Three essays in environmental economics

HARVARD UNIVERSITY
G raduate School o f A rts and Sciences

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Committee on Public Policy
have examined a dissertation entitled
Three Essays in Environmental Economics

presented by FeiYu
candidate for the degree of Doctor of Philosophy and hereby
certify that it is worthy of acceptance.

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Three Essays in Environmental Economics
A dissertation presented

by

Fei Yu

to

The Committee on Higher Degrees in Public Policy

in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in the subject of

Public Policy

Harvard University
Cambridge, Massachusetts

July 2007

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Advisors:
Professor Robert Stavins (Chair)
Professor Dale Jorgenson
Professor Cary Coglianese

Fei Yu

Three Essays in Environmental Economics
This dissertation presents three essays in environmental economics. They address
issues o f environmental economics from macroeconomic, financial markets and program
evaluation perspectives, respectively.
The first essay examines whether air pollutants in the US states converge to
predictable patterns. US data concerning five types o f air pollutant emissions for the
period 1985 to 1999 were analyzed to test whether or not there is convergence in the
manner hypothesized by Stokey’s optimal growth model. The empirical tests show
evidence supporting conditional convergence o f emissions, where each o f the 51 states
converge to different steady states or balanced growth paths. The implied rates o f
convergence are in the comparable range with that o f income convergence.
The second essay employs an event study method to analyze the stock market
response to news o f firms having been awarded membership in the EPA’s National
Environmental Performance Track (NEPT) Program. The results indicate that
participating firms experienced positive cumulative abnormal returns over ten and fifteen
day event windows following release o f news on new memberships. Significant
determinants o f cumulative abnormal returns include R&D, total assets and sales.
The third essay analyzes the effectiveness o f a recently completed World Bank

project in China, where 5,500 rural households were subject to different combinations o f

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improved stoves and behavioral interventions to reduce indoor air pollution (IAP)
exposure. Fixed effects models, random effects models, linear probability models and
matching estimators were used in the analysis. There is significant evidence that the
interventions were effective in reducing indoor air pollution levels, and in reducing acute
respiratory infection (ARI) risks among children under five years o f age. Cost-benefit
analysis shows that both the combination o f stove and behavioral interventions and
behavioral interventions alone generate health benefits far exceeding the costs.
Behavioral interventions alone appear to be more cost effective.

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Table of Contents
Acknowledgements................................................................................................................ vi

Chapter 1.

Revisiting the Environmental Kuznets’ Curve:
Do Pollution Levels Tend to Converge to Predictable P attern s..............1

Chapter 2.

Participation o f Firms in Voluntary Environmental Protection Program:
An Analysis o f Corporate Social Responsibility and Capital Market
Perform ance................................................................................................... 27

Chapter 3.

Measuring Benefits from Interventions to Reduce Indoor Air Pollution in
Rural C h in a .................................................................................................... 60

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Acknowledgements
This has been a long journey, from undergraduate studies at the Dalian University
o f Technology to a doctorate from what in the People’s Republic o f China, my home
country, is considered the world’s most prestigious university. Each step o f the way,
including the Universities o f London and Princeton, has been most challenging and
inspiring, culminating in five-years o f intensive study at the Kennedy School o f
Government, Harvard University, leading to a Doctor o f Philosophy in Public Policy.
Many people have helped me along this journey, most notably my family
members (parents and husband) who provided the encouragement and support needed to
stay the course, and my professors who provided such wise guidance and inspired me to
push at the frontiers o f scholarly endeavor. During my doctoral studies I was blessed by
having a baby daughter, who provided much distraction but without whom my life would
be much less.
Members o f my dissertation committee have been especially helpful in
completing this long journey. Professor Robert Stavins was my supervisor from the

outset and 1 am very grateful to him for introducing me to environmental economics and
helping to chart a course o f studies and research o f such deep interest. I am also very
grateful to Professor Stavins for providing career guidance and for taking the time and
effort to ensure that I get well started in the next chapter o f my professional endeavors.
Professor Dale Jorgenson’s stature in the economics community could have been
intimidating but for his kindness and gentle manner in probing to the core o f subjects o f
inquiry. My first dissertation paper, on whether air pollution emissions in the United
States tend to converge to predictable patterns, originated from a required project in his

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class. Like Professor Stavins, Professor Jorgenson encouraged me to reach high
standards o f scholarship, however difficult theory, data sets and econometric methods
might prove.
Professor Cary Coglianese, the third member o f my dissertation committee,
helped me bridge academe and the policy world by guiding my research on EPA’s
volunteer programs to encourage good corporate practices. With the addition o f
Professor Coglianese, my dissertation committee reflected the spirit o f the public policy
program, for it included three scholars o f distinction from three different fields. I much
appreciated Professor Coglianese’s energetic inquiry and partnership in preparing
research papers, assisted so ably by Jennifer Nash, Executive Director, Corporate Social
Responsibility Initiative, Kennedy School. The association led to one o f my three
dissertation papers.
Many other professors at Harvard have contributed importantly to my
progression. Among these were Professors Alberto Abadie, Majid Ezzati, and Richard
Zeckhauser. Professor Alberto Abadie provided me step-by-step guidance in designing
and executing the econometric procedures employed in one o f m y dissertation papers. I

have also benefited a great deal from inspiring and fun discussions with Professor
Zeckhauser while co-authoring a paper together. Professor Majid Ezzati introduced me
to an important health issue in developing countries, adding another dimension to my
studies.
Fellow students in the Environmental Economics Program o f Harvard University
provided me encouragement and constructive commentary, as well as the opportunity for
me to learn o f their wide ranging fields o f inquiry. Louisa van Baalen, Director o f the

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PhD Program in Public Policy, was a constant friend and always an answer to my
frequent questions.
My research efforts would have been stymied but for the cooperation and
assistance o f a number of people and organizations. In particular, I would like to thank
Julie K. Spyres, Director, Program Development and Member Services, National
Environmental Performance Track, EPA. Also o f particular note, I would like to thank
Center for Disease Control o f PR China for sharing with me its extensive data set on
indoor air pollution derived during a joint study with the World Bank. Professor Majid
Ezzati, Harvard School o f Public Health, and Dr. Enis Baris, World Bank, guided the
study and engaged me in the process, providing the foundation for one o f my three
dissertation papers.
Schumpeter’s description o f capitalism as creative destruction brings to mind my
struggles to first define the subject and then structure theory or empirical research to
develop the hypotheses and counter hypotheses. Certainly there was much destruction
during the process, but hopefully some creativity as well. However, that is for others to
judge.
It has been a great honor and privilege to attend Harvard University. In closing, I

wish to thank the selection committees that approved my application and financial
support, including fellowships from the Belfer Center at the Kennedy School o f
Government and the Graduate School of Arts and Sciences.

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Chapter 1
Revisiting the Environmental Kuznets’ Curve:
Do Pollution Levels Tend to Converge to Predictable Patterns?
1.1 Introduction
The Environmental Kuznets Curve, a possible inverse U-shaped relationship
between economic growth and environmental quality has generated a good deal of
interest. At low levels o f development and income, environmental degradation is largely
the result o f a subsistence economy and relatively low levels o f biodegradable wastes.
W ith commercialization o f the agricultural sector and more extensive resource extraction,
and as industrialization intensifies, environmental degradation worsens. Yet higher levels
o f development and income, however, provide the resources and incentive for more
efficient and environmentally friendly technologies and/or constraints, and environmental
degradation declines (Panayotou 2000). This inverse U-shaped relationship between
economic growth and environmental quality is referred to as the Environmental Kuznets’
Curve (EKC).
If such a relationship can be verified, the policy implications are significant.1
There is the possible prospect of sustainable development, although it depends on factors
o f technology and preference. Further, it suggests the need for research into the turning
point, the degree o f environmental degradation before this point is reached, including
potentially pushing beyond ecological thresholds, and the institutional and policy

1 Although the existence o f the EKC are yet to be proved, the EKC relationship is already playing an
important role in policy-making. For example, the postulated relationship plays a substantial role in
forecasting greenhouse gas emissions. The International Panel o f Climate Change (IPCC) implicitly
assumes an EKC in their forecast o f greenhouse gas emissions.

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conditions required to ensure environmental recovery as development advances to a high
level. Most fundamentally, though, the premise itself requires careful scrutiny.
Using cross-country data for the United States, Grossman and Krueger (1993)
showed an inverted U-shape in the relationship between per capita GDP and ambient
levels o f both sulfur dioxide and suspended particulates. They estimated the GDP per
capita inflection point was in the range o f $4000 to $5,000 (in 1985 US dollars). Selden
and Song (1994) and Grossman and Krueger (1995) later produced more refined
estimates for these and other pollutants, based on better-quality data.
Subsequent studies have been conducted using as dependent variables various
airborne emissions, ambient concentrations o f various pollutants, water pollutants,
deforestation, per capita solid waste, carbon dioxide, lack o f safe water, and other factors.
The independent variable common to most models is income per capita, but some studies
have used purchasing power parity data. Results o f the empirical analysis vary widely:
some show a U-shaped relationship between the selected environmental indicator and per
capita income; some show a downward sloping linear relationship; and yet others show
an upward sloping linear relationship (Panayotou 2000). The estimated inflection points
range from $823 for deforestation (Panayotou 1993) to over $18,000 for carbon dioxide
(Moomaw and Unruh 1997).
The factors contributing to an EKC relationship have been classified into broad
groups. Panayotou (1997) and Islam, Vincent, and Panayotou (1999) identified three

distinct structural forces that affect the environment: (a) the scale o f economic activity,
(b) the composition or structure o f economic activity and (c) the effect o f income on the
demand for and supply o f pollution abatement efforts. The scale effect on pollution,

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controlling for the other two factors, is expected to be a monotonically increasing
function o f income; the larger the scale o f economic activity per unit o f area, the higher
the level o f pollution, all else equal.
Structural change that accompanies economic growth affects environmental
quality by changing the composition o f economic activity toward sectors o f higher or
lower pollution intensity. The composition effect is likely to be a non-monotonic
(inverted-U) function o f GDP; that is, as the share o f industry first rises and then falls,
environmental pollution will first rise and then fall - in relative terms - with income
growth, controlling for all other influences transmitted through income.
Isolated from the scale and composition effects, the income variable reflects the
demand for and supply o f pollution abatement. At low income levels, increases in
income are directed primarily towards food and shelter, and have little effect on the
demand for environmental quality. At higher income levels, increases in income lead to
higher demand for environmental quality (since it is a normal good). Engel’s curve for
environmental quality translates into an inverted-J curve between income and
environmental degradation (Selden and Song 1995). On the supply side, higher incomes
make available the resources needed for increased private and public expenditures on
pollution abatement. Further, they induce stricter pollution regulations to help internalize
environmental externalities.
Grossman (1995) has suggested a fourth structural force or factor contributing to
the EKC relationship - the “technological change effect” . This refers to technological

progress that accompanies economic growth, since wealthier countries can afford to
spend more on research and development. In turn, this contributes to the substitution of

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obsolete and environmentally-insensitive technologies with cleaner ones, leading to
improvements in the quality o f the environment. Policy-induced changes in pollution
abatement technology and use o f more energy efficient technologies illustrate the
influence o f this fourth factor.
There are many theoretical models offering explanations o f the EKC. Some
authors focus on shifts in production technology brought about by structural changes that
accompany economic growth (Grossman and Krueger 1993, Panaytou 1993). Others
have emphasized the characteristics o f abatement technology (Selden and Song 1995,
Andreoni and Levinson 1998). And yet others have focused on preferences and
especially the income elasticity for environmental quality. A few authors have
formulated complete growth models, with plausible assumptions about the properties of
both technology and preferences from which they derive the EKC.
A number o f critical surveys o f the EKC literature have been published. Arrow et
al. (1995) argue that the EKC model as presented in the 1992 World Development Report
and elsewhere implicitly assumes there is no feedback between economic production and
environmental damage, as income is treated as an exogenous variable. This highlights the
importance o f adopting a dynamic optimization model, wherein both income and
pollution are endogenously determined.
There is a seeming disconnect between theoretical models and empirical models.
The income-environment relationship specified and tested in much o f the literature is in a
reduced form function that aims to capture the “net effect” of income on the environment.
Income is used as an omnibus variable representing a variety o f underlying influences,

whose separate effects are obscured. Decomposition models that test the four sets o f

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structural factors contributing to the EKC relationship, outlined above, also seem to lack
rigorous theoretical frameworks.
Another problem is that most studies o f EKC are cross-country studies, with
developed countries on the high end o f the income axis and developing countries on the
low end. In order to infer the environment-income relationship o f a single country over
time, cross-country studies implicitly assume that all countries will follow the same
growth pattern. Critiques argue that the EKC that emerges with cross-country and crosssection analysis “may simply reflect the juxtaposition o f a positive relationship between
pollution and income in developing countries with a fundamentally different, negative
one in developed countries, not a single relationship that applies to both categories o f
countries” (Vincent 1997).
A further source o f concern regarding empirical estimates o f the EKC is the
comparability and quality o f available environmental data. Stem et al. (1996) noted that
pollution data used in environmental Kuznets curve studies are “notoriously patchy in
coverage and/or poor in quality”. For these reasons, a number o f EKC studies involve
only single countries, where the data may be better and more consistent.

Most o f these

studies, except those for the United States, suggest that the EKC relationship is weak and
does not hold over time. However, different studies indicate conflicting results as to the
effects o f growth on the environment (Borghesi,1999).
In what follows, a somewhat different question is probed than the hypothesized
inverse U-shaped relationship between economic growth and environmental quality.

Rather than trying to trace out the EKC, this paper focuses on testing whether pollution
levels in a country (or state/province) tend to converge over time towards the levels

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defined in the steady state and/or the balanced growth path.2 Brock and Taylor (2004)
used OECD data to test convergence predicted by a “green Solow model” and found
significant evidence o f convergence. The models employed for this purpose are those
developed by Stokey (1998); an endogenous growth model and an exogenous technical
change model with pollution as a by-product o f production. The case study is for the
United States, employing 1985-99 data concerning state emissions o f five o f the seven
elements used to measure air quality: CO, NOX, PM10, SO2 and VOC.3
Two hypotheses are tested: (1) emissions at the state-level follow the convergence
process predicted by Stokey using an optimal growth with pollution model; significant
evidence is found supporting the proposed convergence phenomenon; (2) states converge
to their respective steady states rather than the same steady states; there appears to be
significant inter-state differences concerning steady state or balanced growth path
emission levels, reflecting a wide variety o f state-specific characteristics; coefficient
estimates will be biased if the modeler assumes interstate homogeneity.
Section 1.2 following describes in more detail the data and econometric models
used to test these hypotheses. Section 1.3 presents the empirical results and Sector 4
provides the main conclusions.

2 Steady state refers to no growth in per capita income while a balanced growth path refers to common
growth rates in capital, output and consumption.
3 Emissions o f the other two criteria air pollutants, NH3 and PM2.5 are not available for the years from
1985 to 1999.

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1.2 Data and Econometric Models Employed
State-level data for annual emissions o f CO, NOx, SO2, PM10 and VOC4 were
drawn from the National Emissions Inventory o f the US Environmental Protection
Agency (EPA)5. Emission estimates for the years 1985-1999 were constructed using a
‘bottoms-up’ methodology, whereby emissions derived at the facility or county level
were aggregated to the state-level. The emission estimates include non-point, point and
mobile sources. All emissions data are in tons per year. The 1985-1999 data used in this
study were last updated in 2002. Income and demographic data used in the study come
from the US Bureau o f Economic Analysis and the US Census Bureau. All income data
are expressed in 1983 dollar terms. Table 1-1 provides the summary statistics.

4

These pollutants are: carbon monoxide (CO), sulfur dioxide (S 02), particulate matter (PM 10), volatile
organic compounds (VOC) and nitrogen oxides (NOx).

5 EPA's National Emission Inventory (NEI) database contains detailed information about sources that emit
criteria air pollutants and their precursors, and hazardous air pollutants. An extract o f the database for
AirData includes estimates o f annual air pollutant emissions from point, nonpoint, and mobile sources in
the 50 States, the District o f Columbia, Puerto Rico, and the Virgin Islands. EPA conducts a national
inventory o f air pollutant emissions at three-year intervals, and adds the new data to the National Emission
Inventory database. Between inventories, EPA refines and corrects the emissions data, and updates the
database several times. Data are extracted for use in AirData approximately once per year.

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Table 1-1: Summary Statistics of Data
Annual State-Level Data for 51 States: Emissions pc (ton per year), population and income
pc, 1985-1999
Variable

Obs

Mean

Std. Dev.

Min

Max
8.595
1.010

CO

765

0.543

0.596

0.151

nox
pmlO

765
765

0.089
0.205

0.030
0.009

so2

765

0.123
0.196
0.102

0.106

0.004

0.669

VOC

765

0.106

0.103

0.031

1.491

popu

765
765

5000229
14557.910

5509847

453401

33100000

2389.469

9279.550

23175.330

Min

Max

0.105

-2.338
-0.770

2.376
1.295

-0.012

0.200
0.124

-1.253
-0.602

1.358
1.030

pci

1.556

Annual Growth (log difference) for Testing Eq. (2),
Mean

Variable
geo
gnox

Obs
714
714

gpmlO
gso2

714
714

gvoc

714
714

-0.016

0.130

-1.203

1.229

gpopu

0.007

gi

714

0.013

0.010
0.021

-0.038
-0.112

0.069
0.086

-0.005
-0.002
-0.041

Std. Dev.
0.204

85-92 Interval Growth Rates (log difference) and Structure Variables, Testing Eq. (6)
Variable

Obs

Mean

Std. Dev.

Min

Max

geo
gnox

51

-0.036

0.141

0.001

0.073

-0.844
-0.444

0.263
0.153

gpmlO
gso2

51
51

51

-0.019
-0.014

0.089

-0.538
-0.179

0.077
0.461

gvoc
gpopu

51
51

-0.032
0.012

0.084

0.078
0.035

gi
sso

-0.008
-0.192
-12.583

svoc

51
51
51
51
51

0.040

-0.518
-0.015
-0.003
-0.471
-0.379
-12.830
-0.249

spm

51

0.015

-0.445

SCO
snox

0.021

-0.190
-0.424

0.111
0.010
0.013
0.119
0.054
0.171

0.053
0.364
0.078
-12.083
0.021
-0.358

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Table 1-1 (continued)
92-99 Interval Growth Rates (log difference) and Structure Variables, Testing Eq. (6)
Variable

Obs

Mean

geo
gnox

51

0.213
-0.104

gpmlO
gso2
gvoc
gpopu
gi
sso2
SCO

spm
svoc
snox

Std. Dev.

Min

Max

0.285

-0.575

1.337

-0.119
-0.109
0.041

0.093
0.305

-0.362
-1.253

0.185
0.608

0.121
0.299

-0.443
-1.137

0.148
0.987

51
51

0.008
0.016

0.008
0.011

-0.007
-0.008

0.037
0.047

51
51

-0.296
0.144

0.079
0.097

-0.574
-0.242

-0.129
0.402

51
51
51

-0.233
-0.092

0.021

-0.335

-0.170

0.090
0.029

-0.283
-0.094

0.227
0.069

51
51
51
51

-0.037

85-99 Interval Growth Rates (log difference) and Structure Variables, Testing Eq. (6)
Variable

Obs

Mean

Std. Dev.

Min

Max

geo

51

-0.091

0.287

-0.411

1.300

-0.045

0.200

-0.534

0.497

-0.746

-0.227
-0.290
0.122

0.515
0.436

-1.843
-1.702

0.316
0.130

-0.839
-0.201

0.713
0.665
0.830

0.199
-0.079
-0.662

0.066
0.128

-0.115
-0.555
-0.690

gnox
gpmlO
gso2
gvoc
gpopu
gi
Sco
Spm

51
51
51
51
51
51
51

0.319

0.023

-0.096

-0.588
0.121

Svoc

51

51

0.020
0.046

-0.267

0.119

-0.533

0.153

sso2

51

-0.294

0.127

-0.942

-0.109

Snox

51

0.643

0.277

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The five emissions included in the study contribute to a number o f serious health
effects and together they comprise a reasonably comprehensive set o f the main factors
that compromise air quality. CO exposure can lead to high levels o f carboxyhaemoglobin
in the blood and to angina attacks; nationwide, three-quarters o f carbon monoxide
emissions come from motor vehicles (cars and trucks) and non-road engines (such as
boats and construction equipment). NOx is one o f the main ingredients in the formation
of ground-level ozone, which can trigger serious respiratory problems; the primary
sources o f NOx are motor vehicles, electric utilities, and other industrial, commercial,
and residential sources that bum fuels. SO 2 contributes to respiratory illness. Over 65
percent o f S 0 2 released to the air, or more than 13 million tons per year, results from
electric utilities, especially those that bum coal. Other sources o f S 0 2 are industrial
facilities that derive their products from raw materials like metallic ore, coal, and crude
oil, or that bum coal or oil to produce heat. Both NOx and S02 contribute to acid rain.
PM 10 is associated with serious health effects; again the source is largely cars, trucks,
buses, factories, and construction sites. VOC emissions also contribute to particulate
formation, and VOCs and NOx are main contributors to tropospheric ozone pollution,
which is linked to acute and chronic respiratory problems. Motor vehicle exhaust and
industrial emissions, gasoline vapors, and chemical solvents are some o f the major
sources of VOC.6
The econometric models employed are based on Stokey’s optimal growth model
with pollution (Stokey 1998). Optimal growth models provide one general class o f
theoretical foundation for the empirically observed EKC. They also represent an

6 EPA website on six common pollutants: www.epa.gov.

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independent literature o f models o f development. These models use a Ramsey framework
with pollution as a by-product o f production, and there is a trade-off between the
disutility from a pollution byproduct and the utility derived from consumption. In
Stokey’s model, the social planner specifies an optimal emissions standard that must be
achieved. The social planner then chooses paths for consumption and for the technology
in use so as to maximize the utility o f the (infinitely lived) representative household.
Stokey considers a one-sector endogenous growth model with linear technology (AK
model) and a one-sector growth model with exogenous technical change.
Under the endogenous growth model, when environmental regulation is binding,
the economy reaches a steady state7. As the economy approaches the steady state, total
pollution declines if the form of the utility function satisfies certain conditions. Stokey
assumes a standard constant inter-temporal elasticity o f substitution utility function.
When the elasticity o f marginal utility is greater thanl, total pollution declines. The
proportionate decline in marginal utility from increases in consumption is sufficiently
significant that the increase in disutility from pollution, as a by-product o f production,
dominates the increase in utility from consumption. Total pollution along the optimal
path and at the steady state is, in both cases, determined by preference, technology and
discount factors.
Under the exogenous technical change model, there is a balanced growth path
along which capital, output, and consumption all grow at the same rate. In the presence

7 Normally in AK models there are no steady states and no convergence. However, with pollution, output
is produced with the capital stock and the aggregate pollution level as inputs. Thus, the real return to

capital is not the constant A, but something that declines with capital for any fixed level o f pollution. As
utility is concave in consumption and convex in total pollution, it is not optimal to increase pollution
proportionally to the increase o f capital. As the capital stock grows the optimal emission standard becomes
stricter, reducing the real rate o f return. When the emission standard gets strict enough, capital
accumulation ceases (Stokey, 1998).

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o f pollution, the common growth rate is lower than without pollution. Pollution also
grows at a constant rate, which is lower than the common growth rate assumed for
capital, output and consumption. Again, if the elasticity o f marginal utility is greater
thanl, total pollution declines during transition towards and along the balanced path.
Total pollution during transition and along the balanced path depends on preference and
technology parameters and the share o f capital.
Since preference and technology parameters are hard to measure, it is difficult to
conduct tests o f the optimal growth path and the steady state. It is possible, however, to
test the relationship between the common growth rate o f capital, output and consumption
and the growth rate o f pollution emissions. If the economy is on the balanced growth
path, the growth rate o f pollution emissions should be a linear function o f the common
growth rate. Pollution emissions decline if the linear coefficient is negative, which
depends on preference parameters.
Another possible test is o f convergence. Both models predict convergence o f total
pollution emissions - to the steady state for the AK model and to the balanced growth
path for the exogenous growth model. Convergence can be tested through log
linearization around the steady state or the balanced growth path. It should be noted that
it is not assumed here that all economies converge to the same steady state or balanced
growth path. Instead, it may be the case that economies converge to different steady

states or balanced growth paths, reflecting differences in preference, production functions
and endowment.
The relationship between the common growth rate of capital, output and
consumption and the growth rate o f pollution emissions is given by

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(1.1)

Ge = fiG k

Where Ge is the growth rate o f pollution emissions per capita and Gk is the
common growth rate o f capital, output and consumption, again in per capita terms. P is a
constant determined by preference factors.
In standard econometric notation, the specification o f the empirical model is:
(1.2)

Yi = p X ,+ rjZi + eI

Where Y; is the annual growth rate o f pollution emissions per capita; X; is the
annual growth rate of personal income; Z, is a vector o f state characteristics to control for
differences in preference8; and s; is a shock term. It is assumed that Sj-s are independently
distributed with mean zero. A panel data analysis procedure is used to control for statespecific characteristics, and to correct for heterogeneity in the error term. Prais-Winsten
regressions were run for the five pollutants to correct for serial correlation and to produce
panel corrected standard errors (PCSE).
The convergence test is applicable to both the AK model and the exogenous
technical change model. For the AK model, the speed o f convergence when

approximating the steady state is given by9
^ ln^ >
at

-A [ln (£ * )-ln ( £ (l)) ]

(1.3)

Where A is the rate o f convergence, which is a function o f preference, technology
and the discount rate.10 This equation implies that

8 The differences in preference across states are not readily measurable or observable. Initial per capita
income, initial population levels, initial population density, and the population growth rate are included as
control variables.
9 The log linearization technique is used for studying income convergence. (Mankiew, Romer and Weil,
1992; Islam, 1995)

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ln (£ (0 ) = (1 - e ~u) In(E*) + e~u ln(£(0))

(1 .4)

Where E(0) is per capita emissions at some initial date. E* is per capita emissions
at the steady state. Subtracting In(E(0)) from both sides,
In(E(t)) - ln(£(0)) = (1 - e "*) ln(£*) - (1 - e * ) ln(£(0))

(1.5)

In econometric notation, the specification o f the empirical model is:
Yit

=

a , + f3Xlt_T + r]Zlt_T + s

(1.6)

Where Yt t is the log difference o f the initial and end per capita emissions; oti
equals ( l - e -^) ln(£; *), which is a function o f the per capita emissions at the steady
state; X; is the log initial level of per capita emissions; Z^-t is a vector o f control
variables; andf,.( is state-specific shift or shock term. Individual US States may have
different steady states determined by production technology, resource endowments,
institutions etc. and the differences in the steady state could be correlated with both the
growth rate o f emissions and the initial levels o f emissions per capita. If these differences
are included in the error term, the coefficient for the initial level o f emissions could be
biased. In order to avoid such bias, a set o f control variables is included to try and capture
state-specific shifts. Based on this correction, it is assumed that ei t is independent o f the
explanatory variables.11 The theory predicts that if there is convergence the coefficient
for the initial level o f emissions per capita will be negative.
The control variables include initial per capita income levels, initial population
levels, initial population densities, income growth rates, population growth rates and a

10 The half-life is log(2)/A,. Hence, if X = 0.05 per year, then the half-life is 14 years, which means half o f
the initial gap disappears in 14 years. (Barrow and Sala-Martin Xavier, 1999)
11 Such an assumption is common in growth models.

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