenity data.

4.2. Households Used to Estimate the Discrete Choice Model

In estimating the discrete choice models, we focus on households residing in one of the
284 MSAs for which we have complete amenity data. To be included in our sample, a household
must be headed by a person 16 years of age or older who was born in the continental United
States. We exclude households whose heads are in the military or are in certain occupations (e.g.,
logging, mining) that would restrict locational choices. We also eliminate households whose
members are self-employed, because of the difficulty in predicting their wages, and drop
households with negative values of Yy-Py at their chosen locations.15 This leaves over 2 million
households. A 2.5 percent sample of these households yields the 54,008 households described in
Table l.16

We have estimated the discrete choice model for the full sample of households and also
for the two subsamples described in Table 1: households with prime-aged heads (i.e., heads
between 25 and 55) and households with heads over age 55. The results presented in this paper
focus on households with prime-aged heads. As Table 1 indicates, 98 percent of these
households have some labor income, and on average, 93 percent of the income of these
households comes from wages. The hedonic approach, which uses wage and housing cost
differentials to value amenities, is most appropriately applied to prime-aged households. Our
results also suggest that preferences for climate amenities differ significantly between prime-
aged households and households with older heads; hence, focusing on a single demographic
group makes for a cleaner comparison with the hedonic approach.

4.3. Climate Variables

Previous studies of the value of climate amenities have used various measures of climate,
including temperature, humidity, precipitation, and sunshine. Many studies use average summer

14 There were 284 such MSAs in the continental United States in 2000, containing 80 percent of the country's
population.

15 These households may have substantial accumulated wealth (e.g., in real property) that we cannot measure.

16 Computational difficulties led us to use such a small sample of households. However, we have run the mixed logit
model on different samples of this size and find the results to be sufficiently similar.

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17

and winter temperatures (Graves and Mueser 1993; Cragg and Kahn 1997, 1999; Kahn 2009)
or annual heating and cooling degree days (Roback 1982; Blomquist et al. 1988; Gyourko and

Tracy 1991; Albouy 2012), which are highly correlated with winter and summer temperatures.
In studying the impact of climate on agriculture, health, and electricity usage, temperature has
been measured by the number of days in various temperature bins (Schlenker and Roberts 2009;
Deschenes and Greenstone 2011; Barreca et al. 2016). In the context of climate amenities, Fan et
al. (2016) use the number of days below 32 degrees and the number of days above 80 degrees,
while controlling for mean annual temperature. Albouy et al. (2016) use binned data to examine
the impact of temperatures above and below 65 degrees F.

Our hedonic and discrete choice models use mean winter (December-February) and
mean summer (June-August) temperatures, measured as climate normals for the period 1970-
2000. The advantage of mean winter and summer temperatures is that they capture seasonality,
which annual heating and cooling degree days and temperature bins do not. Also, with the MSA
as the unit of observation, it is asking a lot of the data to estimate the impact of temperature when

measured as the number of days in fine temperature bins.

In interpreting temperature coefficients, we note that correlation between winter and
summer temperatures and temperatures during other seasons of the year implies that winter and
summer temperatures will pick up other temperature impacts: the correlation between mean
winter temperature and mean March temperature is 0.98, as is the correlation between mean
winter temperature and mean November temperature. Collinearity among mean winter, summer,
fall, and spring temperatures, however, makes it impossible to include all four measures in our
models.

In the discussion that follows, we focus primarily on results for winter and summer
temperatures; however, the hedonic and discrete choice models also include annual snowfall,
mean summer precipitation, and July relative humidity. The climate variables in the models are
summarized in Table 2. All variables are climate normals: the arithmetic mean of a climate

variable computed for a 30-year period. Following the literature, we also include the

17 Graves and Mueser (1993) and Kahn (2009) use mean January and mean July temperatures; Cragg and Kahn
(1997, 1999) use mean February and mean July temperatures.

18 A mean daily temperature greater than 65 degrees F results in (average temperature - 65) cooling degree days. A
mean daily temperature less than 65 degrees results in (65 - average temperature) heating degree days.

19 Moreover, the number of days per year exceeding 80 degrees—based on climate normal for 1970-2000—is very
small.

20 The temperature and summer precipitation data are for the period 1970-2000. July relative humidity, annual
snowfall, and percentage possible sunshine are measured for the period 1960-1990.

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percentage of possible sunshine, defined as the total time that sunshine reaches the surface of the
earth, expressed as a percentage of the maximum amount possible from sunrise to sunset.

4.4. Nonclimate Amenities

The nonclimate amenity variables used in both the discrete choice and hedonic models
are also summarized in Table 2. These include amenity measures typically used in QOL studies
as well as variables that are likely to be correlated with climate, such as elevation, visibility, and
measures of parks and recreation opportunities. Because both sets of models are estimated using
a single cross section of data, we attempt to avoid problems of omitted variable bias by including
a variety of location-specific amenities in our models.

Many QOL studies include population density as an amenity variable (Roback 1982;
Albouy 2012) or city population (Gyourko and Tracy 1991). Population should be used with
caution in a discrete choice model, since the model is constructed to predict the share of
population in each city (i.e., summing the predicted probability of moving to city j across
households yields the predicted share of population in city j). We therefore do not include
population as an amenity but do include population density, which may proxy amenities that
higher population density supports that are not adequately captured by other variables (e.g.,
better public transportation, restaurants, and live sporting events). We also estimate models with
population density omitted.21

Other (dis)amenities for which we control include air pollution (fine particulate matter,
PM2.5), an index of violent crime, visibility (percentage of hours with visibility greater than 10
miles), square miles of parks within the MSA, elevation measured at the population-weighted
centroid of the MSA, and distance from the population-weighted centroid of each MSA to the
nearest coast. We also include indices from the Places Rated Almanac (Savageau and
D'Agostino 2000) that measure how well each city functions in terms of transportation,
education, health, and recreation opportunities.

4.5. Empirical Specification

The hedonic wage and price equations we estimate are semilog functions, a form
commonly used in the hedonic literature and used by Albouy et al. (2016) in constructing

21 We recognize that ideally we would want to instrument for population density. Although we do not instrument for
population density, we conduct sensitivity analysis by replacing population density with other variables. The results
indicate that the MWTP estimates are robust to these alternative specifications. See Sinha et al. (forthcoming) for
details.

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location-specific wage and housing price indices. When estimating equations (7) and (16),
amenities enter the right-hand side of each equation in linear or logarithmic form, although we
consider quadratic functions of winter and summer temperatures as a sensitivity analysis.

To examine heterogeneity in tastes for climate, we focus on winter and summer
temperatures. In hedonic models, the residuals obtained by estimating equation (7) excluding
winter and summer temperatures are used to estimate local linear regressions (equation 8), which
allow MWTP for summer and winter temperatures to vary by city. In estimating discrete choice
models, we allow the coefficients on winter and summer temperatures to be random.

Specifically, we assume that the coefficients are jointly normally distributed with variance-

covariance matrix E. We compute the distribution of these coefficients for each sample
household, conditional on its chosen MSA, and then average the means of these location-specific
coefficients for all households in a city to compute MSA-specific MWTP for winter and summer

temperatures.

5. Estimation Results

In the spirit of Cragg and Kahn (1997) and Bayer et al. (2009), we compare estimates of
mean MWTP from the discrete choice and hedonic models to see whether the discrete choice
approach yields similar mean estimates of amenity values. We are, however, also interested in
taste sorting. From the perspective of valuing climate, it matters how MWTP for temperature
changes varies geographically: Are households living in areas where temperatures are likely to
increase under future climate scenarios willing to pay more (or less) than the mean for warmer
winters or cooler summers? We approach this by measuring MWTP for temperature changes
conditional on a household's current location.

5.1. Hedonic Results

We begin by examining how climate amenities are capitalized into wages and housing
prices, based on national hedonic price functions. Columns 1 and 2 of Table 3 present climate
coefficients from the hedonic wage and housing price regressions estimated when the MSA wage
and housing price indices from equations (4') and (5') are each regressed on the vector of city-

22 In Sinha et al. (forthcoming), we allow other climate variables to have random coefficients, as well as the
coefficients on moving costs and the Hicksian bundle. These alternative specifications have virtually no impact on
mean MWTP for winter or summer temperature. The sorting patterns we observe for winter and summer
temperatures are qualitatively similar to those we report below.

23 Mean MWTP for winter temperature in an MSA is computed by averaging the means of the winter temperature
distributions for all households in the MSA and dividing by a, the coefficient on the Hicksian bundle.

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24

specific amenities. The last two columns of the table show the climate amenity coefficients
obtained when the QOL indices formed from the MSA wage and housing price indices are
regressed on the vector of amenities.

Table 3 suggests that winter temperature is an amenity that is capitalized primarily into
wages (i.e., wages are lower in MSAs with warmer winters) and summer temperature is a
disamenity that is capitalized primarily into housing prices (i.e., housing prices are lower in
MSAs with hotter summers). Housing prices are higher in MSAs with more sunshine but lower
in areas with more snowfall. At the same time, wages are lower in MSAs with more snowfall.
The wage and housing prices indices from equations (4') and (5') are combined into QOL indices
using traditional (Roback) weights (column 3) and adjusted (Albouy) weights (column 4), and
the impact of climate amenities on the QOL index differs depending on the weights used. The
Albouy weights, which assign more importance to housing prices, suggest that summer
temperature is more of a disamenity than winter temperature; traditional weights, which assign
more weight to wages, assign a higher amenity value to winter temperature.

Table 4 displays MWTP for climate amenities implied by the QOL models, using,

alternately, traditional and adjusted weights. Each model controls for all the amenities listed in
Table 2.26 Models H. 1 and H.2 allow winter and summer temperatures to enter in linear and
quadratic forms. In model H.2, MWTP is computed at the means of each climate variable.
Several points are worth noting. All models imply that warmer winter temperature is an amenity
and warmer summer temperature a disamenity; however, the models with adjusted weights
indicate that summer temperature is more of a disamenity than winter temperature is an amenity
when evaluated at temperature means. When adjusted weights are used, MWTP to avoid an
increase in summer temperature is, on average, over three times as great as MWTP for an
increase in winter temperature ($104 for winter temperature and -$358 for summer temperature
in model H. la). In contrast, the two values are approximately equal in magnitude when

traditional weights are used (e.g., $207 and -$228 in model H.lt).

24 The coefficients of nonclimate amenities are presented in Appendix Table A.3.

25 Appendix Table A. 4 displays MWTP for nonclimate amenities for the four models presented in Table 4.
Appendix Table A. 5 presents the MWTP for climate amenities when results are population-weighted.

26 MWTP in Table 4 is calculated by multiplying the relevant coefficient by the mean income of prime-aged
households.

27 There are other differences in the values attached to climate amenities by the two sets of hedonic models.
Snowfall is a disamenity using adjusted weights but an amenity using traditional weights. Summer precipitation is
an amenity when traditional weights are used but a disamenity with adjusted weights.

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Table 4 assumes homogeneous tastes for climate amenities. We also use the QOL indices
from each hedonic model to estimate flexible, local linear regressions that allow the coefficients
on summer and winter temperatures to vary by MSA. Specifically, we regress the QOL index on
all amenities except for winter and summer temperatures, and then use the residuals from this
equation in a local linear regression with the kernel weights described in equation (8). Following
Bajari and Benkard (2004) and Bajari and Kahn (2005), we enter winter and summer
temperatures in linear form. With only 284 observations, results are sensitive to the bandwidth
chosen for the kernel weights. In general, the smaller the bandwidth, the greater the range of
estimated MWTP values across cities. In Table 5, we present summary statistics of MWTP from
the local linear regressions using bandwidths between 0.4 and 0.9. The MWTP for winter and
summer temperatures for each city are plotted in Figures 1-4 using a bandwidth of 0.7 and in
Appendix Figures A. 1-A.4 using bandwidths between 0.4 and 0.9.

When preferences for temperature are allowed to vary across cities, both hedonic models
suggest that summer temperature is a greater disamenity than winter temperature is an amenity:
the MWTP for warmer winters averaged across all cities is less than half of the mean MWTP for
cooler summers, using either set of weights. At a bandwidth of 0.5 (0.7), mean MWTP for winter
temperature is $95 ($77) using traditional weights and $76 ($63) using adjusted weights. Mean
MWTP to reduce summer temperature by 1 degree is $231 ($186) using traditional weights and
$246 ($194) using adjusted weights.

The sorting patterns implied by the two sets of weights are, however, very different.
Figures 1 and 2 display MWTP for winter temperature by city, plotted against winter
temperature using traditional (Figure 1) and adjusted (Figure 2) weights. The use of traditional
weights (Figure 1) suggests that households that live in cold cities have the greatest MWTP for
warmer winters. The highest MWTP is in Duluth, Minnesota. Households along the Pacific coast
would actually prefer cooler winters. This sorting pattern suggests that households in northern
latitudes—in the East and West North Central and New England census divisions—would be
willing pay the most for the beneficial portion of climate change. Using Albouy weights (Figure
2) suggests that households that enjoy warm winters (households in the West South Central and
South Atlantic divisions) have the highest MWTP for warmer winters, although three MSAs in
the northern United States also have high MWTP. Simply put, the two sets of weights have
sorting patterns that are opposites of one another, which the correlations between winter
temperature and MWTP for winter temperature in Table 5 confirm.

The two sets of weights also yield different sorting patterns for summer temperature
(Figures 3 and 4). With traditional weights (Figure 3), the relationship between MWTP for
warmer summers and summer temperature is upward-sloping: people with the highest MWTP to

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reduce summer temperature (the largest negative MWTP) are those who live in MSAs with
cooler summer temperatures. The relationship between MWTP and temperature turns down at
higher temperatures, although the extent of this negative relationship depends on bandwidth—the
MWTP for cooler summers is higher for households living in the South with smaller bandwidths
(see Appendix Figure A.3). The sorting pattern using adjusted weights (Figure 4) is the opposite
of the pattern in Figure 3. The relationship between MWTP for cooler summers and summer
temperature is fairly flat until 80 degrees and then turns sharply downward. Households in the
South Atlantic and West South Central divisions—which are willing to pay the most for warmer
winters (Figure 2)—are willing to pay the most to avoid warmer summers. As shown in Table 5
and in Appendix Figure A.4, this sorting pattern is robust to choice of bandwidth and agrees with
Albouy et al. (2016, Figure 6, Panel C), who describe residents of areas with warmer summers as
being more heat-averse on the margin.

In comparing hedonic results to the discrete choice results reported below, we focus on
results obtained using adjusted (Albouy) weights. The sorting patterns shown in Figures 2 and 4
(and in Appendix Figures A.2 and A.4) using adjusted weights generally agree with the results

reported by Albouy et al. (2016) even though we use different temperature measures. The
results are also more robust to choice of bandwidth than results based on traditional weights. We
also report discrete choice models based on after-tax income to facilitate comparison with
hedonic results based on Albouy weights.

5.2. Discrete Choice Results

As noted above, we estimate discrete location choice models for various population
groups: households headed by persons between 25 and 55 (prime-aged households), households
whose heads are over 55, and households headed by persons 16 years of age and older (full

sample). In comparing the discrete choice and continuous hedonic approaches, we focus on
prime-aged households because of their strong labor-force attachment (see Table 1). It is,
however, important to note that prime-aged households have different preferences for climate
amenities than households headed by persons over age 55, a point we return to below.

28 In the case of summer temperature, Panels C and D of Figure 6 in Albouy et al. (2016) show MWTP to avoid a
day at 80 degrees (versus 65 degrees) to be roughly constant for households experiencing between 1,000 and 3,000
cooling degree days per year. This agrees with the flat portion of Figure 4. The upward-sloping portion of Figure 2,
which shows households in warmer MSAs having higher MWTP for warmer winters, is consistent with Panel B of
Figure 6 in Albouy et al. (2016) at low values of heating degree days.

29 These results are reported in Table 9, discussed below.

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Table 6 describes the results of estimating our base model for prime-aged households,
controlling for all attributes in Table 2 and assuming homogeneous preferences. Model C.l is the
base model with income measured before taxes, model C.2 is the same model but with income
measured after taxes, model C.3 is model C. 1 with moving costs removed, and model C.4 is
model C.2 with moving costs removed. The base model coefficients have been converted to
MWTP by dividing by the coefficient on the Hicksian bundle. Standard errors are reported for all
MWTP estimates.

Table 6 suggests that estimates produced by the discrete choice approach are two to four
times as large as estimates produced by the hedonic approach, assuming homogeneous
preferences. This is certainly true when the estimates from model C.l are compared with those
from the hedonic model with traditional weights (H.lt) and when estimates from model C.2 are
compared with those from the hedonic model with adjusted weights (H.la). Does this difference
disappear when moving costs are removed from the discrete choice models? Model C.4 shows
that removing moving costs from the model in which income is measured net of taxes brings
MWTP to reduce summer temperature very close to what is estimated using the adjusted hedonic
model but still leaves MWTP for winter temperature about three times what is estimated using

the adjusted hedonic model.

Table 7 presents estimates of MWTP for winter and summer temperatures and other

climate amenities based on four mixed logit models. Our base model (model M. 1) controls for
all the amenities in Table 2, as well as moving costs, and allows the coefficients on winter and
summer temperatures to be jointly normally distributed. Model M.2 is identical to model M.l,
except that income is measured as after-tax income. Both models suggest that on average, higher
winter temperature is an amenity and warmer summer temperature a disamenity. Mean MWTP
to reduce summer temperature by 1 degree is higher than mean MWTP to increase winter
temperature by 1 degree ($627 versus $518 in model M.l; $522 versus $382 in model M.2).
There is, however, considerable variation in tastes. Interestingly, the coefficients on winter and
summer temperatures are negatively correlated: most (but not all) households that prefer milder
winters also prefer milder summers, while those that favor colder winters like hotter summers.32

30 As a sensitivity analysis, Appendix Table A.6 shows how the results of Table 6 are altered when population
density is dropped from the list of nonclimate amenities. Results are robust to the omission of population density.

31 Table 7 in the text reports MWTP for climate variables only. MWTPs for nonclimate amenities are reported in
Appendix Table A.7.

32 Appendix Table A.8 explores the sensitivity of the discrete choice model to the Hicksian bundle entering equation
(11) in quadratic form and to the use of the Cobb-Douglas utility function (equation 11'). Results are robust to these
sensitivity analyses.

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To examine how households sort across locations in relation to their taste for winter and
summer temperatures, we calculate the joint distribution of the coefficients of winter and
summer temperatures for each household, conditional on the household's choice of location. The
means of these conditional distributions are averaged across all households in each city, divided
by the coefficient on the Hicksian bundle, and plotted against city temperature in Figures 5 and

The pattern of taste sorting is similar whether we base location decisions on income

before or after taxes. Households with higher MWTP for warmer winters tend to locate in
warmer cities: the correlation coefficient between winter temperature and mean MSA MWTP is
0.92 in model M. 1 (Figure 5A) and 0.91 in model M.2 (Figure 5B). There is, however, some
variation in mean MWTP across cities at a given temperature. For example, at a mean winter
temperature of 40 degrees, households in the states of Oregon and Washington have a
willingness to pay for a warmer winter that is much higher than the MWTP of households in
Texas. At a mean winter temperature of 50 degrees, households on the Pacific coast are willing
to pay more for warmer winter temperature than households in the East South Central division.
Preferences for summer temperature (Figures 6A and 6B) are even more varied: at a temperature
of 70 degrees, households on the Pacific coast find warmer summers a disamenity; however, this
is less so for people in the West North Central division (e.g., the Dakotas). This is also true at
mean summer temperatures above 80: households in the South Atlantic division find warmer
summers a disamenity, but residents of Texas are willing to pay less to avoid hotter summers
than residents of Florida.

Figures 5 and 6 suggest that, holding temperature constant, MWTP for winter and
summer temperatures varies by region: households in the East North Central census division
appear to find hotter summers less of a disamenity than households that have located on the
Pacific coast. Households in the Mountain states appear to favor colder winters than households
in the Pacific division. Some of this might appear to reflect differences in climate variables other
than temperature, such as differences in summer humidity, precipitation, and snowfall. Our base
model, however, controls for summer humidity and precipitation, as well as snowfall and
sunshine.

33 When preferences for winter and summer temperatures are forced to be uncorrelated, there is a strong association
between MSA mean MWTP for higher temperature and temperature itself: the correlation is 0.96 between MSA
mean MWTP and winter temperature and 0.97 between MSA mean MWTP and summer temperature. It appears that
households that live in warmer cities place higher values on both summer and winter temperatures.

34 Figures 5 A and 6A plot results based on model M. 1, while Figures 5B and 6B plot results from model M.2, which
is based on net-of-tax income.

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Failure to control for moving costs has a large effect on the estimated value of climate
amenities, as well as on the spatial distribution of MWTP for winter and summer temperatures.
Model M.3 (M.4) shows the impact of dropping moving costs from the discrete choice model
when income is measured before (after) taxes. While the mean of the distribution of MWTP for
winter temperature remains positive, its magnitude drops by about 5 percent (15 percent). The
mean of the distribution on the coefficient of summer temperature is even more sensitive: its
magnitude drops by about 38 percent (35 percent) when moving costs are omitted. Table 7 also
indicates the role that moving costs play in taste sorting: when moving costs are omitted from the
base models, the standard deviations on the winter temperature coefficients are no longer
statistically significant. In model M.3, the correlation coefficient between the winter and summer
temperature coefficients switches from negative to positive in sign. Simply put, patterns of taste
sorting are no longer identified when moving costs are removed from the discrete choice model.

This is borne out in Figure 7, which contrasts the sorting patterns from model M.3 when
moving costs are removed with the patterns shown in Figures 5 A and 6A. The top right panel of
Figure 7 still shows a positive correlation between mean MWTP for winter temperature and
mean winter temperature; however, the variation is small, and all MSAs have mean MWTP
within about $20 of each other. The bottom right panel suggests that MWTP for warmer
summers is positively associated with summer temperature. Similar results obtain when using
income net of taxes (see Appendix Figure A. 5). We present these results to show the importance
of controlling for moving costs. Moving costs are highly significant in all discrete choice models
and clearly belong in the models.

5.3. Comparison of Hedonic and Discrete Choice Results

The preceding results make clear that the mean values attached to winter and summer
temperatures using the discrete choice approach are much larger than the values obtained from
the hedonic models we have estimated. Under the assumption of homogeneous tastes (Table 6),
mean MWTP for a 1 degree increase in winter temperature using the base discrete choice model
(model C.l) is three times the estimate obtained from hedonic model using traditional weights
(model H.lt). Mean MWTP for a 1 degree decrease in summer temperature is approximately 3.5
times larger using the discrete choice model. When location choices are based on after-tax
income (Model C.2), mean MWTP for winter temperature is four times the estimate obtained
using the hedonic model with adjusted weights (Model H.la). The corresponding estimates for
summer temperature are $595 (Model C.2) and $358 (Model H.la).

The differences in mean MWTP persist when estimated tastes for climate vary across
cities: mean estimates of MWTP for winter temperature vary with the bandwidth used in the

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hedonic models but are below $115 for all the bandwidths reported in Table 5, for both sets of
weights. Mean MWTP is $382 (s.e. = $104) when the discrete choice model is estimated using
after-tax income. The corresponding mean MWTP for a 1 degree decrease in summer
temperature is $522 (s.e. = $180), twice as large as mean MWTP obtained from the hedonic

model for all bandwidths >0.5 using either set of hedonic weights.

The hedonic and discrete choice approaches also produce very different taste sorting
patterns. The discrete choice models suggest that households sort across locations based on
preferences for winter temperature: there is a strong positive correlation between winter
temperature and MWTP for winter temperature in Figures 5A and 5B. The relationship between
MWTP for winter temperature and MSA temperature resulting from the traditionally weighted
local linear hedonic model (Figure 1) is the reverse: it suggests that households with the highest
MWTP for winter temperature live in the coldest cities.

The sorting pattern produced by the hedonic model with adjusted weights (Figure 2) is
closer to the sorting pattern produced by the discrete choice model: both models project that
households living in Florida and Texas have the highest MWTP for warmer winters, but there are
important differences. In the hedonic model, households in the West North Central division have
an MWTP for winter temperature that is as high as that of households living in the South. In
general, the correlation between MWTP for winter temperature and winter temperature is much
weaker than in the discrete choice model.

The value placed on avoiding hotter summers also differs between the discrete choice and
hedonic approaches. A key result from the discrete choice model is that preferences for warmer
summers and warmer winters are negatively correlated. This leads to the inverted-U sorting
pattern shown in Figures 6A and 6B. Households on the Pacific coast, which have high MWTP
for warmer winters, also have a high MWTP for warmer summers. The same is true of
households that live in the South Atlantic division. In contrast, the sorting pattern produced by
the hedonic model with traditional weights shows a much stronger upward slope: according to
this model, households on the Pacific coast have the lowest MWTP for milder summers of all US
households. The sorting pattern produced by the hedonic model with adjusted weights differs
from both the traditional hedonic sorting pattern and the discrete choice model: it displays a
negative correlation between MWTP for an increase in summer temperature and mean summer
temperature. It projects, as does the discrete choice model, that households in Texas and Florida

35 Although we focus on winter and summer temperatures, the discrete choice model generally produces larger
estimates of MWTP for other climate amenities; see Table 6.

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have the highest MWTP to avoid hotter summers, but it also projects that households on the
Pacific coast have the lowest MWTP for cooler summers.

5.4. What Accounts for the Differences?

Why do estimates of the amenity value of temperature differ between the two
approaches? The discrete choice and hedonic models we have estimated differ in three ways: (1)
the discrete choice model incorporates the psychological costs of moving from one's birthplace,
which the hedonic models do not; (2) the discrete choice model allows for city-specific labor and
housing markets, rather than assuming a national market; (3) the discrete choice model uses
information on market shares (i.e., population), which the hedonic model does not.36

If moving costs prevent amenity values from being fully capitalized into wages and
housing prices, then failure to account for moving costs in the hedonic model should reduce
MWTP estimates compared with those produced by the discrete choice model. Equivalently,
removing moving costs from the discrete choice model should cause discrete choice estimates of
MWTP to fall. This is indeed what happens in both the conditional and mixed logit models. In
Table 6, MWTP for summer temperature in model C.4 (discrete choice model based on after-tax
income, no moving costs) is approximately equal to MWTP in the hedonic model with adjusted
weights (see also columns 2 and 4 of Table 8). The two models still differ, however, in MWTP
for winter temperature. In the mixed logit models, dropping moving costs reduces estimates of
mean MWTP for winter and summer temperatures, but they do not coincide with means
produced by the hedonic model with heterogeneous tastes (compare Tables 5 and 7). Moving
costs therefore do not explain all the differences in mean MWTP between the hedonic and
discrete choice approaches.

To investigate the impact of national versus city-specific labor markets, we estimate the
discrete choice model derived from a Cobb-Douglas utility function (equation 9'), including only
moving costs and city-specific fixed effects (Sj) in the first stage. The second stage of estimation
entails regressing city fixed effects on wages, housing prices, and amenities,

8j = ocylnYj — aH\npj + Ajf? + 
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which we assume vary only by city. In estimating equation (20), we replace Inly by (1 - t) Aj
and lnpy by Aj, the same wage and housing price indices that are used in estimating the hedonic
model. This imposes the assumption of national labor and housing markets on the discrete choice
model. The resulting MWTP estimates, in column (3) of Table 8, show that the assumption of
national labor and housing markets reduces MWTP for both winter and summer temperatures
compared with the base discrete choice model, which assumes city-specific labor and housing
markets. It brings MWTP for a decrease in summer temperature in line with estimates from the
hedonic model (column 4 of Table 8); however, MWTP to increase winter temperature is still
three times what the hedonic model projects.

A third difference between the two approaches arises from the fact that the discrete
choice model uses information on market shares in estimating model parameters, which the
hedonic model does not. This can be seen by rewriting the equation for the second-stage of the
discrete choice model (equation 20), following Bayer et al. (2007), as

Sj/ccy + (~)lnPy - lnYj = Aj^ + Sj /av	(21)

where — is the share of income spent on housing. Equation (21) is similar to the hedonic

CCy

equation, with the QOL index on the left-hand side adjusted by the city-specific fixed effect Sj.
Given this adjustment, there is no reason why the discrete choice model should yield the same
estimates of MWTP as the hedonic approach, provided Sj varies across cities. Maximization of
the likelihood function of the conditional logit model guarantees that each Sj equates the sum of
the probabilities that each household chooses city j to the number of households in the sample
that actually choose that city. Although Sj will also be influenced by other variables that enter
the first stage of estimation, Sj will reflect the number of households living city /; under random
sampling, this will be proportional to city population.37 The use of quantity (share) information
should therefore cause discrete choice estimates of MWTP to differ from hedonic estimates.

Equation (21) helps explain why mean MWTP for winter temperature is higher under the
discrete choice than the hedonic approach. The city-specific fixed effects from the first stage of
the conditional logit model with moving costs (the model in column 3 of Table 8) are more
highly positively correlated with winter than with summer temperature. This raises MWTP for
winter temperature in the discrete choice model compared with MWTP from the hedonic model.

37 In the model of column (3) of Table 8, the correlation between Sj and city population is 0.71.

26

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6. Conclusions

The goal of this paper is to compare the continuous hedonic and discrete choice
approaches to valuing climate amenities—in particular, summer and winter temperatures. While
previous comparisons of the two methods have focused on comparing mean MWTP (Cragg and
Kahn 1997; Bayer et al. 2009) we have focused on comparing how MWTP for small changes in
winter and summer temperatures vary with a household's current location. Preferences for
temperature represent a classic case of taste sorting, and for the purposes of valuing climate
policies, it is essential to measure how MWTP for temperature varies with geographic location.

Simply put, the patterns of taste sorting produced by the two approaches are quite
different. The discrete location choice model suggests that households that place a higher value
on warmer winters tend to live in warmer cities, although there is variation across cities in
MWTP holding temperature constant. The continuous hedonic approach using traditional
weights and local linear regression suggests the opposite: MWTP for an increase in winter
temperature is higher for people living in North Dakota than for those in Florida. The hedonic
results with adjusted weights are a U-shaped function of temperature: MWTP is highest for
people living in the West North Central census division, where it is very cold, and in Florida,
where winters are mild, and lowest in locations where mean winter temperature is between 40
and 50 degrees.

In terms of summer temperature, the hedonic local linear regressions with adjusted
weights suggest that MWTP for cooler summers is negatively correlated with temperature at
current location: people on the Pacific coast and in the mountain states consider warmer
summers to be a disamenity, but less so than people living in the South Atlantic, West South
Central, and East South Central census divisions, who will bear the brunt of hotter summers
under climate change (Karl et al. 2009). The hedonic local linear regressions with traditional
hedonic weights suggest that people living in these census divisions are actually willing to pay
less to avoid an increase in mean summer temperature than people in other parts of the country,
while the discrete choice model estimates that MWTP to avoid warmer summers is highest, for
prime-aged households, in the Pacific, Mountain, and South Atlantic states.

There is also a difference in the mean MWTP across models. MWTP for warmer winters
is lower, on average, in both sets of hedonic models than in the discrete choice case: when taste
sorting is allowed, mean MWTP for a 1 degree increase in winter temperature is less than $100
using either hedonic model (Table 5), whereas it is approximately $400 in the discrete choice
model (model M.2 of Table 7). Mean MWTP to avoid warmer summers is lower in both hedonic

27

-------
models (approximately $170 to $250, depending on bandwidth) than in the discrete choice

38

model, where MWTP is over $500.

These findings raise an obvious question: Why do results differ across models? Bayer et
al. (2009) suggest that it is the inclusion of moving costs in the discrete choice model that causes
their hedonic and discrete choice results to differ. Omitting moving costs reduces estimates of
mean MWTP for winter and summer temperatures in our discrete choice models and brings the
discrete choice estimates closer to estimates from the hedonic models, but it does not account for
all the differences between the hedonic and discrete choice estimates.

The hedonic and discrete choice approaches differ in other ways. The construction of
hedonic QOL indices is based on national labor and housing market equations that assume that
the returns to human capital and the marginal cost of housing characteristics are everywhere
equal. The discrete choice approach, in contrast, treats each city as a separate market and allows
variation in the returns to human capital and in the marginal price of dwelling characteristics
across cities to identify household preferences. As shown in Table 8, assuming national labor and
housing markets in the context of the discrete choice model (but including moving costs) lowers
mean MWTP for an increase in winter and a decrease in summer temperature, compared with the
model with city-specific markets.

The discrete choice and hedonic models also use information on location choices
differently. The city-specific fixed effects estimated in the first stage of the discrete choice model
equate the sum of the probabilities of choosing a city to the number of persons in the sample who
choose the city. In a random sample, this will be proportional to city population. When city fixed
effects are regressed on amenities in the second stage of estimation of the discrete choice model,
population is implicitly used to estimate preferences. This is not the case for the hedonic model.
We show, following Bayer et al. (2007), that the second stage of estimation of the discrete choice
model, assuming national labor and housing markets, is similar to that of the hedonic model,
with hedonic prices adjusted for city-specific fixed effects. There is therefore no reason why the
two approaches should produce identical estimates of mean MWTP for city-specific amenities.

This raises another question: If the hedonic and discrete choice approaches yield different
results, which approach yields the more reliable estimates of the value of climate amenities for
use in evaluating climate policy? We believe that several considerations argue in favor of the

38 The mean estimate for the discrete choice model depends on whether income is after tax or before tax: mean
MWTP for winter temperature is $382 (s.e. = $104) using after-tax income and $518 (s.e. = $144) using before-tax
income. The corresponding estimates for reducing summer temperature are $522 (s.e. = $180) using after-tax
income and $627 (s.e. = $249) using before-tax income.

28

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discrete choice approach. As noted above, the discrete choice approach captures the stylized fact
that the majority of households in the United States live in the same state in which the head of
household was born. Informational and psychological frictions make households less than
perfectly mobile. The discrete choice approach also makes use of spatial differences in labor and
housing markets to identify household preferences, rather than assuming a national labor and
housing market.

Finally, the discrete choice approach is more easily able to measure the impact of urban
amenities on all household groups. The hedonic approach typically focuses on the preferences of
prime-aged households, since a significant fraction of older households have no wage income.
But climate benefits accrue to all households. Table 9 presents estimates of the discrete choice
model for households headed by prime-aged adults, adults over 55, and all households with
heads 16 years and older. Estimates of MWTP based on all households are approximately 40
percent greater than those based on the prime-aged sample. Older households place a higher
value on warmer winters and cooler summers, and it is important to estimate these benefits.

29

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32

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Table 1. Descriptive Statistics of Household Characteristics





Full sample

Prime-aged

Greater than 55





(/V: 54,008)

(/V: 33,180)

(/V: 17,643)

Variable

Description

Mean

Std. dev.

Mean

Std. dev.

Mean

Std. dev.

Age of household head

Age

49.11

17.03

40.79

8.20

69.50

9.41

(mean)















Gender of household head

Male

63.93



67.02



60.60



(proportion)















Marital status of household

Married

52.22



55.43



50.99



head (proportion)















Race of household head

White

82.70



81.13



87.03



(proportions)

Black

13.11



13.97



10.98





Other

4.20



4.91



1.99



Education of household

No high school

12.86



7.56



23.09



head (proportions)

High school

25.96



24.06



29.71





Some college

30.89



33.73



23.65





College graduate

19.33



22.67



12.95





Postgraduate education

10.96



11.99



10.62



Household head movement

Left state of birth

42.65



40.99



47.32



from place of birth

Left census division of birth

32.78



31.28



36.86



(proportions)

Left census region of birth

26.55



24.98



30.85



Household wage earnings

Sum of the wage earnings of all

$49,960

$54,508

$64,098

$55,106

$26,307

$47,544

(mean)

household members













Household wage earnings

Households with zero wage

16.75



2.23



46.94



(proportion)

earnings













Total household income Sum of wage, business, and farm $63,312 $58,671	$69,161 $59,723	$57,294 $58,615

(mean)	incomes and income from other

sources of all household members"

33

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Full sample

Prime-aged

Greater than 55





(/V: 54,008)

(/V: 33,180)

(/V: 17,643)

Variable

Description

Mean Std. dev.

Mean Std. dev.

Mean Std. dev.

Household annual housing

Sum of monthly mortgage

$15,556 $9,082

$16,193 $9,437

$15,481 $8,560

expenditures (mean)

payment or rent, cost of utilities,









insurance, and property taxes







Size of household

1 member

26.16

21.05

36.03

(proportions)

2 members

34.69

27.35

47.68



3 or more members

39.15

51.59

16.28

° Income from other sources would include Social Security income; welfare (public assistance) income; Supplementary Security Income; interest,
dividend, and rental income; retirement income; and other income.

34

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Table 2. Descriptive Statistics of Amenity Variables







Variable

N

Mean

Std. dev.

Minimum

Maximum

Median

Avg. winter temperature (°F)

284

37.339

12.158

9.442

67.922

34.996

Avg. summer temperature (°F)

284

73.309

5.817

60.848

89.733

72.517

Annual snowfall (inches)

284

20.360

21.366

0.000

84.050

18.050

Summer precipitation (inches)

284

10.966

5.057

0.440

23.300

11.932

July relative humidity (%)

284

66.246

10.891

22.500

78.000

70.500

Annual sunshine (% of possible sunshine in 24 hours)

284

60.764

8.323

43.000

78.000

58.000

Avg. elevation (miles)

284

0.197

0.273

0.000

1.620

0.130

Distance to coast (miles)

284

141.096

169.592

0.009

824.451

91.025

Visibility > 10 miles (% of hours)

284

46.053

19.541

5.000

85.500

45.500

Mean PM2.5 (micrograms/cubic meter)

284

12.829

2.884

5.382

19.535

12.818

Population density (persons per square mile)

284

471.767

983.041

5.400

13,043.600

259.050

Violent crime rate (number of violent crimes per 1,000 persons)

284

4.560

2.214

0.069

12.330

4.349

Park area (square miles)

284

192.908

584.303

0.000

5,477.564

24.893

Transportation score

284

50.370

29.181

0.000

100.000

50.280

Education score

284

51.230

29.322

0.000

100.000

51.130

Arts score

284

51.137

29.055

0.000

100.000

51.140

Healthcare score

284

49.201

28.657

0.000

98.300

49.430

Recreation score

284

53.342

28.386

0.000

100.000

54.245

35

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Table 3. Hedonic Wage, Housing Cost, and Quality of Life Regressions



Wage reg.

Housing cost reg.

QOL reg.
Traditional weights

QOL reg.
Adjusted weights

Variable

Coef.

Coef.

Coef.

Coef.



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

-0.0030

-0.0001

0.0030

0.0015



(0.0008)

(0.0020)

(0.0006)

(0.0005)

Avg. summer temperature

-0.0010

-0.0172

-0.0033

-0.0052



(0.0015)

(0.0040)

(0.0010)

(0.0009)

July humidity

-0.0007

0.0020

0.0012

0.0010



(0.0007)

(0.0016)

(0.0005)

(0.0003)

Annual snowfall

-0.0010

-0.0022

0.0004

-0.0002



(0.0003)

(0.0007)

(0.0002)

(0.0002)

Ln(summer precipitation)

-0.0247

-0.0475

0.0128

-0.0031



(0.0111)

(0.0283)

(0.0080)

(0.0067)

Annual sunshine

0.0004

0.0089

0.0019

0.0028



(0.0009)

(0.0022)

(0.0006)

(0.0005)

No. of obs. (MSAs)

284

284

284

284

Adjusted R-squared

0.71

0.74

0.50

0.59

Note: All other amenities in Table 2 are included in the models reported in this table.

-------
Table 4. Marginal Willingness to Pay for Climate Amenities: Hedonic Models, Homogeneous Tastes

Traditional hedonic weights	Adjusted hedonic weights

Model Hl.t	Model H2.t	Model HI.a	Model H2.a

Temperature specification	Linear	Quadratic	Linear	Quadratic

(Base model)	(Base model)

Variable

Coef.

MWTP

Coef.

MWTP

Coef.

MWTP

Coef.

MWTP



(Std.

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.



err.)

err.)

err.)

err.)

err.)

err.)

err.)

err.)

Avg. winter temperature

0.0030

$207

0.0043

$186

0.0015

$104

0.0031

$110



(0.0006)

($42)

(0.0019)

($46)

(0.0005)

($33)

(0.0014)

($41)

Avg. summer temperature

-0.0033

-$228

-0.0228

-$228

-0.0052

-$358

-0.0048

-$355



(0.0010)

($68)

(0.0131)

($68)

(0.0009)

($64)

(0.0158)

($65)

July humidity

0.0012

$84

0.0012

$84

0.0010

$71

0.0010

$71



(0.0005)

($35)

(0.0005)

($35)

(0.0003)

($24)

(0.0003)

($23)

Annual snowfall

0.0004

$29

0.0005

$33

-0.0002

-$16

-0.0001

-$10



(0.0002)

($16)

(0.0002)

($16)

(0.0002)

($11)

(0.0002)

($11)

Ln(summer precipitation)

0.0128

$81

0.0157

$99

-0.0031

-$19

-0.0014

—$9



(0.0080)

($50)

(0.0087)

($55)

(0.0067)

($42)

(0.0069)

($44)

Annual sunshine

0.0019

$129

0.0025

$172

0.0028

$191

0.0030

$205



(0.0006)

($44)

(0.0008)

($57)

(0.0005)

($35)

(0.0007)

($45)

No. of obs. (MSAs)

284



284



284



284



Adjusted R-squared

0.50



0.50



0.59



0.59



Note: MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the regressions
nonlinearly, amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear
covariates are as follows: population density, summer precipitation, and elevation enter in log form, while distance to the
coast enters the model quadratically.

37

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Table 5. Marginal Willingness to Pay for Climate Amenities: Hedonic Models, Heterogeneous Tastes





Winter temperature

Summer temperature



Correlations























WT

WT,









Std.

10th

90th



Std.

10th

90th

MWTP,

WT

ST,

Weights

Bandwidth

Mean

dev.

pctile

pctile

Mean

dev.

pctile

pctile

ST MWTP

MWTP

ST MW1

Traditional

0.4

$113

$81

-$4

$188

-$248

$273

-$622

$44

-0.05

-0.31

0.03

Traditional

0.5

$95

$58

$23

$146

-$231

$181

-$494

-$69

-0.23

-0.44

0.22

Traditional

0.6

$84

$47

$32

$132

-$209

$135

-$414

-$85

-0.36

-0.52

0.37

Traditional

0.7

$77

$39

$46

$123

-$186

$109

-$345

-$81

-0.46

-0.59

0.49

Traditional

0.8

$72

$32

$46

$110

-$165

$93

-$301

-$76

-0.54

-0.64

0.58

Traditional

0.9

$68

$27

$46

$101

-$148

$81

-$265

-$71

-0.61

-0.69

0.65

Adjusted

0.4

$90

$87

$2

$173

-$276

$305

-$530

-$42

-0.51

0.07

-0.53

Adjusted

0.5

$76

$58

$19

$115

-$245

$233

-$424

-$88

-0.58

0.03

-0.53

Adjusted

0.6

$68

$40

$29

$94

-$216

$169

-$358

-$107

-0.61

0.00

-0.56

Adjusted

0.7

$63

$29

$34

$80

-$194

$122

-$314

-$117

-0.60

-0.03

-0.61

Adjusted

0.8

$60

$22

$38

$76

-$179

$90

-$281

-$122

-0.55

-0.07

-0.67

Adjusted

0.9

$57

$17

$42

$72

-$169

$69

-$254

-$123

-0.49

-0.10

-0.72

Note: The mean MWTP across the 284 MSA regressions is weighted by MSA population.

38

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Table 6. Comparison of Hedonic and Discrete Choice Models, Homogeneous Tastes



Model C.l

Model C.2

Model C.3

Model C.4

Model Hl.t

Model HI.a

Variable

MWTP

MWTP

MWTP

MWTP

MWTP

MWTP



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

$599

$406

$540

$358

$207

$104



($147)

($97)

($147)

($96)

($42)

($33)

Avg. summer temperature

-$791

-$595

-$382

-$322

-$228

-$358



($246)

($163)

($278)

($178)

($68)

($64)

July humidity

-$465

-$295

-$445

-$271

$84

$71



($139)

($90)

($125)

($80)

($35)

($24)

Annual snowfall

-$377

-$266

-$122

-$90

$29

-$16



($65)

($44)

($67)

($43)

($16)

($11)

Ln(summer precipitation)

$525

$321

$163

$76

$81

-$19



($188)

($124)

($184)

($118)

($50)

($42)

Annual sunshine

-$151

-$65

-$267

-$133

$129

$191



($153)

($100)

($161)

($103)

($44)

($35)

Note: For the hedonic models, MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the
regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear covariates are as
follows: population density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model quadratically.

Model C.l: Base conditional logit model

Model C.2: Base conditional logit model with income net of taxes
Model C.3: Base conditional logit model with moving costs removed

Model C.4: Base conditional logit model with income net of taxes and moving costs removed
Model Hl.t: Hedonic model with traditional weights
Model HI.a: Hedonic model with adjusted weights

39

-------
Table 7. Marginal Willingness to Pay for Climate Amenities: Mixed Logit Models

M.l: Base model	M.2: Net of taxes	M.3: Omit moving	M.4: Net of taxes+

costs	omit moving costs

Panel A: 1st stage estimates

Variable

Coef.



Coef.



Coef.



Coef.



(Std. err.)



(Std. err.)



(Std. err.)



(Std. err.)



Std. dev.: avg. winter temperature

0.0588
(0.0026)



0.0592
(0.0026)



0.0011
(0.0128)



0.0032
(0.0097)



Std. dev.: avg. summer temperature

0.0592
(0.0068)



0.0612
(0.0066)



0.0352
(0.0215)



0.0525
(0.0174)



Correlation coefficient

-0.6893
(0.0827)



-0.6993
(0.0776)



0.8614
(0.2756)



-0.9433
(0.1297)



Panel B: 2nd stage estimates

















Variable

Coef

MWTP

Coef

MWTP

Coef

MWTP

Coef

MWTP

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Mean: avg. winter temperature

0.0209

$518

0.0210

$382

0.0184

$491

0.0171

$326



(0.0058)

($144)

(0.0057)

($104)

(0.0055)

($146)

(0.0055)

($104)

Mean: avg. summer temperature

-0.0253

-$627

-0.0286

-$522

-0.0145

-$386

-0.0178

-$339



(0.0100)

($249)

(0.0098)

($180)

(0.0108)

($288)

(0.0110)

($209)

July humidity

-0.0208

-$514

-0.0198

-$360

-0.0165

-$440

-0.0156

-$296



(0.0054)

($135)

(0.0052)

($95)

(0.0046)

($124)

(0.0045)

($85)

Annual snowfall

-0.0170

-$422

-0.0176

-$321

-0.0047

-$126

-0.0052

-$99



(0.0026)

($66)

(0.0026)

($49)

(0.0025)

($67)

(0.0025)

($48)

Ln(summer precipitation)

0.1708

$403

0.1517

$264

0.0678

$172

0.0593

$107



(0.0768)

($181)

(0.0752)

($131)

(0.0732)

($186)

(0.0727)

($132)

Annual sunshine

-0.0149

-$368

-0.0125

-$229

-0.0082

-$219

-0.0040

-$75



(0.0060)

($149)

(0.0059)

($108)

(0.0060)

($159)

(0.0059)

($111)

Note: When entering the regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear
covariates are as follows: population density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model
quadratically.

40

-------
Table 8. Comparison of Hedonic and Discrete Choice Models, Homogeneous Tastes



Base discrete

Discrete choice
model with
taxes, no
moving costs

Discrete choice
model,

Hedonic
model,
adjusted
weights



choice model
with taxes

national labor
and housing
markets

Variable

MWTP

MWTP

MWTP

MWTP



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

$406

$358

$344

$104



($97)

($96)

($72)

($33)

Avg. summer temperature

-$595

-$322

-$423

-$358



($163)

($178)

($125)

($64)

July humidity

-$295

-$271

-$207

$71



($90)

($80)

($62)

($24)

Annual snowfall

-$266

-$90

-$167

-$16



($44)

($43)

($28)

($11)

Ln(summer precipitation)

$321

$76

$241

-$19



($124)

($118)

($84)

($42)

Annual sunshine

-$65

-$133

-$30

$191



($100)

($103)

($72)

($35)

Note: For the models in columns (3) and (4), MWTP is computed at mean household income for the prime-aged sample
($69,188). When entering the regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to
compute MWTP. Nonlinear covariates are as follows: population density, summer precipitation, and elevation enter in log form,
while distance to the coast enters the model quadratically.

41

-------
Table 9. Marginal Willingness to Pay for Climate Amenities: Mixed Logit Results, Various Subsamples

All ages
(base model)

Prime-aged

Over 55 years

Panel A: 1st stage estimates



Coef.



Coef.



Coef.



Variable

(Std.



(Std.



(Std.





err.)



err.)



err.)



Std. dev.: avg. winter temperature

0.0666



0.0588



0.0742





(0.0020)



(0.0026)



(0.0039)



Std. dev.: avg. summer temperature

0.0522



0.0592



0.0331





(0.0060)



(0.0068)



(0.0091)



Correlation coefficient

-0.8332



-0.6893



-0.9936





(0.0731)



(0.0827)



(0.1077)



Panel B: 2nd stage estimates















Coef.

MWTP

Coef.

MWTP

Coef.

MWTP

Variable

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.



err.)

err.)

err.)

err.)

err.)

err.)

Mean: avg. Winter temperature

0.0249

$709

0.0209

$518

0.0375

$1,035



(0.0056)

($160)

(0.0058)

($144)

(0.0070)

($199)

Mean: avg. summer temperature

-0.0307

-$873

-0.0253

-$627

-0.0516

-$1,424



(0.0091)

($260)

(0.0100)

($249)

(0.0106)

($301)

July humidity

-0.0269

-$764

-0.0208

-$514

-0.0325

-$896



(0.0049)

($142)

(0.0054)

($135)

(0.0054)

($155)

Annual snowfall

-0.0166

-$471

-0.0170

-$422

-0.0154

-$425



(0.0024)

($70)

(0.0026)

($66)

(0.0026)

($75)

Ln(summer precipitation)

0.1408

$376

0.1708

$403

0.0926

$232



(0.0720)

($192)

(0.0768)

($181)

(0.0823)

($206)

Annual sunshine

-0.0155

-$441

-0.0149

-$368

-0.0111

-$307



(0.0057)

($162)

(0.0060)

($149)

(0.0067)

($185)

Note: When entering the regressions nonlinearly, amenity variables are evaluated at population-weighted means in
order to compute MWTP. Nonlinear covariates are as follows: population density, summer precipitation, and
elevation enter in log form, while distance to the coast enters the model quadratically.

42

-------
Figure 1. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Local Linear Hedonic Model, Traditional

Weights (bandwidth = 0.7)

O
O

a

Traditional Weights QOL, Band = 0.7

O

o

w

Ph
H

o -

o
o

~T~

0

0 AD ogOfi1

o AA ° o + +
o +

~++

o

n o n

AO

A

o ^ o

O

&

~40~

~60

20

Winter Temperature

80

O New England

0

Middle Atlantic

A

East North Central

~

"West North Central

+ South Atlantic

x East South Central

0

West South Central

0

Mountain

A

Pacific



43

-------
Figure 2. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Local Linear Hedonic Model, Adjusted

Weights (bandwidth = 0.7)

Adjusted Weights QOL, Band = 0.7

o

o -

o

° J

m _

i	i	i	i	r~

0	20	40	60	80

Winter Temperature

o

New England

0

Middle Atlantic

A

East North Central

~

West North Central

+ South Atlantic

X

East South Central

o

West South Central

o

Mountain

A

Pacific



44

-------
Figure 3. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Local Linear Hedonic Model,

Traditional Weights (bandwidth = 0.7)

o
o

o -

o
o

o
o

Traditional Weights QOL, Band = 0.7

A
A

AA

A

+ + + + A

5	-	***%*$

&	+	° 0

.	A g	O** aoQ u oo

^ O

W

b	A O	~ +

O c>	D	+ o

S1	A	A	+X« O

'	o o^A aA d	0 o

V*	+ 1

O I *	<>&& 4n°

O _	A ~ n a TlH

rr,	a	riJ . A

o o

A

0ov c?

°o ,0^ * D

% [JD

60	70	80	90~

Summer Temperature

o

New England

0

Middle Atlantic

A

East North Central

~

West North Central

+ South Atlantic

X

East South Central

o

West South Central

0

Mountain

A

Pacific



45

-------
Figure 4. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Local Linear Hedonic Model, Adjusted

Weights (bandwidth = 0.7)

Adjusted Weights QOL, Band = 0.7

~

Afa.	n	^

o |	«	-

o _	~

A

(ft. O

<>

O

+ wo

^jlO

©	**>0 o o

Ph	a°

H0	+

o	+

o _	+

+

+

+

o	+

o

00

^	1	r	i

60	70	80	90

Summer Temperature

O New England

0

Middle Atlantic

A

East North Central

~

"West North Central

+ S outh Atl anti c

x East South Central

o

West South Central

0

Mountain

A

Pacific



46

-------
Figure 5A. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Base Discrete Choice Model

~

o
o
o

—I	1	1	1-

20	40	60	80

Winter Temperature

O New England

0

Middle Atlantic

A

East North Central

~

West North Central

+ South Atlantic

x East South Central

o

West South Central

0

Mountain

A

Pacific



47

-------
Figure 5B. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Discrete Choice Model, Income Net of

Taxes

o
o
m

o
o
o

rT °

, o

U")

o

O _|

A
A

&A A*+'



+

> +
s

+

20

40

Winter Temperature

60

80

O New England

0

Middle Atlantic

A

East North Central

~

West North Central

+ South Atlantic

x East South Central

o

West South Central

0

Mountain

A

Pacific



48

-------
Figure 6A. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Base Discrete Choice Model

O
O

w-

Ph
H

o
o
o

o
o

V")

Summer Temperature

O New England

0

Middle Atlantic

A

East North Central

~

West North Central

+¦ South Atlantic

x East South Central

o

"West South Central

0

Mountain

A

Pacific



49

-------
Figure 6B. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Discrete Choice Model, Income Net

of Taxes

o -

o
o
m

y*
~_

^	A A

8 1 a aaa

O -	A

A

A
&

O
O
ID

60	70	80	90

Summer Temperature

O New England

O

Middle Atlantic

A

East North Central

~

West North Central

+ South Atlantic

x East South Central

o

West South Central

o

Mountain

A

Pacific



50

-------
Figure 7. Impact of Removing Moving Costs on Marginal Willingness to Pay for Temperature by Metropolitan Area

Base Model (Left Panel)

Omit Moving Costs (Right Panel)



;

if D

n



20

40 60 80







Witter T auperatue

o



O «¦«.

£. U-.N^.Tcr,, D

-

BBcScuhCir.nJ

D





mni'Mj -H-3H+ 4++ +

H Ncv Brdird

Witter TanperalLire

£l bici'far*. Cc

* % uf
~ & &.

8

»*~ *



60



70

80

Summer Temperature

90

'

0



70

80

Smun ff Temperature

90

C- Drclu-d













~ NivBriJin]









o *¦



o <««»' C, P..-U









bixhrcramJ

O htanun £. PuiRl



51

-------
Appendix

Table A.1. Summary of Hedonic Wage Coefficients

National
equation

MSA-specific
equations (284)

(Dependent variable: log(wage rate))

Coef.

Mean(Coef.) Std.dev.(Coef.

High school (left-out category is no high school)	0.117

Some college	0.212

College graduate	0.418

Higher education	0.577

Age	0.049

Age squared (divided by 100)	0.000

Married	0.093

Male	0.197

Black (left-out category is white)	-0.082

Other race	-0.086

Speaks English well	0.213

Hispanic	-0.075

Business operations occupation (left-out category is	-0.120
management occupation)

Financial specialists occupation	-0.139

Computer and math occupation	0.010

Engineering occupation	-0.088

Life, physical, and social sciences occupation	-0.206

Social services occupation	-0.354

Legal occupation	-0.023

Teachers occupation	-0.221

Other educational occupation	-0.502

Arts, sports, and media occupation	-0.220

Healthcare practitioners occupation	0.025

Healthcare support occupation	-0.351

Protective services occupation	-0.257

Food and serving occupation	-0.453

Maintenance occupation	-0.485

Personal care service occupation	-0.435

High-skill sales occupation	-0.154

Low-skill sales occupation	-0.227

Office support occupation	-0.316

Construction trades and extraction workers	-0.248
occupation

Maintenance workers occupation	-0.206

Production occupation	-0.346

Transportation occupation	-0.375

Construction industry (left-out category is mining	-0.179
and utilities)0

Manufacturing industry	-0.127

0.098
0.180
0.382
0.546
0.048
0.000
0.092
0.215
-0.070
-0.055
0.126
-0.057
-0.122

-0.116
0.004
-0.073
-0.180
-0.328
-0.039
-0.190
-0.473
-0.243
0.062
-0.330
-0.240
-0.428
-0.472
-0.423
-0.136
-0.228
-0.298
-0.246

-0.192
-0.317
-0.357
-0.180

-0.120

0.038
0.045
0.069
0.074
0.007
0.000
0.021
0.040
0.070
0.054
0.103
0.074
0.067

0.072
0.089
0.083
0.100
0.078
0.127
0.093
0.129
0.094
0.078
0.078
0.106
0.077
0.074
0.114
0.067
0.062
0.049
0.090

0.065
0.084
0.075
0.095

0.107

52

-------


National

MSA-specific



equation

equations (284)

(Dependent variable: log(wage rate))

Coef.

Mean(Coef.)

Std.dev.(Coef.)

Wholesale industry

-0.190

-0.185

0.097

Retail industry

-0.344

-0.339

0.094

Transportation industry

-0.111

-0.084

0.107

Information and communications industry

-0.111

-0.134

0.109

Finance industry

-0.151

-0.175

0.105

Professional and scientific management services

-0.197

-0.220

0.101

industry







Educational and health social services industry

-0.280

-0.267

0.092

Recreation and food services industry

-0.352

-0.370

0.110

Other services industry

-0.348

-0.343

0.101

Public administration industry

-0.123

-0.126

0.095

No. of obs.fc

2,916,211

10,268

16,223

R-squared6

0.41

0.40

0.03

° Since these two industries have a very low number of observations, we bundled them together as the
omitted category.

b For the MSA-specific regressions, the value in the first column presents the average number of
observations and average R-squared value across the 284 MSA regressions, while the second column
presents the standard deviation of the relevant statistic across those regressions.

53

-------
Table A.2. Summary of Hedonic Housing Coefficients

(Dependent variable: log(user costs including
insurance and utility costs))

National
equation

Coef.

MSA-specific equations (284)
Mean(Coef.) Std.dev.(Coef.)

House is owned

0.504

0.464

0.144

3 bedrooms (left-out category is less than 3

0.128

0.160

0.061

bedrooms)







4 bedrooms

0.152

0.208

0.082

5 bedrooms

0.283

0.324

0.110

Greater than 5 bedrooms

0.485

0.500

0.163

2 rooms (left-out category is less than 2

0.137

0.080

0.133

rooms)







3 rooms

0.137

0.053

0.140

4 rooms

0.166

0.075

0.146

5 rooms

0.230

0.126

0.154

6 rooms

0.327

0.218

0.156

Greater than 6 rooms

0.531

0.413

0.176

Complete kitchen

-0.033

-0.104

0.261

Complete plumbing

0.219

0.221

0.212

1 to 10 acres

0.214

0.246

0.140

0 to 1 years old

0.391

0.428

0.157

2 to 5 years old

0.371

0.404

0.158

6 to 10 years old

0.316

0.358

0.150

11 to 20 years old

0.218

0.247

0.127

21 to 30 years old

0.110

0.150

0.122

31 to 40 years old

0.059

0.093

0.113

41 to 50 years old

0.020

0.039

0.089

51 to 60 years old (left-out category is over 61

-0.026

-0.011

0.075

years old)







Number of units in structure: single-attached

-0.158

-0.082

0.105

(left-out category is single family detached)







2 units in structure

-0.055

-0.089

0.107

3 to 4 units in structure

-0.112

-0.135

0.095

5 to 9 units in structure

-0.139

-0.167

0.106

10 to 19 units in structure

-0.114

-0.132

0.127

20 to 49 units in structure

-0.169

-0.154

0.151

Over 50 units in structure

-0.152

-0.190

0.207

No. of obs.°

3,255,748

11,464

18,376

/?-squared°

0.57

0.54

0.07

a For the MSA-specific regressions, the value in the first column presents the average number of
observations and average R-squared value across the 284 MSA regressions, while the second column
presents the standard deviation of the relevant statistic across those regressions.

54

-------
Table A.3. Hedonic Wage, Housing Cost, and Quality of Life Regressions (all coefficients)



Wage reg.

Housing cost reg.

QOL reg.

QOL reg.







traditional weights

adjusted weights

Variable

Coef.

Coef.

Coef.

Coef.



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

-0.0030

-0.0001

0.0030

0.0015



(0.0008)

(0.0020)

(0.0006)

(0.0005)

Avg. summer temperature

-0.0010

-0.0172

-0.0033

-0.0052



(0.0015)

(0.0040)

(0.0010)

(0.0009)

July humidity

-0.0007

0.0020

0.0012

0.0010



(0.0007)

(0.0016)

(0.0005)

(0.0003)

Annual snowfall

-0.0010

-0.0022

0.0004

-0.0002



(0.0003)

(0.0007)

(0.0002)

(0.0002)

Ln(summer precipitation)

-0.0247

-0.0475

0.0128

-0.0031



(0.0111)

(0.0283)

(0.0080)

(0.0067)

Annual sunshine

0.0004

0.0089

0.0019

0.0028



(0.0009)

(0.0022)

(0.0006)

(0.0005)

Ln(population density)

0.0504

0.1302

-0.0179

0.0173



(0.0069)

(0.0168)

(0.0049)

(0.0039)

Mean PM2.5

0.0036

-0.0076

-0.0056

-0.0044



(0.0018)

(0.0042)

(0.0014)

(0.0011)

Violent crime rate

0.0019

-0.0096

-0.0043

-0.0042



(0.0019)

(0.0043)

(0.0017)

(0.0013)

Transportation score

-0.0007

-0.0015

0.0003

-0.0001



(0.0002)

(0.0005)

(0.0001)

(0.0001)

Education score

0.0000

0.0000

0.0000

0.0000



(0.0002)

(0.0006)

(0.0001)

(0.0001)

55

-------


Wage reg.

Housing cost reg.

QOL reg.
traditional weights

QOL reg.
adjusted weights

Variable

Coef.

Coef.

Coef.

Coef.



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Arts score

0.0007

0.0013

-0.0004

0.0001



(0.0003)

(0.0006)

(0.0002)

(0.0001)

Healthcare score

0.0002

0.0013

0.0002

0.0003



(0.0002)

(0.0004)

(0.0001)

(0.0001)

Recreation score

0.0005

0.0009

-0.0002

0.0001



(0.0002)

(0.0005)

(0.0002)

(0.0001)

Park area

0.0000

0.0000

0.0000

0.0000



(0.0000)

(0.0000)

(0.0000)

(0.0000)

Visibility > 10 miles

0.0016

0.0024

-0.0010

0.0000



(0.0004)

(0.0009)

(0.0003)

(0.0002)

Ln(elevation)

-0.0019

0.0035

0.0027

0.0021



(0.0056)

(0.0125)

(0.0043)

(0.0032)

Distance to coast

-0.0006

-0.0011

0.0003

-0.0001



(0.0001)

(0.0002)

(0.0001)

(0.0001)

(Distance to coast)A2

0.0000

0.0000

0.0000

0.0000



(0.0000)

(0.0000)

(0.0000)

(0.0000)

No. of obs. (MSAs)

284

284

284

284

Adjusted R-squared

0.71

0.74

0.50

0.59

Note: MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the regressions nonlinearly,
amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear covariates are as follows: population
density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model quadratically.

56

-------
Table A.4. MWTP for All Location-Specific Amenities, Hedonic Models

Temperature specification

Traditional hedonic weights
Model Hl.t	Model H2.t

Linear	Quadratic

(base model)

Adjusted hedonic weights
Model Hl.a	Model H2.a

Linear	Quadratic

(base model)

Variable

Coef.

MWTP

Coef.

MWTP

Coef.

MWTP

Coef.

MWTP



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

0.0030

$207

0.0043

$186

0.0015

$104

0.0031

$110



(0.0006)

($42)

(0.0019)

($46)

(0.0005)

($33)

(0.0014)

($41)

Avg. summer temperature

-0.0033

-$228

-0.0228

-$228

-0.0052

-$358

-0.0048

-$355



(0.0010)

($68)

(0.0131)

($68)

(0.0009)

($64)

(0.0158)

($65)

July humidity

0.0012

$84

0.0012

$84

0.0010

$71

0.0010

$71



(0.0005)

($35)

(0.0005)

($35)

(0.0003)

($24)

(0.0003)

($23)

Annual snowfall

0.0004

$29

0.0005

$33

-0.0002

ID
1

¦uy
1

-0.0001

O

1

¦uy
1



(0.0002)

($16)

(0.0002)

($16)

(0.0002)

($11)

(0.0002)

($11)

Ln(summer precipitation)

0.0128

$81

0.0157

$99

-0.0031

-$19

-0.0014

-$9



(0.0080)

($50)

(0.0087)

($55)

(0.0067)

($42)

(0.0069)

($44)

Annual sunshine

0.0019

$129

0.0025

$172

0.0028

$191

0.0030

$205



(0.0006)

($44)

(0.0008)

($57)

(0.0005)

($35)

(0.0007)

($45)

Ln(population density)

-0.0179

-$3

-0.0165

-$2

0.0173

$2

0.0173

$2



(0.0049)

($1)

(0.0051)

($1)

(0.0039)

($1)

(0.0038)

($1)

Mean PM2.5

-0.0056

-$384

-0.0056

-$387

-0.0044

-$303

-0.0051

-$350



(0.0014)

($95)

(0.0016)

($110)

(0.0011)

($75)

(0.0012)

($84)

Violent crime rate

-0.0043

-$301

-0.0045

-$312

-0.0042

-$288

-0.0044

-$307



(0.0017)

($116)

(0.0017)

($120)

(0.0013)

($87)

(0.0013)

($89)

Transportation score

0.0003

$23

0.0003

$23

-0.0001

-$9

-0.0001

-$8



(0.0001)

($10)

(0.0001)

($10)

(0.0001)

($8)

(0.0001)

($8)

Education score

0.0000

$2

0.0000

$1

0.0000

$1

0.0000

$0



(0.0001)

($10)

(0.0001)

($10)

(0.0001)

($9)

(0.0001)

($9)

Arts score

-0.0004

-$26

-0.0004

-$26

0.0001

$5

0.0001

$6



(0.0002)

($12)

(0.0002)

($12)

(0.0001)

($9)

(0.0001)

($9)

Healthcare score

0.0002

$11

0.0002

$12

0.0003

$24

0.0003

$24



(0.0001)

($8)

(0.0001)

($8)

(0.0001)

($7)

(0.0001)

($7)

Recreation score

-0.0002

-$17

-0.0002

-$16

0.0001

$4

0.0001

$4



(0.0002)

($12)

(0.0002)

($12)

(0.0001)

($9)

(0.0001)

($9)

Park area

0.0000

-$1

0.0000

-$1

0.0000

$0

0.0000

$0

57

-------
Temperature specification

Traditional hedonic weights
Model Hl.t	Model H2.t

Linear	Quadratic

(base model)

Adjusted hedonic weights
Model Hl.a	Model H2.a

Linear	Quadratic

(base model)

Variable Coef. MWTP Coef. MWTP Coef. MWTP Coef.	MWTP
	(Std. err.) (Std. err.)	(Std. err.) (Std. err.)	(Std. err.) (Std. err.)	(Std. err.) (Std. err.)



(0.0000)

($0)

(0.0000)

($0)

(0.0000)

($0)

(0.0000)

($0)

Visibility > 10 miles

-0.0010

-$68

-0.0011

-$78

0.0000

-$1

-0.0001

-$5



(0.0003)

($21)

(0.0003)

($22)

(0.0002)

($16)

(0.0002)

($16)

Ln(elevation)

0.0027

$965

0.0021

$731

0.0021

$740

0.0017

$614



(0.0043)

($1,531)

(0.0044)

($1,554)

(0.0032)

($1,126)

(0.0032)

($1,123)

Distance to coast

0.0003

$16

0.0003

$17

-0.0001

-$3

-0.0001

-$3



(0.0001)

($3)

(0.0001)

($3)

(0.0001)

($3)

(0.0001)

($3)

(Distance to coast)A2

0.0000



0.0000



0.0000



0.0000





(0.0000)



(0.0000)



(0.0000)



(0.0000)



No. of obs. (MSAs)

284



284



284



284



Adjusted /?-squared

0.50



0.50



0.59



0.59



Note: MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the regressions nonlinearly,
amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear covariates are as follows: population
density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model quadratically.

58

-------
Table A.5. MWTP for Climate Amenities, Hedonic Models (population-weighted estimates)

Traditional hedonic weights	Adjusted hedonic weights

Model Hl.t	Model H2.t	Model Hl.a	Model H2.a

Temperature specification	Linear	Quadratic	Linear	Quadratic

(base model)	(base model)

Variable

Coef.
(Std. err.)

MWTP
(Std. err.)

Coef.
(Std. err.)

MWTP
(Std. err.)

Coef.
(Std. err.)

MWTP
(Std. err.)

Coef.
(Std. err.)

MWTP
(Std. err.)

Avg. winter temperature

0.0025

$172

0.0006

$133

0.0012

$83

0.0001

$60



(0.0005)

($38)

(0.0018)

($44)

(0.0004)

($29)

(0.0013)

($33)

Avg. summer temperature

-0.0006

-$43

-0.0189

-$45

-0.0035

-$245

-0.0149

-$246



(0.0009)

($63)

(0.0149)

($63)

(0.0007)

($48)

(0.0114)

($48)

July humidity

0.0014

$96

0.0015

$104

0.0011

$74

0.0011

$79



(0.0005)

($34)

(0.0005)

($34)

(0.0004)

($26)

(0.0004)

($26)

Annual snowfall

0.0007

$48

0.0006

$40

-0.0001

—$7

-0.0002

-$12



(0.0002)

($16)

(0.0003)

($18)

(0.0002)

($12)

(0.0002)

($14)

Ln(summer precipitation)

-0.0139

-$88

-0.0139

-$88

-0.0178

-$113

-0.0178

-$112



(0.0067)

($42)

(0.0070)

($44)

(0.0051)

($32)

(0.0054)

($34)

Annual sunshine

0.0004

$25

0.0006

$41

0.0018

$121

0.0019

$132



(0.0006)

($42)

(0.0007)

($52)

(0.0005)

($32)

(0.0006)

($40)

No. of obs. (MSAs)

284



284



284



284



Adjusted R-squared

0.51



0.51



0.74



0.74



Note: MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the regressions nonlinearly,
amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear covariates are as follows: population
density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model quadratically. Regressions are
weighted by MSA populations.

59

-------
Table A.6. Comparison of Hedonic and Discrete Choice Models, Homogeneous Tastes (sensitivity analysis)



Discrete choice



Hedonic











Traditional weights

Adjusted weights





Omit



Omit



Omit



Base model

ln(population

Base model

ln(population

Base model

ln(population





density)



density)



density)

Variable

MWTP

MWTP

MWTP

MWTP

MWTP

MWTP



(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

(Std. err.)

Avg. winter temperature

$599

$630

$207

$200

$104

$111



($147)

($149)

($42)

($44)

($33)

($37)

Avg. summer temperature

-$791

-$771

-$228

-$233

-$358

-$353



($246)

($271)

($68)

($72)

($64)

($62)

July humidity

-$465

-$414

$84

$72

$71

$82



($139)

($151)

($35)

($34)

($24)

($24)

Annual snowfall

-$377

-$347

$29

$22

-$16

—$9



($65)

($71)

($16)

($17)

($11)

($13)

Ln(summer precipitation)

$525

$428

$81

$103

-$19

-$40



($188)

($204)

($50)

($49)

($42)

($42)

Annual sunshine

-$151

-$231

$129

$148

$191

$173



($153)

($158)

($44)

($43)

($35)

($36)

Note: For the share and hedonic models, MWTP is computed at mean household income for the prime-aged sample ($69,188). When entering the
regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to compute MWTP. Nonlinear covariates are as
follows: population density, summer precipitation, and elevation enter in log form, while distance to the coast enters the model quadratically.

60

-------
Table A.7. MWTP for All Location-Specific Amenities, Mixed Logit Models

Base model	Net of taxes	Omit moving costs	Net of taxes+

omit moving costs

Panel A: 1st stage estimates	



Coef



Coef



Coef



Coef



Variable

(Std.



(Std.



(Std.



(Std.





err.)



err.)



err.)



err.)



Std. dev.: avg. winter temperature

0.0588



0.0592



0.0011



0.0032





(0.0026)



(0.0026)



(0.0128)



(0.0097)



Std. dev.: avg. summer temperature

0.0592



0.0612



0.0352



0.0525





(0.0068)



(0.0066)



(0.0215)



(0.0174)



Correlation coefficient

-0.6893



-0.6993



0.8614



-0.9433





(0.0827)



(0.0776)



(0.2756)



(0.1297)



Panel B: 2nd stage estimates



















Coef

MWTP

Coef

MWTP

Coef

MWTP

Coef

MWTP

Variable

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.

(Std.



err.)

err.)

err.)

err.)

err.)

err.)

err.)

err.)

Mean: avg. winter temperature

0.0209

$518

0.0210

$382

0.0184

$491

0.0171

$326



(0.0058)

($144)

(0.0057)

($104)

(0.0055)

($146)

(0.0055)

($104)

Mean: avg. summer temperature

-0.0253

-$627

-0.0286

-$522

-0.0145

-$386

-0.0178

-$339



(0.0100)

($249)

(0.0098)

($180)

(0.0108)

($288)

(0.0110)

($209)

July humidity

-0.0208

-$514

-0.0198

-$360

-0.0165

-$440

-0.0156

-$296



(0.0054)

($135)

(0.0052)

($95)

(0.0046)

($124)

(0.0045)

($85)

Annual snowfall

-0.0170

-$422

-0.0176

-$321

-0.0047

-$126

-0.0052

-$99



(0.0026)

($66)

(0.0026)

($49)

(0.0025)

($67)

(0.0025)

($48)

Ln(summer precipitation)

0.1708

$403

0.1517

$264

0.0678

$172

0.0593

$107



(0.0768)

($181)

(0.0752)

($131)

(0.0732)

($186)

(0.0727)

($132)

Annual sunshine

-0.0149

-$368

-0.0125

-$229

-0.0082

-$219

-0.0040

-$75



(0.0060)

($149)

(0.0059)

($108)

(0.0060)

($159)

(0.0059)

($111)

-------
Ln(population density)

0.2094

$6

0.2559

$5

0.2891

$8

0.3361

$7



(0.0494)

($1)

(0.0505)

($1)

(0.0441)

($1)

(0.0453)

($1)

Mean PM2.5

0.0572

$1,416

0.0553

$1,009

0.0546

$1,454

0.0543

$1,032



(0.0164)

($408)

(0.0164)

($301)

(0.0153)

($410)

(0.0153)

($291)

Violent crime rate

0.0006

$15

-0.0018

-$33

-0.0117

-$312

-0.0142

-$270



(0.0142)

($352)

(0.0141)

($258)

(0.0150)

($400)

(0.0150)

($286)

Transportation score

0.0105

$259

0.0099

$180

0.0112

$298

0.0106

$202



(0.0015)

($39)

(0.0015)

($28)

(0.0015)

($41)

(0.0015)

($29)

Education score

0.0043

$106

0.0041

$76

0.0035

$92

0.0033

$63



(0.0016)

($41)

(0.0016)

($30)

(0.0016)

($43)

(0.0016)

($30)

Arts score

0.0043

$106

0.0047

$86

0.0034

$90

0.0037

$71



(0.0018)

($46)

(0.0019)

($34)

(0.0016)

($42)

(0.0016)

($30)

Healthcare score

0.0002

$4

0.0008

$14

0.0002

$6

0.0008

$15



(0.0012)

($31)

(0.0012)

($23)

(0.0012)

($32)

(0.0012)

($23)

Recreation score

0.0124

$307

0.0126

$229

0.0120

$320

0.0122

$232



(0.0016)

($41)

(0.0016)

($30)

(0.0016)

($42)

(0.0016)

($30)

Park area

0.0001

$4

0.0002

$3

0.0001

$3

0.0001

$2



(0.0001)

($1)

(0.0001)

($1)

(0.0000)

($1)

(0.0000)

($1)

Visibility > 10 miles

0.0073

$180

0.0081

$147

0.0009

$24

0.0011

$22



(0.0033)

($82)

(0.0033)

($61)

(0.0035)

($92)

(0.0035)

($66)

Ln(elevation)

0.0895

$12,450

0.0935

$9,578

0.1145

$17,142

0.1166

$12,454



(0.0481)

($6,706)

(0.0477)

($4,891)

(0.0415)

($6,234)

(0.0411)

($4,404)

Distance to coast

-0.0020

-$25

-0.0023

-$25

-0.0012

-$19

-0.0014

-$18



(0.0007)

($14)

(0.0007)

($10)

(0.0008)

($15)

(0.0008)

($11)

(Distance to coast)A2

0.0000
(0.0000)



0.0000
(0.0000)



0.0000
(0.0000)



0.0000
(0.0000)



No. of obs. (MSAs)

284



284



284



284



Adjusted R-squared

0.82



0.83



0.82



0.83



Note: When entering the regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to compute MWTP.
Nonlinear covariates are as follows: population density, summer precipitation, and elevation enter in log form, while distance to the coast
enters the model quadratically.

62

-------
Table A.8. MWTP for Climate Amenities, Mixed Logit Models (sensitivity to specification of utility function)

Cobb-Douglas utility

Base model	Quadratic	Log(wage) in 1st stage

Hicksian	with housing price index

bundle	in 2nd stage

Panel A: 1st stage
estimates

Variable

Coef
(Std. err.)



Coef
(Std. err.)



Coef
(Std. err.)



Std. dev.: avg. winter













temperature

0.0588
(0.0026)



0.0584
(0.0026)



0.0603
(0.0025)



Std. dev.: avg. summer













temperature

0.0592
(0.0068)



0.0572
(0.0069)



0.0555
(0.0070)



Correlation coefficient

-0.6893
(0.0827)



-0.7007
(0.0863)



-0.7624
(0.0851)



Panel B: 2nd stage













estimates













Variable

Coef
(Std. err.)

MWTP
(Std.
err.)

Coef
(Std. err.)

MWTP
(Std. err.)

Coef
(Std. err.)

MWTP
(Std. err.)

Mean: avg. winter













temperature

0.0209

$518

0.0218

$463

0.0190

$590



(0.0058)

($144)

(0.0058)

($126)

(0.0059)

($184)

Mean: avg. summer













temperature

-0.0253

-$627

-0.0266

-$566

-0.0208

-$644



(0.0100)

($249)

(0.0099)

($214)

(0.0102)

($317)

63

-------
July humidity

-0.0208

-$514

-0.0201

-$428

-0.0236

-$733



(0.0054)

($135)

(0.0054)

($118)

(0.0055)

($174)

Annual snowfall

-0.0170

-$422

-0.0170

-$363

-0.0174

-$539



(0.0026)

($66)

(0.0026)

($60)

(0.0026)

($86)

Ln(summer precipitation)

0.1708

$403

0.1755

$356

0.1787

$527



(0.0768)

($181)

(0.0762)

($156)

(0.0784)

($233)

Annual sunshine

-0.0149

-$368

-0.0140

-$297

-0.0177

-$549



(0.0060)

($149)

(0.0059)

($128)

(0.0061)

($192)

Note: When entering the regressions nonlinearly, amenity variables are evaluated at population-weighted means in order to
compute MWTP. Nonlinear covariates are as follows: population density, summer precipitation, and elevation enter in log
form, while distance to the coast enters the model quadratically.

64

-------
Figure A.1. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Local Linear Hedonic Model,

Traditional Weights (various bandwidths)

Traditional Weights QOL, Band = 0.4

0	°

UK"? t
00 i¦ 0 *
4a *

A &

a-

Traditional Weights QOL, Band = 0.6

D*b
~

-+>+ % +
: a8, oT"

~3>	5

Vfltter Temperature

O	o ;

A BacMutf.rcml ~ rc«



O NivB-.tfrrd O !

Traditional Weights QOL, Band = 0.7

+e+a k

\

Traditional Weights QOL, Band = 0.8

a J » o

§-

Traditional Weights QOL, Band = 0.9

O rlv frchjd O I

ii BacMuThCcrnJ ~

D H c a,c*f^J O ¦

P <[1)1111. CE

D Ncv B-,ck«i O <

-------
Figure A.2. Marginal Willingness to Pay for Winter Temperature by Metropolitan Area, Local Linear Hedonic Model, Adjusted

Weights (various bandwidths)

Adjusted Weights QOL, Band = 0.4

X

Whter Temperalue

O »»¦	o

Adjusted Weights QOL, Band = 0.5



Vfittff Temperature

O Ht^fr.Ekxd o

Adjusted Weights QOL, Band = 0.6

&

Witter Temjsntixe

O Ncv	o M,Uk ¦Jl""

Adjusted Weights QOL, Band= 0.7

a. "TSWWffirSWF y

>1



D Nr.- »£kj Band = 0.8

m



# §
/

Vfitter Temperature

D ifc' a.fki-a O

£. DuNutfirirmJ

Adjusted Weights QQL^ Band= 0.9

D Hi'- tt-.fknj O

66

-------
Figure A.3. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Local Linear Hedonic Model,

Traditional Weights (various bandwidths)

Traditional Weights QOL, Band =0.4



o" oS

oo C

& u

Simmer T empemlixe

D Nnp*th«j C ;

Traditional Weights QOL, Band = 0.6

A*	i

+	c * ;?dod 0



Simmer Temperature

~ •llNuih CP

Traditional Weights QOL, Band =0.7

f D

V*

a m a °

i a aA &

48f

o

5 O

t

Sumner T emperalure

Traditional Weights QOL, Band = 0.8

+ ++a

+ a is

4 ° > J,

it

>, ° v

90	60

s-

O Nn> a-ekn) O i

60

70 80

90



Mm in er Temperatue



CJ Ncfechrrf

O a Q«Mtrt,CCr«J ~

E*- - *->«!¦



nl r; >..SB*C0«1 Munii £. F-tflc



Traditional Weights QOL, Band = 0.9

«/+ I &V3

a	°	„ o

+ £ ~ + -a# °

V

*

*<#* lB

*> , ~

Jlift

Simmer Temperame

67

-------
Figure A.4. Marginal Willingness to Pay for Summer Temperature by Metropolitan Area, Local Linear Hedonic Model,

Adjusted Weights (various bandwidths)

Adjusted Weights QOL, Band = 0.4



Sunmer Temperature

Adjusted Weights QOL, Band =0.5

0 *£o

~Uo ' &r

Simmer TemperaCre

O Nw »«knl o

O Nevfcefcrf 0 1

A BucNcntiCEnml ~

Adjusted Weights QOL^ Band = 0.6

Simmer Temperatire

O Ncvtocknl ^ ;

Adjusted Weights QOL, Band = 0.7

Simmer Temperalure

Adjusted Weights QOL^ Band =0.8

*

OGO1



Simmer Temperature

O Nw »«kr Band= 0.9

90	60

Summer Temperatire

Q ;-4c<" Bp.cfcJil O

68

-------
Figure A.5. Impact of Removing Moving Costs on Marginal Willingness to Pay for Temperature by Metropolitan Area Using

Income Net of Taxes

Base, Net of Taxes
(Left Panel)

~ ^
£ln

°n Do



°°°°

Omit Moving Costs, Net of Taxes
(Right Panel)

0

20

40 60
Wiiter T emperatue

80





30

40 00 80
Witter Temperature

C* !'* '¦ Q rfl ud

0 MiUc .-ilr.i

BHcKurt, Cctwri ~ ^CKi-tnt, Cc

 T-ckSluTC

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69

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