FINAL RliPOi-r
Volume 1: Model Revision and Simulation
THE OAP REGIONAL ECONOMETRIC MODEL:
A REVISED VERSION
Prepared for:
Environmental Protection Agency
Office of Air Programs
Research Triangle Park
North Carolina
September 25,1972
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FINAL REPORT
CONTRACT NUMBER 68-04-0039
VOLUME 1: MODEL REVISION
AND SIMULATION
THE OAP REGIONAL ECONOMETRIC
MODEL: THE REVISED VERSION
Prepared for:
Environmental Protection Agency
Office of Air Programs
Research Triangle Park, North Carolina
Prepared by:
CONSAD Research Corporation
121 North Highland Avenue
Pittsburgh, Penns ylvania 15206
T. R. Lakshmanan, Fu-chen Lo, Krishna Moorthi
September 25, 1972
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ACKNOWLEDGEMENT
The research reported here was carried out by
CONSAD Research Corporation under the direction of
Dr. T. R. Lakshmanan. Dr. Fu-chen Lo was the
principal investigator of the effort. S. Krishna Moorthi
'carried out the validation experiments on the revised
model. Rajan Vaswani participated in the preparation
of the Philadelphia case study. Professor p. J.
Dhryrnes of the University of Pennsylvania provided
valuable assistance as a consultant.
In the preparation of this report, CONSAD has
relied heavily on the advice and guidance of Allen
Basala, the project officer. Other EPA staff members
who provided valuable guidance during the various phases
of the project are Dr. Joel Horowitz, Dr. Mike Lerner,
John O'Connor, Ron Campbell and Warren F'reas. To
all of these individuals, grateful acknowledgement is
made.
Any opinions expressed in this report are those
of CONSAD and do not necessarily reflect the views of
the individuals cited above.
ii
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1.0
2.0
3.0
4.0
T ABLE OF CONTENTS
INTRODUCTION AND SUMMARY
.............
THE OAP REGIONAL MODEL:
DEVELOPMENT, UTILIZATION
AND REFORMULATION. . . . .
2. 1
2.2
2.3
2.4
.............
The Regional Economic Model
and the RAP A Program. . . . . . .. . . . . . ...
The Phases of the Economic
Model Development. . . . . . . . . . . . . . . . . .
Model Utilization. . . . . . . . . . . . . . . . . . .
Potentials for Model Refinement. . . . . . . . . .
THE REVISED REGIONAL MODEL. .
3. 1
3.2
3.3
3.4
3.5
3.6
......
. . . .
Model Formulation. . . . . .. . . . . . . . . . . . .
Input-Output Model and
Interregional Feedback Scheme. . . . . . . . . . .
The Manufacturing Block of the
Regional Model. . . . . . . . . . . . . . . . . . . .
Income Determination Block. . . . . . . . . . . . .
Labor Market Block. . . . . . . . . . . . . . . . .
Regional Fuel Demand Block. . . . . . . . . . . .
REGIONAL ECONOMIC IMPACTS OF
AIR POLLUTION ABATEMENT: A
SIMULATION WITH THE REVISED MODEL.
4. 1
4.2
4.3
.......
Alternative Implementation Strategies
and Measures of Their Economic Effects. . . . . .
Total Net Effects of Alternative Strategies. . . . .
Geographical Patterns of Economic Growth. . . . .
Hi
'';'
Page
1
4
'4
9
12
17
18
21
25
33
53
56
59
69
70
75
78
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TABLE OF CONTENTS (continued)
5.0
VALIDATION OF THE OAP ECONOMIC
MODEL: REVISED VERSION. . . . . . . .
. . . . . . . ..
5. I
5.2
5.3
5.4
5.5
6.0
Introduc tion. . . . . . . . . . . . . . . . . . . . . .
Method. . . . . . . . . . . . . . . . . . . . . . . .
Results and Discus sion. . . . . . . . . . . . . . . .
A Comparison of The OAP Model
and the St. Louis Model for the
St. Louis Region. . . . . . . . . . . . . . . . . . .
Conclusion. . . . . . . . . . . . . . .
. . . .
. . . .
ECONOMIC-ENVIRONMENTAL INTERACTION:
A CASE STUDY OF PHILADELPHIA ~ . . . . . . . . . . .
6. I
6.2
6.3
6.4
APPENDIX A:
APPENDIX B:
APPENDIX C:
APPENDIX D:
APPENDIX E:
APPENDIX F:
Air Pollution and Public Policy. . . . . . . . . . .
Improvement in Emissions and
Air Quality Due to Control. . . . . . . . . . . . . .
Change of Property Values in Res ponse
to Cbange of Air Quality. . . . . . . . . . . . . . .
Economic -Environmental Interaction. . . . . . . . .
Manufacturing Investment Functions:
A Cross -Section Estimation with SMSA Data ..
Flow Chart of Validation Program
KRV ALTSC ..................'..
External Validity Results for Manufacturing
Sector By Two-Digit Detail for 1969
...Except YE - bY. . . . .'. . . . . . . . . . . . .
Internal Validity Results by Two-Digit
Detail for 1967 for SIC 0, 24, 29, 31 . . . . . .
Internal Validity Results for Tax
Equations, 1967 . . . . . . . . . . . . . . . . .
Identification of AQCRs with Estimates Off
By More Than I, 2, 3 Standard Errors
(Aggregate Manufacturing). . . . . . . . . . . .
iv
.,
Page
93
93
94
110
. 119
120
125
125
128
139
143
A. I
B. I
C. I
D. I
E. I
F. I
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I
Figure
2. 1
3. 1
4. 1
4.2
4.3
4.4
4.5
4.6
5. 1
6. 1
6.2
6.3
6.4
6.5
6.6
LIST OF FIGURES
Regional Air Pollution Analysis Process
Major Components of the Model
Three- Year Straight Implementation:
Without Government Assistance
Geographic Distribution of Economic
Effects Measured by Change of Regional
Unemployment Rate
Geographic Distribution of Economic
Effects Measured by Change of Manufacturing
Production (Value-Added)
Geographic Distribution of Economic Effects
Measured by Change of Manufacturing Investment
Geographic Distribution of Economic Effects
Measured by Change of Manufacturing Profit
Geographic Distribution of Economic Effects
Measured by Change of Regional Personal Income
Simulation of Manufacturing Product (Va1ue-
Added) in St. Louis Region, 1958 -196 7
Interactions of DCIM, Anderson-Crocker Model
and OAP Model: A Flow Chart
Structure of DCIM
Philadelphia Air Quality Control Region
Sulfur Dioxide Air Quality Before Control (mgm/m3)
Philadelphia Air Quality Control Region
Sulfur Dioxide Air Quality After Implementation of
Clean Air Act Amendment Standards (mgm/m3)
Philadelphia Air Quality Control Region
Particulate Air Quality Before Control (mgm/m3)
Philadelphia Air Quality Control Region
Particulate Air Quality After Implementation of
Clean Air Act Amendment Standards (mgm/m3)
v
Page
6
24
72
81
83
85
87
89
121
129
131
135
136
137
138
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Tables
3. 1
3.2
3.3
3.4
3. 5
3.6
3. 7
3.8
3.9
3. 10
4. 1
4.2
4.3
4.4
4.5
4.6
4.7
5. 1
5.2
5.3
6. 1
6.2
6. 3
6.4
LIST OF TABLES
Regional Share of Manufacturing Industry
Production Functions
Investment Functions
Pre-Estimated Parameters
Wage Equations
Income Determination Block Equations
Labor Market Block Equations
Energy Demand Function
Energy Production Function
Regional Electricity Demand Function
Aggregate Economic Effects on 91 AQCRs
Three- Year Straight Implementation by 1975
Three- Year Straight Implementation by 1975
Three-Year Straight Implementation by 1975
Three-Year Straight Implementation by 1975
Three-Year Straight Implementation by 1975
Economic Effects on Selected AQCRs Under
the Two Alternative Strategies as Measured
by Five Key Variables
Summary of Validation Results, 1969 and 1967
AQCRs Whose Estimates Are Off by 3 or More
Standard Errors of Estimate for Five Selected
Variables are Listed
Simulation of Manufacturing Product
(Value-Added) of St. Louis AQCR
SOx and Particulate Emissions by Two-Digit
SIC Industries in Philadelphia AQCR
SOx and Particulate Emissions Per Unit of
Output ($1 million of Value of Shipment and
Value-Added) by 2-Digit SIC Industries in
Philadelphia AQCR Before .Control
SOx and Particulate Emissions Per Unit of
Output ($lMillion of Value of Shipment and
Value-Added) by 2-Digit SIC Industries in
Philadelphia AQCR After Control
Percentage Changes of Major Economic
Indicators in Philadelphia AQCR in Response
to the Implementation of 312(a) Air Quality
Standards by 1976
vi
....
Page
29
36
46
48
51
55
58
65
66
68
76
80
82
84
86
88
90
113
115
123
145
146
147
148
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1.0
INTRODUCTION AND SUMMARY
CONSAD has developed an operational, policy-oriented regional
economic model, termed the OAP Regional Econometric Model, to
describe the economic system-wide effects of specific air pollution
strategies in 91 metropolitan areas of the United States.
This model
has been utilized in two separate efforts.
The first was a simple demonstration of the model's operation-
ality by simula'ting the effects of strategies that imply different levels
of cost sharing by the government. ':< The second case of utilization
was concerned with the simulation over time of more realistic strate-
gies that reflect the standards promulgated as a result of the Clean
Air Amendments of 1970. ':0:< The performance of the model as evident
from these utilization experiments, while encouraging, suggested the
need for further refinement of the model.
This refinement took the
form of improved model specification and the reestimation of the
greater part of the model with better data.
The respecification of the model encompassed the following: In
the manufacturing block of the OAP Model, a set of new investment
>::o:
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functions with lag distributions ,and a set of production functions with
technological change were specified.
In the regional income block,
the public sector equations were disaggregated to identify different
local government sector tax equations.
This respecified model was then estimated with cross -sections
of time -series data.
The manufacturing sector equations were esti-
mated by the data for the years 1958 through 1967.
This increased
the sample size and improved 'the statistical results of the model.
The reformulated model was validated by a broad range of tests and
has been used to simulate the regional economic effects of alternate
strategies of implementation of air pollution abatement.
Chapter 2 gives a brief review of the history of model develop-
ment and previous experience with the utilization of the model.
Chap-
ter 3 deals with both the conceptual formulation and statistical esti-
mation of the revised model.
In Chapter 4 a simulation analysis with
the revised model is presented.
Both aggregate impacts and regional
patterns of incidence of economic effects are analyzed.
The next
chapter presents a validation of the revised model.
In this chapter,
a series of statistical tests including t-tests, regression tests, dis-
tribution of the estimates in the ranges of standard errors, and non-
parametric tests are presented.
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"
Finally, in Chapter 6, a case study of economic-environmental
interaction in the Philadelphia Air Quality Control Region (AQCR) is
demons tr ated.
This is an attempt to integrate and utilize some exist-
ing modelling efforts such as the Direct Cost of Implementation Model
(DCIM), the property value damage functions and the OAP Regional
Econometric Model.
These modelling efforts describe the changes of
air quality, property damage and the corresponding regional econon~ic
impacts upon the implementation of a given ambient air quality stand-
ard.
3
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2.0
THE OAP REGIONAL MODEL:
DEVELOPMENT, UTILIZATION
AND REFORMULATION
Over the last three years, CONSAD Research Corporation has
developed and demonstrated an operational Regional Economic Model
for the assessment of the effects of air pollution abatement.
This
chapter is addressed to a review of:
The context of development of the model,
A brief review of the development history
and scope of the model,
The utilization experiments on the model,
and
The nature of the reformulation of the
model suggested by the experience in the
policy analyses with the model.
2. 1
The Regional Economic Model
and the RAP A Program
In July, 1968, the predecessor agency to the Office of Air Pro-
grams, Environmental Protection Agency (EP A), initiated a s ys terns
analysis of regional air pollution control.
It was clear, at the outs et,
that this study's contribution to the pollution problem's solution would
be in the integration of contemporary air pollution control deve1op-
ments into a workable analytical tool, rather than in fundamental
research areas.
With this in mind, a tool was developed - - Regional
4
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Air Pollution Analysis (RAP A) - - to demonstrate the usefulness of
looking at the many facets of the air pollution problem in an inte-
grated manner.
The RAPA program is a system of mathematical models
arranged in a modular fashion and relating both engineering and
economic effects of the analysis.
Relations between the major com-
ponents of the system are described in Figure 2..1.
Information on the effects of air pollution is reported in terms
of air pollutant criteria, which are a compendium of today's knowl-
edge of scientific findings on the range of adverse effects of specific
air pollutants and combinations of pollutants on man and his environ-
ment.
Air quality standards that are developed with the guidance of
these air quality criteria are goals established for the protection of
public health and welfare.
They provide a basis for controlling exist-
ing sources of pollution emissions and preventing future regional
growth from adding to the pollution problem.
Regional goals may
reflect more than one air quality standard, insuring minimum air
quality levels, as well as higher levels of air quality, to preclude
any significant deterioration of existing high air quality levels.
The government's role starts with setting air quality standards
which reflect goals for clean air within a specified time period.
After
5
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Figure 2. I
Regional Air Pollution Analysis Proces s
'"
Goals (Air Economic
Quality for -- Abatement -- f---- Sources - Control Cost - Effect (OAP
Emission Strategy Controls Diffusion and Benefit Economic
Standards), Receptor s (Damage) Model
,
Implemen-
tation Plan
>
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"
the air qua.lity standards are set, an effort is made to establish imple-
mentation plans which may set forth regulatory procedures, such as
pollutant source emis sion standards to achieve air quality standards.
Limiting pollutant emis sions through source emis sion standards, along
with other types of regulatory procedures such as zoning regulations
or fuel restrictions, forms an abatement strategy designed to achieve
regional air quality within a specified time period.
To accomplish the task of developing abatement strategies will
require an extensive examination of the factors involved in the air pol-
lution system, such as meteorology, air pollution control technology,
air pollution growth trends, source emission inventories, existing
regional air quality conditions, and regional economic impact.
The
OAP Regional Economic Model was expressly developed as part of the
RAPA program to respond to these requirements of information on the
economic impacts of abatement strategies.
The Federal air pollution abatement legislation requires busi-
nes sand indust;y to control the amount of pollutants that they dis-
charge into the air.
To industry, this requirement means that the
production costs for the same amount of output produced prior to the
legislation will be increas ed in proportion to the required investments
to air pollution control equipment.
Thus, certain industries and re-
gions that have in the past enjoyed the economic advantage of low-cost
7
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production may face some degree of economic decline due to the re-
quirements of pollution abatement.
There would be offsetting economic effects from air quality con-
trol strategies in such regions in terms of (a) increased demand for
the products of the industries that produce pollution control equipment
and low pollutant fuels leading to increased output, employment, and
income in those sectors, and (b) a variety of general economic bene-
fits resulting from increased labor productivity, reduced health ex-
penditures, reduced outlays on physical maintenance of homes and
plants, and savings in agricultural production activities.
Conse-
quently, air pollution abatement leads to changes in economic output,
. labor markets, the availability of capital, as well as redistributions
within the entire economy.
Further, the implementation of air quality
programs would have a variety of other effects, such as tax base
impacts on communities or variations in land use and industrializa-
tion in various regions.
CONSAD has developed a regional economic model that will pro-
vide pollution abatement policy-makers capabilities to assess the
effects of various pollution control strategies.
The CONSAD model
is intended to provide the following types of information for public ~
policy analysis:
8
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1=~'" . .=~_., '-.--'.- --,.~ '....' --- . ......
..
Regional economic changes (e. g., output,
investment, employment, income, and con-
sumption) expected to result from enforce-
ment of varying abatement standards upon
high-emission industries.
Regional economic effects expected to re-
sult from reduction of industrial damage
and growth in air pollution equipment in-
dustries.
Fiscal effects of regional implen~entation
of air quality control programs, including
tax base irnpacts of economic change and
the effects of tax credits upon economic
change and the rate of achievement of
emis s ion standards in terms of the imple-
mentation plan.
2.2
The Phases of the Economic
Model D evelo pment
During the first phase of the RAP A program, CONSAD developed
a Regional Econometric Model of the St. Louis region where RAP A
was explored first in depth.
This model was a time series model that
des cribed the growth patterns of key economic sectors (both high
emis sion and otqer industries) and estimated the regional product,
employment, capital stock and investment change, and value-added
by industry, tax receipts and regional unemployment.
These esti-
mates are sensitive to a variety of air pollution control strategies.
In fact, the economic effects of five hypothetical air quality control
9
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strategies were 'simulated and interpl'eted, using the model for the
St. Louis region. >:<
The next phase of model development was an extension of the
model to 31 large metropolitan areas. ':<>:< These large urban areas
have a varied industrial structure highly representative of the national
industrial composition and comprise a significant segment of national
output.
The structure and outputs of this cross -sectional model are
very similar to those of the St. Louis model.
However, this regional model was structured as though AQCRs
were economically independent of one another.
There was no allow-
ance for interregional effects.
If, for example, Region A instituted
air pollution control and in order to do 50 imported air pollution equip-
ment from Region B, the model simulated the economic impact of
Region A's program on Region A alone, and not on Region B.
Thus,
the regional model gave no indication of the increase in employment
in Region B, resulting from the increased production of air pollution
control equipment for export to Region A.
There was, however, a
source of pessimistic bias in the statement of economic effects of air
pollution abatement embedded in the very structure of the model.
'::o:
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n_. . - ,-.- - -----~-- - ~- -
------'- ~ ~ ~~.'------~--~--
..
The model focused only on the economic impacts of control ex-
penditures and accounted in no way for any benefits which might result
from air quality improvement. ,This again tended to cause unjustifi-
ably pessimistic conclusions about the economic effects of air pollu-
tion control.
CONSAD approached the problem of eliminating these biases and
making some preliminary assessment of the national impact of air
pollution control next.
The cross -sectional Regional Model was re-
structured to eliminate, insofar as possible, the pessimistic bias
induced by structural exclusion of interregional feedback effects and
benefits and to permit preliminary estimates.
A national Input-Output
(1-0) model was introduced to capture (a) a preliminary estimate of
structural changes in the national economy, and (b) to provide an in-
terregional feedback scheme to the AQCRs.
This model, >:' termed the OAP Regional Economic Model, is
operational and policy-oriented and attempts to des cribe the economic
system-wide eff~cts of specific air pollution strategies in 91 major
metropolitan areas in the United States.
Essentially, the model is
a cross-sectional Keynesian-type regional macro model that describes
in considerable detail, the two-digit SIC manufacturing industries,
>:'See CONSAD, QQ. cit.
11
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.,
viewed as leading regional economic growth.
The Keynesian system
and economic base theory are integrated in the regional income deter-
mination block of the model that des cribes regional personal income,
consumption expenditures and local governrnent expenditures and rev-
enues.
In addition, there is a regional labor market block that speci-
fies the employment, unemployment and labor force equations.
Finally, the model describes the regional electricity and fuel
demand patterns by the two-digit SIC industries.
The regional model
is hooked up to a National Input-Output Model (1963) via a Regional
Share (location quotient) matrix.
The 1-0 system is intended to serve
as an external market for the regional economy and to measure the
structural change in the national economy attendant on air pollution
control in the regions.
The regional model was estimated using 1967 data for the 91
largest Standard Metropolitan Statistical Areas (SMSAs). using ordi-
nary least squares except for the income block for which two-stage
least squares was used.
2.3
Model Utilization
The OAP Regional Econometric Model has been utilized in three
sequential steps.
First was the demonstration phase when the m.odel's
operationality was demonstrated.
The second step was the design and
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implementation of a set of realistic utilization experiments that helped
to simulate the economic effects of implementation strategies over
time to 1977.
The third step was the use of the model after reformu-
lation and reestimation of the investment equation and some validation
experiments to assess the economic effects of air pollution strategies.
2.3. 1
Demonstration Phase
The ope rationality of the model system was demonstrated at the
end of this stage of model development.
The OAP specified three
alternative strategies to be tested, with the Regional Economic Model
system as their basis, f014 the control costs envisioned in the 1970
Report to the Congress as required by Section 305(a) of the Clean Air
Act of 1967::' In this report, cost estimates were made of controlling
the emissions of selected pollutants within 100 AQCRs during the fiscal
years 1970 through 1975.
The cos ts reflect the emis sion reductions
of particulates, sulfur oxides, hyd"rocarbons and carbon monoxides in
these 100 AQCRs by 1975.
A computer simulation program of the OAP Regional Economic
Model system was developed.
The Regional Model, using this simu-
lation program, could trace the effects of a variety of policy tools
>:'Fogel, M. E., et al., Comprehensive Economic Cost Stu~
Air Pollution Control Costs for Selected Industries and Selected Re-
gions, Research Triangle Institute, February, 1970, Chapter 4.
13
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such as standards or incentives available to OAP, provided the latter
are converted into inputs consistent with the model logic.
Specifically, three strategies reflecting the same control costs
but different in their incidence of these costs among industries, con-
sumers and government were simulated.
These simulation results
dem.onstrated the operationality of the model.
However, they suggested
[
the need for further model utilization experiments that would lead to a
more thorough utilization of the model than was possible in the devel-
opm.ent and demonstration phase.
2.3.2
Further Model Utilization Experiments
Such utilization experiments were structured in the following
manner.
The first step was addressed to a specification of air pollution
control implementation strategies that introduce a greater realism to
the model utilization and can lead to a more thorough exercise of the
model than was possible in the demonstration phase.
Realism was
introduced in a variety of ways.
First, the standards and costs used
in the strategies were the preliminary estimates corresponding to the
control implied in the Federal Register of August 14, 1971, as promul-
gated by EP A.
Second, since control implementation would take place over a
period extending to 1975 or 1977, the simulation includes the regional
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i---u- -
"'I
economies for the corresponding future years and the incidence of con-
trol costs over time is assumed to be a "step up" function (with the
greatest proportion of the investments occurring closer to 1975 or
1977), rather than a uniform annual expenditure over the period, as
as sumed in the dernons tration simulation.
Since the EP A adminis trator
can extend the period of implelnentation by two years under certain
circumstances, strategies can also differ by implementation periods.
Further, the economies of the AQCRs are likely to be larger in 1973-
1975 than in 1967, and with a more realistic time scheme of cost func-
tions as proposed here, the simulated strategies were likely to be
more realistic.
Third, a greater variety of schemes, inclusive of various gov-
ernment cost sharing provisions, were tried in the strategies.
Fourth, alternative levels of "net" benefits of air pollution con-
trol were assumed.
The ins titution of pollution abatement will result
in increases of productivity, property values, control device produc-
tion and decreases in health expenditures, housing maintenance, etc.
The level of increment of national final demand resulting from such
changes is termed here as "net" benefits.
Estimates of "net" benefits
are hard to come by and two levels are assumed for the simulation.
Six strategies are developed in the light of the above dimensions --
time period of implementation, cost sharing and level of net benefits --
15
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for simulation with the OAP model.
A seventh strategy, termed as
the "mixed" strategy evolves out of the simulation and implementation
of the above six was also tried.
The next step in model utilization was essentially a quantification
of the strategies and updating the economic data in a manner to simu-
late strategies such as those developed in this study.
To facilitate the
use of the model over the implementation period, a num.ber of future
cros s -s ections of the regional economies were developed for the 91
AQCRs using the OBE regional forecasts. >:< The simulation procedures
of the OAP Model were adopted to accommodate the over time and cum-
ulative effects of the strategies in the demonstration phase.
The final step was to apply the model to simulate and assess the
economic consequences of the three strategies.
As air pollution con-
trol requirements are instituted in the nation, the consequent effects
are incident differentially in the various AQCRs.
The primary purpose
of regional economic modelling is to provide quantitative estimates of
such differences among the AQCRs in any particular treatment (strat-
egy) and among different treatments.
The information on such differ-
ences has been assembled and interpreted in depth elsewhere. >:<>:<
>::<>:
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2.4
Potentials for Model Refinement
The various efforts to utilize the model and analyze the results
suggested a number of potential model refinements.
First, it became
obvious that the model should retain its current ability to describe the
variations of economic effects among different geographic areas, but
should also treat the economic changes over time more realistically.
Consequently, the model has been reformulated by pooling the cros s-
sections over a ten-year period, 1958-1967.
This procedure increases
the sal'np1e size, in addition, and improves the efficiency of estimation.
Second, in view of the importance of government cost sharing
schemes in implementation strategies, the need to treat the Federal,
. state and local governments and their component revenue sources in
detail became clear.
Third, since investment expenditures are sensitive to abatement
costs, a more realistic formulation of the investlTIent equations with
an appropriate lag structure is called for.
The OAP Regional Model was revised as described in the next
chapter.
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].
..
3.0
THE REVISED REGIONAL MODEL
Compared to national models and various industry econometric
models, regional models are fewer in number and less sophisticated.
Three reasons underlie this fact.
First, at the national level, good time series data have been
available for most observable economic variables, while data on
other variables such as capital stock are published as the result of
theoretical inquiry.
But at the regional level - - either state or
SMSA -- data are unreliable and unavailable, especially in a contin-
uous time series form.
Second, econometricians began the development of their models
at the national level.
From time to time, different equations and
theories have been tested with the same data base in a well-defined
economy, say the United States.
By repetition of various tests and
the accumulation of experience, national models calibrated to good
theoretical structures are now available.
On the other hand, regional
models often deal with C!-ifferent geographic units, each often with its
unique data base.
Further geogr~phic and cultural environments
vary and socioeconomic structures differ from region to region.
Third, theoretically speaking, macro-economic models are
usually based on well-established economic theory in their formulation.
18
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"
The regional models, however, do not have a unified theory of
regional growth to draw upon.
Various available concepts such as
economic base theory, location theory, gravity concepts, migration
theory, and especially the concept of "distance" emphasized by re-
gional scientists for some time are much harder to integrate into an
overall hiera'rchical system.
In spite of these shortcomings, some
notable regional models have been recently estimated. ~:~
An example of a regional econometric model developed specific-
ally for EPA to assess regional economic effects of environmental
control strategies is the OAP Regional Economic Model. ~:":~ The OAP
Model was estimated with cross-sectional data for 91 AQCRs.
~:~See Frederick W. Bell, "An Econometric Forecasting Model
for a Region, " Journal of Regional Scienc_e...! Vol. 7, No.2, 1967;
B. H. Tuck, An Aggregate ..!ncome Model of~~mi-Au~~.!..
Alask~ E~~omY2 Anchorage, Federal Field Development Committee
for Development Planning, 1967; T. R. Lakshmanan and Fu-Chen Lo,
A Regional Growth Model of Puerto Ri£o: An Analysis of Municipal
Growth Patter.,ps and Public Investments, Pittsburgh, Pa., CONSAD
Research Corporation, September, 1970; Robert Crow, "Econometric
Model of the Northeast Corridor, " (mimeograph) MATHEMATIC A,
October, 1967; Daniel B. Suits, "Econometric Model of Michigan, "
(mimeograph), 'Research Seminar in QuantItative Economics of the
University of Michigan; Norman J. Glickman, "An Annual Econometric
Model of the Philadelphia SMSA, 1949-1.966," (mimeograph), Ph. D.
Dissertation, Department of Economics, University of Pennsylvania,
November, 1968; Yukio Kaneka, "An Econometric Approach to Annual
Forecast on Regional Economy by Local Government, II Paper and Pro-
ceed~~2 The Second Far East Conference of Regional Science Associ-
ation, 1965, University of Tokyo Pres s, Tokyo, 1967; pp. 119 -144.
>:<~:
-------
."
Utilization of the OAP Model suggested the need for explicitly
introducing the time element for use in policy simulation.
So a re-
formulation of the OAP Regional Economic Model into a dynamic model
has been found necessary.
Specifically, a reestimation of the greater
part of the model with pooled cross -section and time series data has
been carried out here.
This approach provides three advantages:
A dynamic model that incorporates the inter-
relationships between economic growth and
the effects of control will be more realistic
for the over time policy simulation than the
the use of the trend projections used so far.
By pooling cross -section and time series
data, the sample size will increase consid-
erably. Therefore, statistically, more effi-
cient estimates of model parameters can be
expected.
The advantage of cross ",s.ectiona1 observations
of policy impacts among different regions still
remains. Therefore, as an operational tool,
policy impacts over time and over different
geographic units can be investigated in this
reformulated model.
The revised model extends the data to the period of 1958 through
1967.
Details of the revised model are given in two parts, a section
on formulation, followed by the actual e.stimation of the model.
20
-------
3. 1 Model Formulation
There is a fundamental difference between the economy of
metropolitan regions and the national economy.
The former is based
on an open economy where growth and development is closely related
to its capability to carryon external trade with other regions.
The
latter is rather more self -contained by its nature.
The concept of
"export-base" or economic base theory, has been the core of the ana-
lytical frameworks of urban economies since its first appearance in
1928. >:~ However, the measurement of the economic base multipliers
originally based on a calculation of ratios between export-oriented
(or basic) employment and local-oriented (or service) employment
has been changed by using the concept of output level, say value
added, instead of employment. ~'<*
>:~Haig, Robert M., Major Economic Factor~ in Metr?politan
Growth and Arrangeme~.!. Vol. I, Regional Survey of New York and
Environs, New York, 1928. See also Thompson, Wilbur R., A
~ace to Urbal?- .Economics, Resources for the Future, 1965:-
~'<>~As an early exaxnple, see Leven, Charles L., "Measuring the
EC,onomic Base, " Papers and Proc.eeding~ Vol. 2, The Regional
SClence Association, 1956.
21
-------
This later development now takes into account different produc-
tion structures among local industries, so that factor intensities of
capital and labor may contribute different weights to the mu:ltipller.
Since manufacturing industries are more capital-intensive, the
role of manufacturing industries in regional growth becomes decisive
in that they usually dominate the value of exports (greater than 80
percent of the total value-added in some cases). *
Moreover, the dimension of space or distance plays an important
role in the modelling of a system of regions.
In other words, the in-
teraction between regions must be treated in the model.
Tinbergen':":'
has argued that one of the simpler ways of dealing with such problems
is to classify industries into regional, national, and international.
It
if therefore quite safe to treat manufacturing industry as an export-
oriented industry in the regional growth model.
Some of the recent
--
- \
),'
-------
"
'!
::j
...
succes sful regional econometr ic models explicitly or implicitly
embody a causal relationship of manufacturing industry and the over-
all regional growth. >:,
The change in measurement from employment to value-added
in economic base theory has not only improved the applicability of
the regional multiplier in recent regional growth analysis, but also
seems to be consistent with the familiar Keynesian-type trade multi-
plier in the open economic system.
By treating manufacturing sectors as export-oriented industries,
the OAP Model framework is essentially block recursive, followed by
a regional income determination block and labor market block.
One
additional block, namely interregional feedback scheme, was intro-
duced to treat interregional interaction of a system of regions.
In
order to measure fuels and electricty demands in response to air
pollution control strategies, a fuel demand block was added to com-
plete the model.
The maj or components of the model are given in
Figure 3. 1.
>:'A typical and succes sful model of this nature if Frederick W.
Bell, Q.E.. cit.
[.
,
23
-------
"
FIGURE 3. 1
MAJOR COMPONENTS OF THE MODEL
1-0 Model and Inter-
regional Feedback
.---- ------1
I ,
I I
I J
I J
National I
1-0 Model I
I
I
J
I I
I I
4!1~:
I
J
I
-,
I:
Regional
Market
Share
Matrix
I
I
I
I
I
l- - -
- - - -
-----
Regional Model
,. . - - - - - - . ~
J
I
- - - - - - - - . - -. I
I
I
I
- - - - -
Manufac-
turing .
Industries
I"
I
I
A ,
I '
1
I .
Regional i r
Economy, I Electricity
Income r--~ and Fuel
consumpt'i0l Dernand
Government
t .
Regional
Labor.
Market
I
I
J
- - - --'
I
I .
-----.--
- - - -
-- -----
24
-------
3.2 Input-Output Model and Interregional Feedback Scheme
As emphasized earlier, a region's growth is closely dependent
upon its capability to carryon external trade with other regions.
How-
ever, the formulation of an interregional 1-0 system of this scale, say
. a 20-sector regional 1-0 system with 100 SMSAs, will create a matrix
of 2000 x 2000, requiring information that is largely non-existent. >:<
A national 1-0 system linked to a regional market share matrix is
therefore introduced to serve the role of external market for the
regional economy and to capture the regional feedback.
It is argued that the regional share of the national market by
industry, or location quotient, is relatively stable.
(See Table 3. 1. )
By definition:
I'
I
x..
b.. = 2
1J x.
J
where:
b..
1J
is the regional market share, or location quotient,
industry produced in the ith region;
is the output of ~th industry in the ith region;
is the output of jth industry in the nation.
of jth
x..
1J
X.
J
>:
-------
-~-,"""""-~-- ,
In the regional model, only manufacturing industries were treated as
export-oriented industries; so the demands of regional manufacturing
products are determined by the. regional matrix share or the location
.quotient and national demand by each manufacturing industry.
Thus,
XR = BX ,
(l)
where:
matrix XR = [;x:..] is the regional share of demand for manufactur ing
lJ
products at national market;
matrix B = [bij] is the regional market share (or location quotient)
coefficient matrix;
. matrix X = contains diagonal elements Xj which is the total national
demand by each manufacturing industry.
By introducing a national I -0 model, the menu of final demand by
sectors can be captured by the inverse matrix:
x = {I-A)-ly.
(2 )
where:
matrix A is the national 1-0 coefficient matrix;
Y is a vector with element y. which is the final demand of sector j;
J
X is a vector with element x. which is the gros s product or value of
J
shipment by sector j.
26
-------
...
The link provided between the regional model and the national
1-0 model is best explained in the following manner: since the
regional model has manufacturing industries as export-oriented
industries, demands for manufacturing products remain to be deter-
mined at the national markets.
The 1-0 model and the regional share'
matrix serve to link the regions with the nation, or time series data
of national product by industry x., can be a set of exogeneous vari-
J
abIes to the model.
Some data on air pollution control i~pact are obtainable only at
the national level, for example, rough estimates on benefits accruable
from air pollution control.
These estimates can be' treated at the
national level by the 1-0 model and distributed through the regional
share matrix to the regions.
Assuming an equilibrium economy, air
pollution control costs will shift up supply curves of high emis sion
industries (which are manufacturing industries) and cut down the
production levels of such industries in each region. * Since
manufacturing. industries are export-oriented, changes in regional
),'(LeSourd, D. A., ~al., Comprehensive Study of Specified Air
Pollution Sources to Assess Eco~<2.mic 1i;!jects of Air Quality Stan-
dards, Research Triangle Institute, December, 1970.
27
-------
...
manufacturing production will generate a sequence of interregional
effects and feedbacks from other regions, including the regions under
study and the rest of the United States.
The use of the national 1-0
model and regional market share matrix as proposed here, provides
a reasonable simulation of these interregional"effects.
In the revised model, regional market share matrice s we re
estimated with time series data from 1958 to 1967 based on Census
of Manufacturing and Annual Survey of Manufacturers data.
For
those AQCR s without a complete time se r,ie s data, the coefficients
are estimated by data on 1958, 1963 and 1967.
Standard errors
as sociated with each estimate are also obtained.
The results show
a remarkable stability of the coefficients as shown in Table 3. I for
all manufacturing. ~~
National products by manufacturing industries over time can
be taken as a set of exogeneous variables to the model.
Therefore,
equation (1) can be given as:
Xijt = bijXjt
i =
j =
t =
1, . . . n (regions)
1,... m (industries)
1,...T (years)
;'
-------
, -
AQCR
Code
1
2
3
4
5
6
7
8
9
10
11
12
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Table 3.1
Regional Share of Manufacturing Industry
AQCR
New York, New York
Chicag 0, I1linoi s
Los Angeles, Calif.
Philadelphia, Pa.
Detroit, Michigan
San Francisco, Calif.
Boston, Mass.
Pittsburgh, Pa'.
St. Louis, Mis souri
Washington, D. C.
Cleveland, Ohio
Baltimore, Maryland
Minneapolis-St. Paul,
Minnesota
Houston, Texas
Buffalo, New York
Milwaukee, Wisconsin
Cincinnati, Ohio
Louisville, Kentucky
Dallas, T exa s
Seattle -Eve rett, 'Vash.
l-
-------
AQCR
Code
39
40
41
42
43
44
45.
46
47
48
50
51
52
53
54
55
61
63
64
66
67,
68
69
70
71
72,
73
74
75
76
77
78
80
81
~ --- ~--_.
----.- ---
Table 3.1
(continued)
':
AQCR
Chattanooga, T cnn.
Men.phis, T enne s see
Salt Lake City, Utah
Oklahoma City, Oklahoma
Onlaha, Nebraska
Honolulu, Hawaii
Beaum,ont-Port Arthur-
Orange, Texas
Charlotte, N. C.
Portland, Maine
Albuquerque, N. M.
El Paso, Texas
Las Vegas, Nevada
Fargo-Moorhead, N. D. ,
Minne s ota
Boise, Idaho
Billings, Montana
Sioux City, Iowa
Allentow n-B ethlehen.-
Easton, Pa.
Bake l' sfield, Calif.
Davenport-Rock Island-
Moline, Iowa, !llin'ois
Grand Rapids/Muskegon-
Muskegon Heights, Migh.
Greensboro, N. C.
Harrisburg, Pa.
Jacksonville, Florida
Knoxville, Tenn.
Nashville, Tenn.
Peoria, Illinois
Richmond, Virginia
Rochester, New York
Saginaw IBay City, Mich.
Scranton IWilke s Bar re-
Hazelton, Pa.
Syracuse, New York
Tulsa, Oklahoma
Youngstown- Warren,
Ohio
Albany-Schenectady-
1'roy., ,Ne\\,. Y~rJ.~~~~,~~-u
:E stimated
Regional
6ha re (PIn \
.226
,-296
. 18 1
. 128
.225
.088
.360
.149
. 072
.035
. 068
. 031
.014
. 015
. 025
. 037
.586
. 041
.279
. 384
.239
.252
.126
.205
.238
.297
. 301
.883
.260
.270
~ 421
.177
.480
1~]8 3
Standard
Error
.011
. 003
. 015
. 015
. 003
. 006
. ,05 1
.006
. 003
. 003
.003
.003
. 001
. 000
. 001
. 005
.058
. 002
.011
.026
.045
. 068
.001
. 005
.012
.008
. 004
.041
.020
.010
.011
.013
.009
. .
."'- q () 8,"..,~
-------
AQCR
Code
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Table 3.1
( continued)
AQCR
Bingharnton, New York
Charleston, S. C.
Charleston, W. Va.
De s l\1oine s, Iowa
Fresno, Calif.
Fort Wayne, Indiana
Jackson, Mississippi
Johnstown, Pa.
Lancaster, Pa.
Mobile, Alabalna
Nor £011<:- Portsmouth /New-
port News-Hampton, Va.
Raleigh/Durham., N. C.
Reading, Pa.
Rockford, Illinois
Sacramento, Calif
South Bend, Indiana
Utica-Rome, New York
Wichita, I-
-------
whe re :
x.. tis manufacturing product (value added) of industry j, in region i,
IJ,
year t
b.. is regional market share of manufacturing industry j in region i
IJ .
x. is national manufacturing product (value added) of industry j in
J
year t
For example,
x =
5,37,t
. 1249 x
(.004) 37, t
which indicates that trans portation equipment production (SIC 37) in
Detroit (AQCR 5) is 12.49% of the national output in that industry and
that the standard error of such estimates is . 004.
32
-------
,'"
3. 3 The Manufacturing Block of the Regional Model
It has been suggested earlier that for a regional model, the ex-
port sector usually plays an impo'rtant role.
Regional export is st'rongly
related with metropolitan's interindustrial structure.
Thomas s en,
Bell, Glickman, and Klein* link exports also with the Gross Nationa.l '
Product (GNP).
However, it is important that the export sector be
disaggregated.
The reason is that the inter -industrial structure of a
large metropolitan area may be quite different from that at the
national level.
As suggested by location theory, regional resource
endowments and other socio-economic characteristics determine the
industr ial structure of a local economic unit.
Therefore, the use of
a GNP trend is a less desirable indicator of external market demand
than national outputs by industry.
Moreover, the present model is designed to measure the eco-
nomic impacts of air pollution control, and it is more realistic to
observe the impact for each major manufacturing industry at the
two -digit SIC l~vel.
*See H. Thomas s en, ItA Growth Model for a State, " S~uthe..!E..
Economic Journal, No. 24, 1957, pp. 123-139;
-.-~deri~kW. Bell, "An Econometric Forecasting Model for a
Region, " Journal of Re[ional Science, Vol. 7, No.2, 1967;
Norman J. Glickman, "An Annual Econometric Model of the
Philadelphia SMSA, 1949-1966," (mimeograph), Ph. D. Dissertation,
Department of Economics, University of Pennsylvania, November,
1968;
Klein, L. R., "The Specification of Regional Econometric Models, "
Papers, Regional Science Association, Vol. 23, 1969. pp. 153-166.
33
-------
The two-digit SIC manufacturing industries included in the
regional model are:
SIC
20
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
Industry
food and kindred products
textile mill products
apparel and related products
lumber and wood products
furniture and fixtures
paper and allied products
printing and publication
chemicals and allied products
petroleum and coal products
rubber and plastics products
leather and leather products
stone, clay, and glass products
primary metal industries
fabricated metal products
machinery, except electrical
electrical machinery
transport equipment
instruments and related products
miscellaneous products.
The manufacturing block consists of the following equations:
. r.t «, 1-«.
X. . = A. e J N.. Jt K"t J
. yt J Y Y
"ijt = (1 - 4j) Xijt
Il'J't = a. (1. .t 1 - 4.. K"t 1) + b, (n"t - n. .t 1) + C. K..
J lJ.- J lJ - J lJ lJ - J lJt
Kijt = Kijt-1 + Iijt - 4jKijt
K"t
Wl'J't = a. + b,W"t 1 + c. (~)
J J lJ - J Lijt
34
(3)
(4)
(5)
(6)
(7)
-------
I
I'
The details of formulation and estimation of each set of equations
follows.
3. 3. 1 Production Functions and Capital Shares
Equation (3) is a typical Cobb-Douglas production function.
In this formulation, a measure of te'chni~~i change "e rjt has been intro-
duced.
This gives a separate measurement of production efficiency
over time by labor and capital.
The results are shown in Table 3.2.
The technical change
coefficients, rjt show a 2-5% increase in the productivity of labor
and capital annually.
The parentheses under each estimated coeffi-
cient shows the standard error, followed by the regression coeffi-
cient R2 and sample size in each estimation. >:'..
>,'
-------
Table 3.2
Production Functions
. r.t a.. I-a..
X A e J N..~ K.. J
=
. ijt j 1J 1Jt
R2 Sample
SIC In Ai A. r. In a. a. Size
1 1
All mfg. 1. 3154 3.7262 0.0324 -0.6539 0.5200 0.9927 370
(0.0107) (0.0020) (0.0001)
20 1. 2037 3.3326 0.0215 -0.9177 0.3994 0.9814 330
(0.0175) (0.0033) (1. 3010)
22 1. 0552 2.8727 0.0327 -0.5428 0.5811 0.9680 160
(0.0283) (0.0053) (0.8563)
23 1.8111 6. 1170 0.0229 -0.5362 0.5850 0.9760 210
(0. 0274) (0.0051) (1.0394)
24 1. 1606 3.1919 0.0496 -0.5589 0.5718 0.8964 40
(0.0475) (0. 0089) (0.4089)
25 1. 5174 4. 5602 0.0384 -0.5494 0.5773 0.9889 120
(0. 0256) (0.0048) (0.0000)
26 1. 0571 2.8781 0.0169 -0.6783 0.5075 0.9768 250
(0.0166) (0.0031) (1.0252)
27 1. 6053 4.9794 0.0227 -0.5594 0.5716 0.9877 270
(0.0137) (0. 0026) (0. 7586)
28 0.8850 2.4230 0.0320 -1.2118 0.2977 0.9561 260
(0.0279) (0.0052) (1. 6355)
29 0.3416 1.4072 0.0533 -1. 1451 0.3182 0.8143 80
(0. 0397) (0.0074) (1. 0068)
30 1. 3139 3.7205 0.0262 -0.6797 0.5068 0.8598 130
(0. 0394) (0.0074) (1. 1580)
31 1. 5805 4.8573 0.0252 -0.4959 0.6090 0.9695 100
(0.0331) (0.0062) (0.5047)
°36
-------
...
Table 3.2
(continued)
R2 Sample
SIC In Ai A. r'o In (t (t. Size
1 1
32 1. 1051 3.0195 0.0256 -0.7615 0.4670 0.9575 240
. (0.0187) (0.0035) (0.0001)
33 1. 1214 3.0690 0.0421 -0.6053 0.5459 0.9283 25'0
(0.0228) (0. 0043) (1. 2586)
34 1. 4037 4.0701 0.0389 -0.5939 0.5522 0.9394 330
(0.0148) (0. 0028) (0. 0001)
35 1. 4979 4.4723 0.0434 -0.5936 0.5523 0.9815 280
(0.0142) (0.0027) (0.9407)
36 1. 6552 5.2343 0.0252 -0.6388 O. 5279 0.9846 230
(0.0196) (0. 0037) (1. 0229)
37 1. 5521 4.7213 0.0457 -0.5794 0.5602 0.9596 230
(0. 0227) (0.0042) (1. 6513)
38 1.7540 5.7776 0.0221 -0.6069 0.5450 0.9362 90
(0.0320) (0. 0060) (0.6944)
39 1. 5356 4.6439 0.0139 -0.5895 0.5546 0.9757 130
(0.0318) (0.0060) (0.6947)
-37
-------
Equation (4) is an identity defining the gross profit as residuals
of value added and wage bill.
Since a Cobb -Douglas production func-
tion is homogeneous of degree one
ax
n = (X - aN
. N) =
ax
aK
'K
=(l-a.)X
The capital share coefficients (1 - a.), can be obtained from
J
Table 3.2.
3. 3.2 Investment Functions and Capital Stock
It is argued that the investment behavior of manufacturing indus-
tries will be considerably effected by the pollution control expenditures
likely to be made in response to recent legislative requirements.
Although such expenditures involve both investment and operating
costs of control, they are non-productive, and may have a sequential
impact over time on investment behavior of production capacities of
manufacturing industries.
In a recent survey Jorgenson>:< indicated that most recent
investment studies were formulated on the flexible accelerator model
>:'Jorgenson, D. W., "Econometric Studies of Investment Behav-
ior: A Survey", Journal of Economic Literature, Vol. 15, 1971,
pp. 1111....1147.
38
-------
of investment, focusing on the time structure of investment behavior
directed to achieving a desired capital stock.
Howeve r, the specifi-
cation of desired capital varying among alternative theories; further,
time structure of investment expenditures is different among many
empi r ic al studie s.
No attempt is made to review the various
approaches here.
It may suffice to indicate that the new formulation
will be based on the neoclas sical theory of optimal accumulation of
capital in the formulation of desired capital stock. ':'
The case of the neoclassical theory of optimal accumulation of
capital is to determine optimal (desired) capital stock which maxi-
mizes n.et worth.
According to Jorgenson':":'
(a)
NW =
.roo
-rt
e
[z (t)
T (t) ]
d t
Net worth (NW) is the sum of the discounted value of the
difference between revenue
Z (t) and rental outlay of capital ser-
vices T(t) integral over time with a discount rate of r.
Under
>.'
-------
neoclas sical conditions of production, maximization of net worth
is subject to two constraints, namely, the production function and
that replacement is proportional to capital stock.
(b)
x = A La
KP
(c)
r+
= I -aK
Equation (b) is a Cobb-Douglas production function, where X, L, and
K are output, labor and capital inputs respectively.
I-t- is rate of
cbange of capital stock (net investment), I is gross inves.tment and
o is depreciation rate of capital.
By maximizing net worth in equation (a) subject to (b) and (c)
the desired capital K+is determined as follows >:<
'(d)
K+ =
X
Pc
* In detail formulation see Jorgenson, ££.. cit., pp. 43-53.
~<* User cost of capital is defined as
c = q [ 1 - UV a + 1 - UW
l-U l-U
where q is the price of capital good, U the rate of direct taxation,
V the proportion of replacement changeable against income for tax
purpose, W the proportion of the cost of capital allowable for tax
purpose, r the cost of capital or interest rate and a is replacement
rate. In the later study, capital gain or loss on assets has been
added to this formulation. .
r ]
40
-------
...
where fJ is capital share coefficient or elasticity of output with re-
spect to capital from a Cobb- Douglas production function (3) and
C is the user cost of capital.
The user cost of capital is the implicit
price that the capital stock must earn to pay for itself and is, in
general, a function of the price of the stock, the cost of capital
funds to the firm, and any tax treatment accorded to capital stock>:":<.
+
Given the desired capital stock Kt ' the time scheme of in-
vestment behavior to complete the delivery of the demand capital
1S considered to be lag distribution.
This is to say, that on the investment orders, which represent
the difference between desired capital and actual capital holdings
(K + - K ), only a certain fraction is delivered in each period.
t t
ao ' a 1 ' a 2' ....
o :::::; a
-< 1
i = O. 1, 2, ....
1
In his pioneering study of investment behavior, Koyck
suggested a lag distribution with a series of geometrically declining
weights.>:< The- actual investment at time t will be the sum of a
weighted fraction of investment projects initiated in all previous
periods (Xt - i,
i = 0,
1, 2,
. . .. )
1+ =
t
a
o
x + al X 1+....
t t -
o n Xt - n +
*In an earlier estimation of investment equations! Almon's
weights were also used. See Appendix A.
41
-------
Koyck as sumed that
a =
1
Xa,o
0:2 =
Xa =
1
X2 a
o
- - - - - - - - - -
an : X a
n- 1
=
n
= X 0-
o
than
(e)
r+ =
t
cP
L:
i = 0
a.
o
X 1 X
t - i
Suppose the investment plan started in each time t is given by
the difference between optimal capital stocks at time periods t and
t - 1
Xt = (K; - K t - 1 )
A fraction of the above will be delivered each time according to Koyck
lag distribution; then the actual investment at time t will be
(f)
r+ = a
.t 0
00
.L:
1 = 0
X i (K+ - K+ 1 .)
t-i t--1
42
-------
I.
,,-
Then (f) can be transformed to -,'
(g) It = }'It~ 1 + 40 [Kt - Kt 1 ]
Substituting (d) into (g) to get
(h)
+ +
It = X It- 1
r~
L Ct
Xt~~
- Ct-~
+ 4.ofJ
Assume that the user cost is relatively homogeneous, then,
( X't X't 1 ) 1 ( )
-L - J - :'Z - Xjt - Xjt- 1
Cjt Cjt-l C
Therefore Equation (h) becomes
(i)
ao fJ
C
[ Xjt - Xjt-l]
+ Vjt
Ijt = AIjt-l +
-'-
-" Suppose L is a lag operator that by definition
i
L Xt = Xt- i
"
j =1, . . . , n
and I is an identity operator that IXt=Xt> then equation (5) becomes
1+ .
t = ao
00 .
L: Xl Xt-i =
i=o
ao Xt
I
I - XL
Apply 1- A L to both sides
+
It =
X It~ 1
+ a oXt
Therefore,
+ +
It = A It-l + ao
[K; -
Kt~ I]
Statistical Foundations
See Dhrymes, P. J. Econometrics:
tion. pp. 509-517.
43
and Applica-
-------
"I
This foundation is thus a generali~ed version of the accelerator model.
With a Cobb-Douglas Production function (3), by definition, gross
profit" is a fixed proportion to output X
"jt = PXjt
Then equation (i) becomes
(j)
01-
I'
jt
=
+
A Ijt-l
+
a
o
C
[ 0 jt -
o jt- l] + v jt
_.
H 1+. h '.
owever, IS tenet Investment; therefore, the formulation for
gros s investment It will be
ao
(5)
It
=
x (It- 1 -
o Kt- 2 ) +
C
(Ot - 0 t-l) + oKt + Vt
The results of estimation of Equation (5) by pooling cross -section
data of 1958 through 1967 is given in Table 3.3.
The capital stock identities are given as
(6)
K10J't = K"t 1 + loot - o.K't
lJ - lJ J lJ
j =
1, ... m
Some data and pre -estimated parameters need further explanation.
Depreciation rates for all manufacturing industry and each of two
digit SIC industries were estimated from actual depreciation and
44
-------
gross book value of fixed assets of 1957 U. S. data. ~:' The time series
data of capital stock by metropolitan regions and by 2 -digit SIC indus-
tries are non-existant.
Therefore capital output ratios of U. S. in
1958 were applied to the value added by regions by industries in 1958
to obtain the initial capital stock.
That is
Kij 1958 = 4j . Xij 1958
where 4. is capital output ratio of industry j of U. S.
J
Using Kij 1958 as bench mark estimates of regional capital stock by
industries in the base year 1958, time series estimates of capital
stock. were derived as follows:
Kijt = Kijt-l + Iijt - 6jKijt
where initial capital stocks, K.. , investment I. .t and depreciation
1J 0 1J
rates, 6. are given.
J
The pre -estimated depreciation rates and
capital-output ratios are given in Table 3.4.
:o:
-------
Table 3.3
Investment Functions
a.o
1.'t = .(Io't 1 - o.K.'t 1) + - (nOOt -nOOt 1) + o.Koot
1J J 1J - J 1J - C 1J 1J - J 1J
40 00 Sample
SIC Xo c R2 Size
1 1
All manufac- 0.9913 0.0778 0.0692 0.9519 342
turing (0. 0284) (0.0112) (0. 0008)
20 0.6910 0.0104 0.0719 O. 9270 297
(0.0492) (0. 0094) (0.0010)
. 22 0.6579 0.0146 0.0540 O. 7821 144
(0. 0693) (0.0123) (0.0017)
23 0.0026 0.0035 0.1108 0.9240 189
(0. 0784) (0. 0014) (0. 0026)
24 0.3907 0.0355 0.1108 0.9240 36
(0.1592) (0.0310) (0. 0086)
25 0.4474 0.0561 0.0692 0.7815 117
(0.0878) (0.0145) (0. 0029)
26 0.2955 0.0550 0.0703 0.6179 225
(0.0651) (0.0489) (0.0033)
27 0.5496 0.0057 0.0765 0.9284 243
(0. 0608) (0.0185) (0. 0023)
28 0.8550 0.0909 0.0699 0.8721 234
(0.0368) (0.0136) (0.0023)
29 0.4138 0.0510 0.0860 0.6952 72
(0.1320) (0. 0250) (0. 0069)
30 -0.0191 -0.0168 O. 1027 0.7023 117
(0.1023) (0.0442) (0.0055)
31 0.5388 0.0662 0.0704 0.7333 90
(0.0879) (0.0065) (0. 0042)
46
-------
"\
Table 3.3
(continued)
Xo dO R2 Sample
SIC c ~' Size
1 1
32 0.5454 0.0087 0.0751 O. 7295 216
(0. 0667) (0.0187) (0. 0023)
33 0.2936 -0.0714 0.0811 0.8627 225
(0.0671) (0. 0230) (0. 0028)
34 0.4472 0.0899 0.0837 0.8488 297
(0.0542) (0.0205) (0. 0026)
35 1. 0472 -0.0060 0.0830 0.9330 252
(0. 0549) (0.0091) (0.0023)
,
36 0.5226 0.0622 0.0963 0.8648 207
(0.0702) (0.0136) (0.0041)
37 0.7500 0.0517 0.0878 0.8704 207
(0. 0467) (0.0095) . (0.0036)
38 0.4549 0.0761 O. 1882 0.8970 81
(0. 1248) (0.0153) (0.0138)
39 0.2270 0.0518 0.0594 0.8728 117
(0.0920) (0.0092) (0. 0023)
47
-------
Table 3.4
Pre -estimated Parameters
Indus try Output-Capital !
Depreciation
rate OJ ratio
A 11 Man£. .0662 1.271
SIC 20 . 0674 1.394
22 .0525 1.043
23 .0906 6.032
24 .0915 1. 126
25 .0737 2.415
26 .0539 ..799
27 .0686 2.142
28 .0669 .952
29 .0614 .409
30 .0618 1. 381
31 . 0755 4.053
32 .0646 .966
33 .0560 .769
34 .0700 1. 670
35 . 0722 1.696
36 .0738 2.353
37 . 0738 2.353
38 .0671 3.276
39 .0732 2.389
48
-------
.
._~-~-- --...-."
3.3. 3 Wage Equations
Wage differentials among regions in the U. S. have been observed
by many studies. ,,'< Theoretically, such regional wage differentials can
be eXplained by production factor ratios, namely capital labor ratio
on the assumption that (1) production function is neo-classical and
homogeneous of degree one, (2) wages and rentals are equal to their
marginal productivities, respectively.
More precisely, with a Cobb-
Douglas production function it can be shown that if capital labor ratio
in region 1 is greater than region 2, then wage rates in region 1 will
be greater than that of region 2 and vice versa. >:<>:'
Scully has empirically estimated the cross -sectional wage
equations and finds that the capital-labor ratio seems to be a signif-
icant explanatory variable in his estimation. >:<>:<>:' By pooling
over time of cros s -section data, the bargaining power of unions is
~'See Block, J. W., "Regional Wage Differentials. 1907 -1946",
Mon~ Lab. Rev~, April, 1948, pp. 371-77, Gallaway, L. E., "The
North-South Wage Differential", Review of~.s.9..~mi~_aEd Statistics..l
Aug. 1963, Vol. 45, pp. 264-72.
"'<>~See Lo, Fu-chen, "A Two -Region Growth Model with Imper-
fect Mobility of Factors ", Ph. D. thesis, University of Pennsylvania,
1968.
>~>:'>:'Scully, G. W., "Interstate Wage Differentials: A Cros s Sec-
tion Analysis ", American Econom.ic Review, Vol. LIX, 1969, pp.
-----
757-773.
49
-------
"\
is likely to be reflected in a "mark up over years ".
Therefore, a
lag variable was introduced in the wage equation which gives
(7)
K"t
W"t = a. +b,W"t 1 +c. (~)
lJ J J lJ - J Lijt
The results given in Table 3. 5 suggest a good fit of the equation.
The'
coefficients of capital-labor ratios are positive in most cases, as
expected by theoretical formulation, and als 0 significant.
Only in
three cases (SIC 25, 31, 32), are negative signs evident; however,
they are statistically insignificant.
50
-------
Table 3. 5
Wage Equations
K"t
W"t 1J
= a. + b,W"t 1'+ c. (-)
1J J J 1J - J LOot
1J
Sample
SIC a b' c R2 Size
All manufac- 1. 1145 O. 7018 O. 1043 0.6239 342
turing (0.2095) (0. 0339) (0.0162)
20 O. 6795 0.7869 0.0649 0.8264 297
(0.1282) (0.0297) (0.0110)
22 0.3423 0.7973 0.096J 0.8979 144
(0.1103) (0.0341) (0.0173)
23 0.3372 0.8391 0.4095 0.8836 189
(0.0941) (0.0371) (0. 0999)
24 0.2159 0.8502 O. 1113 0.9053 36
(0.2426) (0.0689) (0. 0505)
25 0.6296 0.9048 -0.0202 0.8067 117
(0.2119) (0. 0459) (0. 0614)
26 0.9218 0.8302 0.0096 0.8394 225
(0.1413) (0.0288) (0. 0040)
27 0.8674 0.8341 0.0492 0.8068 243
(0.1616) (0. 0333) (0.0217)
28 1. 1 72 0.8115 0.0077 0.7347 234
(0.2057) (0. 0360) (0. 0044)
29 1. 2442 0.8122 0.0065 0.7606 72
(0.4726) (0. 0773) (0. 0034)
30 1. 0146 0.7910 0.0299 0.7177 117
(0.2694) (0. 0529) (0. 0240)
31 0.8352 0.8104 -0.0342 0.6110 90
(0.2676) (0. 0866) (0. 0743)
51
-------
"I
Table 3. 5
. (continued)
R2 Sample
SIC a b c Size
32 0.6770 0.9211 -0.0059 0.8329 216
(0. 1702) (0.0287) (0. 0085)
33 0.8643 0.8877 0.0030 0.8459 225
(0.1678) (0. 0295) (0. 0054)
34 1. 0987 0.6757 0.1651 0.6255 297
(0.2172) (0. 0417) (0. 0289)
35 0.6009 0.9338 0.0059 0.8837 252
(0. 1423) (0. 0227) (0. 0 158)
36 0.6556 0.9144 0.0097 0.8797 207
(0. 1427) (0. 0247) (0.0149)
37 3.1635 0.5444 O. 04 11 0.3193 207
(0.4106) (0. 0586) (0.0302)
38 1.9113 0.6317 O. 1368 O. 7056 81
(0.3780) (0.0786) (0.0516)
39 O. 9781 0.8064 0.0216 0.7007 117
(0.2602) (0. 0564) (0.0182)
52
-------
,"
3.4
Income Determination Block
Integration of the Keynesian system. and economic base theory
can be best explained by the income determination block of this model,
(8) Y it = f(C't 4 X. 't G't)
1 J 'lJ 1
(9) Cit = f(Yit' Cit-1)
(10) G't = f (T it)
. 1
(11) P 0 A
Tit = T. + Tit + Tit
1t
(12) ~t = f (A, )
1t
( 13) 0 f[Y (~)J
Tit = 1t
(14) A f[(TP; TO) (~)it. ~TP+TO) Yit]
Tit
=
it, P't
1 'ThiS model-.is a cros s - sectional regional growth model. Thus, the
national influence upon a local economy can be measured by the regional
market share of the output in each manufactur ing industry.
Since
manufacturing is also regarded as export-oriented, the level of pro-
duction (value-added), ~ X... also reflects the role of economic base
j 1J
theor y in Equation (8).
Regional consumption Cit and local govemnent
expenditure also are included in regional income determination.
Equation (9) is a typical consumption function.
Equations (10) through (14) give local government revenues and
expenditures sub-block.
Equation (10) is merely a simple relation
53
-------
...
between local government expenditure, Git' and total local govern-
ment revenue, Tit. Equation (11) is an identity that treats total local
government revenue as the sum of three components: local property
p
tax, Tit, other local ta.."{es and revenues,
o
Tit'
A
Tit'
Equation (12) is a
and federal and state
transfer payment to the local government,
property tax equation that states that local property tax is a function
of gr'oss assessed property value, Ait.
Equation (13) relates other
Y
local taxes and revenues to per capita income of region, (p) it' and
regional income Y.
Finally, a behavior equation of federal and state
transfer payment to local government is given in Equation (14). >:~
Transfer payment to the local government, TA, is determined by the
local taxes and the total local revenue effort (TP +To) IT, regional per
Y
capita income ( p ), per capita local tax, (TP+To) IP, and regional
income Y.
The results are given in Table 3.6.
Since there is a dearth of
consistent time series data for most of the variables contained in this
block, the equations in this block (i. e., (11-14) were reestimated with
1967 data.
Equations (8) through (10), as well as those in the labor
market and fuel damand blocks, are the previously estim.ated equations
(May 15, 1971).
They are presented here for com.pleteness.
>:
-------
Table 3.6
Income Dete rmination Block Equations
-,
(l0)
( 11)
(12)
(14)
(8)
Yit = . 4284 ~ Xijt + .9481 Cit + 2.840 Git
(.0564)J (.0661) (.309)
(9)
Cit = 137.99 + .6133 Yit + .01214 Cit-1
(50.09) (.0057) (0012)
Git = 23.4227 +.9421 Tit
(4.108) (.0048)
Tit = T~t +T? + TAt
1 It 1
( 13)
'IT:' =0.568 A't
it (.0071) 1
T~= -.0045 (:!.. )'t + .0121 Y't
t p 1 1
1 (.0016) (.0008)
A TP+ TO Y
Tit = 317. 84 - 81 5. 72 ) it - . 0272 ( -p )it
'I
(80.76) (154.7) (.0125)
TP + TO
+ 1. 055 ( - ht + . 0471 (Yht
(.367) P (,0021)
Note:
Y: Regional income
C: Regional consumption
G: Local government expenditures
'I: Total local revenue
TP: Local property tax
o
'I : Other local taxes and revenues
'IA: Federal and state transfer payment
A: Gross assessed value of regional property
P: Population
55
(R 2=. 997)
(R2=.992)
(R2=.998)
(R2=.915)
(R2=.756)
(R 2=.881)
-------
r
3. 5 Labor Market Block
In a recursive fashion, level of export activities by manufac-
turing block and regional income generates derived demand of labor
in the regional labor market.
The labor market block includes the
following equations:
(15) Nit = f(Y't - 2:X. 't)
1 . 1J
J
(16) Nit = N't+2:NFt
1 . J
J
(17) Lit = f(N it' U it)
Lit - Nit
(18) Uit = ----
Lit
In Equation (15), employment in the sectors other than manufacturing
industries, Nit' is a function of the non-manufacturing incon~e,
(Y't - 2:X. 't), which is approximated by taking the difference between
1 . 1J
J
regional income and total value added by manufacturing industries.
Equation (16) is an identity that shows that total regional employment,
N it' is the sum of employment in the sector other than manufactur ing
industr ies.
Nit' and manufacturing employment~Nijt' were deter-
J
The re gional labor
mined in the manufacturing block of the model.
56
-------
force, Lit' is given as a function of total regional employment, Nit'
and regional unemployment rate, V it' in Equation (17).
Finally,
regional unemployment rate, Vit' is defined in Equation (18).
The
results are given in Table 3. 7.
57
-------
Table 3. 7
Labor Market Block Equations
(15). Nit = 56.36 + .1032(Y. -2;X"t)
(9.52) (.0016) it j lJ
"
(R 2=.978)
(16 )
Nit = Nit + ~Nijt
J
(17)
Lit = -13.958 + 1. 0392Nit + 361. 37Ui
(2.080) (.0009) (55.97)
(R 2=.999)
(18 )
Lit - Nit
U1't = ----- x 100
Lit
---
Note:
N: Regional employment in the sectors
turing industries
Y: Regional income
2;X,: Manufacturing value added
, J
J
N:
L:
.U:
othe r than manuf ac -
Total regional employment
Regional labor force
Regional unemployment rate
58
-------
3. 6 Regional Fuel Demand Block
It has been obs erved that the burning of coal, fuel oil and natural
gas to produce power and heat is one of the most important sources
of particulates, sulfur oxides, and nitrogen emission to the air.
Coal,
coke, fuel oil, natural gas and electricity are also the most important
energy sources available to the manufacturing industries in the nation.
Demand for energy increases as the manufacturing output increases.
However, each type of manufactur ing industry differs from the other
in the production process; therefore, the type of fuels and combina-
tion of different type of fuel and electric power also differ from indus-
try to industry.
On the other hand, it is true that there are substitutional rela-
tions among the different types of fuel and/or electricity to produce
the energy (power and heat) necessary for any given level of product
of an industry.
Hence, industry may choose an optimal combination
of fuels and electricity which minimizes the total cost of energy.
This
is to say, the prices of fuels and electricity also affect the demand
for each type of fuel or amount of electricity in the production process
of each type of manufacturing industry.
Therefore, if the price of
electricity or any type of fuel changes, then the demand for the fuels
59
-------
."'
and electricity changes according to a new optimal combination which
minimizes the total cost of the energy.
As the air pollution control policy is implemented, sulfur con-
tent in coal and fuel oils will greatly affect the price because of in-
creased demand for low sulfur fuels and their limited supply.
Prices'
of natural gas and electricity (partly by the increase in production
cost) tend to change becaus e of changes in demand and supply rela-
tions .
Demand for energy, and hence fuels, like the dernand for labor
or capital is an induced demand from moderation.
Therefore, an
appropriate way to incorporate an energy demand model into the
regional model would be to reformulate the production functions in
the re gional model.
A production function describes the maximum output obtainable
from every possible combination of inputs.
Some of the inputs are
substitutable for one another while others are non-substitutable and
are proportiona.l to the output.
A general production relation can be
conceived of various types of inputs, with substitutional relations
among a group of inputs categorized into a number of sub -groups.
Between any pair of sub-groups of inputs there is no substitutional
relation.
Further assume that inputs for a given industry have been
60
-------
L
"
classified into 3 groups of inputs.
Since there is no substitutional
relations among those 3 inputs, the productions function can be given
as
x = min (1. X ~ X -al X3)
a l' a2 2 '
1 3
Each group I s input is proportionate to the output.
However, within
each group of inputs there are substitutional relations:
X.
1
= f(x x x. ),
i l' i2' ..., in
(i=1,2,3),
f has all propertie s of a neo -clas sical production function.
Therefore,
X = min[~f1(Xll' ..., x1n)' ~f2(X21 + I, ..., x2n)'
~ f 3 (x31 + 1, ..., X3n)] .
Assume that X is gross product (or value of shipments of a given
industry, V is its value -added, Z is energy requirement in this pro-
duction, M is other intermediate good.
Then
(1 1 1')
X = min - V, - Z, - M .
a1 a2 a3
61
-------
Thus, we can derive the relation between value-added and total
energy as:
a2
Z = --V
al
that is, energy demand is proportionate to the value -added.
Cost of energy equals the sum of the costs of all types of fuels
which is the product of price qr and the quantity demand of fuel Ee'
For the 19 manufacturing industries we have':':
(19)
2;E .. q . = a. V..
r IJ rl J IJ
r
0= 1, ...,19).
On the other hand, a Cobb -Douglas type of energy production function
can be introduced which specifies the technical relation between fuels
as inputs and total energy produced.
Suppos e there are fi\Te type s of
fuel, then:
(20)
5
Z.. = B.. n
IJ IJ r = 1
,9ij
E ..
rlJ
(j = 1, ..., 1 9 ) ,
(21)
E ..
~=
Esij
qsi ,9rj
---
qri f3 sj
0=1, ..., 19)
(s f. r, r, s = 1,
...,5).
':'For notational convenience, E5 has been used for electricity
instead of Q, tbus E5ij == Qi" And El, E2, E3, and E4 represent
coal, coke, fuel oil, and naiural gas, respectively. Not all two-
digit SIC manufacturing industries use all five types.
62
-------
Equation (20) gives the energy production by each manufacturing
industry while equation (21) is simply derived from the equilibrium
condition that price ratio betwe.en two types of fuels equals the ratio
of marginal productivity of fuels. ':'
Residential and other non-manufacturing industry demands of
electricity are given as:
(22)
Qci(t) = f[Ci(t)] ;
(23)
Qi(t) = f[Yi(t) -~Vij(t)];
J
Qi (t) = 2:[Qij (t) + Qci (t) + 6i (t)].
(24)
Equation (22) relates regional industrial demand of electricity to
regional consumption, while in equation (23) the demand of electricity
by other industries is a function of non-manufacturing regional income.
Equation (24) gives the total regional demand for electricity.
-----
':
-------
This block of equations, estimated by cros s -section data of 1967
earlier, is presented here in Tables 3.8, 3.9, and 3. 10.
64
-------
Table 3.8
Energy Demand Function
Z.. = a' V..
1J J 1J
Industry a.
. SIC J
20 2. 13525
22 3.04152
23 0.74246
24 2.57780
25 1. 33572
26 3.97124
27 0.61895
28 2.79554
29 9.43424
30 2.83225
31 1. 15811
32 6. 14368
33 10.68980
34 2. 10111
35 1. 34915
36 1. 19740
37 1. 35564
38 1. 00903
39 1. 44677
65
-------
Table 3.9
Energy Production Function
1'1' 1'2' 1'3i 1'4' 1'5'
Z . - B. E J E J E . E ,I E J
i.1 - .1 Ii.1 2ij 3ij 4i.1 5ij
SIC B.. "Yl ."Y 2 "Y3 "Y4 "Y5 R~
Code 1.1
20 . 1 7. 304 . 0993 . 0 . 11 07 .2250 . 5651 .984
(. 0597) (. 0687) . (. 0908) (. 0820)
22 19.563 . 1133 . 0 . 1 544 . 1070 .6254 .976
(5.246) (.0523) (. 0786) (. 0429) (. 1204)
23 21. 914 . 0 .0 . 0934 . 0822 . 8244 .998
(7.570) (. 05 72) (.0359) (. 0817)
24 19.061 . 0 . 0 . 1707 .1110 .7183 .970
(3_.693) (.0337) (. 0323) (. 0493)
25 23.206 .0882 . 0 .0873 . 1243 .7002 .995
(4.134) (. 0237) (. 0282) (. 0280) (.0618)
26 20.941 .2150 . 0 .1318 . 1378 .5154 .930
(4. 732) (. 1233) (.0961) (.0995) (.1390)
27 19. 616 . 0 . 0 . 0670 .1325 . 8006 .982
(L 963) (. 0206) (.0352) (.0503)
28 12.312 . 1564 . 0 .0587 .2067 .5782 .920
-(4..514) (. 0798) (. 0618) (.1109) (.1352)
29 3.063 . 0 . 0 . 0620 .5371 .4009 .959
l-=- 700) (.0594) (. 1387) (.1308)
30 14.935 . 0 .' 0 . 1030 . 1236 . 7734 .989
(1.617) (.0307) (. 0347) (. 0436)
31 17.965 .1191 . 0 . 1535 . 1105 .6169 .941
(12.313) (.0318) (. 0387) (.0199) (.0601)
32 9.?86 . 1382 .' 0 . 0818 .3780 .4020 .857
(2.476) (. 0785) (. 0455) (.1195) (. 0857)
66
-------
.--..,. .- - ~ -~ -~--
. I .
~
Table 3.9
(continued)
33 19.482 .0465 . 1838 . 1062 .2293 .4342 .983
(4.450) (.0195) (. 0852) (.0546) (.0701) (. 0982)
.'
34 17.059 . 0352 . 0 . 1108 .2338 .6202 .993
(1. 719) (.0173) (.0588) (. 0762) (.0691)
35 __t9.981 .0688 . 0 . 1087 .1656 .6569 .987
(2. 734) (.0363) (. 0663) (. 0597) (. 0687)
36 16. 827 .0493 . 0 . 0800 . 1567 .7139 .955
(2. 912) (.0142) (.0391) (. 0436) (. 0556)
37 1'7.572 .0905 . 0 .0717, . 1345 . 7032 .990
(5. 738) (.0321) (. 0406) (.0394) (.0536)
38 18~982 .1141 . 0 . 1159 . 1199 .6500 .969
(8. 577) (. 05 9 1) (. 0226) (.0197) (.0593)
39 20.846 .0608 . 0 . 1289 . 1437 . 6666 .985
(4. 008) (.0182) (. 0436) (.0661) (. 0980)
67
-------
Table 3. 10
Regional Electricity Demand Function'
------1}
(22)
(23)
(24)
Q. = .0472C.
Cl 1
(.0022)
(R2=.880)
Q. = .07947(Y.-2:X..)
1 (.0042) 1 j IJ
2
(R =. 846)
Q. ,= Q + Q. + 2:Q. .
1 ci 1 . IJ
, . J '
68
-------
4.0
REGIONAL ECONOMIC IMPACTS OF
AIR POLLUTION ABATEMENT: A
SIMULA TION WITH THE REVISED MODEL
I
As air pollution control requirements are instituted in the nation,
the consequent effects are incident differentially in the various AQCRs.
The primary purpose of regional economic modelling is to provide
quantitative estimates of such differences among the AQCRs in any
particular treatment (strategy) and among different treatments.
The second purpose of the model is to provide information on
such differences among regions and among strategies that is useful in
assessing implementation strategies.
For example, it is possible to
argue that the "perfect" strategy is one in which each AQCR suffers
" the same degree of economic hardship.
Exact measurement of such
a condition is impossible, since there is no single measure of eco-
nomic hardship.
However, the use of this regional model permits
useful estimation of the degree of differences in the treatment of
AQCRs necessary to achieve some degree of unifo"rmity in the effects
of implementation of pollution control requirements.
Other forms of targeted assistance (differenti.~l cost sharing,
etc. ) are also possible.
Consequently, the regional model can be
used to design and assess such "mixed" implementation strategies
(in which different AQCRs are treated differently) by trial and error,
69
-------
so that some guidance may be available to EP A officials to achieve
some degree of equity among AQCRs in control implementation.
This chapter is addres sed to a description of the effort directed
to both of the above purposes of the revised OAP Regional Econometric
Model.
First, it opens with a brief description of the framework anal-
yses of economic impacts and the rationale for the measures of impact
of control us ed in this chapter.
It proceeds to a comparative descrip-
tion of the economic effects over time aggregated over 91 AQCRs under
the alternative strategies.
Next, it provides a comparison of strate-
gies in terms of the geographic pattern of incidence of economic effects,
specifically, the geographic distribution of economic hardships.
4. 1
Alternative Implementation Strategies
and Measures of Their Economic Effects
Two alternative strategies were formulated for simulation
through the revised model. >:< These two strategies assume the prelim-
inary EPA cost estimates based upon the standards resulting from the
EPA Federal Register of August 14, 1971.
Thus, they both assume
the same aggregate costs for 91 AQCRs over the implementation period.
>:'These are the first two of the seven strategies formulated and
simulated in the earlier model utilization experiments. See CONSAD
Research Corporation, The OAP Regional Economic Model Utilization,
Phase I,2.£.. cit., pp. 9-30.
70
-------
i ~~~-
Howeve'r, they differ in the following manner:
."
Strategy 1:
(Straight
Implementation)
Strategy 2:
(Extended
Implementation)
The actual implementation period is assumed
to be 1973-1975. This is because states are
expected to get their implementation plan
approval and regulations in force by the end
of fiscal year 1972. No additional govern-
mental financial assistance than what is
implicit in the existing tax structure is pro-
vided.
Same as Strategy 1, except that it allows all
AQCRs to extend the target year to 1977, as
the maximum extension permitted by law,
without any financial assistance from the
gove rnment.
Given this difference in implementation costs, the geographic
and time incidence of control costs vary among AQCRs (apart from
their differences in terms of industrial composition).
These varying
levels of control costs lead, in turn, through the operation of the com-
plex interrelationships of regional economies (as captured by the OAP
model) to a range of effects on high emission industries, consumers,
employment, taxpayers, local governments, and regional growth.
The simulation of the strategies through the OAP model provides
a large number of measures of these economic effects (Figure 4.1).
Figure 4. 1 gives a sample output for the Pittsburgh AQCR in the year
1975 under strategy 1.
of outputs.
There is a list of variables and four columns
The first column - - "without control" - - shows economic
projections without any air pollution control.
The second column --
71
-------
FIGURE 4. 1
r i1 1< U~ '( f. Mi 5 T iUI I C: Ii T I H P L E~) r: iJ T .~, TIC i-j -
\'j I r 11 () t) r GO V E I~ N f1 F: (J T A :.; ~ ! s r {\ fJ C E
TOTAL NET EFFECT uF ALL CONTROL SrHATEGIES PU~SUfU
I tJ T HIS RUN
A (~ C H
PI,TSHUkGH,
P A. j
B
MAN U FA C T l) i~ IN C; 1 ~ID U 5 T HIE $
V A l U E A !J [) E D (n ILL 1 0 IJ S )
PKOFIT (MILLIONS)
IMVlST~lNl (MILLIUN~)
CAP iTA L 5 T 0 ( K (11 ILL I U i~ 5 )
E t1 P L 0 Y t~ f.. N T (J (J nos I
-J 0 T H [ P. I I~ D U S H, I E 5
N
EMPLOY~[NT (JUDU 5)
TotAL P~HSUNAL INtONE FUR THE REGION (MILLIONS)
. R E (, ! 0 II ALe 0 i IS U 1"0 P T I 0 j.; (M ILL ION'::) ) .
TOT A L HE c. 1 UNA L E. H~' L (j Hi E I JT (1 0 L.) n S)
REG 10tJAL LJi4Ei'WLCiYI"1f>n (PERCEI,n I
TOTAL LAUOR FORCE (JUUO SI
G 0 V U, IH I U I T f-( EvEr j U E F idJ H THE H t. <1 1 0 i~ (r-, ILL I 0 I'! 5 )
G 0 V E I{ r J 1'1 E r J T i~ EvE:: HUE F P lJ t1 PRO P f. Ii T Y T A XES (M ILL I U N S )
GOVEfn~r1U:T Rt.vEI'JUE OlHU< THAr~ PI.aQ7 -8U.8U9 -0.aLf3e
6.>23./169 626S.(}09 -611.8llS -1.03'13
IG5'i.72J IOS/.OOI -b.761 -0.829Lj
'1.00/1 '1.00U 0.7993 19.9817
110J.R1H 1101.U'18 -9.111 -O.d27S
73J.177 7 2 '/ . U ,~ U -~.26'7 -U.7,27
JllJ.42(; 31U.Lf27 U.O U.U
9Uol/~8 80.86:; -2.01'1 . -2.272S
J3J.20J 32~.26U -7.777 -2.3693
1'176.77'1
1-1 u. 333
J6LJ.96'i
'-iU::>.476
1'159.219
696.18'+
36U.28U
4U2.7S:.
-1t3.722
-ILj.322
-1.3'12
-3.057
-1.283U
- 2..iJ 5 7 2
-U.3726
-0.7S91
-------
"with (T -1)" - - provides the projection of the variable in column 1
with air pollution control to year T -1 (which is 1974) but before con-
trol is applied in 1975.
It shows the cumulative effects of control
through 1974 before control of 1975.
The third column shows "net
change" of control in year 1975 and the last column shows percentage
change of control in year 1975.
An assessment of these effects is
best organized by identifying from among this long list a few indica-
tors of strategic importance to the purpose at hand.
The purpos e at
hand is:
To compa're alternative strategies in terms of
effects aggregated over 91 AQCRs.
To compare the alternative strategies in terms
of the degree of adverse effects in different
AQCRs.
To explore the geographic patterns of impacts
in terms of industries, regions, government
and communities.
To describe the geographic patterns of these
effects in terms of the locational factors, in-
dustrial structure and economic histories of
these AQCRs. The objective of this specula-
tion is to identify to s'ome degree the transi-
tional adjus tment problems in severely affected
AQCRs.
The measures that appear to be relevant from these criteria for five
major economic indicators in the regional economy are as follows:
73
-------
...
Measure
1.
2.
3.
4.
5.
Manufacturing production (value -added)
Manufacturing investments (for production)
Regional personal income
Unemployment rate
Manufacturing gros s profit
The rest of this chapter interprets the results of the simulation of the
various strategies in terms of these five measures.
74
-------
i......-.
4.2
Total Net Effects of
Alternative Strategies
This section presents the effects of the two major strategies
aggregated over all these 91 AQCRs.
The 91 AQCRs included in the
current study are the major metropolitan areas of the United States.
They account for 64 percent of the regional personal income, 56 per-
cent of total labor force, and 60 percent of the total manufacturing
industries in the United States. >:' In general, these AQCRs have a
lower than national average of agriculture and mining production but
a higher than average of manufacturing, transportation, wholesale-
retail trade, finance and service sectors.
Table 4. 1 provides the economic effects aggregated over 91
AQCRs under two strategies, namely, a straight implementation by
1975 and an extended implementation by 1977. >:0:'
Several points are fairly evident when these tables are examined:
The economic effects under the different strat-
egies are sufficiently different to suggest that
the regional economies are sensitive to the
*Persona1 income projections of the United States and regional
aggregations for the year 1967 and manufactur ing production percent-
ages in 91 AQCRs is estimated from Census of Manufactures, 1967.
>:o:'For a detailed description of control strategy alternatives, see
T. R. Lakshmanan, F. Lo, and R. Byrne, The OAP Regional Eco-
nomic Model Utilization, Volume I, Simulation and Analysis, prepa.red
for the Environmental Protection Agency, by CONSAD Research Corp-
oration, Pittsburgh, Pennsylvania, January, 1972.
75
-------
Table 4.
A
. .. . .
-.J
0"
.ggregate conomlC ec s on s
Three Year Straight
Implementation Five-Year Extended Implementation
Regional 1973 1974 1975 1973 . 1974 1975 1976 1977
Employment (1000) ' I .
without control 588.41 617.44 648.05 588.41 617.44 648.05 679.86 7.13.42
Change with control -.70 -1.84 -2.96 -.25 -. 54 I 1. 81 -2.47 -1.65
Percentage change -. 12 -.30 -.46 -.04 -.08 -.28 -.36 -.23
Manufacturing I
. Value-added ($ billion)
without control 188.50 195. 50 202.75 188.50 195.49 202.75 210.55 218.65
Change with control -.39 -.95 -1. 42 -. 14 -.28 -.97 -1.18 -.48
Percentage change -.21 -.49 -. 71 -.07 -. 14 -.48 -. 57 -.22
Regional Personal
Income ($ billion)
without control 561. 69 589.23 618.19 561. 69 589.23 618.19 648.40 680. 16
Change with control -.54 -1.37 -2.16 -. 19 -.38 -1. 38 -1. 77 -.92
Percentage change -. 10 -.23 -.34 -.03 -.06 -.22 -.27 -.14
Manufacturing
Investment ($ billion)
without control 13.97 14.50 15.04 13.97 14.49 15.03 . 15.62 16.22
Change with control -.35 -.83 -1.19 -. 12 -.25 -.86 -.99 -.27
Percentage change - 2. 53 -5.87 -8.66 -.87 -1.71 -5.86 -6.92 j. -1. 97
-1 -
Manufacturing G ros s Profit
Value -added minus wage
bill ($ billion)
without control 89.79 93.15 96.63 89.78 93.14 96.63 100.38 104.27
Change with control -.21 -.67 -1. 28 -.07 -.20 -.68 -1.15 -1.17
Percentage change -.24 . -.72 -1. 33 -.08 -.22 -. 71 -1. 16 -1.15
E
. Eff
t
91 AQCR
-------
differences in the strategies. The different
economic indicators move in the same consis-
tent direction among the strategies.
Expected1y, the economic indicators of the
manufacturing sector (high emission) show the
greatest range of differences on a percentage
scale among the strategies. The regional
economy and government indicators show a
narrower 'range of variations.
Extension of the implementation period fron~
three to five years in each case reduces the
aggregate adverse economic effects. This is
to be expected in view of the spread of conti'ol
costs over a longer period. Further, the re-
gional economies of 1977 are larger than those
of 1975 and the control costs may be a smaller
percentage of the aggregate regional economies.
More specifically, Table 4. 1 shows that, with straight imp1e-
mentation by 1975, manufacturing production (measured by va1ue-
added) in these AQCRs will decrease 1. 42 percent by 1975.
Further,
investment in manufacturing industries (for production capacity) will
drop from $15 billion to $12.6 billion which is about a 16 percent drop.
Personal income is expected to decrease 0.34 percent while the unem-
p10yment rate will increase by 0.46 percent.
This indicates that the
manufacturing sector, bearing the brunt of the control costs, will be
more sensitive to the air pollution control compared with regional
income, and unemployment rate.
Manufactur ing gross profits will
drop about 2. 3 percent.
Consequently, when comparing the 1973-1975
77
-------
strategies with 1973-1977 strategies, it is clear that extension of the
time of implementation is likely to help.
4.3
Geographical Patterns
of Economic Growth.
The previous section dealt with only the aggregate effects of 91
AQCRs during the implementation periods with and without two-year
extens ions.
However, behind these aggregate patterns ties a wide vari-
ation in economic effects among the different AQCRs.
For example,
if implementation is required by 1975, manufacturing production
(value-added) will drop 0.8 percent by 1975.
However, there will be
28 out of 91 AQCRs which have one percent or more reduction in the
manufacturing production, and six AQCRs will be in the range of 3.0
percent and over.
It also shows that most of the AQCRs seriously adversely
affected are located in the heavily-industrial north-central (Michigan,
Ohio, Indiana, Illinois) and central-east (Pennsylvania, West Virginia)
states.
AQCRs located in the west and south, in general, do not seem
to be affected by air pollution control and some are even better off.
Therefore, air pollution control under Strategy 1 may conceivably
lead to a 10cationa1 redistribution of the economic activity of the nation
as a result of increased growth in the newer metropolitan areas and
the greater econon~ic pres sure on the older heavy industrial areas.
78
-------
1-
The degree of economic impacts upon each AQCR can be ana-
lyzed by identifying the AQCRs into different groups as shown in
Tables 4.2 through 4.6 for five variables, and geographic distribu-
tion of the corresponding tables are given in Figures 4..2 through
4.6.
Regional unemployment rate (Table 4.2 and Figure 4.2)
Manufacturing value-added (Table 4.3 and Figure 4.3)
Manufacturing gross profit (Table 4.4 and Figure 4.4)
Manufacturing investment (Table 4.5 and Figure 4.5)
Regional personal income (Table 4.6 and Figure 4.6)
A more detailed result on two groups of AQCRs, namely, AQCRs
with regional unemployment rate expected to increase 0.5 to one per-
cent, and AQCRs with unemployment rate expected to increase one
percent and over, are shown in Table 4.7.
79
-------
Table 4.2
Three-year Straight Implementation by 1975
AQCRs with less than. 49 percent increase in the regional unemployment:
l.
3.
4.
6.
7.
10.
11.
12.
14.
15.
20.
21.
22.
23.
24.
25.
New York
Los Angeles
Philadelphia
San Francis co
Boston
Washington, D. C.
Cleveland
Baltimore
Minneapolis
Houston
Dallas
Seattle-Everett
Kansas City, Mo.
San Diego
A tla nta
Indianapolis
26.
27.
29.
30.
3l.
32.
33.
34.
35.
39.
40.
41.
42.
44.
48.
50.
Miami
Denver
Portland, Oregon
Providence
Phoenix
Tam pa
Columbus
San Antonio
Dayton
Chattanooga
Memphis
Salt Lake City
Oklahoma City
Honolulu
Albuquerque
E1 Pas 0
5l.
53.
66.
67.
69.
7l.
73.
74.
78.
81.
87.
88.
92.
95.
96.
99.
Las Vegas
Boise
Grand Rapids, Mich.
Greensboro, N.C.
Jacksonville, Fla.
Nashville
Richmond, Va.
Rochester, N. Y.
Tulsa, Okla.
Albany- Troy.
Fort Wayne
Jackson, Miss.
Norfolk/Newport
Rockford, Ill.
Sacrame nto
Wichita
AQCRs with an increase in unemployment rate between. 50 and. 99 percent:
2. Chicago
5. Detroit
8. Pittsburgh
9. St. Louis
16. Buffalo
17. Milwaukee
18. Cincinnati
19. Louisville
28. New Orleans
36. Birmingham
37. Toledo
- 43. Omaha
46.
47.
55.
6l.
64.
68.
70.
72.
75.
77.
82.
Charlotte
Portland, Maine
Sioux City, S. D.
Allentown-Easton
Davenport
Harrisburg, Pa.
Knoxville, Tenn.
Peoria, Ill.
Saginaw/Bay City
Syracuse
Binghamton, N. Y.
- 83. Charleston, S. C.
84. Charleston, W. V.
85. Des Moines
86. Fresno, Callf.
90. Lancaster, Pa.
91. Mobile, Ala.
93. Raleigh/Durham
94. Reading, Fa.
97. South Bend, Ind.
98. Utica-Rome
100. York, Fa.
AQCRs with an increase in unemployment greater than 1.0 percent:
38.
45.
52.
Steubenville area
Beaumont, Texas
Fargo-Moorehead
54.
63.
76.
Billings
Bakersfield, Calif.
Scranton area
80
80.
89.
Youngstown- Warren
Johnstown, Fa.
-------
00
.....
. Geograph' . Figure" 2
b lC Dlstri)' -.
y Change f . uhon of E
o Regional U conomic <'f:
nem 1 ...J .ects M
. P oyment R t easured
. a e
. .
'. '. .YIJ ~
\;> . ~,.-
. ..._,,J"
I
\~ .
q52 ~ ~ .
) r./~ .' .' .
'\ 'J~'f-r ,,,./
I 0~4 .~i ~/~ \ \~/
~ '\ 1 71 7 5~ 7 -q 8 \ ( ~I
-........--.. . ' ~/. 16 7 ~CI. : I . '] .
f55 U;--'-: j 6 5. '82 8~,:.1"
43 (l) CD85 ~. (!)2. ~ -.----/ 1 .8 7.~.' >-.1,3fo
'\ 1"1\64! w9JJ3 i . 0.0 1 OOrr\.~w\ vj::?,
'f"" . "" 8 7C!J ,8.. 6 8>t'~ 6 I
-, L 33 O\\fJ. "': .\4)
~22 \. 1% increase' \\ .
-------
Table 4. 3
Three-year Straight Implementation by 1975
AQCR s with a decrease in Manufacturing
than. 99 percent:
1. New York
2. Chicago
3. Los Angeles
4. Philadelphia
5. Detroit
6. San Francisco
7. Boston
11. Cleveland
12. Baltimore
14. Minneapolis
15. Houston
17. Milwaukee
18. Cincinnati
19. Louisville
20. Dallas
21. Seattle -Everett
22. Kansas City
23. San Diego
24. Atlanta
25. Indianapolis
26. Miami
AQCRs with a decrease
1.0 and 2. 99 percent:
8. Pittsburgh
9. St. Louis
10. Washington, D. C.
16. Buffalo, N.Y.
32. Tampa
36. Birmingham, Ala.
37. Toledo
52. Fargo:'Moorehead
27.
29.
30.
. 3l.
33.
34.
35.
39.
40.
4l.
42.
43.
44.
46.
47.
48.
50.
5l.
53.
64.
66.
Production (Value Added) of less
Denver
Portland, Ore.
Providence
Phoenix
Columbus
San Antonio
Dayton
Chattanooga
Memphis
Salt Lake City
Oklahoma City
Omaha
Honolulu
Charlotte, N. C.
Portland, Maine
Albuquerque
El Paso
Las Vegas
Boise
Davenport/Moline
Grand Rapids
67. Greensboro, N. C.
71. Nashville
72. Peoria, Ill.
73. Richmond, Va.
74. Rochester, N. Y.
75. Saginaw/Bay City
77. Syracuse
81. Albany Area
82. Binghamton, N. Y.
84. Charleston, W. Va.
87. Fort Wayne, Ind.
90. Lancaster, Pa.
93. Raleigh/Durham
94. Reading, Pa.
95. Rockford, Ill.
96. Sacramento
97. South Bend
98. Utica Rome, N.Y.
99. Wichita
100. York, Pa.
in Manufacturing Production (Value Added) of between
55.
6l.
68.
69.
70.
76.
78.
Sioux City, S. D.
Allentown/Easton area
Harrisburg
Jacksonville, Fla.
Knoxville, Tenn.
Scranton, Pa.
Tulsa
80.
83.
85.
86.
88.
9l.
92.
Youngstown/Warren
Charleston, S. C.
Des Moines
Fresno, Calif.
Jackson, Miss.
Mobile, Ala.
Norfolk, Va. area
,AQCRs with a decrease
28. New Orleans
38. Steubenville area
in Manufacturi ng Production of over 3 percent:
45. Beaumont/Orange 63. Bakersfield, Calif.
54. Billings 89. Johnstown, Pa.
82
-------
.~ ~r-- .
/ ~,,-., I ... . yo
.'{> . v-
..._~~ I
Figure ,:.3
Geographic Dis :r ibu :ion of .
Measured by Ch' EconOffilC Effects
ange of Ma f .
(Value-Added) . nu acturmg Production
00
VJ
\~ . .
cb52 Lx ~ . '....'
\ I ~ ~--:,.., '47 ./
) .( \.~rr .., '(W'
:0~ ~ ~ 75' 7 i1708~\ (\17 .
I . 17,. 16 (!) #, . 4~ .
/ .) U6. .82 8 ~~-"r....1 .
'"'--... \_~5 5- '\' \'30
. 55 '\0- 1 7 1:-'
43~' CD8S.J Z' . 91;37' . ~O I o~~-0S7 61
'~ )064! 87~ 33 0\& ': 68(1;;'~ . 94
~ . ~ 072 r..3~ .J03~.~~:li --90
022 \ 2'5 :0li.J' ./ 1 O~\:\; .
i 9 ~88 1
. C 191 .
~5! \ ~.~\
034~5W~. ~. ~~~.9\'
. ..;/ 32
. r A > 1m . .
\ \;# -/0 lncreas e ~
. \ 26.
CD 0..50 - 0.99 increase '\:f2J
o <.. o. 49 increas e -" ,/
-------
Table 4.4
Three-year Straight Implementation by 1975
AQCRs with a decrease in Manufacturing Investment of less than 9.9 percent:
1. New York
3. Los Angeles
4. Philadelphia
5. Detroit
6. San Francisco
7. Boston
11. Cleveland
14. Minneapolis
15. Houston
17. Milwaukee
18. Cincinnati
19. Louisville
20. Dallas
21. Seattle -Everett
22. Kansas City, Mo.
23. San Diego
24. Atlanta
25. Indianapolis
26. Miami
27. Denver
30. Providence
31. Phoenix
33. Columbus
34. San Antonio
35. Dayton
38. Steubenville area
39. Chattanooga
40. Memphis, Tenn.
41. Salt Lake City
42. Oklahoma City
43. Omaha
44. Honolulu
46. Charlotte
47. Portland
48. Albuquerque
50. El Paso
51. Las Vegas
53. Boise, Idaho
64. Davenport
66. Grand Rapids
67. Greensboro
71. Nashville
72. Peoria
73. Richmond
74. Rochester
75. Saginaw/Bay City
81. Albany/Troy
82. Binghamton
84. Charleston, W. Va.
87. Fort Wayne, Ind.
90. Lancaster, Pa.
93. Raleigh/Durham
94. Reading .
95. Rockford
96. Sacramento
97. South Bend
98. Utica-Rome, N. Y.
100. York, Pa.
AQCRs with a decrease in Manufacturing Investment of between
percent:
2. Chicago
9. St. Louis
10. Washington, D.C.
12. Baltimore
16. Buffalo
29. Portland, Ore.
45. Beaumont/Orange
52. Fargo-Moorehead
54. Billings
61. Allentown area
69. Jacksonville, Fla.
76. Scranton
77. Syracuse
83. Charleston, S. C.
10.0 and 19.9
85. Des Moines
86. Fresno, Calif.
88. Jackson, Miss.
91. Mobile, Ala.
92. Norfolk, Va. area
99. Wichita
AQCRs with a decrease in Manufacturing Investment of more than 20 percent:
8. Pittsburgh
28. New Orleans
32. Tampa
36. Birmingham
37. Toledo
55. Sioux Falls, S. D.
63. Bakersfield, Calif.
68. Harrisburg, Pa.
84
70. Knoxville, Tenn.
78. Tulsa
80. Youngstown/Warren
89. Johnstown, Pa.
-------
00
,\Jl
031
. ~ '~4 I
" 0~...
" .'{)
.~2~~
. 'yO
. .;,;-
""-''''''~ I
'.
Figure 4.4 '
Geographic Distribution of Economic Effects
Measured by Change. of Manufacturing Investment
(t) 54
027
I
I
048'
G)99
780 '
04 ~ \ ' . 40 ,
~ I I' 36 024 \~
. 0201--1 0 i (
. \ ~8191.~'")
45~ ,.M>../-<-=~~9'
03415e&J~~ . " . .
.7 ,<2
r 0 > 1% increase "~6) ,
\ CD O. 50 - 0.99 increas e Ig,
./
o < 0.49 increase
-------
Table 4. 5
Three- Year Straight Implementation by 1975
"
AQCRs with decrease in Manufacturing Profit of less than. 99 percent.
1.
3.
6.
7.
14.
15.
19.
20.
22.
23.
New York
Los Angeles
San Francisco
Boston
Minneapolis
Houston
Louis ville
Dallas
Kansas City
San Diego
24.
25.
26.
27.
29.
30.
33.
35.
39.
40.
Atlanta
Indianapolis
Miami
Denver
Portland, Ore.
Providence
Columbus
Dayton
Chattanooga
Memphis
44.
50.
5!.
67.
74.
84.
87.
95.
96.
Honolulu
El Paso
Las Vegas
Greensboro
Rochester
Charleston, W. Va.
Fort Wayne
Rockford, Ill.
Sacramento
AQCRs with decl.'ease in Manufacturing Profit of between 1. 0 and 2.99
percent.
2.
4.
5.
9.
11.
12.
16.
17.
18.
21.
31.
32.
34.
41.
Chicago
Philadelphia
Detroit
St. Louis
Cleveland
Baltimore
Buffalo
Milwaukee
Cincinnati
Seattle-Everett
Phoenix
Tampa
San Antonio
Salt Lake City
42.
43,
45.
46.
47.
48.
64.
66.
69.
71.
72.
73.
75.
77.
Oklahoma City
Oma ha
Beaumont/Orange
Charlotte, N. C.
Portland, Maine
Albuquerque
Davenport
Grand Rapids
Jacks onville
Nashville
Peoria
Richmond
Saginaw /Bay City
Syracuse
81.
82.
85.
86.
88.
90.
91.
93.
94.
97.
98.
99.
100.
Albany-Troy
Binghan'lton
Des Moines
Fresno, Calif.
Jackson, Miss.
Lancaster, Pa.
Mobile, Ala.
Raleigh/Durham
Reading, Pa.
South Bend, Ind.
Utica-Rome
Wichita
York, Pa.
AQCRs with a decrease in Manufacturing Profit of more than 3 percent.
8.
10.
28.
36.
37.
38.
39.
Pittsburgh
Washington, D. C.
New Orleans
Birmingham
Toledo
Steubenville
Fargo -Moorehead
53.
54.
55.
61.
63.
68.
70.
Bois e
Billings
Sioux City
Allentown area
Bakersfield, Calif.
Harrisburg, Pa.
Knoxville, Tenn.
86
76.
78.
80.
83.
89.
92.
Sc'ranton area
Tulsa, Okla.
Youngstown- Warren
Charleston, S. C.
Johnstown, Pa.
Norfolk area
-------
G Figur 4
eograph" " e. 5
M le DlSt- °b
easured b rl ution '01 E .
y Change of M eonomie Eff
, ' anulactur' ects
. ", mg Profit
00
-J
..~~
~ Z' .' ~.'
~52 " ,., "," ~'
,)~ ,~.
\ ) 'fjr-'r: ' \ V
(I @~ 17/ ~ 75 . 7 i77_q8~\ I ~(
~\ 16 $(»" \ .1
I . 6 .' 9
. 55 95- 5 .' 82 8 ~._,. "
64 9113 ' .0 1 0 O(j) 0 '0::;?"
. \~ CD. 81(!! ,0,8 68Q~' 61
-, ~CD72 ~33 O\O~. G£~1)
'" (0) 3 '" 38;" - --" "'.' >~ / . 94
~22 2'5 . 'Z/,f V ",-~w w
(p99: 9 ~\ .uJ.r -I' f 1i?\12. -90
I I' W. --<..~J
. -19 84 . 'l\j." '
78 ::-l.- )-1 / 73CTD _0
o ,_J . ,92
(D42 \' 2 11 10 10 .;)
40 . 39' CD93 /..c-c!) .
j ',. ' f
-~( '36 \024~83 .
, ~ 0 1 .'
\ (1)88' '
~ ! 91 ;
(j) 34 45; ,tr1"\ ~
j~'-=~~->--V~ ~~ ,
'f b3\
. 0 > 1 "
~ '" ,:" mcrease ~
@ 0.50 - 0 \ 26
r--. .99 increase ~
~ < 0 4 ' --7
. 9 Inereas e ./ /'
054
~41 I
027
,~' 44
. / ~'''::c, I
-------
Table 4.6
Three- Year Straight Implementation by 1975
AQCRs with decrease in regional personal income of less than. 49
percent.
1. New York 29. Portland, Ore. 67. Greensboro
3. Los Angeles 30. Providenc e 69. Jacksonville
4. Philadelphia 31. Phoenix 71. N as hville
5. Detroit 32. Tampa 73. Richmond
6. San Francisco 33. Columbus 74. Rochester
7. Boston 34. San Antonio 78. Tuls a
10. Washington, D. C. 35. Dayton 81. Albany-Troy
11. Cleveland 40. Memphis 83. Charleston, S. C.
I? Baltimore 41. Salt Lake City 86. Fresno, Calif.
14. Minneapolis 42. Oklahoma City 87. Fort Wayne
15. Hous ton 43. Omaha 88. Jackson, Miss.
20. Dallas 44. Honolulu 91. Mobile, Ala.
21. Seattle-Everett 46. Charlotte, N. C. 92. Norfolk, Va. area
22. Kansas City 47. Portland, Maine 93. Raleigh/Durham
23. San Diego 48. Albuquerque 94. Reading, Pa.
24. Atlanta 50. El Paso 95. Rockford, Ill.
25. Indianapolis 51. Las Vegas 96. Sacramento, Calif.
26; Miami 53. Bois e 99. Wichita
27. Denver 66. Grand Rapids 100. York, Pa.
AQCRs with decrease in regional personal income between. 50 and. 99
percent.
2. Chicago 39. Chattanooga 76. Scranton area
8. PittsQurgh 52. Fargo-Moorehead 77. Syracuse
9. St. Louis 55. Sioux City 82. Binghamton
16. Buffalo 61. Allentown area 84. Charleston, W. Va.
17. Milwaukee 63. Bakersfield, Calif. 85. Des Moines
18. Cincinnati 64. Davenport 90. Lancaster, Pa.
19. Louisville 68. Harrisburg, Pa. 97. South Bend, Ind.
28. New Orleans 72. Peoria, Ill. 98. Utica-Rome
36. Birmingham, Ala. 75. Saginaw /Bay City
AQCRs with decrease in regional personal income of more than 1. 0
percent.
37.
38.
45.
Toledo
Steubenville
Beaumont - Orang e
54.
70.
Billings
Knoxville, Tenn.
80.
89.
Youngstown- Warren
Johnstown, Pa.
88
-------
GeographO ~igure 4.6
M lC Dlst "b
easured b rl ution of E
y Change of R "conomic Eft
egLOnal P . ects
ersonal I
ncome
00
-.!)
-------
Table 4. 7
Economic Effects on Selected AQCRs Under the Two
Alternative Strategies as Measured by Five Key Variables
Strategy 1 (1975)
. .
. p.
... u 6 ...
Q) CI) ~ .~
~ H '+-<
C!) Q) Q) Q) C!) Q) 0 Q)
r-I :>
n! bl) bl) . bl) ~ bl) ~ bJ)
:> ~ ~ ~ ~ ~ ~ ~ ~ s:::
Seiected n! H ro n! n! ro
.,.c: .,.c: .,.c: .,.c: ...c:
AQCRs ~U ~l) bl)U bl)U ~U
C!) 0
~~ ~~ (:t:(~ (:t:(~ ~~
2 Chicago -.95 -16.11 -. 53 .61 -1..68
5 Detroit -.56 - 5. 93 -.42 .63 - 1 . 28
.'
8 Pittsburgh -1. 56 - 21. 90 -.84 . 80 -4.48
9 St. Louis -1. 04 -14.62 -.62 . 71 - 2. 11
16 Buffalo -1. 20 -16.05 -. 91 .87 -2.89
17 Milwaukee. -.54 -4.72 -. 58 .90 -1. 21
18 Cincinnati -.75 -9.92 -.62 .75 -1. 09
19 Louisville -.62 -7.87 -.64 . 81 -.75
28 New Orleans 3.20 75.47 -.82 . 53 4.92
36 Birmingham 1. 97 33.91 -.95 . 76 3.21
37 Toledo 1.82 24.59 1. 12 . 97 3. 15
43 Omaha -. 71 -7.04 -.44 . 74 f-1. 14
-
46 Charlotte -.52 - 2. 12 -.31 . 53 1. 47
47 Portland, Me. -.67 -6.12 -.38 . 56 1-1. 54
55 Sioux City, SD 2.50 96.79 -.54 .60 3. 56
61 Allentown Area -1. 30 11. 36 -.77 .82 4. 181
64 Davenport -.68 -4.97 -.56 .60 1. 321;
90
.
. Strategy 2 (1976)
. .
. P.
4-> U 6 ...
Q) CI) ~ .~
~ ' C!) H .....
r-I Q) :> Q) Q) Q) Q) 0 Q)
ro bl) bl) . bl) ~ bl) ~ bl)
:> ~ ~ s::: ~ ~ ::> ~ ~ ~
n! H n! n! ro n!
.,.c: .,.c: .,.c: .,.c: .,.c:
~U ~U bl)U bl)U ~U
Q) C!)
~~ ~~ (:t:(~ (:t:(~ ~~
-.69 - 11. 24 -.41 . 52 -1. 89
-.41 - 4. 16 -.34 . 55 -1.44
-1. 19 ""16.99 -.65 .60 -4.31
-.73 -9.93 -.47 .60 -2.28
-LOI -13.66 -.82 . 76 -2.22
-.45 - 3. 96 -.47 . 72 -. 97
-. 53 -6.35 -. 39 .54 -1.28
-.40 -4.46 -.46 .69 -1. 01
-2. 58 -61. 47 -.66 .42 -4.49
-1. 38 -23. 16 -.70 .64 -3. 91
-1. 39 -18.76 -.88 .81 -3.22
-.65 -7.80 -.36 . 54 -. 58
-.54 -2.74 -.27 .38 -.63
-'.62 -6.56 -. 31 .47 -.78
-2.08 -90.62 -.42 .43 -2.43
-1. 16 -10.37 -.64 .60 - 2. 74
-.65 -5.43 -.46 .40 -. 57
-------
Economic Effects on Selected AQCR' s (continued)
Selected
AQCR s
68 Harrisburg
70 Knoxville
""
72 Peoria, Ill.
75 Saginaw/
Bay City
77 Syracuse
Q)
~ Q)
ro 0.0
:> ~
cd
...c:
J:PU
~~
Strategy 1 (975)
" .
...
II)
Q) Q)
:> b.O
P P
H cd
...c:
J:PU
~~
.
u
P
1-1 Q)
.0.0
~ P
cd
...c:
b.OU
Q)
p:;~
-2.34 -40.31 -.88
-2.67 - 50.01-1. 14
-.80
-.74
-.77
82 Binghamton NY -. 56
" "
-5.36 -.56
-1. 33 -.57
-4.71 -.55
-4.99 -.50
83 Charleston, SC -2.18 -10.99 -.40
84 Charleston,
, :' W. Va.
85 Des Moines
-. 51
-1. 22
86 Fresno, Calif. -1. 92
90 Lancaster, Pa. ~.52
91 Mobile, Ala.
93 Raleigh/
Durham
94 Reading, Pa.
97 South Bend
98 Utica /R orne
100 York, Pa.
J
1. 21
-.77
-.61
-.56
-.60
-.50
-2.97 -.53
12.09 -.66
12.51 -.48
-5.37 -.51
11.86 -.42
-3.47 -.34
-5.92 -.45
-4.88 -.51
-5.58 -.57
-5.45 -.40
.
p.
S
Q) Q)
P b.O
~ P
ro
...c:
o.oU
Q)
p:;~
...
....
.....
o Q)
J.i b.O
p.. P
cd
....c:
J:PU
~~
.88" -4. 87
.97
.61
.88
.84
. 78
. 53
.52
.79
. 88
.61
.50
.92
.59
. 82
.94
. 52
-3.39
-1.6"11
- 2. 06
- 2. 56 J
-1.721
-4.43
-. 98
2.82
2.64
2.25
2.47
2. 18
1. 99
1. 40
1. 491
1. 061"
91
Strategy 2 (1976) -
. .
. u 0...
Q) '" S '"
II) p ....
::s Q) H "-'
.-I Q) Q) Q) Q) Q) 0 Q)
ro bO :> co . b.O P b.O J.i t1)
:> p ~ ~ ~ ~ :::> ~ ~ !::
cd H ro cd cd ro
...c: ...c: ...c: ...c: ...c:
J:PU J:PU b.OU b.OU J:PU
Q) Q)
~~ ~~ p:;~ p:;~ ~~
-2.15 -43.26 -.73 .63 -2.68
""
- 2. 37 -49.40 -.94 . 71 - 2. 1 7
-.73 -5. 15 -.47 .44 -.99
-.63 -1.15 -.44 .66 -1. 55
~.76 -6. 18 -.45 . 58 -1.19
-.53 -6.01 -.44 . 59 -.85
- 2. 11 -12.35 -.34 .38 -2.27
-.46 -2.64 -.48 .47 -.72
-1.01 -10.30 -.52 .60 -2.18
-1. 66 -12.66 -.38 .64 -1. 50
-.58 -7.13 .46 .44 -. 99
-1.18 -12.22 .37 . 39 -1. 43
-.81 -5.42 . 27 .62 -.87
-.62 -6.51 . 38 .41 -.94
-. 53 -5.57 -.41 . 58 -.68
-.54 -6. 13 .45 .66 -.86
-.46 -5.06 . 39 .40 -.66
-------
I
Economic Effects on Selected AQCR s (continued)
Strategy 1 (975)
. .
. p.
«> ..... u E .....
(J) s::: .,..
::1 .....
«> «> «> H «> «> «> 0 «>
.-i >
ro b/.) b/.) p; b/.) s::: b/.) H b/.)
:> s::: s::: s::: s::: ~ s::: ~ s:::
Se lected ro H ro ro ro ro
...£: ...£: .,.!:1 .,.!:1 ....c:
AQCRs ~U ~U b/.)U b/.)U ~U
Q) Q)
~~ ~~ p:;~ p:;~ ~~
38 -Steubenville -4.85 -7.78 -4.72 1.60 -8.42
Area 45 Beaumont,. Tex.-3. 48 -18.-23 -4.25 1. 01 -1. 53
152 .Jf'argo/ -
Moorehead -2.95 -17. 90 -.63 1. 10 -6.39
54 nillings -3.05 -18.15 -1.30 2.01 -4.61.
63 Bakersfield -7.13 -45.09 -.77 . 70 9.61
76 Scranton Area -1. 32 -13.78 -.92 1. 68 -7.43
I-
80 Youngstown/ -1.71 47.75 1. 24 1.06 4.71
Warren
89 Johnstown, Pa. -3.50 ~ 30.53 -1.53 1. 51 -8.76
92
.
,
- Strategy 2 (1976)
.
. .
. u p.
Q) "'" E "'"
(J) s::: .,..
::1 Q) H .....
.-i Q) Q) Q) Q) Q) 0 Q)
ro b/.) > b/.) p; b/.) s::: bO H b/.)
:> s::: s::: s::: s::: ~ s::: ~ s:::
ro H ro ro ro ro
.,.!:1 .,.!:1 ...£: .,.!:1 .,.!:1
.;:pU .;:pU b/.)U b/.)U .;:pU
Q) Q)
~ '" ~~ p:;~ p:;~ ~~
'-<~
-3.76 -3.94 4. ~ 5 1. 50 -11. 55
- 2. 81 -14.77 3.75 .80 -1. 39
:
-2.64 -24. 15 -.39 .66 -2.93
-2.86 -18.13 -1.09 1. 48 -2.77
5.88 -38.37 -.62 1. 33 -7.63
-1. 61 -27.07 -.85 1. 19 -2.87
-1. 49 -43.45 1. 01 .76 - 3.37
- 3. 17 -31.17 1.27 1. 05 -4.97
-------
5.0
VALIDATION OF THE OAP ECONOMIC MODEL:
REVISED VERSION
5. 1
Introduction
The essential stages of the development of a simulation model
may be represented as systems analysis, synthesis, verification,
validation and inference. >:< The previous sections have dealt with anal-
ysis, synthesis and inference.
This section deals with "validation"
and the next section deals with "verification" in the sense in which
Fishman and Kiviat>:<>:< segmented the problem of checking the reliability
of the model:
validation- -testing the agreement between the behavior of
the simulation model (1. e., the estimates) and the real
system (1. e., the actuals),
verification--ensuring that the model behaves in special
cas es as the experimenter /model- builder intends.
Section 5.2 discusses the methods used in this study for the
validation of the OAP Regional Economic Model in its revised form:
t-test, distribution over intervals of 1, 2, and 3 standard errors,
regression between estimates and actuals and the non-parametric U -test.
* Mihram, G. A., "Some Practical A spects of the Verification
and Validation of Simulation Models, " Operational Res earch Quarterly,
VoL 23, No.1, Mar ch 1972.
*>:< Fishman, G. S., and Kiviat, P. J., "Digital Computer Simula-
tion: Statistical Considerations, " Rand Corp. (RM-5387), Santa Monica,
Calif., 1967. (Also published as "The Statistics of Discrete-Event
Simulation, "Simulation, 10, page 185).
93
-------
"'
Section 5.3 presents the results with a brief discussion.
Then the
conclusions of validation are summarized in section 5.4.
5.2
Method
5.2.1
General
In accordance with Fishman and Kiviat, ~:' Van Horn~:'>:' defines
validation as lithe process of building an acceptable level of confidence
that an inference about a simulated process is a correct inference for
the actual process. II Mihram>:":'~:' has surveyed the literature on the
methods available for the validation of simulation models defined as
above.
From the literature, five methods have been'adopted as the
most suitable for the present validation.
By testing validity by five
different methods and noting how far their results converge or diverge,
greater confidence can be placed on the predictions from the model.
* Fishman, G. S., and Kiviat, P. J., op. cit.
>:0:' Van Horn, R., "Validation, II in liThe Design of Computer
Simulation Experiments, II (ed. T. H. Naylor), Duke Univers ity Pres s,
Durham, 1969, pp. 232-251.
*>:,>:, Mihram, G. A., op. cit., pp. 2,5- 27.
94
-------
1-
5.2.2 The Model
The main components of the OAP Regional Economic Model~:c
are 120 equations in the manufacturing sector to predict the six
variable s - -employment, value added, investme nt, profit, wage rate,
and capital stock- ":'for the manufactur ing sector of 19 two-digit SIC
detail industries and one aggregate of all 19 two digit-detail industries.
There are also 15 equations in the other sectors combining manufacturing
and non-rnanufacturing as pects for varaibles such as pers onal incorne,
governrnent expenditure, consumption, labor, employment (total),
unemployment, non-manufacturing em.ployment, electric consumption
of four kinds and taxes of four types.
The model can be considered to consist of equations of the general
form YE. .=f. (X..) where YE.. is the esti.mate of the actual dependent
1J J 1J 1J .
variable Y.. for Air Quality Control Regions i = 1, 2, ... , 91 for
1J
industrial sectors j = 1, 2, ... , 20, "all manufacturing industries II
together being included in the twenty.
* Please see Section 3.0 for details.
95
-------
5.2.3 Validation Tests
By definition of validation, validation consists in building an
acceptable level of confidence that YE.. are in agreement with Y...
1J 1J
It has been stated earlier that five different methods will be used
for this purpose.
The five different methods of comparison of YE
and Y.. used in this study are the following:
1J
the difference between the means of actuals Y and estimates YE; (2)
(1) applying t-test to detect
finding how many and which AQCRs have estimates off by 1, 2, or 3
standard errors of estimate; (3) doing regression of the form YE=a+bY;
(4) doing regression of the form YE=bY; .and (5) doing a distribution-
free non- parametr ic test to detect differences between YE and Y.
In the next pages, the different methods are discussed in detail.
The twenty manufacturing sectors and the aggregate sector are
taken up separately.
Hence, the subscript j is omitted in the following
dis cus s.ion.
5.2.4 The t-test.
The aim is to compare the means of the two sets of observations
of Y. and YE.. and test the null hypothesis that the means are not differ-
1 1
ent.
This can be done by calculating the t- statistic,
Y - YE
t =
J c:~ )
+(S~E )
n -1
2
96
-------
'I
where:
Y
= mean of Yi for i =1,2, ... , nl
YE = mean of YE. for i = 1, 2,
1
... , n2
sy
= standard deviation of Y.
1
sYE = standard deviation of YE i
It can be shown that t follows student's t-distribution with (nl + n2 - 2) .
degrees of freedom. ~~ Suppose the calculated t is less than the tabulated
value of t-distribution for (nl + n2 - 2) degrees of freedom at a probability
of 0.05.
Then the researcher can state that the means of Y. and YE.
1 I.
are not significantly different at accepted c,onfidence levels.
Thus, there is the desirable result of actuals and estimates being
equal on average if the computed t-statistic is smaller than approxi-
mately 1. 986.
(Note that this is not what is expected when usually t-
test is us ed to show that two groups are in fact differen9
5.2.5 Standard Error of Estimate
In forecasting time-series, it is desirable to have as few of the
estimates as possible, off by more than three standard errors of esti-
mate from the a-ctuals.
This is based on the normality assumptions of
regression.
The report shows in turn:
>,'< Snedecor, G. W., and W. G. Cochran, "Statistical Methods, II
Ames, Iowa, Iowa State University Press, 1968, pp. 100-103.
97
-------
How many AQCRs have estimates within one
standard error of estimate from actuals,
How many AQCR s have estimates within a wider
interval of two standard errors of estimate
from actuals, and
How many AQCR s have estimates within a
still wider interval of three standard errors
of estimate from actuals.
Then the report identifies the AQCR s which have more error of
estimate than each of these intervals.
For such AQCR s, the simulation
results may be qualified by judgment.
It may be noted that in a normal distribution, only two-thirds of
the points need be within one standard error, only 95 percent of the
points need be within two standard errors, and 99 percent fall within
three standard errors.
(This statement is to caution the reader against
any hasty conclusions on four or five AQCRs being off by more than two
standard errors. )
It is also worth noting that these percentage guidelines will not
apply if the distribution of actual data is far from the normal distribu-
tion.
98
-------
5.2.6 Regression YE. :: a + bY. + e.
ill
The validator wishes to check !he assumption of the USer of the
model that the change in Y - estimate equals the change in Y -actuals
for most AQCR s with a high probability.
To do this, a general linear
function is fitted between YE. and Y. as YE. :: a + bY. + e. by linear
. 1 1 1 1 1
2
squares regression. The R of this regression shows what proportion
of the variance in actuals is reflected in estimates.
. 2
A high R closer
to 1 is desirable.
If b is found to be significantly different from unity,
the as sumption of changes in YE. reflecting changes in Y. is in valid. >:<
1 1
To test the hypothesis that b is not different from unity, the
following procedure is adopted following J. Johnston. >:0:< The regression
YE. :: a + bY. + e. can be expressed in the standard matrix form,
ill
Y = X ~ + U, for convenience in following standard treatises on regres-
sian.
For the significance test, the assumption has to be made that the
residuals U. are normally and independently distributed with 0 mean
1
>:< Meier, R. C., W. T. Newell and H. L. Pazer, "Simulation in
Business and Economics, " Englewood Cliffs, New Jersey, Prentice-
Hall, 1969, pp. 294-295.
>:<>:< Johnston, J., "Econometric Methods, "McGraw-Hill, Inc.,
New York, 1963, pp. 115-18. The test could not be done in a
theoretically pure form. Hence the following discussion of assump-
tions.
99
-------
. 2
and constant vanance (1 over different AQCR s.
If this assumption
can be made, (} can be estimated by the least-squares estimate
,. - 1
~ = (XIX) X'Y.
With the same as sumptions, ~ is normally distr ibuted
2 -1 2
with variance (1 (XIX) where (1 is the constant variance assumed over
all the AQCRs for U.
2 . I' 2
(1 1S estimated by (1 = the residual sum of squares
n
2
L e.
. 1 1
1=
(n - k)
where k is the number of parameters, equal to 2 here, and e. = YE. -
1 1
a - bY..
1
The aim is to test the null hypothesis that B., (the jth element
J
of ~ ) is not different from ~ .'
J
It can be shown that
t
=
A
~ j
- ~ .
J
~ (12
. a..
JJ
has the t-distribution with n-k degress of freedom, where a.. is the
JJ
- 1
jth diagonal element in (XIX) . >:< If the hypothesized value ~. = 0,
J
the usual t-statistic printed in regression program outputs is obtained.
In trying to prove that b= 1 in the relation YE = a + bY + ei' ~ 2 is
taken as 1.
If the computed t is more than the critical value of t
* Johnston, J., op. cit., p. 118.
100
-------
~~.~..: '::" .'';:;:~'';;~..-...........-:-:..,- -,,----,,-~ '.
tabulated for the t-distribution at the accepted confidence level of 0.05,
(approximately 1. 986 at the degrees of freedom in this study), b has to
be taken as different from 1.
Then changes in estimates do not dupli-
cate changes in actua1s exactly.
The assumption of 'Ihomoscedasticity, II 1. e., of constant variance
(12 for the population of residuals; often cannot be made with the cross-
sectional data of the present study, especially in the case of AQCRs
with a large number of small AQCRs and a small number of large
AQCRs.
In such cases, the t-statistic for the difference of b from
unity calculated as above can be an overestimate leading to the wrong
inference that b is different from 1. Inferences from such a test can
be misleading to the extent the population residuals are heteroscedastic. >:'
>,'< Johnston, J., "Econometric Methods, "op. cit., pp. 207-11
has suggested a method to correct for heteroscedasticity if the form of
deviation from homoscedasticity is known for each AQCR. The correction
could not be done in this study since the form is unknown with present data.
In'the homoscedastic case, it was assumed that the residuals U have
a constant variance (12. Instead of that, in the heteroscedastic case, the
residual variance
E(UU') 2 0 0 2 1/>'1 0 0
= (11 . . = (I . .
2 0 1/>. 2 .
0 (I 0
2 '. .
o .
0 0 . 1 />..
n
o 0 2
.(1
n
If A is the diagonal matrix with ith element v>::.
(footnote continued on page 102)
it can be shown
101
-------
1\
The closer (I. is to (I.,
J J
i. e. ,
2 ~
the closer the R of the original
regression was to unity, the more is the t-test in validation regression
affected in reliability due to violations in assumptions.
This can lead
to the ironic conclusion that the best regressions by the usual criteria
of high R2 and significant regression coefficients are also the worst by
the validation test with t = (b-l) / standard error of b. ~~
(footnote continued from page 1 01)
"
that the least squares estimator (J is really
I' - 1
LJ = (XI,\2X) X'A2 Y,
val' (~) = 0"2 (X'A2 X)-l,
with
A is not known for the data in the present study. The homoscedastic
estimate ~ h = (X'X)-l X'Y is still an unbiased estimate, but Val' ( ~ h)=
0"2 (XI X) -1 is different from actual. (30hnston, op. cit., p. 209).
>:' The following-example illustrates the dilemma. Referring to
Table 3.3 in Section 3.3.1, in SICO (all n~anufacturing), the estimating
equation for investment has R2=0.952 with all regression coefficients
significant at 0.01 level. Thus, it is a satisfactory equation by the usual
criteria of regression. Referring to the Table 5.1 in Section 5.3 giving
the results of validation for SICO, for investment,
YEi = -0.953
(3.595)
+
1.044
(0.016)
Yi + e.
1
2
the numbers in parentheses being associated standard errors. The R
is 0.9861 showing that the variance in actuals accounts for 98.6 percent
of the variance in YE, i. e., alnlOst all the variance in estimates.
Since 1. 044 is an unbiased estimate of b, changes in YE. are on the
average only 4. 4 percent more than corres ponding changes in Y i' which
means the estimated changes are very close to actual. But the low biased
estimate of standard error of b equal to'O. 016 gives t for HO:b=l as
(1.044 - 1)/0.016 = 2.75, which is signficantat 0.05 level. This suggests
the misl.eading inference that YE is far different from Y since b is far
different from 1. On the other hand, in SIC 29, the estimc..ting equation
for investment has R2=0. 695 \vhich is not so satisfactory; and in validation
YE=a+bY, it shows up in the value of b being 0.7057, nearly 30 percent
off from 1. But the standard error of b is 0.27. This gives the mis-
leading inference that b is not different from 1, since t for HO: b= 1 is
(1-0.7057)/0.27=1. 08 which is not significant at .05 level.
102
-------
"
The heteroscedasticity of the residuals could not be corrected
without further assumptions which may need exploratory work into
the form of heteroscedasticity for justification.
Therefore a weaker
test was adopted as below.
In the regressions YE. = a + bY + e., if
1 1
b is numerically close to +1 and statistically significantly different
from 0 by the t- statistic t = b/ standard erro; of b, b is taken to be
not different from 1, since the estimate of b with homos cedastic
assumption is an unbiased estimate of the actual b. >;< Then a small
change in YE. equals the corresponding change in Y..
1 ,1
A still weaker
result would be that b is not numerically close to +1, but is positive and
significantly different from O.
Then the observer can say that a change
in YE estimates a part of the corresponding actual change cons istently.
If b is far different from one or b is not signficant at all, the estirnation
of change can be declared as poor.
5.2.7 Regression YE. = bY. + e.
111
If a is nearly zero really and the validator forces the regression
YE. = a + bY. + e. as in
1 1 . 1
1 . 2
putationa errors 1n R ,
5.2.6 on such data, there will be serious com-
b and its standard error.
Therefore, (or such
cases, it is desirable to fit a regression without intercept YE. = bY. + e..
1 . 1 1
If b is not significantly different from 1 in this case, YE. = Y..
1 1
The
estimates themselves are equal to actuals, a stronger result than the
previous one that changes in estimates reflect changes in actuals.
>:< Johnston, J., op. cit., p. 209.
103
-------
...
5.2.8 Non- Parametric Test- - .
(Mann- Whitne y U - Test)
The validation tests mentioned previously have the limitation
that they assume normal distributions for the population for the differ-
ent variables.
The t-test assumes in addition tile homogeneity of
variances of estimates and actuals. * The results of validation rnay
be prejudiced by thes e as sumptions.
Therefore it is des irable to
test the difference between estimates and actuals without making such
assumptions.
A non-parametric test wi~l serve this purpose.
,
The non-parametric test chosen was the Mann-Whitney U-test.
This is one of the most powerful of the non-parametric tests; it is a
most useful alternative to the paran1etric t-test when the researcher
wishes to avoid the assumptions of the t-test. >:<>:<
Suppose two independent samples have been drawn from two
populations, population A and population B.
The Mann- Whitney U -test
tests whether the two populations have different distributions.
>.'< Siegel, S., "Non-parametric Statistics for the Behavioral
Sciences, II McGraw-Hill, Inc., New York, 1956, p. 19.
>.'<>:< Siegel, S., op. cit., p. 116. Mihram, G. A., ("Practical
Aspects of Simulation Models, II Operational Research Quarterly, Vol. 23,
No.1, March 1972, pp. 26- 7) suggests the Mann- Whitney U - test,
Kolmogorov-Smirnov 2- sample test and the Wald- Wolfowitz Runs test
as non-parametric tests suitable for validation. The other tests
suggested are the chi- square test and the median test. Following the
comparison of these tests in Siegel, S., op. cit., pages 126, 136, and
144-45, the Mann-Whitney U-test was preferred as the best test of dif-
ferences in location and variability for the sample-sizes in this study.
104
-------
...
The hypotheses are as follows:
Null Hypothes is, HO:
A and B have the same distribution, i. e., the probability
that an observation from A is larger than an observation
from B is exactly one-half. If a is an observation from
population A and b is an observation from population B,
HO can be stated briefly as:
HO:
Probability (a >b) = 0.5
The alternative hypothesis, HI:
A and B have different distributions,
i. e. ,
HI:
Probability (a >b) :-I O. 5.
Calculation of U -Statistic*
Let nl be the number of cases in the smaller (A) of two indepen-
dent groups and n2 be the number of cases in the larger (B).
The obser-
vations from both groups are combined and the combination is ranked
in order of increasing size, being careful to retain a tag on each obser-
vation as to which sample it came from.
The U - statistic U is given by
the number of times that an observation in the sample with n2 cases
precedes an ob~ervation in the sample with nl cases.
This is practi-
cally computed by the formula
U = nl n2 + n1 (n1 + 1)/2 - R 1
* Siegel, S., pp. 116-127.
105
-------
r
I
...
where
R 1 = sum of the ranks assigned to the sample A, when the
whole combination is ranked I, 2, 3, ....
The' computed U is tested against values of the sampling distri-
bution of U under HO' given in published tables>''< for the larger sample
I:
I;
I
Ii
size up to 20.
For n2 greater than 20, the sampling distribution of U
approaches the normal distribution regardless of the distribution of
the samples.
For a given U, the equivalent normalized statistic Z
u
is given by
U - n 1 n2 /2
nl n2 (nl + n2 +1)
12
Z
u
=
If the computed Z is larger than the tabulated critical value (1. 96) of the
u
the normal distribution at a confidence level of O. 95, the null hypothes is
is rejected and the two samples, (estimates and actuals) are cons idered
to have different distributions.
A two-tailed test has been done since
the hypotheses in this study are as follows:
Null hypothesis:,
HO: Y estimates and Y actuals are not different in their
dis tr ibutions;
Alternative hypothesis:
HI: Y estimates are stochastically larger or smaller than
Y actuals.
>,'< Siegel, S., pp. 271-77.
106
-------
..
Only the normalized equivalent of the U-statistic is presented in the
results since most of the samples are larger than 20, and the regular
U-statistic critical values are not tabulated for n greater than 20.
2
5.2.9 Computer Program
A flow chart based on this section is given in Appendix B.
This served as the basis for the computer program in FORTRAN IV
developed for IBM 370/165.
The program took 20 to 50 seconds for
validation of estimates for one year, depending on the printout of
some or all data and some or all results for checking.
5.2. 10 Data Used for Validation
The model was es timated us ing data from 1958. to 1967.
There-
fore, to validate the model, it is desirable to compare the actuals and
estimates for a period other than that, preferably closer to 1972 when
the model is applied to policy decisions.
The only year outs ide 1958-
67 and closer to 1972 for which data was available was 1969.
Hence,
data for 1969 was used to validate the model in the manufacturing sector.
To compare the estimates and actuals for 1969, the estimates for
1969 have to be computed first.
For this, actual data from 1968 is
necessary since the investment and wage equations involve lagged
variables.
Unfortunately the variables for 1968 are available only by
states (not by AQCR) and only for all manufacturing (without 2-digit
industry detail).
Therefore, 1968 data by AQCR and 2-digit detail
was approximated as below.
107
-------
1--- --------------
A pproximation of 1968 Data
The problem is to get approximations to 1968 data without
prejudicing the validation by depending on either the 1958-67 data or
the model being validated.
The solution adopted was to project back-
wards from 1969 data assuming that the growth rate of any industry in
any AQCR from 1968 to 1969 was the same as the growth rate of the
aggregate manufacturing sector in the state or states in which the AQCR
lies, in the same period of 1968-1969,
i. e. ,
variable
i,
j, 1968 = variable i, j, 1969 x
variable
si,
variable
si,
1968
1969
for,
AQCR i, industry j, state s. in which AQCR i lies,
. 1
where, "variable" stands for en,ployment, wage bill, value added,
investm ent, and capital stock.
Missing Data Problems
In the manufacturing sector, if data are missing in any of the
unlagged independent variables in 1969 or lagged independent variables
in 1968, the particular dependent variable could not be estimated for
that AQCR and SIC.
This reduced the sample size to a low figure in
SIC 24, 29, and 31.
Then the question arises whether the validation
results are affected by the small sample size.
In such cases, the
validation results comparing estimates and actuals for 1967 were
computed in addition to 1969.
108
-------
Validation of first differences could not be done since actual
data for 1968 were not available.
In calculating the 1969 estimates,
the approximated 1968 data for independent variables play only a minor
role supporting the actual 1969 data.
Therefore, there was some
justification for using them.
But using the approximations as actual
independent variables for 1968 to estimate dependent variables for
1968 and to calculate first differences in actuals of dependent variables
would vitiate the very basis of validation, namely the comparison of
the real system with the estimated system.
The comparison would
now be between one estimate and another estimate.
Therefore, first
differences were not validated due to miss ing data in 1968.
In the non-manufacturing sector, the only year with data avail-
able for income, unemployment, etc., and taxes, was 1967.
Th ere-
fore, the only way is to compare estimates and actuals for 1967 for
which the parameters were estimated.
Thus, due to missing data, the "external validity" of the non-
manufacturing sector could not be checked; only its "internal validity"
could be checked.>:' For the manufacturing sector, both internal and
external validity were tested.
>:'Hermann, C., "Validation Problems in Games and Simulation, "
Behavioral Science, 12, page 216.
109
-------
5.3
Results and Di.scussion
5. 3. 1 Summary
Table 5. 1 shows a summary of the main results of validation for
the manufacturing sector (1969) and the other sectors (1967) for the
whole economy. Column 0 shows the SIC code of the industry considered,
and the symbol of the variable.
For 2-digit SIC detail, the symbols
mean the followi ng:
N = Employment (Manufacturing)
v = Value-added
I
= Investment
n = Profit
W = Wage rate
K = Capital stock
"Other sectors" variables are named directly in the table.
Column 1
gives the year whose actual data were compared with estimates for
validation of the econometric model.
This may be 1969 or 1967 or both.
Column 2 gives the non- parametric U - statistic in normalized form.
If it is greater than 1. 96, the actuals and estimates are different i.n their
distribution at a confidence level of 0.95.
Columns 3 to 5 can help to check how far the estimates from the
model are different from the actual on the average.
Column 3 gives
110
-------
...
the mean of the actual data of the variable considered in the year shown
in column 1 for the relevant industry.
By comparing the estimate mean
in column 4 with the actual mean in column 3, the observer can notice
if they are too different.
The t-statistic in column 5 is the difference
between actual mean and estimate mean, standardized by the standard
error of the difference.
By comparing the computed t-statistic with
values given in published tables of the t-distribution, an asterisk has
been marked wherever the estimate mean is different from the actual
mean.
If the es timatep are reasonably good, there should be only a
small number of asterisks.
In other words, a low t-test result shows
the model is working well; a high t-test result with an asterisk shows
that the model is not working well for the particular industry, variable
and year.
Columns 6 to 10 give a measure of different levels of divergence
of model estimates from the actual.
The standard error of estimate of
each regres sion equation is us ed as a device to measure the deficiency
in prediction.
This is given in column 6.
Column 7 shows the actual
number of observations for which this check was done.
(This may be
less than the total number of AQC'Rs since data were missing for some
in the validating year).
Column 8 gives the most stringent test of error
in prediction by the model.
This is the number of AQCRs for which
estimates are accurate within one standard error.
If this count is a
111
-------
...
high proportion of the total number of AQCRs, obviously the model is
excellent in estimation.
Some AQCRs did not fall within this interval.
To find whether
all these were far wrong or only some of them were.. the interval is
widened.
A count is made as to how many AQCRs are accurate within
two standard errors.
The results appear in column 9.
If column 9
includes most of the AQCRs, the model is good.
Column 10 extends
the idea to an interval of three standard errors.
A regression of the form YE = a + b (Y actual) was estimated.
If the model is good, the t-statistic of b in column 11 must be signifi-
cant (larger than the critical t around 1. 7).
Also, the value of b in
column 12 must be near one.
The R2 of this regression in column 13
shows the proportion of the variance in YE explained by the variance
in Y.
This should be as close to one as possible.
Columns 14 to 16
repeat tb, b, R2 fo'r the regression YE = bY without intercept.
Table 5.2 shows the AQCRs whose estimates are off by three
standard errors of estimate for five selected variables.
Now the results are discussed for the different sectors.
5.3.2 Manufacturing Sector
Table 5.1 shows the validation results for the aggregate sector.
The first section is the manufacturing aspect for the year 1969.
For
all six variables (employment, value-added, investment, gross profit,
112
-------
L- .-
Tabb 5. 1
Summary of V?-lidati01:' :(~esults t 1969 and 1967
I
['
o
1
2 3 4 5 6 17 8 9 J;"
Norm-J f Stand. 'No. No. of ObV3,
,.
alized, - Act".. ~ ~ Est. Er ror of with in Inten
U-sta-i M.e,',i ~1\jean t of Est Ob fo. I" I'
tistie ~ Y f. Ye S~at. S . n' Y-tls Y:t2~-'i-' --
1.85 In. t-208.6 .7923.8 5933 49
1.83 2271. f2811.9 .90 236.8 59 27 43
. 30 144., 1 49. 8 . 1 7 3 1. 0 .59 51 57
.12 ,1074. ~-: ; 1090. 4 .06 202.5 59 51 56
1.09! 6.::, 6.81.19 .3 59 38 56
.15 1187. '.: 1774.3 .03 31. 5 59 38 54
S'J
57
Variables
Mfg. Ernployrncnt NM
Mfg. Value-added VM
Mfg. Investment 1M
Mfg. Gross Profit M
Mfg. Wage Ratc '\VM
l\1fg. Capital 1<1\0'1
Year
1969
1969
1969
1969
1969
1969
59
57
Mfg. Ernployment N:rvf 1967 1. 08 181.0 193.9 .30 23.8 56 41 53 56
Mfg. 'Value-c~dc1ed VM 1967 1. 00 1552.4 1682. 1 .35 236.8 89 67 ~ 80 88
Mfg. Investment 11\1 1967 .05 f 161..6 160. 1 . 03 31. 0 56 45 54 5~
Mfg. Gross Pr of iL M 1967 . 15 ! 736.E: 745.1 .05 202.5 89 80 86 8',
Mfg. Wage Rate 'W:lV1 1967 .36 6., ~:' 6.5 .45 . 3 56 39 55 56
Mfg. Capital 1<1\1 1967 .73 1484. 1 1602.6 .37 327.3 56 45 50 54
11967
Ree10nal person:.1.l ineOl1.1C Y N.A. 4416.9 4478.1 .06 469. 5 91 77 86 87
Local govt. expe oditur e G 1967 " 375.2 375.2 . 00 3"5. 05 91 78 85 88
Regional consurnption C 1967 " 2.844.7 j 2846. 7 .00 411.6 91 76 81 91
R egiona 1 total ':~mpl. 1,T~ 119671 11 458.8 .05 83.07' 91 I 75 86 89
'.i 1 453.4
Regionallabol' [cree L 11967 II 475~~ I 469. 7 .05 84.23 91 76 86 88
Regional unern p1. rate U 1967 " . 0.3 ,..) i' 0323 .97 .0105 91 67 85 88
- .. mployment of nOI1-' I
. nianufaetu"ring N .11967 " 337.E 339.0 . 01 79.26 9J. 76 85 88
Total olee. eonsumptl0,i QT 11967
II 628.7 694.9 .43 443.5 91 82 86 88
Residential UGe QC 1967 11 173.9 139.2 1. 24 95.6 91 77 87 88
Manufacturing use QM 1967 11 145~ 0 334.4 3.25>: 418.5 91 80 86 88
Other industrial use Q 1967 " 308..3 308.3 1. 36 211. 5 91 75 84 90
c
Taxes--
Total local revenue T 1967 . 22 370. 3. 321.4 .41 235.0. 82 69 77 80
l-'ropcrt.y tax T p 1967 .66 148.2 158. 1 . 21 76.6 82 70 76 79
Other taxes To 1967 2. 82~:: 32.5 I '30.8 .11 51. 0 82 74 79 80
Federal and state aid T A 1967 .65 189. 5 I 132.5 .92 257.5 82 62 78 81
I
113
-------
Table 5,.1 (continued)
Summary of Validation ~esults, '1969 and 1967
o 1 ."- 11 12 13 ] 4 I 15 I 16 J
-
YE = a: + bY YE = bY
.
tb b RZ, ~b' b RZ
,
Variabl es Year
M.fg. Employment NM 1969 133.4 1.18 0.99 165.4 1.19 . 99
Mfg. Value-added VM 1969 107. ~ 1. 26 0.99 136.8 1. 25 . 99
Mfg. Investment 1M 1969 64~ 1 1. 04 ~ 99 8:;>.2 1. 04 .99
Mfg. Gross Profit M 19()9 57.5 1. 06 .98 72. 9 1. 04 . 98
Mfg. V{age Hate "\V]\'1 1969 32'.9 .80 .95 208.8 1. 02 .87
Mfg. Capital KM 1969 270.4 .99 0.99 348.0. .99 . 99
Mfg. Employment NM 1967 100.1 1. 00 .99 n. a. n. a. n. a.
Mfg. Value-added V.1\-1 1967 12 O. 2 1. 03 . 99 " " "
. -
Mfg. Invef;tInent 11"1 1967 43.7 .99 .97 II " II
Mfg. Gross Profit 1967 71.9 1. 06 .98 " II "
I\'J
Mfg. Wage Hate '\'IM 1967 19.8 .84 .88 II II "
M,fg. Capital EM 1967 50. 7 1. 12 .98 II " "
-.
Regional personCll income Y 1961' 152. 0 . 99 0.99 " II "
Local govt. c;.:pe neli t Ul" e G 11967! 196.2 1. 00 0.99 II " II
Hegiona1 consumplion C 19671 105.4 .99 . 99 " II I II
I
Region(~l total empL N~ ]967 86.0 . 95 . 99 " '" II
. .L I
Hegional labor force L 1967 88.5 .95 .99 II " II
,Regional nnernpl. rate U 1967 20. 0 1.52 .82 " i II II
I Enlployment of non-
m'an'ufacturing N 1967 63.2 .98 . 98 II II "
Total clcc. consumption 01' 1967 27.8 1.32 .90 II " "
Residenlial use 0c 1967 22.0 .94 .84 " " II
Manufacturing u.se QM 1967 15.5 2.37 . 73 II II "
Other industrial use Q 1967 20.5 ~ 81 .82 II " "
Taxes--
Total local revenue T 1967 29.9 .89 .92 33. 0 .89 .92
Property tax T p 1967 35. 0 .98 .94 39.6 1. 00 . 94
lather taxes To 1967 16.8 . 73 . 78 17.9 : 75 . 77
r - -._. . .. - ...
i Federal and state aid TA 1967 12. 1 ' .81 .64 l 13. 1 . 79 . 64
,
n. a. = not available.
11 J:t
-------
j-
TABLE 5.2
AQCRS Whose Estimates Are Off by 3 or More Standard Errors of
Estimate for Five Selected Variables are Listed Below>:'
Variable
AQCR s Off by 3 or mOJ;e standard errors.
of estimate
Manufacturing
Value-added (69)
1 New York
2 Chicago
3 Los Angeles
4 Philadelphia
5 Detroit
7 Boston
8 Pittsburgh
9 St. Louis
11 Cleveland
20 Dallas
Manufacturing
Gross Profit (69)
1 New York
5 Detroit
Manufacturing
In vestment (69)
NONE
Manufacturing
Wage rate (69)
NONE
Manufacturing
Capital Stock (69)
1 New York
15 Houston.
Regional personal
income (67)
19 Louisville, Ky.
Regional
unemployment (67)
90 Lancaster, Pa.
>:'It appears that estimates of some large AQCRs tends to fall off by
three standard errors of estimates which indicates the existence of
a strong heteroskedasticity of the model. . See pp. 100-103.
115
-------
wage rate and capital stock), the means of actual and estimate are
quite close.
All the t-statistics are lower than the tabulated value of
1. 986 for 110 (=2 x 56 - 2) degrees of freedom at a confidence level of
0.95.
Therefore, none of the variables in the aggregate manufacturing
sector has the model estimates different from the actual on the average.
All the normalized U-statistics are less than 1. 96.
This shows that
the distributions of estimates are not different from that of the actuals.
Thus, the model is good in predicting the six variables regarding loca-
tion and validity.
This can be stated with 95 percent confidence.
Next, the proportion of observations falling within one, two and
three standal.d errors is considered.
A standard to compare is the
normal distribution which has more than two-thirds of the observations
within one standard error, nearly 95 percent within two standard errors
and nearly 99 percent within three standard errors.
In Table 5. I, the
columns 8, 9 and 10 giving the number of observations within intervals
of 1, 2 and 3 standard errors show the results to be good for the first
six variables for the manufacturing sector for 1969.
The results of the regression YE = a + bY and YE = bY in Table
5. 1 (continued) show that generally the coefficient b is nearly equal to
one numerically and is significant at 0.95 confidence level by the t-
statistic being greater than the tabulated t-statistic (1. 673 at 54 degrees
of freedom and 1.662 at 87 degrees of freedom).
This shows that
116
-------
"
changes in the actual V'a1!'l;;'.L~.!] are predicted well by the changes in
the estimates used by ffue:s~',"<':cl.
Appendix C
gives i ;~. . iled results by 2-digit detail for manufac-
turing (1969).
In Table 5.1, below lhe results of external validity tests using
1969 data, the results :(')f l;;'..fl1l.'..:cnal validity tests using 1967 data are
presented.
These res'lilts '.upport the conclusions of the external va-
lidity tests.
Appendix D
gives the internal validity results by 2-digit detail
for 1967 for selected industries, viz., 23, 29, 31, where the external
validity results are cnreliah}e due to sample size being too small
because of missing d
-------
...
5. 3. 3 Other Sectors
The internal validity results (1967) for the national economy in
variables like personal income, unemployment, consumption, electric
power consumption and taxes are summarized in Table 5. 1.a and band
Appendix E.
External validity tests could not be done due to lack of
data in other years.
Most of the results show validity except unemploy-
ment, electric consumption in manufacturing and other taxes.
Changes in unemployment rate are overestimated since b = 1. 52
and significant.
But t-test shows that still the estimate of unemploy-
ment rate is not significantly different from the actual.
(The t-statistic
0.97 is much less than the critical value of 1.96 at 180 degrees of
freedom).
In the case of electric consumption for Hlanufacturing, there is
overestimation of change and the estimate is significantly different by
t-test from the actual.
But such an error is unavoidable since its
regression parameters were not based on actual data but on estimated
data from other variables.
Other taxes fail the U - test, but are not different on the average
in estimates and actuals by t-test.
118
-------
Variables like wage rate and unemployment perform well in the
usual test of nearly 95 percent of the observations falling within two
standard errors, although their distribution is flatter than the normal.
5.4
A Comparison of the OAP Model and the
St. Louis Model for the St. Louis Region
The previous section provided a full-scale evaluation of the
model.
This section presents a comparison of the actual values of a
key economic variable for the St. Louis AQCR and the estimates as
simulated through the OA P Regional Econometric Model and the St.
Louis Regional Model. ~:~
The St. Louis Regional Model is a time series econometric
model estimated for St. Louis;~ while the OAP Regional Model has
been estimated with cross -section data pooled over ten years for 91
AQ CR s.
A comparison of the simulations through the two models
should throw some light on the performance ~ time of the OAP
Regional Econometric Model for a specific AQCR.
Manufacturing product {value-added} by aggregate manufacturing
sector and each of 2-digit SIC sectors from 1958 to 1967 as estimated
':'For details of the St. Louis Regional Model, see CONSAD Re-
search Corporation, An Economic l\10del System for the Assessment
of Air Pollution Abatement, Appendix A: A Model to Assess the Eco-
nomic Effects of Air Pollution Abatement in the St. Louis AQCR, pre-
pared for the Environmental Protection Agency, May 15, 1971.
119
-------
by the two models are compared with the actuals in Figure 5. 1.
Table 5.3 compares these two forecasts with the actuals for all man-
ufacturing products by each year.
It appears that both models provide
a good forecast of the aggregate manufacturing sector.
However, the
performance of the two models is more variable for the 2 -digit SIC
sectors.
5.5
Conclusion
Different validation tests of the revised OAF Regional Economic
Model converge to the following conclusion:
the model estimates
almost all variables with satisfactory accuracy in almost all industrial
sectors even in a time period two years after the estimation period.
This is all the more interesting since the model parameter estimation
was limited by lack of full data at the time of estimation in many cases.
The model seems to have some difficulty in predicting the cyclical
downswing in value added and employment in 1969.
This suggests one
direction for further study: the inclusion of cyclical capacity utiliza-
tion factors or a national cyclical economic indicator like GNP as an
exogenous variable in the estimation and simulation of the model.
The
performance of the model may be improved by this extension.
120
-------
u ZOO'
I 121 L
~9' bO 1,4 ' ~7 59 . b ' d ' /.. ,~ ' :7
1958 0' OZ oJ ,~ .~ lq~ti 6\ ~) "
(mUllonl)
450
Figure 5.1
Simulation of Manufacturing Product
(Value-Added) in St. Louis Region,
St. loulo /I'clO~ 19 5 8 19 6 7
AU ma.nutact\lrins Product (Vah.l~ }'dded) -
/.
/
'"
400
/
/
S. L.R. F'or~cast /'
~/A
/;'//
/."/.
.4.:
,#
OAP Foree-Aftt .~
..._~.
- -,:- ,,:%' Actual
350
)00
150
h"'"
/
zoo
1958
60
.
0)
66
67
62
04
6'5
0'
59
(mUlion.)-
450
H5
/
/."-" -::--...:.- 7
-------
Figure 5. 1 (cQntinued)
J.. j
" ,I,
(milJlon.)
(,"111100'\
.300 '
St. tout. ReRIon
Manufac:turlng prnnuct (Value .Adried)
~rslc H
!
/,
51. I..oull H.er,ion
Manu{aclurlnr/. product (V.tue Added) of 51G 34
.~1000
100
,"
,.,.
/
650
/
..----
--
/
/
,.,.
----~
/-
OJ'\P ForccaU / /' .
~,.~~~.....,
- - - :/' A
- ~ Actual.
'\'
./
. Z~9
,.,.
'"
/
zoo
550
S. L. R. For('casl
'"
,.,.
/
/ ~ QA P Forecnst
ISO
S. J.... R. Forecast
/
--.,,' """
~ /'
....-- ~ """""',-/
----
......,
400
59
60
~l
(/'1
(,)
~)
05
h6
'(,7
59
6'0
/,)
62
i'J
64
6\
66
67
1958
1958
St. Toui. ~eRion
".tanuhcturing product (Value J\ddrd) or ~ic 3q
.'
(mI1Hons)
lZ!o
St. I ouis '~('5:ion
'hnur.ctutbr. pn'ldt:C't p"aluc Add~d) o[ ,CJC 35
75
0." P Ie I'.~':i\st
(n,11110n8)
~OO ,
Z50
/
/
/
/
//
"'/
~.
,,- ~-.
OAP Forf'COt.!iot /~/./
5.1... R. Furt:'cast ~ - ::;."""':
?~~tU'1
100
"\!OO
50
Actual
--
- --
- -
....-
,15'0 ,.
Z~
59
.
'60
,
61
1958
19~
6l
,
6J
'64
i.5
6"
, 67
5~
GO
/,)
(,I.:
tJ
14 .
is
I-t
'b7
1SuJ1110n.'
Zso
St. Louts H~gion I
ZlS Manu(aclurin;: product (Value Added) of SiC 36 I
I
I
,.lOO .,.,
.,.,
I
OA P For~cast /
,I~ --..l.- I
-- ---/
.,.,- --
/'
S. L. R. Fort-cast -"
'UO , - .-'
-,-'-'-'-'~
U!.
I S~ to ~I 6~
ius ,) t~ 6S 6& '61 122
" .
-------
TAB LE 5. 3
Simulation of Manufacturing Product
(Value Added) of St. Louis AQCR
"'?
All Manufa.cturing Product SIC 20
Actual OAP SLR OAP SLR
Year Forecast Forecast Year Actual Forecast Forecast
1958 2382.0 2Lf17.1 2459.,~ 1958 352.6 362.8 3S7.6
1459 2673.'1 2631.1 2631.d 1959 360.0 369.0 373.0
19<:'0 2699.S 2733.7 2684.4 1960 371.7 371 .2 378.1
1 ':161 267Li.6 2768.lJ 2699.5 1 C) 6 1 366.5 386.5 383.~~,
1962 2B3S.9 28U5.1 2928.3 1962 371.5 39S.7 329.1'
1963 3D26.3 3061.0 3073.5 1963 377.2 39 'i . 2 ,399.6
1 (/6 4 3227.9 32Lf8.5 3271.1 1 "64 'i23.7 LfO'i.5 414.9
1 r)6:) 3'~21..2 )'187.5 3552.2 196:> 399.7 '115.0 419.0
1 C) 6 6 379'i.O 3791.3 40 <> 4.3 1966 Lf150l '125.7 444.8
1967 38ULf.8 'i086.3 1967 4'i8.8 '1'13 . 1
SIC 26 SIC 7..7
OAP SLR Actual OAP SLR
Year
Year Actual Forecast Forecast Forecast Forecast
----~
1.958 "65.6 7 1 . 7 6 t. . It 1958 1 1 'i . 'i 1'22.7 112.0
1459 66.7 72.7 66.:> 1959 126.0 122.8 12l.~)
lenO bU.7 7'1.8 6 7 . ~~ 1960 135.9 120.7 L2,1.1
1 C) 6 1 6'i.7 -, 6.2 (;. 8. {t, 1 ')61 132.1 129.5 11.9.9
1962 69.3 80.2 70.3 1962 1 3 'i . 9 139.9 1 'I', .,
-IU."
1963 6 'i . 1 77.0 70,,7 1963 137.8 lLf9.8 13'.f.6
1 "64 7 1 .7 80.9 73.2 1 " 6 It l'i5.Lf 163.5 151.6
196:> 73.n 83.6 7501. 196:.1 ISO.A 16R.Li 162.2
1966 7 1 . J 8S.0 81.6 1966 1517 . 9 173 . 8 l04.~
1967 77. Ii 87.U 1967 .169.2 179.3
SIC 32 SIC 33
OAP SLR OAP SLR
Year Actual Forecast Year Actual Forecast Forecast
Forecast
1.950 liS. 9 1 1 'i . 3' 1 0 () 0 b 1958 205.2 206.9: 18'5.2
1959 12 S. 5 122 . 9 123.3 1959 233.3 233.0 ?26.b
1960 130.0 12/~.3 120.d' 1960 199.2 235.0 232.11
t C)6 1 127 . 1 12Lf.(J 110.91 11)61 22S.1 2'i2.3 206.9
1962 129.8 125.7 123.01 1962 238.9 261 .9 227.8
1963 122.6 J2'i.S 129. j! 1963 270.8 300.8 245.3
1 " 6 It 126.8 126.2 136. T 1 "64 3'01 .8 33'i.0 2'13.2
196:> 13S.'i lLfU.'1 143.7 196:> 322."1 369.6 341.9
1966 1"1':>.5 1'i8.7 149.9 1<;66 'i07.'i Lf21.Lf 38B.3
1967 1 Lf I 03 IS'i.U 1967 3'i8.9 1./22.5
123
-------
TABLE 5.3 (continued)
"
SIC 34 SIC 35
Actual OAP SLR Act ua 1 OAP SLR
Year Forecast Forecast Year Forecast Forecast
1958 I 7 I .6 159.2 192.6 1958 J ,~ 9 . 2 IS 'J . 5 1')4.2
1459 I a I.! 166 . I 175.7 1959 168.} 166.0 169.7
19t-O 177 . 3 1 7 ,~ . B 176.1 19t-O 177.U 173.2 170.::>
t 1:161 182.8 18'J.'~ 176.1 1 I) 6 1 161 .5 172. U 1 70.0
1962 18101 192.5 186.4 1962 182.5 183.2 182.4
1963 192.0 203.2 192.2 1963 J as.1f 19'i.6 183.2
1 (/ 6 it 200.1 2 I 5.2 2 0 6 . It lC164 2UO.8 2 1 ,~ . 5 205.8
196:5 225.5 236.7 224.7 196:> 217.0 22'J.7, 223.a
1 <) 6 6 2'i3.1 2'i9.9 248.2 1966 2'i1.2 .255.1 250.4
1967 265.0 277.9 1967 25'i.6 '298.1
STC 36 SIC 37
OJ\p SLR Actual OAP SLR
Year
Year Actual Forecast Forecast Forecast Forecast
1958 1 ;.2 . 6 1958 'iOs.o ''J12.7 403.2
136.6 15~;.5 1459 'i95.2 If '16. I 5U7.2
1959 150.5 I 6 3 . 1 1 ;,9 . 3 l 136301 751 . 1 835.3
196:> 161.6 1 'I" . 5
1966 992.0 8 5 9 " ~ .072.1.
1966 1 7 1 .4 ,202.1 1~16.!
1967 2 I 3 . 3 2J'~.2 1967 92~;.5 927.0
SIC 39
OAP SLR
Year Actual Forecast Forecast>:~
1958 8'~ . 0 79. 7'
1959 10(J.l 8'1.5
19t-O 102 . I 92.7
11)6 1 10£3.2 92. 1
1962 11(;.9 90.S
1963 33.5 50.'1
lC164 3S.2 51f.S
1')6:> 35.3 5 I . 1
1966 3 I . If 'is.O
1967 3(\.4 S I . Lf
),~
Data not available in this model.
. - '_.._-~ -
124
-------
6.0
ECONOMIC-ENVIRONMENTAL INTERACTION:
A CASE STUDY OF PHILADELPHIA
6. 1
A ir Pollution and Public Policy
. Effects upon those external to, or not associated with, consurnp-
tion or production activities--like blowing soot over one's neighbors--
are described as externalities, spillovers of simple external effects.
Externalities explain to a large degree why reliance on autonornous
control mechanisms of the market leads to results less than desirable.
They are, in a sense, the heart of the air pollution problem.
Technological externalities, which are more or less direct effects,
but not priced, that one decision unit imposes on another, are an inherent
and normal part of the production and consumption process in highly
developed economies.
They become progressively more important
over time as population and level of economic activity increase.
They
cannot be realistically treated as somewhat occasional anomalies in
an otherwise smoothly working economic system.
An approach to compensate the parties adversely affected is not
feasible in the case of the technological externality of air pollution,
which has the nature of a public "bad." Damages caused by air pollu-
tion, in general, are incident in varying degrees on individuals and
property such that compensation schemes may have to be infeasibly
125
-------
complex.
Further, given the growing concept of dealing with air pol-
lution problems as a management of common property resources,
private exchange cannot be expected to assign accurate relative values
to alternative uses of the air resource. >:, Consequently, it becomes a
function of the government to adjust the framework for voluntary eco-
nomic exchanges so as to lead to efficient resource allocation.
A whole series of proposals have been advanced to deal with
problems as sociated with setting standards and stimulating the pro-
gress toward improved air quality.
None of these proposals, at least
in the current stage of our knowledge, appea'rs to be perfect for the
pu'rpose at hand.
Neither does it appear that anyone of this imperfect
lot clearly dominates.
The existence of systematic interdependencies between economic
and environmental systems imply that any piecemeal remedies sug-
gested from a normative approach may pose serious problems. >:<
Further, the emission standards, fuel regulations, and financial in-
centive structure that may make up a typical pollution control strategy
may be so diverse that normative models may be complex and risky.
>:'Kneese, A. V., "The Environmental Pollution: Economics and
Policy, II American Economic Review, £.1, 1971, pp. 153 -166.
>:o:'Solow, R. M., "The Economist's Approach to Pollution and its
Control," Science, 173, 1971, p. 499.
126
-------
Instead, information based on system-wide analysis of abate-
ment strategies could be generated from positivist models.
Such
models will generate empirical information to a typical policy plan-
ner's question: If abatement strategy A is implemented, what are
the likely consequences in terms of:
Costs of control to various industries?
Levels of air quality to be achieved?
Levels of damages?
Impacts on regional economy?
This chapter represents one such attempt at integrating three
types of models that can be simulated to provide such information.
A case study of Philadelphia to demonstrate the interaction between
economic and environmental systems is provided.
These three models are:
The Direct Cost of Implementation Model
(DCIM), >:<
Property damage functions by Anderson
and Crocker,** and
The revised OAP Regional Econometric
Model.
>::o:
-------
"
The interactions between the models are presented in Figure 6. 1.
These three models are combined together to provide a case study of
economic-environmental effects in the Philadelphia AQCR.
Section 6.2 describes the procedures used to estimate emission
and air quality levels before control and emission and air quality
levels after the implementation of a control strategy predicated on
the implications of the Federal Register of August 14, 1971.
Section
6.3 discusses how an objective measure of benefits due to air pollution
control, namely property value, is expected to improve in Philadelphia
due to air pollution control with the interesting second-order effects
of increased tax revenues.
Section 6.4 studies the effects of air pol-
lution control on the regional economy of the Philadelphia AQCR.
6.2
. Improvement in Emissions and
Air Quality Due to Control
The costs, emis sions and air quality estimates presented here
were obtained from simulations on the Direct Cost of Implementation
Model (DCIM);:' 'developed by CONSAD.
DCIM is an eclectic assembly
and refinement of three extant models il).to a cost-effecti venes s model
>:'See CONSAD Research Corporation, Vol. I: Executive Summary;
Vol. II: The Structure of DCIM, NEFM and REFM; Vol. III: NEFM
and REFM Results; and Vol. IV: Users I Manual, prepared for the
Environmental Protection Agency, February, 1972.
128
-------
r---
I Em
I E
I
I
I
I
I
L
Figure 6.1
Interactions of DCIM, Anderson-Grocker Model
and OAP Model: A Flow Chart
u
I ,
Waste Generation Waste Disposal Cost Model
and Distribution .. and Control . Cost DCIM
. Emission . Standards -~ estimation
. Air quality . Control
technology
i~ s7~f~tors~ Property damage
m1S Slons per I function Anderson-
nit of output I . Property value Crocker
I Model
I
I
'-r----- - ---I
,
Regional Economy Regional Regional
Production Economic Impact Economic Impact OAP
-
. Income (first l'ound) (second round) Model
. Employment Cost impact . Cost-benefit
impact
129
--~,_._---.'~,-.,.---~_..,.., -;'"- ...,----
-------
of air pollution control.
Essentially, it comprises the Control Cost
segment of the Implementation Planning Program':' developed by TRW
Systems Group, the SORTCON and INTCODE segments of the Ernst
and Ernst cost-effectiveness model':":' and a SORTDEV routine with
selected modification relevant to certain optimizing strateg ies.
Figure 6.2 is a macro flow chart of the various component programs
of DCIM.
The input data for the model, cons isting of the four categories
below, are of the type generally collected and used by air pollution
control authorities:
Emission Source Information,
Regional Information,
Control Device Information, and
Meteorological Information.
DCIM was simulated on data obtained for the New York and Philadelphia
AQCRs.
Emission source information was obtained from EPA in the
form of a Source File.
This file consists of a detailed history of all
sources within the AQCR along with their emiss ion rates, rate capaci-
ties, operating time, etc.
Regional information cons ists of fuel costs
>:'TRW Systems Group, Air Quality Implementation Planning Pro-
grarn, Vols. I and II, prepared for the Environmental Protection
Agency, National Air Pollution Control Administration, November 1970.
>:o:'Ernst and Ernst, Application of Cost-Effectiveness Analysis to
Air Pollution Control, prepared for the Department of Health, Educa-
tion and Welfare, Consumer Health Service, Consumer Protection and
Environmental Health Service, April, 1970.
130
-------
Figure 6. 2
Structure of DCIM
...
Emis sion
Source In-
formation
Regional
Information
SORTDEV
Control
Cost
Program
Control
Device In-
formation
INT CODE
SORTCON
131
-------
L
1\
and utility costs and was collected by CONSAD staff.
information is pre-set in the Control Cost program.
The control device
Meteorological
information was obtained from EPA as the Source Contribution File.
This file is the output of the A ir Pollution Concentration Segme nt~:c de-
veloped by TRW.
It lists annual average air quality levels before con-
trol at selected receptor locations in the AQCR.
Fo'r example, in the
Philadelphia AQCR there are 270 such receptor locations.
The file is
really a matrix which details the number of sources and the amount of
pollutants contributed by each to every receptor.
One of the strategies simulated for the Philadelphia AQCR was the
least cost strategy which met emis s ion standards laid down by the 312 (a)
amendment to the CleaD Air Act of 1970.
The standards laid down by the Clean Air Act Amendment are as
follows:
SIC Code
Proce s s Code
Specified EMRAT
(l b. Ih r. )
. 6
.4104.10:-4
(RATCAP)
+ . 6004
.19
.5 (Max. Process
Rate)
4 (Max. Process
Rate)
3. 59 (MPR) 0.62
17.31 (MPR) 0.16
Any
xo
xo
2819
XO
02
4953
01-05
Otherwis e
contin'u'ea.
~:cIbid .
132
Rated Cap.
(MBTU Ihr. )
< 10
10 < RATCAP < 104
> 104
Max. Proc. Rate
< 30 tons Ihr.
> 30 tons Ihr.
-------
Any
2819
Otherwise
XO
02
1.46 (RATCAP)
6.5 (MPR)
10% of sulfur input
to plant
Most of these standards are functions of the rated capacity of a
. plant and the maximum process rate that the plant can achieve.
The
rated capacity and maximum proces s rate are input variables and are
a part of the emission source information input to the control cost seg-
. . .
ment.
For every source en1is sion standards are calculated based on
the above table.
-
Four distinct possibilities can occur -- both 502 and
particulate standards are met, both are not met or either 502 or
particulate is met and the other is not.
In the first cas e, the model
will pick the device with the least total annual cost.
In the other three
cases, the model will pick the device that comes closest to meeting the
standards.
This will be done on the bas is of total emis s ions (both 502
and particulate) being compared with total emissions required by the'
standards.
It must be noted that the total annualized costs generated
by DCIM consist of. operating and maintenance costs and investment
costs and are predicated upon the double declining method of deprec ia-
tion over the estimated life of the control device.
Once appropriate devices have been selected for each source
the model then calculates the resultant reduction in ernissions, based
133
-------
"
on reduction efficiencies of each device, and the resultant air quality
at each receptor.
Since the outputs generated by DCIM can very easily
be identified at the two-digit SIC level, the results can readily be used
to perturb other regional econometric models in order to evaluate the
effects of pollution control on regional economies.
Some of the results obtained for the 312(a} standard strategy for
the Philadelphia AQCR are presented below.
(Each number was obtained
by combining all the 1033 point sources in Philadelphia).
1.
Annual Emissions in Tons
Pre- control
Post- control
% Reduction
SO
x
Particulate
798,000
141,180
300,600
25,410
62.36
82.00
2.
A nnual A verage A ir Quality in mgms 1m 3
Pre- control
Post- control
% Reduction
SO
x
Particulate
52.58
72.20
12.89
38.85
75.53
46. 19
Figures 6. 3 and 6. 5 show the base year sulfur dioxide and parti-
culate air quality.
Figures 6.4 and 6.6 show the sulfur dioxide and
particulate air "quality after the implementation of Clean Air Act Amend-
ment Standards.
A 11 distances shown a~ong the axes in the figures are
in kilometers, the numbering being in standard UTM coordinates.
134
-------
45CC
t1 ti G ;-
J< - . -
44&C
447(,
446C
4<150
445C
4440
444C
443C
442C
L '1 -
..-::t;"
4~CC
43 9~
43Sf
43 7 ~
4360
436;
4350
435'
4340
43.; ,
4330
433
4320
432
420
430
450
46.0
480
500
51'0
520
530
540
550
560
Figure 6. 3
Philadelphia A ir Quality Control Region
. Sulfur Dioxide A ir Quality Before Control (mgm/ m 3)
135
,
-------
420 430 44(}' ~:r.~ :(JO 470 480 490 500 510 520 530 540 550 560
::::--C 1---- --- -----.--------------- ::::
, . ~ ---.--; --~-r----l--------- --------- 4480
1 ~_._"'~..., -;7 .--- .~.--i---_._.. -"~-i---'-' -.--- -- ---_.- ---
~ /'1 I !
, Pi/' ';, '- Buck COl~1tYI ! 4470
.1 }-;r--r/1~~",I~--r---r---:-~~~~:r-I--_---;--- 4460
-,' ~~! ~:-T- 'J;.~'~1:~~'~e :;'~~-~'lr~J~"-"r'----"'t ....', ~I n .y-""'Ir'-- ' r~"'--~r-."-'~ -.
I '.-7, ''-' tIt I ,'', I
4450 -' :'-.>J_,--+--~~~:?:.:;~~m y -j-_._-_l_--~'---~t--fS-,.--t,-~."--;--_.-1_-_. ..--. 4450
4440 1__; ! -f\1\sJc-l-~J" ~- ~J~-J~l:--i------J 4440
4430 -1...--' -!-__Li::J~_...' _ilia_- ---.L----.~ :.__.~----I- 4430
. . r .. ,;"; , . Ii. t
! C 11e ste . C'onritr L) i \ /'" 0' ,,'~i urli!ngton/ 1 !
! ; t i"". ~ I I !)
4420 : l___~: -;.,-,{riel' wA- e .._C....{-o-..-I/..... '-'.!.._-- E~::~.~Y...---L-- ...~..... ......L..__.....- .. 4420
I ! i 1/ ~ I i l'fr:i1..> If' i \ i ; I \ \
i I If ,;, '/: unt : 1....;/ /;..y"\~ :'! : It 1
. !! G \; L" i ~O ! ".::-;:.::t:O \ ;. \!.! .
4410 - -_--..:_----.;.-- -....2- ---"~:7--:" ,,-..:/-'-_0'...-::::- ::~-~~-' -,-Ca: (1-e~I1:,,~--~:'-'--.-0" '--:-"-'-"\"---"--~- 4410
. ; " ;;""; }'! ~",?; Y A" ; '- ; \ : \ I ~ I . I
! 'I/i ;' t/~~I ~ 4P: i (5 °fl1ty\+-,- '... \ I' ! \
1,00 ,..c.-:._----_.._..~___L L.'-_-__. '..-..._.\~~~~<:: ~.~t~~t,~\ .L....----~-_..~'~...__..- ,----..----;..,., '."- ;...1 ......_..-~. 44:00
c!..-._._-'--'--~'-{' Hi'" .'; : y; '- L ; [ ) \' ; \1
i i \: I;" J: . I ~ ,-, 1 ;; ;
4390:' I \ ! : I I; j : ; !..; i! \! 4390
1--\'-\" "Nr:~~t'~7(( -'''r'--'~'--ll''"--'''''' -'I,'''~~r~-''''~';' _......,\ :~.- .._'~". .' --.. r"'" -.-, ~ ~'. --'1 ',... r
4380: I \ ~.;::, "\: '-, " ; ,"- ~ : ! I ~ ; j 4380
'I I\'--i,- . """..n~7i-&rtI-.Go""ty.-:- -----;--- ---,---;---1'-- !,\::~?H-T
~ 1" i . !!, I ! !
43 70 ~--;_. \--_.~~-"....i-rt~,--..I.--.- '. --......'.-,-..... ,.. .",...(.~-~- ._L~..,..~...-...~--L--.......!,- ,""" .:..............!.. 437 C
. I \: \ ,""'\. I ' : : . ! I I I I
: I ~ ;' '\'; i ! ( I !j I I' j !
\' ' "\~.) I . ! j ! I. I ! I
4360, i.", : ~ ''\ :\ i ;! ii- _..__..J----_.- J. 436C
1--1l--~-"---'~;-;f"\/~ -"i.._..-;-,_.--t--I~'--""11"--"~~:j'---- '1 ~ 1
4350: -: --~~---~_---i~:_L__j_---i-----i--+--- -ccl'~-""-" .+.......---!- 435 C
4340 ;1-- I , !--J-+~~_L.J-__~----~-----r--~-.-~ 434 (
I I , ! I II " : ! : I .' Ii!
! ); I I , : I I ~ I
4330 ------"j..,,~_._~~--_..~.____.2 - -1-..--_- .-i----_-_L_...__...L.---..-. :_..___L--~~---_!......._.. L-..-l.- 433 (
4320 _LJ__LJ._- LJ_.__--I__.._!_.___L~__--:_-_J_.J-_.J----L-j 432 (
. C1 . I :;,. '
420430 441,(0450 460470480 490 500510 520 530540 550 560
. . .
r-~- -
4480
4470
4460
Figure 6.4
Philadelphia 1t~jr Quality Control Region
Sulfur Dioxide ..l~irQuality Afte3 Implementation
Amendment St;:C,2"ldards (mgrn/m ) .
136
of Clean A ir Act
.....
-------
:::: ~.~ ~__~[_~4~~.~~O. 4r~__~7~j;5°~~0~._. sL-:::2~.~:~3.~~4~0~~~_~S_6~ :::.'
4480 _1_] I ,/. I I - .-- ------- -- 446'
i 1----I-----i7 .-- '"'--I~-'--l-''' ..- -----i-- -
4470 ----~-~~---~!'-r~tBUCk~__~"-tl:ty.__+. -drLrl--- -~ --.- 447'
446 0 ~---_!_-_J_-,J--.L. -_J::Sl_J--.--1f.~___...i.-_~~ [;~~d-~i]--~j--'--"l-' 4 4 6 i
I ' i /. I I ' ',. I I , I' I
j . ,/'.U! 1\1 Ol~~:gom!e : I :' I i
44S0 t-:j7~!:-_.~+.:;~tnIY -I!--~t--'>"I: ~~-I-~-"::b;!',' !
4 440 _IL_....!._._-_!......_-_...;--_._~.\~-:>,,;..__.~ _.,--....1~~~. -,~~ ..__.~:-:[_._---+....... ...1...,......;'........._,.. 44~!
i I i j \.--; '--- ~ i . , ........;; ;:/ ! . i .: I
! !'. I I /\ " ' : /Y i ! I ; ~
4430. .---' ~....- -' ~._..._._...~-- ----_.; --;:) -..-; ~./:. -: \:B' d cJ .( i"}<--..~. ---....-!...-....- ~~_._, "--'-'''~'---'I- 4 ~ 3 .
Chester; COl1lity ;) 1 I ""( ~,. .~. ~' 'Burli;ng' nj i ~
: . ...... \''''' ~ - ,,:>' ! t , \
412 0 . ; ~ ! (, i L r . ,-' ~ \ G 0 II t r ! : I 4 .< 2
. - ~--~"---'-T'-'-"'-")--f" 'Qc-lawa rh~ -)-'j" --t.J~.. _../_01.!_,-...~-- "'i,-'--.i---~'+'''''''-~'--'''--'' -=
. ! I. 1/ OOl1nb~ '~l >. r-:".- '. ./,; ! " i I \ ;
r (' I ) . '--....",. >'~.., . , , t I .
, , \: i ! ;...- -;: : .... / \, ! I ~ .
-1410 /'-"'-';---"--'i'--"---"+-'~"~'-"{--:~'" ~i~:~{;- <;~~,-_.- :--i-C" ; '.d.c:p ;'''---~i'-~-'~i'''----I~- ..,. --- . --.----_!..\. 4 ~ H
I ! "( : P-"I~! ; :, o,unty\,~.,.., ~ I ;
I,.. ,I I, . I / . I . ," , I;
fO r------~---'-- ~-/....~......._....~.. .--//..... - ...;. 9Xo~is.\~ ~~.~~r....-.~\ ,~_..._--:-.__.,-->,_.__.+.__.._+........_~...(-...._.+ 4~ ('.
c.._--:---"';'T i I /. . Couoty ~ '-l . i : i \ . i
I I ., I If' iI' I -,. .' : \
4390 +~-"":-\-'--j~!
-------
:::: 42~4~~4_~JO_~6~~7_~- 48~90_~0~--.-=1~_:2~__._:3~~4.~_~~~ ::::
. +=--l=--'J~~:.~-Ii ~l.-I)~==~==~=- =-=-- 4480
I -j-„-~I~UCkL~~J..._L__J~r-- -------- 447C
4460 I -~!~ ~t- ~h~~t~d~~~~-J,~.--.-111.~-----; )-~„:;J-l~~--j---T 446C
! '.,~, 1 I I" ,I L) r I
4450 _, i"7 ---~--~~_':C~~?nty -1-_.~l._---'>~.~_._--_':-'_:"'~--\...._..- ,'--"-' -;-_-!~---4- 4450
4440 !-6 -L.L:iJt--'--_J..--i-j-' ,~~.--i.d' --it- _L__.1.___.I 444C
I II' il' i \.",) '~~ :.' : ! /-f" I Ii. ! I
I I /\ ~. l " .,
443 O. .--+---i----~-..,--t.._)..~: ._,,--~. ;.P , }ua.._.!._..~._, \"'-'--+'~'-I.._.._.,~.____.I,- 4430
! Cl1estel'( Courity :) ! \-----r ~o"; --/;.; 'Burl ;ngtonj ! i
. . , . ""', \ .... . \ '7 ~. /if'; t ~ . 1 \
. 4420 I {----'-Tj! -_._-.j~?/r; law~re-'-;~.~U----'-1~!-\~'h_~~~::n ('-'1-"'--''''\1..... ,----1----,,-- .. 442C
. i i ;. ountYj l.'v-'/I"-- \; : \! ; 1 i
, r 1 \: : ' "r" ._# ~ ': ....... I \. i \ 1 n!' .
4410 - ._-,:_---";'-_'''_''_''':-c._---.:-~.~:7..."",. ';..-...,,/": ~;.:::~~~_.- :.-\~Gai;nd-e~n ~...}.;~_:._.---,:,--,----,- "... --- --.---.-1-. 441 C
: i :.-'" ~ . :../,. ,'; i . r ; \ ; i 'I j \
i I " i I ,,'- ! : ! ' C 0 U ~' !:
, i (; I / .... " \. .;'''''''''' ~ I .
: 0 0 ~_._-_..~-_.. - ~ -"/....1,,~...._.....~.._..-f./---'-'~,,,,\ ..QJ.9.~~ ~.C; ~!.9?'......\,~ --,..._.;,._._-_.~-,~...,--_..j-~...---._..1."......' .._~..\ ......-.+ 440 C
-.---:.----;-."(' ; i 1./' ~. County ~ '-l ; : i I . i
! I \,' 'I I J \ I ; I -, I ; . t : ,
4390 ~---'i- j_. -"N\~~.--.;\....;./.....+,,_._.~..t..--.,..... ~ ,,'--+.-.~....~ \......-\. ~..... 00_+".-' .-. \..~. ~_..,! .-'. --.j ',..- .j.' 4390
I I \ C~stl~ ~ ~ i' 1 I "-1 j \' I I \ ~ j
: I I . \: '\ " : i'- , . , I : ; i 438C
4380. '~-'-'-0'OU~\'''-7---5-a-1.'''11'r'1.-GO''UHt~r.._.....-.. ._-,,"~~.- _.."".~._..--;.__.-,---_.'-_OO '\--'I"'--~ :
I \ : : I (i I. ;! i 'I j ""v', ~
\ : ;, I, i : . . I; I ~ i
! \ : : r.t! 1; i! i ~ . : ;
. 4370 ,--.;.-. ~"-'--"~""/"i'( ..-. --"~"-'- , ----'-"'-~-"... ... ...__..~~--_.._.--- -"'"'T'~'-''''-''''-'-''--~'''-''''' -:".... ...". :" 4 3 7 C
! I, \ i \'~"': i i ; I ! I II I' !) I
. '; \ \ \, . I I \ '
4360 \ ;: \, f\ ! : ! i . t ~!
l-n-t-- ~/~-r--.i-.-.-r--r---t--r-'-.----i.---l 4360
43 50 ;;'---""-"~?~';':-'---T' ""--'1--"4'--.' : + --"+'-~'--+--"'-"r'''--''-i---''''''r-'''-''-J--'''---:' 435C'
4340 L-l--~_.L_.j___J -_.L.,~,j._~ --_!.. -~.._J...__.J_~,~J~_..~J~--,~_L__L_.-L 4340
! I) j ! i i ~ : ; : j i j ! j
433 0 l__~_..~".~"._--,.._~.J.--_.__..l- .-J-__-_L~.j___..,_..L__.. ~.____._L___t~w_~!..._.._..L_-.._L 433 C
4320 LJ._J_L_._L- L__L_J.__.L- -_.~--_L.J-_-J._l-J mc
. I I "
420 .430 440 450 460 470 480 490 500 51'0 520 530 540 550 560
4480
4470
Figure 6.6
Philadelphia A ir Quality Control Region
Particulate A ir Quality After Impleme ntation
Amendment Standards (mgm/m3)
of Clean A ir Act
138
-------
6.3
Change of Property Values in Response
to Change of A ir Quality
The improvement in real estate values due to reduction of air
pollution appears to be one of the best objective measures of the benefits
of air pollution control.
In recent quantitative studies on this topic,
some statistically significant damage functions have been estimated
relating pollution dosage and real estate values for different pollutants
in different regions. ~< In this section, such a function will be applied
to the simulated change in air quality due to control in Philadelphia
to estimate the consequent improvem.ent in property values and property
tax assessments for that city.
Most of the damage functions have been estimated in a logarithmic
form of regression equations. >~>:'
>,'< Anderson, R. H., and T. D. Crocker, op. cit.
Crocker, T. D., "Some Economics of A ir Pollution Control"
with Special Reference to Polk County, Florida," Report to the U. S.
Public Health Service, 1968.
>,'<>:< Anderson, R. H., and T. D. Crocker, op. cit., p. 175.
139
-------
Let
A = Property value (sale price)
S = Dosage of SO
x
P = Dosage of Particulate,
*
X. = Other explanatory variables, i = 1, 2, ... , V
. 1
Then the damage function is given
(1)
A = ea S-a p-fJ
V
n
i= 1
'Y'
X 1
i
Suppose change of air quality is presentented in the form,
quality with control = quality without control - improvement
in quality due to control,
i. e.,
S' = S - AS;
P' = P - A,P
Then the new value of property with air pollution control will
be A', given by
(2 )
A' = e a (S - AS) - a
(P - A P)-fJ
V
n
i= 1
'Y'
X 1
i
Dividing (2) by (l)
~' = (s~ Asf
(3 )
(p- :p) - fJ
* The other variables are median family income, the percentage
of property classed 'as dilapidated, the percentage of each tract's units
more than 20 years old in 1959, the percentage of occupied hous ing
each tract inhabited by non-whites, each tract's distance from the
central business district and the median number of rooms in housing
"..
un 1o..S .
140
-------
I--~.-'"''''-''' -~_.- - .--
The percentage increment of property value due to changes in SO and
x
particulate concentrations, as suming other explanatory variables to
. . b A' - A 1 . (A ~. 1)
remain the same, lS glven y .A x 00, 1. e., A - x .100.
The above result is applied to the data for Philadelphia AQCR
as follows. From Section 6.2, the pre-control air quality measures
of SO and particulate concentration are
x
3
S = 52. 58 Mgm/m
3
P = 72.20 Mgm/m .
and
The standards assumed in the Clean Air Act Amendment, 1970
(referred to as 312(a) Standard) will reduce the SO and particulates in
x
Philadelphia AQCR to the levels of
3
12.89 Mgm
3
= 38.85 Mgm
S - as =
and
P - ap
Consequently,
S - as
S
P - a P = O. 5381
P
= 0.24488
and
Substituting these and regression estimates of a and {3 >:c into (3)
~I = (.2449)-.0712
(.5381)-.0610
= 1.06439
>,'c The estimates of a , {3 for Washington, D. C., were adopted as
substitutes for those of Philadelphia which are not available. The
estimates are from Anderson, R. J., and T. D. Crocker, Ope cit.,
p. 175, Type I equation.
141
-------
"
From the calculation above, an increase of approximately 6.44
percent can be expected in the property value in Philadelphia AQCR
due to the application of air pollution control to meet the standards of
the 312{a) Amendment of the Clean Air Act, 1970.
In dollar terms,
the property value will rise from $9.2 billion before control to $9.8
billion after control, i. e., an increas e of $593 million.
If this is
the case, this substantial increase in property value will lead to an
increase of $29.6 million in property tax assessments in Philadelphia.
This shows that the tax revenue of govermnental bodies may increase
substantially due to the application of pollution control measures.
Thus
the actual social cost of pollution control may be les s than it looks at
first sight.
The results also suggest that the study of second-order
effects in economic- environmental interactions can be a valuable
addition to the present tools for policy decisions.
142
-------
,">
6.4
Economic-Environmental Interaction
It is almost impossible for any model system to give ,>
:HTlplete
coverage of the complexity of interdependencies between ccc., .'mic and
environmental systems in reality.
In this section, it merely lltilizes
the information provided from other models as des cribed in Sections
6.2 and 6.3 to give a demonstration on how an integrated study can be
conducted by the use of some existing modelling efforts.
By the use of the DCIM system the air qualities and the emission
levels in Philadelphia AQCRs were obtained (Section 6.2).
Emissions are by-products of econornic activities, in particular,
from production processes of various industries that
E.. = f (Q.,process rate)
1J J
Eij = £ (Qj, process, etc.)
where E.. is type i emis sion from industry j
1J
Q. is level of production of industry j
J
Suppose emission E.. is in proportion to the level of productic)a
1J
e.. =
1J
E..
1J
Q.
J .
Where e.. is type i emission per unit of output of industry j, or it may
1J
be called 'Iemission factor" of industry j.
Upon the implementation of the air quality standards required by
the law, emission reductions can be expected with corresponding
143
-------
improvement of the ambient air qualities.
Thus, the emission per
unit Q output with pollution control can be measured
e* =
ij
(E" E''')
1J - 11
Q.
J
where e>':. is type i emission per unit output of industry j with air
1J
pollution control,
E'.. is type i emission reduction by industry j with implementa-
1J
tion of air quality standards.
The DCIM system described in Section 6.2 also provides the emissions
by Standard Industrial Code (SIC) 4-digit categories.
Emissions by two-digit SIC ilidustries were estimated for the
DCIM output (Table 6. 1).
Based on such information, emissions per
unit of production by two-digit SIC industries can be estimated.
Value
of shipment and value-added were used for measurement of the produc-
tion levels of each industry.
Table 6.2 gives emissions per million
dollar of value of shipment and value-added by two-digit SIC industries
in Philadelphia AQCR.
By the implementation of 3l2(a) standards,
elTIissions per unit of output were considerably reduced as shown in
Table 6.3.
The costs of the implementation of 3l2(a) standards were then
introduced to the OAP Regional Economet'ric Model to lTIeaSUre the
overall regional economic impact.
The simulation results of Philadel-
phia AQCR in year 1976 are given in Table 6.4, column 2.
144
-------
Table 6. 1
SOx and Particulate Emissions by Two-Digit
SIC Industries in Philadelphia AQCR
(unit: tons /day)
Industry SO Particulate
x
SIC 20 12.754 3.176
22 4.998 4.819
26 11. 481 .689
28 268. 152 25.948
29 392.806 68.303
32 2.673 6.547
33 24.208 71.517
34 0 .020
37 4.089 .354
39 85.284 6.788
49 1,350.203 140.133
Other 29.782 58.526
TOTAL 2,186.43 386.82
145
-------
Table 6.2
SOX and Particulate Emis sions Per Unit
of Output ($1 Million of Value of Shipment
and Value -Added) by 2 -Digit SIC Industries
in Philadelphia AQCR Before Control
SOx Particulate
--
Tons per year Tons per year
Industry per $1 million Tons per year per $1 million Tons per year
SIC of value of per $1 million of value of per $1 million
shipment of value -added shipment of value -added
20 2.235 5.692 0.5566 1. 4175
22 3.298 7. 140 3. 1796 6.884
26 5.425 10.218 0.3256 0.6132
28 56. 112 72. 195 5.4297 6.9861
29 95.240 348.333 16.5608 60.57
32 2.892 4.578 7.0826 11. 214
33 7.241 13.034 21.3912 39.083
34 0 0 0.0065 0.0091
37 1. 389 1. 599 O. 1202 O. 1384
39 187.296 280.945 14.9075 22.361
146
-------
Table 6.3
SOX and Particulate Emissions Per Unit
of Output ($1 Million of Value of Shipment
and Value-Added) by 2-Digit SIC Industries
in Philadelphia AQCR After Control
SOx Particulate
Tons per yea'r Tons per year
Industry per $1 million Tons per year per $1 million Tons per year
SIC of value of per $1 million of value of per $1 million
s hi pment of value - added shipm ent of value-a~
20 0.842 2.144 0.1001 0.255
22 1. 242 2.689 0.5723 1.239
26 2.043 3.848 0.0586 O. 11 0
28 21. 132 27. 189 0.9773 1.257
29 35.867 ..J31. 182 2.9809 10.903
32 1. 089 1. 724 1. 2748 2.019
33 2.727 4.909 3.8504 7.035
34 0 0 O. 0011 0.002
37 0.523 0.602 0.0216 0.025
39 70.536 105.804 2.6833 4.025
, 147
-------
Table 6.4
Percentage Changes of Major Economic Indicators
in Philadelphia AQCR in Response to the Implemen-
tation of 312(a) Air Quality Standards by 1976
Percent Changes of Percent Changes of
Cost Impacts Cost Benefit
Variables (first round) Impac)ts {second
round
Manufacturing Industries .'
Value added - .43% - .10%
Gros s profit -1. 01 - .67
Investment -6.24 -6.05
Capital stock - .53 - .52
Employment -1. 00 1. 62
R egiona1 Income - .23 . 14
Regional Employment - .27 .49
Local Tax Revenues - .20 .96
148
-------
However, the benefits such as changes in property value as de-
scribed in Section 6.3 may have some positive economic impacts as
the result of air pollution control.
Assume a 6.4 percent property
value increase in Philadelphia and introduce to the OAP Regional
Econometric Model for a second-round simulation. >:< Some positive
economic impacts can be expected in Philadelphia':<>:< as shown in
column 3 of Table 6.4..
The changes in economic activities, such as manufacturing pro-
duction, again, are expected to change the level of emissions and
hence the corres ponding air qualities in the Philadelphia AQCR.
By
using the emission factors, or emissions per unit of output, the re-
gional emissions and air qualities can be projected.
':<111. the first-round simulation of the OAP Regional Econometric
Model, taken as exogenous information, and then emissions and hence
air quality changes lead to a change of the property value was intro-
duced to the model for second-round simulated.
>:":
-------
APPENDIX A
MANUF ACTURING INVESTMENT FUNCTIONS:
A CROSS-SECTION ESTIMATION WITH SMSA DATA
A. 1
-------
. .
As indicated in Chapter 3, investment functions with Koyck's
distribution were formulated in an earlier version both for g,ross
investment or a net investment equation as follows:
(1)
It
=
" + 1.Z (nt-I - nt-z>] HKt-1 + Ut
(3)
A.2
-------
Data
Cross-section data for manufacturing industries by SMSA in
years 1965, .1966 and 1967 were used.
A maximum sample of 56
SMSA's is included; this is due to the fact that in years 1966 and 1965
data on the Annual Survey .£!..Manufacturers includes only 56 out of
91 SMSA' s under current study.
Some parameters used in the estimation need further explanation.
Depreciation rates for all manufacturing industries and each of
two-digit SIC industries were estimated from actual depreciation and
-,-
gross book value of fixed assets of 1957 U. S. data. -.' Capital data were
also estimated by using capital output ratios of U. S. applied to the
value added by region by industries. ~:o:'
Finally, Almon's weights were derived as described before.
Her
original estimation only included some two-digit SIC industries.
There-
fore, the paralneters froln non-durable or durable industries were
applied to those two-digit SIC industries not inluded in her study.
durables: SIC 24,25,32-39
non-durables: SIC 20,22,23,26-31
These parameters are summarized in Table 1.
~,
. U. S. Department of Commerce. Bureau of the Census. 1958
Census of Manufacturers. Vol. 1, Summary Statistics. Section 9 I'Sel-
ected Costs and Book Value of Fixed Assets. 11
** -
From the same source of data, capital-output ratios were
estimated from value added and gross book value of fixed assets.
A.3
-------
TABLE:l
SOME PRE-ESTIMATED PARAMETERS
.
Indus try Depreciation Output-Capital i Almon's Annualized Weights
rate ratio Al A2
All Man£. . 0662 1.271 .' 514 .406
SIC 20 . 0674 1.394 .561 .401
22 .0525 1.043 .728 .269
23 .0906 6.032 .616 .291
'. '"
24 . 0915 1. 126 .441 .490
l.. . . . . .
25 .0737 2.415 .441 .490
26 .0539 ..799 .557 .415
27 .0686 2.142 .616 .291
28 .0669 .952 .413 .519
29 .0614 .409 .845 .029
I 30 .0618 1. 381 .480 .408
.. .'
31 .0755 4.053 .616 .219
32 .0646 . 966 .491 .462
33 .0560 .769 .441 .490
. .
34 . 0700 1. 670 .441 . :'.490
. .
35 .0722 1.696 . 541 .338
36 . 0738 2.353 .429 .447
37 . 0738 2.353 .429 .447
38 . 0671 3.276 .441 .490
39 .0732 2.389 \J .441 .490
A.4
-------
, Res lilts
..
Ii
. Equations (1), (2) and (3) are estimated with ordinary least
square regres sion melhod with. cros s- sectional data.
In these equations
t represents year 1967, and t-l and t-2 are years 1966 and 1965
respectively.
The results are summarized in Tables 2, 3, and 4.
In each
table, the parentheses under each estimated coefficient shows the
standard error, and followed by the regres sion coefficient R Z and
sam.ple size in each estimation.
All three models seem to be superior to the previous estimates
of the investment equations in th.e Regional Model.both in theoretical
,0,
'I'
. formulation and empirical results.
Equation (1) in Table 3 using gross investment by SMSA
industry in 1967 as dependent variables and estimating the depreciation
rate by the model gives a reasonably good fit; it shows a better fit then
in Equations (2) and (3) (Tables 2 and 4)
,
For previous investment functions see CONSAD Research
Corporation An Econo:::::1ic Model System for the Assessment ..£!'..Effects
..£!'..Air Pollution Abatement prepared for Office of Air Program, EPA,
May 15, 1971.
.'
A.5
-------
TAB LF 2
EQUA TION {2) ':: Net Investment as Dependent Variable with Koyck
Lag Structure - "
~t - ~ K~ = b 1 I~t_l - ~Kt- ~ + bZ [fit - '\- J
I
Indus try b 1 coefficient b2 coefficient R2 Sample Size
All Man£. 1. 0202 . 1225 .938 56
(.0354) (.0182)
.
SIC 20 .9911 .0430 .768 49
(. 0804) (.0469)
22 . ..0779 .0750 .232 26
(. 0762) (.0251)
23 1.0086 .3945 .999 37
I
(.0113) (. 0802)
24 1.0113 .0655 .610 20
(.1078) (.0571)
25 1. 0242 . 1279 .970 34
(.0267) (.0420)
26 .6790 .3002 .530 41
(.1059) (.0816)
27 1. 0664 .0039 .989 47
(.0219) (. 0582)
28 .6571 .0390 .785 41
(. 0-534) (.0706)
29 1. 0629 .3618 .848 13
"(.1174) (. r099)
..
30 .0026 .2647 .136 25
(. 1460) (.0995)
31 1. 0850 .0762 .992 15 .
(. 0282) (.1027)
A.. 6
-------
I --
_0
TAB LE 2
(continued)
Industry b1 coefficient b2 coefficient R2 Sample Size
SIC 32 .6621 -. 0048 .396 46
(.0885) (.0546)
33 1.0138 -. 1392 . 741 36
(. 1099) (.0651)
34 1. 04 99 .0410 .905 51
(.087) (. 0282)
35 1. 0124 . 1109 .850 47
, (.0507) (. 0420)
-
36 1. 1623 .2076 .960 37
(.0331) (.0575)
37 1. 1692 . 0690 . 975 35
(.0354) (. 0207)
38 1. 1407 .2063 .995 22
(.0270) (.0156)
39 1.0539 . 0864 .995 30
.. (.0126) (.0032)
-
I,
v
A.7
-------
"
TAB LE 3
EQUATION (1):
Gross Investment as Dependent Variable with Koyck
Lag Structure -
I
"
It = bl [ILl - !Kt-IJ + bzl n t - nt-I] +-b3 Kt
Industry bi coefficient b2 coefficient b3 coefficient R2
All Man£. 1. 0753 . 1204 .0680 .976
(.0511) (.0181) (. 0012)
SIC 20 .6770 .0599 .0576 .888
(. 1444) (.0449) (.0038)
22 .0872 .0991 . 0483 .938
(.0739) (.0284) (.0026)
23 .0246 . 0117 .0047 .992
(.0178) (.0111) (.0016)
24 .4425 .0697 .0551 .837
(.0850) (.0263) (.0044)
25 .3812 .1329 .353 .617
(.1959) (.0367) (.0116)
26 .3556 . 1595 . 0892 .845
(.1314) (. 0824) (.0102)
27 .5701 .0540 . 0440 .924
(.1129) (.0501) (.0055)
28 .6569 . 0386 .0670 .907
(.0565) (.0786) (.0045) -
29 .4198 .2175 .4201 .889
(.3870) (.1310) (. 2073)
30 .0216 .2759 .0603 .694
(.1491) (.1141) (.0068)
31 -.2701 -.0963 -; 0124 . .807
(.1235) (.0357) (.0080)
A.-8
-------
-"
TAB LE 3
(continued)
Industry b1 coefficient b2 coefficient b3 coeffident R2
,.
SIC 32 .6447 -.0008 .0658 .805
(.1370) (.0601) (. 0069)
.. 33 ,. .3376 .0428 . 1346 .928
(. 1624) (.0627) (.0161)
.' '., 34 .2940 .1138 . 0444 .972
(.1107) (.0223) (.0036)
. . 35 .2178 .0157 .0459 .927
(.1629) (.0388) (.0052)
. . ., 36 .4331 .0407 .0409 . 900
(.1102) (. 0455) (. 0049)
37 .4392 . 0284 .0439 .942
. .
(.1074) (.0145) (.0050)
38 . 1706 .0760 .0262 .992
(.0994) (:0148) (.0042)
. . . . . 39 .4529 .0906 .0369 .996
(. 04 99) (.0013) (.0030)
A.9
-------
TAB LF 4
EQUA TION ~3.):~'. Gross Investment as Dependent Variable with
A1mon1s Annualized Weights ..
"
It = bl [AI (nt- nt-I) + AZ(nt-l - n t-z)] + bz Kt
I Industry b 1 coefficient b coefficient i' R2
2
A 11 Man£. .1964 .0471 .768
(.0990) (.0029)
SIC 20 .0813 .0413 .839
(.1076) (.0027)
22 . 1430 .0498 .938
. (. 042 8) (.0024)
23 .0032 .0025 .992
(.0149) = (.0001)
24 . 1068 .0314 .823
(.0197) (.0029)
25 .2258 .0105 .543 .
(.0759) (.0017)
26 .2792 . 1012 .819
(.1854) (.0117)
27 .0429 .0168 .879
(. 0979) (.0017)
.
28 .9369 .0531 .726
(.2073) (.0095) ..
..,
I . . .6343
29 . 1700 .888
(.1317) (.0586)
.
30 .0138 .0678 .631
, (.0376) (. 0066)
31 -.1050 .0054 .784
(.0465) (. 0007)
v
A.I0
-------
TABLE 4' - . (continued) ... .
'. -, ~ . . .."
. .....,. .
Industry b 1 coefficient b2 coefficient R2
SIC 32 -.2580 .0878 .719
(. 1 6 7 4) (.0052)
33 .. -.0623 .1536 .918
(. 1146) (.0071)
. . 34 .3390 .0298 .961
(.0831) (. 0027)
35 .0214 .0390 .926
(. 0852\ (.0016)
36 -.2068 .0247 .877
. .
(.0792) (.0014)
37 -.0029 .0234 . 913
(.0267) (.0013)
38 . 1606 .0167 .992
(.0204 (.0003\
. . 39 .2118 .0076 .989
(.0050) (.0005)
A. 11
-------
L
I
Both the pre-estirn.ated depreciation rates in Table 1 and
--
estimated depreciation rates with cross-section data seem to be
higher than Jorgenson-Stephenson's estinlates of 2 to 3 percents with
...1....'..
time series data of 1947-1960. -,".,
~:<* Jorgenson, D. W. and J. A. Stephenson [8J
A.12
-------
..
BIBLIOGRAPHY
(1J Almon, S., tiThe Distributed Lag between Capital Appropriatiohs
and Expenditures", Econornetrica 33, 1965, pp. 178-196.
[zJ Dhrymes, P. J., Econometrics: Statistical Foundations and Appli-
cations, Harper & Row, New York, 1970.
[3J ' Distributed Lags: Problems of Estimation and
Forn:m1ation, Holden-Day, San Francisco, 1971.
[4J Evans, 1'\11. K., Macroeconornic Analysis, Theory, Forecasting, and
Control, Harper & Row, New York, 1969.
[5J Jorgenson, D. W., "Capital Theory and Investrnent Behavior, II
AJnerican Economic Review, 33, 1963, pp. 247-259.
[6J ' tlAnticipations and Investment Behavior, tI in The
B rookings Qnarte rly Econorn.etric Model of the United State s, J. S.
Duesenberry, G. Fr~lnan, L. R. KEen and E. l-
-------
APPENDIX B
FLOWCHART OF VALIDATION PROGRAM KRVALTSC
B. 1
-------
Repeat
once for
LYR=LYR-
FLOWCHART OF KRVALTSC PROGRAM:
ESSENTIAL ASPECTS
Read model paramters
for all sectors: PRINT
I"
I
ead (T - 1) actual data
-~y SIC detail; (PRINT)
Read L YR actual data 11
b SIC detail; (PRINT~
I
Compute ACTUALS not
directly read in (PRINT)
or all manufacturing sectors
comput YESTIMA TES from
model paramters and
XACTUA LS; (PRINT)
i
Yes
cb
No
B.2
-------
"
For aggregate sector, compute
YESTIMATES (PRINT
Create scratch-file of all variables
YE and Y actuals, for ECON Pro ra
For each manufacturing sector,
and aggregate, Do TTEST be-
Do UTEST between Y and YE
( PRINT )
Print Summary T able for t and
U tests .
/ I
. For each sector, and aggregate I
read data YE and Y. Do modified
regression YE=a+bY calling ECONVA
ECON; VAlidation Modification
PRINT AQCR.S with estimate s off
b 1,2,3 standard errors
distribution and
Do regression YE=bY .
.. ,
B.3
-------
"
APPENDIX, C
EXTERNAL VALIDITY RESULTS FOR MANUFACTURING
SECTOR BY TWO-DIGIT DETAIL FOR 1969
EXCEPT YE=bY
C. 1
-------
","
AGGREGATE OF ALL 19 SIC's
. Stand. . No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Interval tb b R2
- - Y2:S Y2"2S Y:!:3S
SIC 0 Statistic Y YE Stat. Sy. n
. I
Variables
(Manufacturing) .
'.
Employment N 1.8488 172.361 208.589 .7947 " 23.755 59 33 49 55 133.440 1. 1804 .9968
Value Added V 1. 8273 2271.607 2811. 880 . 8972 236.775 59 27 43 49 107.763 1. 2575 .9950
,in-vestment I .2987 " 144i-361 149.817 . 1716 31. 035 59 51 57 59 64.099 1.0444 ,.9861
~
['.. Gross Profit n .1211 1074.517 1090.382 .0645 202.526 59 51 56 57 57.519 1. 0589 .9828
Wage Rate W 1.0899 6.667 6.841 "1. 189" 0.2936 59 38 56 59 32.870 0.7988 .9490
Capital Stock K O. 1588 1786.972 1774.311 . 0306 31. 507 59 38 54 57 270.372 .9887 . 9,992
~
. .
-------
FOOD AND KINDRED PR ODUCTS
(J
.
,
- Stand. I No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b RZ
- - -" Y2"ZS Y:!:3S
Sic 20 Statistic Y YE Stat. S\'. n yrs
-
Variables . .
~
(Manufacturing)
Employment N 1. 3580 13.333 15.812 .8127 2.535 54 37 46 53 85.933 1. 1605 .9929
Value Added V .8848 228.352 252.842 .4626 41. 080 54 45 50 53 105.617 1.0829 .9953
Investment I .4139 14.798 14.240 . 1336 4. 107 53 49 50 52 30.935 .7909 . 9484
Gross Profit IT .2028 144.355 137.148 .2297 19.229 54 44 51 52 78.561 . 9402 . 9915
Wage Rate W .9647 6.026 6.160 .9070 .2872 54 43 52 54 28.025 .9045 .9367
Capital Stock K .1422 165.086' 163.848 .0333 4.628 53 38 46 51 160.737 1.0042 .9980
~
"
I
VJ
I
-------
TEXTILE MILL PR ODUCTS
I '
Stand. No.
I
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b RZ
- - -A '"'. Y:!:3S
Sic 22 Statistic Y YE Stat. Sv. ( n Y2-S Y2"2S
"
Variables . .
(Manufacturing)
..
Employment N .0 11. 100 13.507 . 5259 .979 17 9 11 12 55.420 1. 2245 .9948
Value Added V . 0 97. 178 111.061 . 3611 15.627 17 12 14 16 46.730 1. 1406 . 9927
~ Inve.stment I . 0 6.012 I 5.845 .0749 1. 944 17 14 17 17 24.514 . 9127 .9740
>I: Gross Profit n . 0 46.027 40.708 . 3311 7.228 17 12 14 17 40.492 .8738 . 9903
Wage Rate W .0 4.667 4.841 . 8457 .210 17 11 17 17 18. 075 1. 0434 .9532
Capital Stock K .0 93,0 199 92. 117 . 0319 1.912 17 9 13 14 76J 80 .9755 .9973
"
I
-------
APPAREL AND RELATED PRODUCTS
U1
I
Sta.nd. ,No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. 'ob. Within Inte rval tb b R2
- -A yi2S Y2:3S
Sic 23 Statistic Y YE Stat. Sv. n y:tS
. I
Variables' . .
(Ma n ufactur i ng) I
Employment N .9568 17.235 19.649 .2320 9.510 37 35 36 36 262.358 1. 1120 .9995
Value Added V .8811 145.734 155.072 . 0999 116.658 37 37 37 37 152.391 .9991 .9985
Investment I .2929 3.778 2.740 .4547 2.372 36 31 34 35 64. 318 .6527 . 9916
Gross Profit IT .0595 68.504 60.480 .1879 46.856 37 36 36 36 138.933 .8376 .9981
I
Wage Rate W 1. 2270 4. 142 4.305 . 9264 .236 - 37 27 36 36 33. 124 1. 0061 . 9682
Capital Stock K .. 0338 24.664 24.706 . 0027 2.455 36 36 36 36 1261.757 1.0039 .,cr9~
" I
o
-------
LUMBER AND WOOD PR ODUCTS
()
1
. Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Interval tb b R2
- -~~+
l'ic 24 Statistic Y YE Stat. Sy. , n Y-S Y_2S Y-3S
Variables . . I
i
(Manufacturing) . :
Employment N . 0 5.813 7.869 1.509E .416 8 0 1 2 12.799 1. 3194 . 9588
Value Added V .0 64.875 85.227 1. 344 ~ 3.401 8 0 1 2 11. 480 1.2548 .9492
I Investment I .0 4.234 4.302 .0431 .543 8 2 6 6 7.220 .6046 .8796
Gross Profit n . 0 30.712 27.779 .4906 1. 546 8 3 4 6 11.211 .8732 .9468
Wage Rate W .0 5.934 6.318 .8319 .306 8 2 8 8 17.330 1. 0356 .9771
Capital Stock K . 0 57.625 550212 .2068 .5415 8 0 0 1 73.663 .9960 .9987
. i
-.
I I
0'
-------
FURNITURE ,AND FIXTURES
o
Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rva1 tb b R2
- ry:tS Y2-2S Y2:3S
.]ic 25 Statistic Y YE Stat. Sy. n
.
~
Variables ' , .
(Manufacturing)
'.
Employment N . 0 6.888 9.087 .7734 .833 17 4 11 13 42. 144 1. 2554 . 9911
Value Added V . 0 73.171. 89.437 .5287 8.300 17 4 14 14 52.282 1. 1795 . 9942
Investment I .0 2.224 2.113 . 1664 .754 17 15 17 17 15. 737 1. 0588 .9391
Gros s Profit IT . 0 33.302 30. 929 .1950 2.166 17 9 12 16 50.548 .9508 .9938
Wage Rate W .0 5.633 5. 587 . 1947 .316 . 17 17 17 17 60. 120 .8793 .9956
Capital Stock K p;0 30,,296' 29.396 .786 .. 7589 17 11 14 15 311. 002 .9669 09998
"
I
--.J
-------
PAPER AND ALLIED PRODUCTS'
n
, .
:00
I
I
I I
I Stand. t No. I
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. 'ob. Within Inte rval tb b R2
- - -yi"s Y-+2S Y+3S
-l3ic 26 Statistic Y YE Stat. Sy. n
Variables' . . I
(Manufacturing) :
Employment N .8941 7.8968 8.820 .4554 ..747 31 19 26 2"7 81. 001 1.1235 .9954
Value Added V .7532 95.854 104.199 .3414 9. 151 31 22 29 29 51.956 1. 0673 .9890
Investment I .5408 7.764 9.031 .6129 3.949 28 22 25 28 11.37 1. 1562 .8262
Gross Profit IT .0634 48.704 47.208 . 1244 5.057 31 25 28 29 36.66:= .9227 .9782
Wage Rate W .2323 5.949 5.984 .2800 .218 31 30 31 31 46. 77: .8364 . 9865
Capital Stock K . 0328 124. 125 124.453 .0101 3.9661 28 27 28 28 398.52~ .. 9946 49998
-. I
-------
PRINTING AND PUBLICATION
-.!J
Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b R2
SIC 27. - I -"~-"'. yi3S
Statistic Y YE Stat. Sy. t n Y -5 Y2"2S
- .
~
Variables . .
(Manufacturing) :
..
Employment N 1. 0854 15.102 17.980 . 4547 1. 510 45 28 37 39 185.787 1. 2093 . 9987
Value Added V .8191 204. 383' 211.639 .0792 97.854 45 44 44 45 98.492 .9165 .9955
investment I .5744 9. 561 8.924 . 1843 3.956 43 40 43 43 59.104 1..0208 . 9881
Gross Profit n . 2219 103.168. 87.558 .3237 55.764 45 43 44 44 88.449 .7474. . 9944
Wage Rate W . 5124 6.290 6.365 .5273 .256 45 41 45 45 58.675 .8616 . 9874
Capital Stock K ! 1771 98.658 99. 021 .r 00781 4.. 0198 .43 39 42 43 756.462 .9923 .9999
".
in
, .
-------
<
SIC 28
-
Variables
(Manufacturing)
Employment N
Value Added V
,...,.) Investment I
\.J '\
o
Gross Profit n
Wage Rate W
Capital Stock K
.
-.
Normal-
ized U -
Statistic
1.4193
1.6559
.2099
.0591
. 2366
.. 1944,
Actual
Mean
Y
11. 340
288.755
23.675
208.142
6.975
309. 144
CHEMICALS AND ALLIED PR ODUCTS
-
Estimate
Mean
YE
16.271
389.739
24.966
202.792
7.010
I 306. 739
i
I
I
I
t-
Stat.
1.4707
Stand.
Error
of Est.
Sy.
. '
1.911
1.1857 43.969
. 1339
7.647
.099217.505
.1959
.0303
.339
,7.743
I ~;.
, :b.
No. of observations
l--Y1ithin Inte rva1
y:!:S Y2"2S Y2"3S
30
11
30
8
29
27
30
21
30
29
'22
29
18
17
29
27
30
23
24
24
29
28
30
26
tb
27.920
51.081
61.083
54.446
43.609
78.486
b
1.5082
1.2911
1.0375
. 9149
, .8399
.9974
R2
"
. 9641
.9890
. 9925
. 9903
. 9850
.9955
-------
PETROLEUM AND COAL PRODUCTS
Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b R2
-" Y2-2S I Y:!:3S
SIC 29. - Y2"S
Statistic Y YE Stat. Sy. n
.
Variables . .
(Manufacturing) :
" .'
Employment N .0 7.667 I 14.466 2..6087 2.983 6 0 4 4 4.154 1.8098 . 7648
V~lue Added V .0 257.330' 1.4806 53.544 6 0 3 4 12.184 1.2952 . 9672
. 388.,174
~ Investment I .0 92.846 84.234 .2596 16.015 4 1 3 4 2.572 .7057 .6518
:: Gross Profit n .0 193.780, 175.448 .3147 18.642 6 4 5 5 14.541 . 7970 .9768
Wage Rate W .0 8. 206. 8.430 .6209 .3108 6 4 6 6 6.588 . 9892 . 8945
Capital Stock K 719...176 ' 735..612 .. 0631 16,,250 29.666 .9966
.0 4 2 4 4 .9884
-.
I I
-------
RUBBER AND PLASTICS PR ODUCTS
I Stand. I
No.
Normal- Actual Estimate Error of No. of observations
SIC 30 ized U - Mean Mean t- of Est. . .ob. Within Inte rval tb b R2
- Y:!S Y2"2S Y:!:3S
Statistic Y YE Stat. Sy. n
- I
Variables' " .
(Manufacturing)
.. ,"
Employment N 1. 0551 9.725 12.019 .7590 1.246 20 8 14 16 51.050 1. 2381 ~ 9928
Value Added V 1.0550 111.736 136.663 .7147 28.800 120 15 17 19 35.716 1.1957 . 9853
o Investment I .0 9.687 9.355 .0894 4.582 13 10 13 .13 9.628 . 7801 . 8843
~ Gross Profit IT .0812 55.837 55.108 .0459 13.933 20 19 20 20 .30.130 . 9489 .9795
Wage Rate Vi . 2976 5.640 5.705 .2711 .361 20 19 20 20 47.217 .. 81 3 3 .9915
Capital Stock K .0 92.016 I 94," 059 # 0614 4? 6 14 13 11 13 13 204.806 1.0190 . 9997
"
-------
<
LEATHER AND LEATHER PRODUCTS'
()
" 1 t
- Stand. . No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b R2
SIC 31 - -Y!S !Y2-2S Y:!:3S
Statistic Y YE Stat. Sy. n
- I
Variables . .
(Manufacturing) :
.'
Employment N .0 8.318 9.741 .3326 . 769 11 6 8 9 96.622 1. 1805 .9989
Value Added V .0 57.295 65.398 . 2993 12.030 11 10 10 10 25.367 1.2016 . 9847
Investment I .0 1. 279 1.137 .2954 .742 11 10 11 11 8.428 . 7123 . 8751
Gross Profit IT .0 22.993 22.402 .0624 4.048 11 9 11 11 25.371: 1.0066 .9847
Wage Rate W .0 4.163 4.122 . 1841 I .370 11 11 11 11 59.648 . 7689 . 9972
Capital Stock K . 0 14.138 13.988 ., 0253 ..7486 11 10 10 11 79.231 ..9727 . 9984
.
-.
(
~_."-----
......
w
-------
Stand. ,No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean I Mean t- of Est. ob. Within Inte rval tb b R2
SIC 32 - -J'; '"' Y:!:3S
Statistic Y YE Stat. Sy. I n YIS Y2"2S
-
.
Variables . . .
(Manufacturing)
"
Employment N 1.5198 6.418 7.526 . 8894 .933 33 20 27 30 58.287 1.1440 . 9907
Value Added V 1.0708 '97. 841 111.384 .7165 14.159 33 24 28 32 49.760 1.1234 . 9872
(' Investment I .5707 7.769 8.259 .3074 3. 026 33 29 32 33 16.523 . 8850 . 8947
:i; Gross Profit n . 1475 53.087 52.149 .0985 5.862 33 26 32 33 43.722 . 9745 .9835
Wage Rate v\[ .0577 6.845 6.828 .0833 .338 33 32 33 33 57.195 .8752 . 9903
Capital Stock K ;1603 101.233 100,236 .0546 3.056 33 27 32 33 165.744 ".9920 .9988
..
I I
STONE. Cl;AY, AND GLASS PRODUCTS.
-------
PRIMAR Y METAL INDUSTRIES
(J
t
Stand. ~ No.
Normal- Actual Estimate Error of No. of observations
SIC 33 ized U - Mean Mean t- of Est. 'ob. Within Inte rva1 tb b R2
- ~ -" Y2-2S I Y:!:3S -
Statistic Y YE Stat. Sy. n yi-s
~ I
Variables' . .
(Manufacturing)
"
Employment N 1.3966 17.936 23.425 .9048 3.297 36 21 25 29 88.624 1.3105 . 9956
Value Added V 1.1375 274.867 339.736 . 7023 90.386 36 26 34 34 91.410 1.2025 .9958
f Investment I .5887 32.875 33.452 .0535 15.676 34 27 33 34 ' 20.408 . 9041 .9264
Gros s Profit IT .0113 131.396 124.817 .1661 48.810 36 34 36 36 54.607 . 9129 .9884
Wage Rate W .1577 7.661 7.654 .0412 .289 36 35 36 36 56.567 .8741 .9892
Capital Stock K ...0123 374.716 374..969 .0022 15. 981 34 30 32, 33 150..306 .9999 . 9985
" I
I
......
U1
-------
"
FABRICATED METAL PRODUCTS
. Stand. i
f No.
Normal- Actual Estimate Error I of No. of observations
ized U - Mean I Mean t- of Est. ob. Within Inte rval tb b R2
SIC 34 - ( -iTS I Y2-2S I Y:!3S
Statistic Y YE Stat. Sy. n
- .
Variables ' '
(Manufacturing)
"
Employment N 1.3119 17.154 20.935 .7280 16.651 46 44 46 46 118. 983 1.197.9 .9968
Value Added V 1. 1401 229.564 271.591 .6040 59.736 46 39 41 44 154.408 1. 1738 .9981
o Investment I . 1252 12.722 13.253 . 1550 6.102 44 43 43 44 44.737 1.0767 . 9790
I
;: Gross Profit IT I
.4295 )07.290 102.799 . 1558 11.639 46 38 42 43 74.698 .9777. .9920
Wage Rate \V .9761 6.864 I 7.009 1.0414 .512 46 43 46 46 20.136 . 7609 .8999
Capital Stock K .0584 141.371 I 140~674 . 0176 6.212. 44 41 44 44 43 5. 7 98, . 9967 .9998
.
-.
I
-------
MACHINERY, EXCEPT ELECTRICAL
-J
Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rva1 tb b R2
SIC 35 - ~--'" Y:!:3S
Statistic Y YE Stat. Sy. n Y2:S Y+2S
-
.
Variables . .
(Manufacturing)
Employment N 1. 4957 21.002 28.174 1.2494 3.029 49 18 30 37 69.028 1. 2768 . 9900
Value Added V 1.3606 314.556 400.480 .9812 44.507 49 21 33 42 95.858 1. 2459 . 9948
.; Investment I .4877 1 7. 467 19.552 .4434 5.395 47 42 45 46 68.975 1. 1193 . 9904
.-
Gros s Profit II .0533 149.463 140.827 . 2447 16.478 49 35 42 45 46.882 . 9545 . 9786
Wage Rate Vi . 4725 7.398 7.489 .5110 . 2828 49 46 49 49 77.864 . 9155 .9921
Capital Stock K .1096 188.958 188..497 &0097 5.628 47 30 41 44 194.829 1~0023 . 9988
"
I I
10
.......
-------
ELECTRICAL MACEINERY
C)
Stand. IN
f o.
Normal- Actual Estimate Error I of No. of observations
ized U - Mean Mean t- of Est. . 'ob. Within Inte rval tb b R2
Sic 36 _. I -y+S '-Y+2S Y1=3S
Statistic Y YE Stat. Sy. n
-
Variables' . .
(Manufacturing)
Employment N . 7745 24.338 27.956 .4620 ' 5. 723 39 35 36 38 6 1. 524 1. 1891 . 9901
Value Added V . 7 145 319.796 377.751 . 5691 55.648 39 29 33 35 1 06. 914 1.1836 . 9967
Investment I . 08 11 1 7. 61.1 17.575 . 0077 8.054 37 35 36 37 25 . 157 1. 0114 . 9461
Gross Profit IT .1149 145.519 15 O. 976 .1229.' 29.472 39 33 36 37 37.961 . 9631 .9743
Wage Rate W . 1449 7. 096 . 7. 128 .1694 .300 39 38 39 39 71. 975 .. 8 8 41 . 9927
Capital Stock K . 2649 41. 840 I 144.854 .0728 8.268 37 35 35 36 235.058 1.0119 . 9993
I
" I
~
to
-------
TRANSPOR T EQUIPMENT
()
- Stand. I No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. -~~iE..Inte rVc;.l tb b R2
Sic 37 - ~ YIS Y2"2S. Y:t3S
Statistic Y YE Stat. Sy. n
-
Variables . .
(Manufacturing)
Employment N 1. 2980 27.674 38.229 . 9416 12. 538 35 27 32 33 60.500 1. 3932 . 9908
Value Added V 1.2040 435.426 559.231 . 6923 135.587 35 24 32 33 52.252 1. 1998 .9877
Investment I .1840 27. 061 26.128 . 0846 16. 927 34 33 34 34 69.874 .9096 . 9933
Gross Profit IT I
. 3935 195.935 191.500 . 0578 98.935 35 31 33 34 25.200 .8435 . 9491
Wage Rate Vi 1.4154 7.962 7.783 . 7980 .836 35 31 35 35 51.206 .5713 . 9872
Capital Stock K .0981 244.463 245.936 .0157 1"7. 353 34 32 33 34 269.382 1. 0177 . 9995 I
.
"
I
-
~
-------
INSTRUWENTS AND RELATED PRODUCTS
o
I I Stand. t No.
I of observations
Normal- Actual Estimate Error i of No.
SIC 38 ized U - Mean Mean t- of Est. ! ob. Within Inte rval tb b R2
- ! -A V2-2S Y:!:3S
Statistic Y YE Stat. Sy. n yiS
- I I
.
" !
Variables I - -
(Manufacturing) I
I
!
i
Employment N .0 14.125 16.207 .3300 2.677 16 12 14 15 75.921 1.2130 .9974
Value Added V . 0 262.713 224.782 .2768 91.726 16 15 15 15 21. 291 .6690 .9679
Investment I .0 13.602 19.101 .4907 8.328 115 12 13 14 29.841 1.2260 . 9845
Gros s Profit IT .0 153.. 511 119.534 .3600 56.776 16 14 15 15 41.496 .6499 . 9914
Wage Rate '.v .0 7. 281 7.055 .8041 .486 116 15 16 16 16.191 .8025 .9457
I I ~ J I
I I
! I ! I
Capital Stock K .0 83.32f ! 94. 211 . 1949 I 8.688 15 10 12 14 -340.844 1.1393 .9999
I
I I
-. I I
I i I
! I
I
I
I I
N
o
-------
MISCELLANEOUS PRODUCTS
I~
I I Stand. ! No.
Normal- Actual Estimate E)~ror I of No. of observations
SIC 39 ized U - Mean Mean t- of Est. ! "ob. Within Inte rva1 tb b R2
- -~ yi"2S I Y2:3S
Statistic Y YE Stat. Sy. : n yiS
- , i
Variables' I " "
!
(Manufacturing)
,"
Employment N .6222 11. 445 12. 266 . 1363 2.592 20 18 19 20 207.469 1. 0691 .9996
Value Added V .0271 122.536 120.617 .0323 29.344 120 I 20 20 20 93.621 1.0131 . 9978
In'\.'estment I .0 3.923 2. 981 . 5688 1.900 18 16 17 18 16.293 . 8 249 .9396
Gross Profit 11 .3787 59.861 54.577 . 1940 10.291 120 16 19 20 80.702 .9334 . 9971
I
I
I I
Wage Rate W .1082 5.558 5.510 . 2906 .410 120 I 20 20 20 43.223 .8172 . 9899
Capital Stock K :O 49.014 47~857 . 0442 1. 929 18 I IS 16 17 193.208 ".9724 . 9995
I
'. I
I
I
-------
()
N
N
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + E
, I
SIC 0 SIC 20 SIC 22
Aggregate of all 19 SIC s Food & Kindred Products Textile Mill Products
tb b. R2. tb b R2 .t b R2
Variables
(Manufacturing)
Employment N 165.355 1. 1914 .9966 11 7. 348 1. 1722 .9928 78.956 1.2208 .9951
Value Added V 136.844 1.2499 .9950 139.776 1.0934 .9951 66.971 1. 1417 .9932
Investment I 85.221 1.0416 .9863 35.082 .8399 .9367 34.038 .9398 .9738
Gross Profit n 72.922 1.0407 .9824 105.259 .9444 . 9916 57.888 .8789 .9909
Wage Rate W 208..834 1. 0224 .8742 220.231 1.0203 .9223 155.329 1.0373 .9561
Capital Stock 347.967 .9903 .9992 211. 421 .9992 .9980 108. 89.9 .9817 .9974
-------
,',
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY, + f
()
SIC 23 SIC 24 SIC 25
Apparel & Related Product~ Lumber & Wood Products Furniture and Fixtures
b. 2 b R2 b R2
tb R' tb .t
Variables
(Manufacturing)
Employment N 265.935 1.1161 .9994 40.400 1.3496 .9641 58. 10C 1.2865 .9904
Value Added V 143.695 1.0068 .9980 35.639 1.3063 .9546 70.82E 1. 1992 .9939
Investment I 64.850 . ,6600 .9906 9.267 .8464 .6526 22.938 .9934 .9369
Gross Profit IT 138.498 .8425 .9979 34.437 .9005 .9534 69.57<1 .9404 .9939
Wage Rate W 194.'014 1. 0384 .9681 134.202 1. 0641 .9797 251.622 .9900 .9798
Capital Stock 1390.279 i.0036 1.000 148.134 .9629 . 9976 429. 85~ .9684 .9998
N
I,J.)
-------
(')
N
~
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE= bY+ E
SIC 26 SIC 27 SIC 28
Paper & A llied Products Printin~ and Publication Chemicals & Allied Pro.
. tb b. R2. tb . b R2 tb b R2
Variables
(Manufacturing)
Employment N 120.092 1. 1200 .9956 210.152 1. 2048 .9987 41.35( 1.4664 .9640
Value Added V 76.740 1.0777 . 9892 87.029 .9370 .9929 72.91, 1. 3213 .9883
Investment I 17.874 1. 1.602 .8326 63.315 .9970 .9864 74.83t 1. 0428 .9927
Gross Profit II 52.816 .9462" .9776 81. 163 .7616 .9920 72.29 .9438 .9886
Wage Rate W 322:539 1.0046 . 9468 334.242 1.0100 . 9579 264. 18, 1.0032 .9477
Capital Stock 535.289 .9988 .9998 736. 044 .9943 .9999 114.801 .9947 .9956
-------
()
.
N
U1
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + f
SIC 29 SIC 30 SIC 31
Petroleum & Coal Products Rubber & Plastics Prod. Leather & Leather Prod.
b 2 R2 R2
. t R' tb b t b
b
Variables
(Manufacturing)
Employment N 14.975 1. 8789 .8105 80. 927 1. 2368 .9931 137.969 1. 1760 .9990
Value Added V 27. 11 7 1.4705 .9521 56.072 1.2113 . 9858 36.104 1.1701 .9849
Investment I 8.096 ..8693 .7170 14. 128 .8707 .8692 13.035 .8055 .8587
Gros s Profit n 29. 171 . 8821 . 9672 46.407 ".9700 .9797 38.174 .9890 .9857
Wage Rate W 11 L 528 1. 0271 .91.43 147.034 1. 0075 . 9342 ~05. 690 .9863 .9164
Capital Stock 76.255 1.0171 .9967 322. 354 1.0208 . 9997 116. 10~ .9814 .9984
-------
()
N
0'
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + E
SIC 32 SIC 33 SIC 34
Stone, Clay, and Glass
Prod ucts Primary Metal Industries Fabricated Metal Prod.
b . 2 b R2 b R2
. tb R' tb . t
Variables
(Manufacturing)
Employment N 100..732 1. 1628 . 9906 116.342 1.3087 .9957 49.739 1.2062 .9968
Value Added V 86.556 1. 1333 .9875 115.207 1.2153 .9957 95.397 1. 1772 .9981
Investment I 26.372 ..9885 .8769 25.839 .9433 .9236 57.643 1.0623 .9790
Gross Profit II 76.051 . 9797 .9840 68.872 . 9265 .'9881 94.073 .9703 .9920
Wage Rate W 310~636 . 9958 . 9715 414.171 .9981 .9695 79.418 1. 0182 .7978
Capital Stock 286.655 . 9908 .9989 196.565 1.0002 .9986 ,54.665 .9961 .9998
-------
(')
N
-.]
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + E
SIC 35 SIC 36 SIC 37
Machinery, Except
Electrical Electrical Machinery Transport Equipment
. t b R2. tb b R2 t b R2
b
Variables
(Manufacturing)
Employment N 89.155 1. 3043 .9892 76.552 1. 1737 .9899 75.644 1. 3891 .9910
Value Added V 124.623 1. 2570 .9947 137.935 1. 1827 .9968 61. 080 1.2252 . 9866
Investment I 90.382 1.1193 . 9906 34.056 1.0054 .9475. 77.800 .9236 .9925
Gros s Profit II 61. 725 .9493 .9790 47.324 .9896 .9729 29.024 .8772 .9446
Wage Rate W 460:.894 1. 0108 .9814 363.075 1.0027 .9747 98.561 .9695 .4980
Capital Stock 254.636 f. 0004 . 9988 300.146 1. 0156 .9993 311.47<1 1. 0142 .9995
.J
-------
()
. .
N
00
1969
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + E
I ] . SIC3 8 [ SIC 39
Miscellaneous Products
Instruments & R elated Prod
b 2 R2 . 2
tb R' tb b t b R
Variables
(Manufacturing)
Employment N 83.356 1. 1833 . 9963 252. 930 1. 0098 . 999b \
Value Added V 21.371 .7182 .9501 108.513 1. 0041 . 9977
Investment I 31. 439 1. 2634. . 9812 20.061 .8013 . 9410
G'ross Profit II 35.598 . 6758 .9841 97.004 .9264 . 9971
Wage Rate W 131. 547 .9668 .9091 229. 115 . 9898 . 9460
"
Capital Stock 386.732 1.1370 .9999 235.011 .9736 .9996
-------
"
APPENDIX D
INTERNAL VALIDITY RESULTS BY TWO-DIGIT DETAIL
FOR 1967 FOR SIC 0, 24, 29, 31
D. 1
-------
VALIDA~~ :ON WITH 1966-67 )A'~A
AGGREGATE OF ALL 19 SICs
Stand. ,No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b R2
SIC 0 - -yiS 1'2"2S Y2"3S
Statistic Y YE Stat. Sy. n
~
.
Variables ' '
(Manufacturing) "
Employment N 1.0824 181. 016 193.922 .2999 I 23.755 56 41 53 56 100.107 .9973 .9945
Value Added V .9964 1552.367 1682.135 .3547 236.775 89 67 80 88 120.232 1.0287 .9939
t Investment I .0524 161.555 160.097 .0331 31.035 56 45 54 55 43.682 .9360 .9720
{'\ Gross Profit n . 1498 736.784 745. 148 .0499 202. 526 189 80 86 87 1. 0583
71.893 .9833
Wage Rate W . 3550 6.462 6.526 .4535 .293 56 39 55 56 19.779 .8431 .8765
Capital Stock K :7274 1484.059 11602.636 .3694 327.348 56 45 50 54 50.670 1. 1172 .9790
" I
I I I I
-------
VALIDATION WITH 1966-67 DATA
WITHOUT CONSTANT YE = bY + E
AGGREGA'I.'E OF ALL 19 SICs
tb b R2
SIC 0
Variables
(Manufacturing)
Employment N 112. 643 1.0263 . 9925
Value Added V 137.175 1.0450 . 9932
Investment I 60.302 .. 9628 . 9708
Gross ProfitTI 84.857 1.0433 I .9828
I
1.0076 I
Wage Rate W 174.870 .8447
Capital Stock K 68.246 1.0997 .9789
I
I
D.3
-------
Lumber and l/food Products, 1967
.. i
I
t)
,po.
t .
. Stand. No.
:
Normal- Actual Estimate Error of No. of observations R2
ized U - Mean Mean t- of Est. ob. Within Inte rval tb b
, - -y+S Y+2S Y:!:3S
SIC 24 Statistic Y YE Stat. Sy. n
~ .
. .
Variables
(Manufacturing)
Employment N l.'4347 2.225 2.797 . 9315 .4185 20 8 16 19 46.669 1. 1875 . 9913
.,
Value Added V 8927 ~1, 240 26.389 .8463 3.4006 20 13 15 17 27.916 1.2560 .9762
i Investment I ! O. '0 '. 965 1. 240 ' . 9272 .5428 19 12 17 18 5.508 .8566 . 6198
\
'\
Gross Profit IT ,.2976 9. 744 9.095 ..2795 1. 5459 20 17 18 20 25.942 .9517 .9725
.
Wage Rate Vi .9468 5.067 5.298 .8522 .3064 ~ 20 9 18 19 9.583 1. 088 1 .8270
Capital Stock K 0.0 17.875 2 1. 2 18 . 6199 2. 3088, 19 ' 10 14 16 32.723 1. 1 502 .9835
I
- I
f "
I
.;
-------
Petroleum and Coal Products, 1967
U"1
.
: Stand. . No.
"
Normal- Actual Estimate Error of No. of observations R2
' ob. Within Inte rva1 tb b
ized U - Mean Mean t- of Est.
SIC 29 _. Stat. Sv. -yETYf2S-Y+3S
Statistic Y YE n
I
- ,
.
. .
Variables
(Manufacturing) "
Employment N . 0 1 4.062 6.035 1. 06 11 2.9826 13 10 13 13 13.836 1. 3243 . 9407
Value Added V . 0 135.619 149.240 . 2496 53.5436 13 9 13 13 10.382 . 9367 .8990
. Investment I .0 30.955 25.885 '. 3944 16.0152 13 10 11 13 8. 154 .6612 .8451
Gross Profit n .O 102. 787 92.465 . 2542 18. 6418 13 12 12 12 31.422 .8585 .9880
Wage Rate W . 0 8.090 7.689 , 1. 935~ .3108 13 9 9 11 1. 003 .2563 .0003
Capital Stock K . 0 244.489 1273.045 . 3 115 40.6846 13 9 12 13 37.580 1.0771:'.9916
r "
It)
-------
Leather and Leather Products, 1967
. ,
Stand. No.
Normal- Actual Estimate Error of No. of observations
ized U - Mean Mean t- of Est.. ob. Within Inte rval tb b R2
-,., Y2-2S Y!3S
SIC 31 - Sy. Y:!S
Statistic Y YE Stat. n
-
Variables' . .
, .
(Manufacturing) '.
Employment N .0 .6~ 073 6.290 . 0713 . 76 91 15 11 12 13 16.932 1. 0219 . 9533
,
Value Added V . 0 . 4,6.576 45.585 - . 0460 12. 0298 15 13 15 15 38.350 .9298 . 9906
Investment I . 0 .887 1. 006 .2678 . 7422 15 12 14 14 5.689 1. 1 967 . 6921
tJ
C' Gross Profit n . 0 20.485 18.211 . 2414 4. 0480 15 13' 14 14 34.332 . 8761 . 9883
Wage Rate W . 0 4.162 6. 759 .9260 . 3702 15 13 14 14 .5431 3.1580 -.0530
..
Capital Stock K . 0 10. 746 12. 781 .4067 3.2176 15 12 15 15 :,40220 10 2008 .9953
t -.
I I
-------
t:1
--J
1967
RESULT OF REGRESSION WITHOUT CONSTANT
YE = bY + E
SIC 24 SIC 29 SIC 31
.
I 2 b R2 t b R2
I tb b. R ~b
Variables
(Manufacturing) '
I
'
EmptOyment'N 72.335 1. 23 12 . 9897 21. 075 1. 4102 . 9382 22.297 10 027 .9566
Value Added V 46.532 1. 2475 .9774 15.600 1. 0 1 9 1 . 8934 48.910 .. 9486 .9902
Investment I 9.740 1. 0954 . 5514 11. 469 . 7351 .8327 7.856 1. 1676 .7132
Gross Profit II 43. 775 . 9400 . 9737 44. 5 18 . 8783 . 9879 45.327 . 8815 .9890
Wage Rate W 63.732 1. 0464 . 8349 45.277 . 9474 . 5277 2.482 1. 6456 . 0170
Capital Stock 52.506 1. 1 719 . 9838 57.811 1. 0994 . 99 15 74.986 J.. 1 957 .9956
-------
APPENDIX E
INTERNAL VALIDITY RESULTS FOR TAX EQUATIONS
1967
E.1
-------
-
Variables
-
-
Total Local
Revenue, T .-
Property 'Tax,
.TP
M
Other Taxes, TO
N
'.
Federal and State
-Aid, TA.
".
Normal-
ized U -
Statistic
"
0.2171
0.6610
2.8185 *"
0.6512
,
Actual
Mean
-
Y
370.256
148. 186
32.532
189.536
TAXES AGGREGATE', 1967
Estimate
Mean
YE
321. 436
158.138
30.787
132.510
t-
Stat.
Stand.
Error
of Est.
Sy.
. .
.4095 234.956
.2110
76.632
. 1139 I 50. 962
.9168 257.531
!
I No.
I
I of
I :b.
I
I
No. of observations
~_~~thin A~e r:v~!. tb
I y:FSTY2-2S ! yi3S
82
69
82
70
82
74
82
62
77
76
79
78
80
79 .'
80
81
19. 8511
35.0025
6.8275
2.0910
b
.8894
. 9841
. 7283
. 81 24
R2
. 9166
.9379
. 7770
.6419
-------
TAXES AGGREGATE, 1967
WITHOUT CONSTANT YE = bY + E
tb b R2
Variable
Total Local Revenue, T 33.0376 0.8855 0.9175
Property Tax, TP 39.5730 1. 0006' 0.9374
Other Taxes, TO 17.9185 0.7469 0.7737
Federal and State Aid, T A 13.1045 0.7911 0.6440
E.3
-------
APPENDIX F
IDENTIFICATION OF AQCRs WITH ESTIMATES OFF BY
MORE THAN 1, 2, 3, STANDARD ERRORS
(AGGREGATE MANUFACTURING)
F. 1
-------
1969, AGGREGATE MANUFACTURING
Variable
I AQCR s Off by 1 to 2 Standard Errors
of Estimation
Employment
5 .Detroit, Mich.
6 San Francis co, Calif.
8 Pittsburgh, Pa.
12 Baltimore, Md.
14 Minneapolis -St. Paul, Minn.
16 Buffalo, N. Y.
17 Milwaukee, Wis.
18 Cincinnati, Ohio
20 Dallas, Texas
21 Seattle-Everett, Wash.
22 Kansas City, Mo.
25 Indianapolis, Ind.
26 Miami, Fla.
30 Providence- Pawtucket, R. I.
40 Memphis, Tenn.
74 Rochester, N. Y.
AQCR s off by 2 to 3 standard errors of estimation
7 Boston, Mass.
9 St. Louis, Mo.
11 Cleveland, Ohio
15 Houston, Texas
19 Louisville, Ky.
67 Greensboro, N. C.
AQCRs off by 3 or more standard errors of
estimation
1 New York, N. Y.
2 Chicago, Ill.
3 Los Angeles, Calif.
4 Philadelphia, Pa.
F.2
-------
1969, AGGREGATE MANUFACTURING
~
Variable
AQCR s off by 1 to 2 standard errors of estimation
Value Added
6 San Francisco, Calif.
18 Cincinnati, Ohio
21 Seattle- Everett, Wash.
22 Kansas City, Mo.
23 San Di.ego, Calif.
25 Indianapolis, Ind.
26 Miami, Fla.
29 Portland, Ore.
31 Phoenix, Ariz.
33 Columbus, Ohio
35 Dayton, Ohio
36 Birmingham, Ala.
61 Allentown-Bethlehem-Easton, Pa., N. J.
67 Greensboro, N. C.
76 Scranton/Wilkes 'Barre-Hazelton, Pa.
100 York, Pa.
I
I
I.
I
I,
AQCRs off by 2 to 3 standard errors of estimation
12 Baltimore, Md.
14 Minneapolis -St. Paul, Minn.
16 Buffalo, N. Y.
17 Milwaukee, Wis.
24 Atlanta, Ga.
30 Providence- Pawtucket, R. 1.
AQCRs off by 3 or more standard errors of
estimation
1 New York, N. Y.
2 Chicago, Ill.
3 Los Angeles, Calif.
4 Philadelphia, Pa.
5 Detroit, Mich.
7 Boston, Mass.
8 Pitts burgh, Pa.
9 St. Louis, Mo.
11 Cleveland, Ohio
20 Dallas, Texas
F.3
-------
1969, AGGREGATE MANUFACTURING
Variable AQCRs off by 1 to 2 standard errors of estimation
Investment 5 Detroit, Mich.
8 Pitts bur gh, Pa.
12 Baltim.ore, Md.
15 Houston, Texas
19 Louis ville, Ky.
21 Seattle- Everett, Wash.
- ._-.. .--.... -.-
AQCRs off by 2 to 3 standard errors of estimation
2 Chicago, Ill.
4 Philadelphia, Pa.
AQCR s off by 3 or more standard errors of
estimation
Variable AQCRs off by 1 to 2 standard errors of estimation
Profit 3 Los Angeles, Calif.
8 Pittsburgh, Pa.
19 Louis ville, Ky.
67 Greensboro, N.C.
74 Rochester, N.Y.
AQCRs off by 2 to 3 standard errors of estimation
15 Houston, Texas
AQCR s off by 3 or more standard errors of
estimation
1 New York, N. Y.
5 Detroit, Mich.
F.4
-------
1969, AGGREGATE MANUFACTURING
Variable
AQCRs off b
1 to 2 standard errors of estimation
Wage Rate
5 Detroit, Michigan
22 Kansas City, Mo.
26 Miami, Fla. .
28 New Orleans, La.
30 Providence- Pawtucket, R. I.
32 Tampa, Fla.
39 Chattanooga, Tenn.
40 Memphis, Tenn.
49 Lawrence-Haverhill/Lowell, Mas s.
70 Knoxville, Tenn.
71 Nashville, Tenn.
73 Richmond, Va.
74 R 0 ch est e r, N. Y.
i 76 Scranton/Wilkes Barre-Hazelton, Pa.
90 Lancaster, Pa.
98 Utica-Rome, N. Y.
99 Wichita, Kan.
00 York, Pa.
I AQCRs off by 2 to 3 standard errors of estimation
15 Houston, Texas
19 Louisville, Ky.
67 Greensboro, N. C.
AQCR s off by 3 or more standard errors of es
estimation
Variable
I AQCR s off by 1 to 2 standard errors of estimation
Capital Stock
2 Chicago, Ill.
3 Los Angeles, Calif.
4 Philadelphia, Pa.
5 Detroit, Mich.
7 Boston, Mass.
9 St. Louis, Mo.
12 Baltimore, Md.
F.5
-------
1969, AGGREGATE MANUFACTURING
16 Buffalo, N. Y.
17 Milwaukee, Wis.
18 Cincinnati, Ohio
19 Louisville, Ky.
30 Providence- Pawtucket, R. 1.
64 Davenport-R ock Island -Moline,
67 Greensboro, N. C.
72 Peoria, Ill.
74 Rochester, N. Y.
Iowa, Ill.
AQCRs off by 2 to 3 standard errors of estimation
14 Minneapolis-St.
27 Denver, Colo.
95 Rockford, Ill.
Paul, Minn.
AQCR s off by 3 or more standard errors of
estimation
1 New York, N. Y.
15 Houston, Texas
F.6
------- |