THREE ESSAYS ON THE ECONOMICS OF TRANSITIONING TO CLEAN ENERGY

By

Minsu Kim

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A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

Agricultural, Food, and Resource Economics—Doctor of Philosophy
Economics—Dual Major

2024

ABSTRACT

Human activities have caused widespread, rapid, and intensifying climate change. Overshooting

1.5 ◦C is inevitable in 2024, while substantial scientists have warned that irreversible changes will

settle down in many places over the Earth after a 2 ◦C increase since 1850-1900. We must find a

way to mitigate climate change, study its impact on our society, and build sustainable communities.

Nevertheless, it isn’t easy to find a socially desirable implementation of an environmental policy

due to its complexity and various stakeholders. This dissertation contributes to finding socially

desirable ways of tackling climate change in energy transition.

The first chapter, titled “Incentivizing capital investments in electric vehicle attributes to stim-

ulate demand,” studies the optimal purchase and investment subsidization of electric vehicles (EV)

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to stimulate investment. The US government has subsidized electric vehicles (EV) with a constant

purchase subsidy of $7500 to replace internal combustion engines (ICE). In this chapter, I analyze

the theoretical model consisting of firms’ dynamic Bertrand game of price and investment and a

government’s dynamic Stackelberg game with firms. I run this theoretical model by estimating

data for every vehicle model sold in the US from 2008 to 2019 and calibrating the model by the

collocation method. I show that the two dynamic policies have the same trend, in which the optimal

intervention begins at high values to spur early adoption before falling and approaching zero as EV

firms’ capital grows. In the two dynamic policies, the optimal policy intervention is very high at

the capital level in 2024: $10694 to $16073 (purchase subsidy) and $17.06 billion to $40.58 billion

(investment subsidy). Then, the optimal policy shrinks rapidly as EV capital increases. Dynamic

purchase and investment subsidy increase the total net present value social net benefit by $2.32

trillion (3.84%) and $1.44 trillion (2.39%) compared to zero policy and by $923 billion (1.49%)

and $47.7 billion (0.08%) compared to the current constant policy. Governments should strongly

intervene in the market first, gradually reducing their policy as the new business grows.

The second chapter, titled “Peer effects in electric vehicle adoption,” captures the peer effect of

EV adoption in Michigan. The market competitiveness of EVs has been improved as many countries

have introduced policies for stimulating EV adoption. A prior understanding of consumer behavior

is required because those policies try to alter the choices of consumers or firms in the market. There

is little literature on the peer effect on EVs, while substantial literature focuses on the consumers’

substitution pattern of vehicles. Consumers may hesitate to purchase an EV at first; however, if

they observe more EVs in their neighborhood, on the road, or in parking lots, their reluctance to

purchase an EV may be resolved. I adopt the spatial error and autocorrelated models and compared

the results with other spatial models with panel data by ZIP Code Tabulation Area (ZCTA) from

2013 to 2019 in Lower Michigan to address the spatial dependent trend. It shows that one increase

in cumulative EV adoption at the same ZCTA will increase next year’s EV adoption by 0.326 to

0.352 cars. One cumulative EV adoption increase in the same ZCTA has the same impact as an

income increase of $1125 to $1254. The policy should be set to adopt the EV aggressively to take

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advantage of the peer effect, which strengthens the aggregate demand for EV adoption.

The third chapter, titled “The impact of transnational municipal networks on local energy

consumption,” is co-authored with Dr. Sun-Jin Yun and published in Urban Climate. Local

governments are essential to the successful implementation of climate policies. They know where

funds should be allocated and how to increase efficiency at the local level. Transnational municipal

networks (TMNs) have galvanized local climate action by sharing best strategies and supporting

communication. This study asks whether and to what extent the International Council for Local

Environmental Initiatives – Local Governments for Sustainability (ICLEI), one of the major TMNs

in climate action, affects local energy consumption in South Korea. We use a staggered difference-

in-differences (DID) method, which is a robust alternative under staggered treatment, with a strongly

balanced panel dataset across 226 Korean counties between 2005 and 2019. We find that ICLEI

membership leads to a significant decrease in energy consumption per capita 4.53% to 6.62%

with county membership, 8.91% to 9.00% with state membership, and 11.8% to 21.4% with both

county and state membership. In addition, state membership shows a growing impact on energy

consumption reduction, while county membership has a weaker trend. The results are statistical

evidence of the role of TMNs in local energy policies. The central government may increase the

effectiveness of its energy policy by selectively supporting ICLEI members.

In loving memory of my grandparents and maternal grandfather, who loved me so much. It would
have been nice to complete this earlier. I love you always, maternal grandmother.

To my wife, Jieun, for her sincere love and being my unflagging supporter.

To my little cutie son, Ethan, whom I care for.

To my parents, Taeho and Sunhee, for their wholehearted support of my study.

To my cat, Tofu, for unexpected bites to wake me up.

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ACKNOWLEDGEMENTS

My journey started from my juvenile to contribute to a sustainable future and has now reached

this huge milestone. This would not be feasible without all the support from a group of people.

I am truly blessed to have those family, friends, collaborators, mentors, and reviewers who have

supported, encouraged, and motivated my journey.

I would like to thank all the committee members for helping me polish the research. First, I

really appreciate the support of Dr. Richard Horan, who has served as my advisor for five years

through my Ph.D. program. I was very happy when discussing ideas on theoretical models with

him and was always surprised by his intelligent ways of refining research ideas. I cannot forget

the moment when he became my advisor, and I look forward to our future collaborations. Next,

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I would like to thank Dr. Scott Swinton, who is my committee member for the graduate research

symposium and my dissertation committee. His extensive research experience greatly helped me

polish research ideas and papers, leading me to the next level of research.

I also especially thank Drs. Soren Anderson and Justin Kirkpatrick. They became my committee

members after several attempts to invite them, and it would be one of the best choices in my Ph.D.

program. Soren sincerely advised my research, and conversations with him always made me feel

connected to current mainstream environmental economics literature. Justin broadens my view of

research on peer effects on environmental goods. His comments considerably improved the second

chapter and made me jump into the peer-effect literature. I sincerely appreciate their unstinting

support, and I look forward to our future collaborations.

Other collaborators outside my committee have contributed to my research journey and pro-

fessional growth. Dr. Simone Valle de Souza, who was my research assistantship supervisor for

two and a half years, always supported me throughout my program.

It is my luck to have her

as my supervisor for research projects. Dr. Ki Hong Kim and Mr. Yutae Kim’s insights into the

automobile industry greatly helped me get my bearings in the first chapter. The third chapter could

not have been polished well without the support of Dr. Sun-Jin Yun, who is the co-author of the

third chapter and a Professor of Energy and Environmental Policy at Seoul National University.

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I also especially thank Dr. Rania Lachhab and Mr. Gi Heung Kim for their insight on staggered

difference-in-difference methods in the third chapter. I am also incredibly grateful to the substantial

number of reviewers at the academic conferences where I presented this research.

In addition, I want to thank the many supporters from the Department of Agricultural, Food, and

Resource Economics (AFRE), the Office for International Students and Scholars, and the Graduate

School at Michigan State University (MSU). They helped me focus on my research and Ph.D.

program. I especially thank Dr. Robert Myers, who was the former Chairperson and Professor in

AFRE, for securing funding for me when I arrived at MSU. I also thank Dr. Nicole Mason-Wardell,

who is the Associate Chairperson and Associate Professor in AFRE, for her unwavering support

and help for my program. Dr. James Sears, who is the chair of the job placement committee, also

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incredibly helps me focus on my research by advising me a lot about job searching.

I am also thankful for the invaluable support from friends and family. I thank MSU friends for

your warm friendship and support: especially Dr. Ming Fang, Dr. Judhajit Chakraborty, Sungmin

Cheu, Seowoo Lee, Saera Oh, and Jin Ho Lee. Enjoyable conversations with close friends in Korea,

such as Seven Stars and other pals, are invaluable sources of refreshment for me throughout the

program. I also thank my parents, Dr. Taeho Kim and Sunhee Kang, and dear brother, Geonwoo

Kim, for their unchanging support, which made me focus on my academic journey. I cannot forget

the unexpected bites of my adorable friend, Tofu, which made running optimization thrilled.

Finally, I would want to take my hat off to my wife, Dr. Jieun Seo. She has been an indispensable

pillar of my life with her unfailing love and support through a global pandemic and my graduate

studies, even as she was making the same journey as a postdoc. I am always proud of you for

what we have done and what we will do. I look forward to our journey ahead and hope it will be

enjoyable. In addition, I special thank to my little cutie and adorable son, Ethan, who has been my

motivation. I hope this research contributes to climate mitigation and energy transition, which will

make a sustainable future for Ethan and future generations. If it makes any little contribution, it is

by standing upon the shoulders of giants. I hope to make a change for all of us, as all we have to

decide is what to do with the time that is given to us.

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TABLE OF CONTENTS 

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii 

CHAPTER 1 INCENTIVIZING CAPITAL INVESTMENTS IN ELECTRIC VEHICLE 
ATTRIBUTES TO STIMULATE DEMAND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 
1.2 Market Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 
1.3 Calibration and Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 
1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 
1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21 
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 
APPENDIX 1.A: Tables and Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 
APPENDIX 1.B: Demand Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 
APPENDIX 1.C: Solving Optimal Decisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47 
APPENDIX 1.D: Collocation Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49 

CHAPTER 2 PEER EFFECTS IN ELECTRIC VEHICLE ADOPTION . . . . . . . . . . . . . . . . . . . 50 
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50 
2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52 
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56 
2.4 Empirical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .60 
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .63 
APPENDIX 2.A: Tables and Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 

CHAPTER 3 THE IMPACT OF TRANSNATIONAL MUNICIPAL NETWORKS ON LOCAL 
ENERGY CONSUMPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 
3.2 Background, Data, and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .86 
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89 
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .93 
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96 
APPENDIX 3.A: Tables and Figures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101 

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AFRE Department of Agricultural, Food, and Resource Economics

LIST OF ABBREVIATIONS

AIC Akike Information Criterion

ATE Average Treatment Effect

BIC Bayesian Information Criterion

CAFE Corporate Average Fuel Economy

CDP Carbon Disclosure Project

CO2eq Carbon Dioxide Equivalent

COVID-19 Coronavirus Disease 2019

CPI Consumer Price Index

CS Consumer Surplus

CS estimator Callaway & Sant’Anna estimator

DE Damage from social costs of carbon

DID Difference-in-Differences

Eq Equilibrium

EV Electric Vehicle

FFE Two-way Fixed Effect in Group and Time

FOC First-Order Condition

GCom Global Covenant of Mayors for Climate & Energy

GDP Gross Domestic Product

GE Governmental Expenditure

GexCom Global Executive Committee

GHG Greenhouse Gas

HJB Hamilton–Jacobi–Bellman

HP Horsepower

ICE Internal Combustion Engine

ICLEI International Council for Local Environmental Initiatives – Local Governments for Sus-

tainability

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IID Independent and Identically Distributed

IPCC Intergovernmental Panel on Climate Change

K-ExCom Korea Executive Committee

KEA Korea Energy Agency

LED Light-emitting Diode

LHS Left-hand Side

LL Log-likelihood function value

MNL Multinomial Logit

MPG Miles per Gallon

MPGe Miles per Gallon of Gasoline-Equivalent

MSRP Manufacturer-Suggested Retail Prices

MSU Michigan State University

NOx Nitrogen Oxides

OLNPP One Less Nuclear Power Plant

OLS Ordinary Least Squares

PS Producer Surplus

R&D Research and Development

RE Renewable Energy

RexCom Regional Executive Committee

RFE Two-way Random Effect in Group and Fixed Effect in Time

RHS Right-hand Side

SAC Spatial Autocorrelation Model

SAR Spatial Autoregressive Model

SCC Social Costs of Carbon

SDM Spatial Durbin Model

SEC U.S. Securities and Exchange Commission

SEM Spatial Error Model

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SNB Social Net Benefit

SOx Sulfur Oxide

TMN Transnational Municipal Network

TOE Tonne of Oil Equivalent

TSNB Total Net Present Value Social Net Benefit

TWFE Two-way Fixed Effect

US United States of America

ZCTA ZIP Code Tabulation Area (ZCTA)

ZEV Zero-Emission Vehicle

ZIP Zone Improvement Plan

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CHAPTER 1

INCENTIVIZING CAPITAL INVESTMENTS IN ELECTRIC VEHICLE ATTRIBUTES
TO STIMULATE DEMAND

1.1

Introduction

One of the most pressing concerns facing humanity is climate change. The IPCC (2022) argued

that global temperature increase should be kept below 2◦C to avoid irreversible systematic change

in global ecology and below 1.5◦C to avoid this safely. Achieving either goal requires substantial

cuts to carbon emissions. It is in this context that we need to consider transportation, one of the

main carbon-emitting sectors. In 2019, 29% of domestic carbon emissions in the US came from

transportation (US Environmental Protection Agency, 2020), and over 90% of fuel is petroleum-

based (US Environmental Protection Agency, 2020). Fortunately, we have an alternative to reduce

heavy carbon emissions: electric vehicles (EV). Curbing the temperature growth urgently requires

replacing petroleum-based vehicles with carbon-free vehicles, such as EV.

Growing evidence shows that consumers care more about price and attributes than the power

source when purchasing a vehicle (Jackman et al., 2023). Graham (2021) found that commonly

accepted advantages of EV are lower operating costs, such as maintenance and repair costs, and

better driving and environmental performance with less noise. The disadvantages are high purchase

cost, lower driving range, and long charging time. Zhang et al. (2018) found that consumers are

concerned about the price and attributes of EVs in their purchase: high price (23%), short driving

range (38%), inconvenient charging (21%), and short battery life (13%).

US governments have tried changing the market price factor with a constant subsidy. Changing

the market price affects consumer demand. The government has subsidized plugged-in electric and

electric vehicles via the American Clean Energy and Security Act (2009) since 2010. This law

sets a minimum credit of $2,500 for vehicles with at least 5 kWh battery capacity plus $417/kWh

beyond 5 kWh of capacity, capped at a maximum credit of $7,500.

In 2022 summer, the new

Inflation Reduction Act changed the details and conditions of subsidies; however, it maintained the

maximum subsidy at $7500. Therefore, the constant maximum subsidy at $7500 exists from 2010

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until now and in the future, considering the difficulties of the US legislative process.

It is worth noting that these decisions are driven to achieve EV adoption goals rather than to

maximize social net benefit (Rapson & Muehlegger, 2023). The current constant subsidy may

not, however, achieve maximum social welfare for two reasons. First, the optimal subsidy should

be changed over time in response to market change. Specifically, the optimal subsidy must be

set so that intertemporal marginal benefits and costs are the same, mindful that consumers are

concerned about the market price and attributes for their decision. If the EV attributes improve

dramatically over time, then consumers may be willing to buy an EV at a higher price, which means

that governments will need to provide less subsidy to achieve the same replacement effect.

In

recent decades, for example, EV driving range has markedly increased: the maximum range from

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100 miles to 375 miles, and the median range from 70 miles to 240 miles, between 2011 to 2019

(US Department of Energy, 2021). Maxwell & Decker (2006) found that responsive regulation is

required to achieve maximum social welfare because voluntary investment may lead to a suboptimal

equilibrium. Recent studies indicated that future implications would need to consider long-term

market growth and innovation via investment to achieve social optimality. Clinton & Steinberg

(2019) pointed out that subsidies will not improve welfare if they only take benefits from emission

reduction. Long-term EV market growth, production cost savings, or accelerated innovation could

substantially impact net welfare. Langer & Lemoine (2022) found that technological progress

would reduce the government’s expenditures by 77% to 95%. Therefore, the optimal policy will

shift as EV attributes improve and the price decreases. Second, subsidization in the current market

endogenously affects the subsidy in the future market by stimulating EV investment. This is because

the current subsidy improves future EV attributes and decreases prices. EV firms’ current profit

increases with more market sales due to purchase subsidies, allowing them to invest more in EV

capital. The firm’s investment in its capital will make for better vehicles in the future, which lessens

the subsidy required. The literature recognizes the necessity of considering the dynamic mechanism

of investment stimulation by the policy. Holland et al. (2016) argued that EV subsidization may

lead to lower production costs due to learning by doing and will increase adoption in the future.

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Luo et al. (2019) found that the government has to pay a much higher subsidy if it does not consider

the efficiency improvement in automated vehicles due to the subsidy itself.

Despite such agreement, the literature has not yet taken market dynamics into account when

studying subsidies or taxes. Market dynamics are especially important for products in the early

stage of business that are good at addressing externality but not market-competitive due to price and

attributes. The improvement of attributes by firms has been missed in previous models (Gulati et al.,

2017). In addition, most estimations of regulatory cost disregard the possibility of technological

innovation (Harrington et al., 2000). Previous attention focused on the constant optimal policy in

a static framework (Holland et al., 2021; Langer & Lemoine, 2022). More recent literature has

started to focus on the need to consider the dynamic effect of subsidies. Dynamic subsidization

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generates better outcomes than subsidies determined in a static framework (Chen & Hu, 2018; Luo

et al., 2019). For example, Luo et al. (2019) found that a higher initial subsidy helps to quickly

penetrate the initial stage where the benefit from the automated vehicle is lower than its cost. Langer

& Lemoine (2022) analyzed the dynamic subsidies for residential solar in California, focusing on

the demand side dynamic decisions, and found that the efficient subsidy increases over time.

This chapter makes two main contributions. To the best of my knowledge, this chapter is

the first to identify the optimal policy path, considering market dynamics on the production side

caused by the subsidy itself. Thus, it meets the recognized need to consider the dynamic impact

of subsidization. The recent work of Langer & Lemoine (2022) analyzed the optimal policy

path considering consumers’ value and price discrimination; however, they assumed that there is

no induced technological change, a gap that this chapter addresses. This chapter fills this gap

by theoretically and numerically identifying the optimal policy path in the presence of market

dynamics arising from capital investments. To do this, I develop a dynamic market model and

estimate demand and production relations using real market and investment data. I established a

dataset of all vehicle models sold in the US from 2005 to 2019 and SEC filing reports of firms to

estimate demand and production functions.

Second, this chapter compares a purchase subsidy and an investment subsidy. As we discussed,

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consumers care about price and attributes. Therefore, governments may subsidize the purchase

price to change the price or subsidize the investment to change attributes. The literature suggests

robust evidence of welfare being increased by enacting various types of individual instruments:

purchase subsidy (DeShazo et al., 2017; Clinton & Steinberg, 2019), purchase tax (Xiao & Ju,

2014), adoption subsidy of residential solar (Langer & Lemoine, 2022), and investment subsidy

(Jiang et al., 2018; De Groote & Verboven, 2019; Dong et al., 2019). Nevertheless, there is little

literature that compares policies. Anderson & Sallee (2016) shows important findings that market-

based policies are better than standards-based policies in fuel economy, not EV adoption. The main

policies for EV production in the US are standards-based: the Zero-Emission Vehicle (ZEV) and

Corporate Average Fuel Economy (CAFE) mandates. According to Bloom et al. (2019), an R&D

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tax credit is the best innovation policy with the highest quality and conclusiveness of evidence and

net benefit. Aghion et al. (2016) show that firms innovate more on EVs and less on ICEs when they

face higher tax-inclusive fuel prices. Acemoglu et al. (2012) argue that the optimal policy involves

both taxes and subsidies so that excessive use of carbon taxes is avoided. Therefore, this chapter

compares two market-based policies on price and investment.

1.2 Market Model

I develop a market model that considers consumption, production, and policy decisions, as

diagrammed in Figure 1.1. Individual consumer behavior is modeled as a discrete choice, responsive

to the vehicles’ price and attributes. Consumers have time-invariant preferences and are myopic.

Firms decide the price and investments to maximize profits with experience curves enhancing

attributes and reducing production costs by accumulated capital—they play a dynamic Bertrand

game of price and investment. After observing all market dynamics, the government may provide

purchase subsidies to intervene in consumer choice or investment subsidies to alter firms’ choices

considering the social cost of carbon together. This naturally builds a dynamic Stackelberg game

in that a leader (a government) has the advantage of moving first, and followers (firms) move later,

taking the leader’s action as given (Abou-Kandil & Bertrand, 1987). Archsmith et al. (2022) argue

that the rate of EV adoptions in the United States is determined by three forces: intrinsic growth

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in demand for EVs (attributes improvement), production cost declines (market price decrease), and

government stimulus of the industry (capital accumulation). All three factors are embodied in the

model.

1.2.1 Consumers

I assume that individual consumer behavior follows a discrete choice model with a multinomial

logit (MNL) model. They decide to buy ICE or EV, which means both vehicles are sufficiently

substitutable, as assumed by Acemoglu et al. (2012). The discrete choice model is convenient for

studying the probability of choice in a given market size. An MNL model is simple and easily gives

approximate results in transportation applications Mau et al. (2008), who used MNL because their

focus was to estimate aggregate consumer behavior. They assume that each estimated coefficient

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is identical to all consumers. This chapter accepts this assumption because I have aggregate-level

data only, and the US automobile market size has remained constant in recent decades. The total

number of new vehicle sales since 2000 has ranged around 17 million (US Bureau of Economic

Analysis, 2022), except for the economic crisis (marked as gray) and its recovery. I assume that

consumers will buy an ICE or EV no matter what the current subsidy level is. This model fits the

US automobile market, which exhibits a constant market size and fierce competition. The discrete

choice model shows that if firm A produces a product with the same price and attributes while

competitors make the same product with better attributes and lower prices, firm A’s market sale

decreases.

I assume there are 𝑀 = 17𝑚𝑖𝑙𝑙𝑖𝑜𝑛 vehicle sales each year, either an EV (indexed by 𝑒) or an

ICE (indexed by 𝑓 ). There is no non-purchase option for this group. This means that the market

for a new car is mature in the US, which makes firms compete for market share. Consumers make

their purchase decision in response to the vehicle’s price, 𝑝 𝑗 (for 𝑗 ∈ {𝑒, 𝑓 }), and attributes. If a

government subsidizes the purchase of a vehicle 𝑗 with 𝜂 𝑗 , then the purchase price will be 𝑝 𝑗 − 𝜂 𝑗 .

Consumers are assumed to be indifferent to price and subsidy but only care about the out-the-door

price, following DeShazo et al. (2017) and Li et al. (2017). Consumers have the same preference

for price and attributes regardless of their demographics, as Langer & Lemoine (2022). They

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are not forward-looking and will not delay their purchase with an expectation of future attribute

improvement. Consumer 𝑖’s indirect utility from its discrete choice of a vehicle 𝑗 is 𝑢𝑖 𝑗 , its average

is ¯𝑢 𝑗 , and the market share of a vehicle 𝑗 is 𝑠 𝑗 .

𝑢𝑖 𝑗 ( 𝑝 𝑗 , 𝑥 𝑗𝑥 𝑗𝑥 𝑗 , 𝑦 𝑗𝑦 𝑗𝑦 𝑗 , 𝑧 𝑗 , 𝜂 𝑗 ) = 𝛽𝛽𝛽𝑥 𝑗𝑥 𝑗𝑥 𝑗 + 𝛾𝛾𝛾𝑦 𝑗𝑦 𝑗𝑦 𝑗 + 𝛿 𝑗 𝑧 𝑗 − 𝛼( 𝑝 𝑗 − 𝜂 𝑗 ) + 𝜖𝑖

¯𝑢 𝑗 ( 𝑝 𝑗 , 𝑥 𝑗𝑥 𝑗𝑥 𝑗 , 𝑦 𝑗𝑦 𝑗𝑦 𝑗 , 𝑧 𝑗 , 𝜂 𝑗 ) = 𝛽𝛽𝛽𝑥 𝑗𝑥 𝑗𝑥 𝑗 + 𝛾𝛾𝛾𝑦 𝑗𝑦 𝑗𝑦 𝑗 + 𝛿 𝑗 𝑧 𝑗 − 𝛼( 𝑝 𝑗 − 𝜂 𝑗 )

𝑠 𝑗 (𝑝𝑝𝑝, 𝑥𝑥𝑥, 𝜂𝑒) =

∫

(cid:214)

𝜖

𝑗≠ 𝑗 ′

𝑃( ¯𝑢 𝑗 − ¯𝑢 𝑗 ′ − 𝜖)𝑃(𝑑𝜖) =

𝑒 ¯𝑢 𝑗 ( 𝑝 𝑗 ,𝑥 𝑗𝑥 𝑗𝑥 𝑗 ,𝑦 𝑗𝑦 𝑗𝑦 𝑗 ,𝑧 𝑗 ,𝜂 𝑗 )
(cid:205) 𝑗 ∈{𝑒, 𝑓 } 𝑒 ¯𝑢 𝑗 ( 𝑝 𝑗 ,𝑥 𝑗𝑥 𝑗𝑥 𝑗 ,𝑦 𝑗𝑦 𝑗𝑦 𝑗 ,𝑧 𝑗 ,𝜂 𝑗 )

(1.1a)

(1.1b)

(1.1c)

where 𝛼 > 0 is a parameter related to prices. 𝜂 𝑗 is purchase subsidy per vehicle purchase; and I only

consider for EV subsidy, which means 𝜂𝑒 ≥ 0 and 𝜂 𝑓 = 0. 𝛽𝛽𝛽 = (𝛽1, · · · , 𝛽3) and 𝛾𝛾𝛾 = (𝛾1, · · · , 𝛾3)

are parameter vectors related to 𝑥 𝑗𝑥 𝑗𝑥 𝑗 and 𝑦 𝑗𝑦 𝑗𝑦 𝑗 , and 𝛿 𝑗 is a parameter related to 𝑧 𝑗 . I use the similar

6

attributes used in Berry et al. (1995). There are two types of attributes. First, capital-dependent
𝑇 = (𝑥1 𝑗 , · · · , 𝑥3 𝑗 )𝑇 , include: 1 for power-weight ratio (Horsepower per curb

attributes, denoted 𝑥 𝑗𝑥 𝑗𝑥 𝑗

weight), 2 for fuel economy (miles per fuel of dollar value), and 3 for maximum driving range

(miles).

I do not consider charging time in this model because of charging patterns and that

charging efficiency is largely due to the technology of charging stations rather than the vehicle 1.
𝑇 = (𝑦1 𝑗 , · · · , 𝑦3 𝑗 )𝑇 , including

The other attribute type is capital-independent attributes, denoted 𝑦 𝑗𝑦 𝑗𝑦 𝑗

1 for wheelbase, 2 for height, and 3 for width. Firms can make any level of these attributes without

significant capital accumulation. 𝑦 𝑗𝑦 𝑗𝑦 𝑗 are important to resolve omitted variable problems but are not

used in the final model. 𝑧 𝑗 is a binary variable indicating the type of vehicle: EV or ICE. 𝑧𝑒 = 1

if 𝑗 = 𝑒, and 0 if 𝑗 = 𝑓 and vice versa. It captures consumer preference for each type. The final

term, 𝜖𝑖, is an idiosyncratic preference and is assumed to be independent and identically distributed

(i.i.d.). Consumer 𝑖 will choose vehicle 𝑗 if and only if 𝑢𝑖 𝑗 ≥ 𝑢𝑖 𝑗 ′, ∀ 𝑗 ′ ≠ 𝑗.

Equation (1.1c) shows the market share for a vehicle 𝑗 derived from the random utility model

following McFadden et al. (1973) and Berry et al. (1995). 𝑝𝑝𝑝 = ( 𝑝𝑒,

𝑝 𝑓 ), 𝑥𝑥𝑥 = (𝑥𝑒𝑥𝑒𝑥𝑒, 𝑥 𝑓𝑥 𝑓𝑥 𝑓 ), and

1According to Lee et al. (2020), 86% of EV owners indicate that home is the most common charging location
chosen by PEV owners: at home only (53%), at home and other places (33%), at work only (8%), and at public only
(3%). The factors for charging time are battery capacity (how many battery cells are deployed) and technology of
charging ports such as level 1, level 2, or DC fast chargers, not EV technology. All EVs have used the same type of
batteries until 2024, Li-ion battery. There will be a significant improvement in battery charging and capacity if the
solid-state battery is commercialized in the future.

6

𝑧𝑧𝑧 = (𝑧𝑒 𝑧 𝑓 ). Vehicle 𝑗’s market share is a function of both vehicles’ prices and attributes.

In

Equation (1.1b), ¯𝑢 𝑗 represents the mean utility from purchasing a vehicle 𝑗. The expected market

share at the aggregate level, 𝑠 𝑗 (𝑝𝑝𝑝, 𝑥𝑥𝑥, 𝑧𝑧𝑧, 𝜂𝑒), is deterministic with vehicles’ prices and attributes. 𝑦 𝑗𝑦 𝑗𝑦 𝑗

are removed by assuming that 𝑦𝑒𝑦𝑒𝑦𝑒 = 𝑦 𝑓𝑦 𝑓𝑦 𝑓 . The market share scales exponentially with a product’s

attractiveness and exponentially downwards with the sum of price and attributes. The total of all

market shares is necessarily 1, i.e. 𝑠𝑒 + 𝑠 𝑓 = 1. This is the logical consistency requirement, with

no non-purchase option, introduced by Cooper & Nakanishi (1988) (also see Huang et al. (2013),

for a review).

1.2.2 Producers

In the model, two aggregated EV and ICE producers compete with each other as per Ma et al.

7

(2020). The two aggregated firms thus articulate the competition between entire ICE and EV firms

rather than among individual firms, brands, and models. The investment decision of automobile

companies is made at the headquarters of a global company that owns its entire brands, and the

benefit of investment returns to entire ICE or EV models within the firm or the entire ICE or

EV market through spillover effects. Then, the model includes the experience curve by treating

accumulated capital as a state variable and investment as a control variable. Attributes and unit

production costs are assumed to follow the experience curve with accumulated capital. This means

that the investment will promote technological advances that can increase product value in two

ways: cost reduction that leads to lower prices and better performance (Gale & Klavans, 1985).

Therefore, unit production cost and attributes are assumed to depend on capital accumulation

on the experience curve. We should consider that EV and ICE have different maturity. ICE has

more than 100 years of history and has almost fully developed its technology, market segmentation,

and strategy, EV firms, being young, have much more potential to dramatically improve attributes

and decrease production costs with capital investment, even if their market prices were initially too

high for their attributes (Holland et al., 2021). Acemoglu et al. (2012) argued that the study of

environmental policies must include the endogenous response of different technologies to proposed

policies. I embody this by having the experience curve concept for technology innovation.

7

The experience curve means that the cost of production is exponentially decreased with business

growth. I assume that the unit production cost depends on capital, not quantity. The unit production

costs of 𝑗, 𝑐 𝑗 (𝐾 𝑗 ), are assumed as a function of cumulative investment in physical capital stock for

𝑗, 𝐾 𝑗 . The same power function is used for attributes because the investment in capital has similar

effects in cost reduction and attribute improvement in the early-stage business.

𝑐 𝑗 (𝐾 𝑗 ) = 𝜙 𝑗 𝑐0 × 𝐾 𝜙 𝑗𝑐1
𝑥 𝑗𝑙 (𝐾 𝑗 ) = 𝜙 𝑗𝑙0 × 𝐾 𝜙 𝑗𝑙1

𝑗

𝑗

, where 𝑙 ∈ {1, 2, 3}

(1.2a)

(1.2b)

where 𝜙 𝑗 𝑐0 and 𝜙 𝑗 𝑐1 are production cost parameters and 𝜙 𝑗𝑙0 and 𝜙 𝑗𝑙1 are attributes parameters.

Capital-dependent attributes, 𝑥 𝑗𝑥 𝑗𝑥 𝑗 , are modeled as a function of cumulative capital investment.

𝑙

indicates each element in 𝑥 𝑗𝑥 𝑗𝑥 𝑗 : 𝑙 = 1 for power-weight ratio, 𝑙 = 2 for fuel economy, and 𝑙 = 3 for

maximum driving range. Experience is usually defined as cumulative production (Samadi, 2018);

however, Schmidt et al. (2017) found that cumulative investment affects future cost decrease along

the experience curve. Therefore, this paper defines experience as the capital stock, the results of

cumulative investment. The dependent variable is expressed as a power function of experience

(Hayward & Graham, 2013).

The firms’ optimization problem with the per-period net income of a firm 𝑗, 𝜋 𝑗 , profit minus

investment cost, and the law of motions of capital accumulation are defined as follows. 𝜌 is the

discount rate over time. 𝜃𝑒 is the investment subsidy for EV investment, and 𝜃 𝑓 = 0 as 𝜂 𝑓 = 0.

𝐾𝐾𝐾 = (𝐾𝑒, 𝐾 𝑓 ) is a vector of 𝐾 𝑗 , and 𝜏𝜏𝜏 = (𝜂𝑒, 𝜃𝑒) is a policy vector.

8

8

∫ ∞

0

max
𝑝 𝑗 , 𝐼 𝑗

𝑒−𝜌𝑡 𝜋 𝑗 (𝑝𝑝𝑝, 𝐼 𝑗 , 𝐾𝐾𝐾; 𝜏𝜏𝜏)𝑑𝑡

𝑠.𝑡. (cid:164)𝐾 𝑗 ,

(cid:164)𝐾− 𝑗 , 𝐾 𝑗 (0) = 𝐾0 𝑗 and 𝐾− 𝑗 (0) = 𝐾0− 𝑗

𝜋 𝑗 (𝑝𝑝𝑝, 𝐼 𝑗 , 𝐾𝐾𝐾; 𝜏𝜏𝜏) = ( 𝑝 𝑗 − 𝑐 𝑗 (𝐾 𝑗 ))𝑠 𝑗 (𝑝𝑝𝑝, 𝑥𝑥𝑥(𝐾𝐾𝐾); 𝜂𝑒) 𝑀 − 𝜓 𝑗 (𝐼 𝑗 ) + 𝜃 𝑗

(cid:164)𝐾 𝑗 = 𝐼 𝑗 − 𝜇𝐾 𝑗

𝜓 𝑗 (𝐼 𝑗 ) = 𝜈𝐼2

𝑗 , 𝜈 > 0

𝜌𝑉𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) = max
𝑝 𝑗 , 𝐼 𝑗

[𝜋 𝑗 (𝑝𝑝𝑝, 𝐼 𝑗 , 𝐾𝐾𝐾; 𝜏𝜏𝜏) +

𝜕𝑉𝑗
𝜕𝐾 𝑗

(𝐼 𝑗 − 𝜇𝐾 𝑗 )
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:123)(cid:122)
(cid:125)
(cid:124)
(cid:164)𝐾 𝑗

+

𝜕𝑉𝑗
𝜕𝐾− 𝑗

(𝐼− 𝑗 − 𝜇𝐾− 𝑗 )
]
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:125)
(cid:123)(cid:122)
(cid:124)
(cid:164)𝐾− 𝑗

(1.3a)

(1.3b)

(1.3c)

(1.3d)

(1.3e)

One firm’s net income depends on both firms’ capital via attributes in the market share. In addition,

firms are assumed to respond to the subsidy myopically as consumers did for attributes. They will

9

not consider that their strategies may affect future subsidies. To simplify the game, I adopt an

open-loop game, which means each firm takes the other firm’s choices, as well as policy instrument

choices, as being time-dependent rather than being specified as feedback rules (Basar & Olsder,

1982). This is not an uncommon approach, but it does mean the game is not subgame-perfect.

In Equation (1.3c), (cid:164)𝐾 𝑗 is the law of motions, 𝐼 𝑗 is an investment in a vehicle 𝑗, and 𝜇 is the

depreciation rate of capital, which is the same for all capital stocks. To simplify problems, I assume

that the capital is immediately accumulated from investment decisions, which takes much longer in

the real automotive business. The aggregated investment of two aggregate firms, EV and ICE, will

accumulate the aggregated capital. Thornton & Thompson (2001) shows that learning spillovers

are significant in productivity growth, and the market failures may be modest. 𝜓 𝑗 (𝐼 𝑗 ) is the cost

of investment, where 𝜈 is a cost parameter related to investment and is expected as 𝜈 > 0.

In

dynamic programming, this results in investments being spread over time rather than all at once to

achieve a steady state immediately. The convex investment cost is assumed for EV by Creti et al.

(2018). Barnett & Sakellaris (1998) said it is common for researchers to assume a quadratic form

for investment cost.

Equation (1.3e) is Hamilton-Jacobi-Bellman equation. 𝑉𝑗 is the maximized long-term profit

that solves Equation 1.3. Firms have choice variables (price and investment) and state variables

9

(capitals). The right-hand side has current period profits, 𝜋 𝑗 (𝑝𝑝𝑝, 𝐼 𝑗 , 𝐾𝐾𝐾, 𝜏𝜏𝜏), and the other terms

represent the marginal value of capital times changes in both firms’ capital, which are the longer

run value to the firm of changes in the capital stock.

(cid:164)𝐾 𝑗 is the capital accumulation. The value function has an interaction term between firms,

𝜕𝑉 𝑗
𝜕𝐾 𝑗 is the price of capital accumulation, and
(cid:164)𝐾− 𝑗 .

𝜕𝑉 𝑗
𝜕𝐾− 𝑗

The capital change of a firm can affect the other’s value function via this term. Both value functions

will be solved together because 𝑉𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) contains both (cid:164)𝐾 𝑗 and (cid:164)𝐾− 𝑗 .

The firms’ optimality condition for the price is to set the marginal benefit and marginal cost

as the same. The F.O.C. for the price of a vehicle 𝑗 is 𝑠 𝑗 𝑀 = −( 𝑝∗

𝑗 − 𝑐 𝑗 )

𝜕𝑠 𝑗
𝜕 𝑝 𝑗

𝑀. The left-hand

side is the marginal effect of price on sales. If there is a marginal increase (decrease) in price,

firms will observe a marginal increase (decrease) in revenue as 𝑠 𝑗 𝑀 > 0. The right-hand side is

the marginal effect of price on market share. If there is a marginal increase (decrease) in price,

firms will also observe a marginal decrease (increase) in market share as

𝜕𝑠 𝑗
𝜕 𝑝 𝑗

= −𝛼𝑠𝑒𝑠 𝑓 < 0. Firms

find optimal prices when the marginal benefit from a higher price matches the marginal cost from

a lower market share, and vice versa. By solving the F.O.C. for the prices, the optimal feedback

price rule for each period is gained, 𝑝∗

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏), which depends on the capital of both firms subject

0

1

to given policy instruments.

𝑒 (𝑝∗𝑝∗𝑝∗, 𝐾𝐾𝐾; 𝜂𝑒) = 𝑐𝑒 +
𝑝∗

𝑓 (𝑝∗𝑝∗𝑝∗, 𝐾𝐾𝐾; 𝜂𝑒) = 𝑐 𝑓 +
𝑝∗

1
𝛼
1
𝛼

+

+

1
𝛼 exp[𝛽𝛽𝛽(𝑥𝑒𝑥𝑒𝑥𝑒 (𝐾𝐾𝐾) − 𝑥 𝑓𝑥 𝑓𝑥 𝑓 (𝐾𝐾𝐾)) + 𝛿𝑒 − 𝛿 𝑓 − 𝛼( 𝑝∗
1
𝛼 exp[𝛽𝛽𝛽(𝑥 𝑓𝑥 𝑓𝑥 𝑓 (𝐾𝐾𝐾) − 𝑥𝑒𝑥𝑒𝑥𝑒 (𝐾𝐾𝐾)) + 𝛿 𝑓 − 𝛿𝑒 + 𝛼( 𝑝∗

𝑒 − 𝜂𝑒 − 𝑝∗

𝑓 )]

𝑒 − 𝜂𝑒 − 𝑝∗

𝑓 )]

(1.4a)

(1.4b)

This optimal price has its term on the right-hand side due to market share. For my numerical

analysis, I approximate the equations with Lambert-W equations to get the optimal price as a

function of other terms, not including itself. Lambert-W function, 𝑤, is the function satisfying
𝑤𝑒𝑤 = 𝑥, where 𝑤 = 𝑊0(𝑥) for 𝑥 ≥ 0 (Disney & Warburton, 2012; Lehtonen, 2016). Therefore, we

can convert the exponential equations into linear ones using the Lambert-W equation as suggested

by Lehtonen (2016). The result is ˇ𝑝∗

𝑗 (𝐾𝐾𝐾; 𝜂𝑒), described in Equation (1.C.1.3) in the Appendix

1.C.1. Note that the approximated optimal price is now only a function of both firms’ capital and

given subsidy. One way to validate approximation is to compare the results with the literature.

10

From Equation (1.C.1.3),

𝜕 𝑝𝑒
𝜕𝜂𝑒

≈ 0.262, which means that EV prices will be increased by $262 under

$1,000 of subsidies, and subsidy-inclusive EV price will be decreased by$738.

𝜕 𝑝 𝑓
𝜕𝜂𝑒

≈ −0.262,

which means that ICE prices become $262 lower under $1,000 of EV purchase subsidies. This

corresponds to Muehlegger & Rapson (2022) saying that every $1,000 of subsidies lowers subsidy-

inclusive EV prices by $730 to $850.

The firms’ optimality condition for investment is when marginal benefit and marginal cost

are the same. The F.O.C. for an investment in a vehicle 𝑗 is

𝑒 (𝐼 𝑗 ), where
intertemporal values of investment, which equal the marginal value of capital, and 𝜓′

= 𝜓′

𝜕𝑉 𝑗
𝜕𝐾 𝑗

is the

𝜕𝑉 𝑗
𝜕𝐾 𝑗
𝑗 (𝐼 𝑗 ) is the

marginal cost of investment. As a result of solving the F.O.C. for an investment, we will get two

feedback functions, 𝐼 𝑗 (𝐾𝐾𝐾, 𝜏𝜏𝜏) = 1
2𝜈

𝜕𝑉 𝑗
𝜕𝐾 𝑗 . It may be noted that the optimal investment depends on

subsidies. Purchase subsidies affect the optimal subsidy because the firm’s profits depend on its

market share, which depends on this subsidy. Investment subsidies for EV firms even affect the

ICE firm because each firm has interaction terms with each other through the capital accumulation

in Equation (1.3a). Capital investment of competitors will affect long-term profit maximizing via

competition with price and attributes in the future market. These feedback rules can be substituted

into the HJB equation. Appendix 1.C. 1 describes how to get this optimal investment.

The feedback rule for investment is fully identified as a function of capital under a given policy,

1

1

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏). 𝐼∗
𝐼∗

𝑗 has both firms’ capital and policy terms via

𝜕𝑉 𝑗
𝜕𝐾 𝑗 . By substituting the optimal price,
𝑗 (𝐾𝐾𝐾; 𝜂 𝑗 ), 𝑥𝑥𝑥(𝐾𝐾𝐾), 𝜂𝑒) = 𝑠 𝑗 (𝐾𝐾𝐾; 𝜂𝑒). Now, the HBJ equation in Equation

the market share is now 𝑠 𝑗 ( ˇ𝑝∗

(1.3e) is substituted with the feedback rule for price and investment as follows.

𝜌𝑉𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) = 𝜋 𝑗 ( ˇ𝑝∗ˇ𝑝∗ˇ𝑝∗(𝐾𝐾𝐾; 𝜂𝑒), 𝐼∗

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏)) +

𝜕𝑉𝑗
𝜕𝐾 𝑗

(𝐼∗

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) − 𝜇𝐾 𝑗 ) +

𝜕𝑉𝑗
𝜕𝐾− 𝑗

(𝐼∗

− 𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) − 𝜇𝐾− 𝑗 )

(1.5)

With the optimal price and investment, the per-period consumer and producer surplus are

described as the function of both firms’ capital.

𝐸 [CS(𝑝𝑝𝑝, 𝑥𝑥𝑥, 𝑦𝑦𝑦, 𝜂𝑒)] =

𝑃𝑆(𝐾𝐾𝐾; 𝜏𝜏𝜏) =

𝑀
𝛼 ln[

∑︁

𝑗 ∈{𝑒, 𝑓 }

∑︁

𝑒 ¯𝑢 𝑗 ( 𝑝 𝑗 ,𝑥 𝑗𝑥 𝑗𝑥 𝑗 ,𝑦 𝑗𝑦 𝑗𝑦 𝑗 ,𝑧 𝑗 ,𝜂 𝑗 )]

(1.6a)

𝑗 ∈{𝑒, 𝑓 }
(cid:104)(cid:16)

ˇ𝑝∗
𝑗 (𝐾𝐾𝐾; 𝜂𝑒) − 𝑐 𝑗 (𝐾 𝑗 )

(cid:17)

𝑗 (𝐾𝐾𝐾; 𝜂𝑒)𝑀 − 𝜓 𝑗 (𝐼∗
𝑠∗

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏)) + 𝜃 𝑗

(cid:105)

(1.6b)

11

From the discrete choice model, the expected individual consumer surplus (CS) is gained by

the log-sum of the exponential of the average utility of each choice, suggested by Small & Rosen

(1981), in Equation (1.6a). The aggregate consumer surplus is calculated by multiplying individual

expected utility by the total market size of 𝑀. The rate of return is gained by taking partial

derivatives with respect to 𝐾 𝑗 , which is similar to the adjoint condition in a typical optimal control

model.

𝜌 + 𝜇 =

𝜕𝜋 𝑗
𝜕𝐾 𝑗
𝜕𝑉 𝑗
𝜕𝐾 𝑗

+

(cid:164)𝐾 𝑗 +

𝜕2𝑉 𝑗
𝜕𝐾 2
𝑗
𝜕𝑉 𝑗
𝜕𝐾 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:124)

𝜕2𝑉 𝑗
𝜕𝐾 𝑗 𝐾− 𝑗
𝜕𝑉 𝑗
𝜕𝐾 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)

(cid:164)𝐾− 𝑗

(cid:125)

𝑑 (

)/𝑑𝑡

(cid:123)(cid:122)
𝜕𝑉𝑗
𝜕𝐾 𝑗
𝜕𝑉𝑗
𝜕𝐾 𝑗

(1.7)

2

1

The left-hand side is the return adjusted for depreciation, 𝜇, and the rate of return, 𝜌, that the

firm could earn elsewhere, an opportunity cost of its own investment. Therefore, the left-hand side

is the depreciation-adjusted rate of return. Optimally, the firm’s own investments must generate

a return equal to the depreciation-adjusted rate. This return is the RHS of Equation (1.7). The

first term of the right-hand side is the marginal profit gains from capital investment, divided by

the marginal value of capital to produce a rate of return. The marginal profit term includes a

price effect on changing demand due to capital accumulation and, therefore, improved attributes,

as well as benefits from reduced production costs. The second term of the right-hand side is a

capital gain or loss that reflects proportional increases (gain) or decreases (loss) in the marginal

value of its own capital.

𝜕2𝑉 𝑗
𝜕𝐾 2
𝑗

is the direction and speed of capital gain or loss by their own capital

accumulation, and

capital accumulation. Assuming

𝜕2𝑉 𝑗
𝜕𝐾 𝑗 𝐾− 𝑗 means the direction and speed of capital gain or loss by the competitor’s
< 0, then there is a capital loss when the capital stock is

𝜕2𝑉 𝑗
𝜕𝐾 2
𝑗

> 0, there is a capital gain with investment due to increasing returns to capital at given

increasing due to their being diminishing returns to capital at given
𝜕2𝑉 𝑗
𝜕𝐾 2
𝑗
𝜕𝑉 𝑗
𝜕𝐾 𝑗

> 0. If

𝜕2𝑉 𝑗
𝜕𝐾 2
𝑗

= 0, there is no motivation to capital gain or loss. The capital gain and loss term

𝜕𝑉 𝑗
𝜕𝐾 𝑗

> 0. Vice versa, with

also includes a capital spillover effect through the market. The last term indicates the rate of capital

gain or loss from the other firm’s capital investments. It may capture that other firms’ investments

12

may induce (1) capital loss by losing relevant technicians, researchers, and scientists and increasing

wage expenses due to headhunting for experts or (2) mutual capital growth due to capital spillover

effects.

1.2.3 Government

In this model, governments decide their subsidy level after observing all market dynamics,

playing a dynamic Stackelberg game with firms. The Stackelberg game has been widely applied to

policy-making problems in which a government is a leader, and the target industries are followers

(Rahimi et al., 2021). A substantial literature in environmental economics applies Stackelberg gam-

ing to analyze the interaction between regulators (leader) and industries (followers) over emissions

trading (Hong et al., 2017), environmental tax (Carlsson, 2000; Canton et al., 2008; Jiang et al.,

3

1

2023; Krass et al., 2013), international agreement (Eichner & Pethig, 2015; Finus et al., 2021),

acid rain (Baron, 1985) and investment (Maxwell & Decker, 2006). In this game, governments try

to maximize their objective goals, such as consumer and producer surplus, subsidization cost, and

social cost of carbon.

Government expenditures here are the sum of all government expenditures on subsidization.

The per-period government expenditure, GE, is defined as GE(𝐾𝐾𝐾; 𝜏𝜏𝜏) = 𝜂𝑒𝑠∗

𝑒 (𝐾𝐾𝐾; 𝜂𝑒)𝑀 + 𝜃𝑒. The first

term is the expenditure for purchase subsidization, and the second is the expenditure for investment

subsidization. This chapter does not account for the instrument interaction; therefore, 𝜂𝑒 × 𝜃𝑒 = 0.

Their interaction is beyond the focus of this study.

This chapter only considers carbon emission as an externality arising from the automobile

market because externalities such as 𝑁𝑂𝑥, 𝑆𝑂𝑥, and/or particle matter emissions or batteries’

disposal are negligible or insignificant2. I consider the carbon emission from driving of EV and

ICE. EVs do not emit carbon dioxide during driving, but modern economies heavily depend on

fossil fuel power plants to generate electricity. Thus, EV driving’s carbon emission comes from

2Based on the dataset of Maier et al. (2023), the avoidable social cost of all other air pollution by replacing ICE
with EV is just 1.7% to 9.1% of the social cost of carbon by urban, suburban, and rural areas and by small, medium,
In addition to that, both ICE and EV generate the cost of disposal, and there is growing evidence
and large cars.
of decreasing the disposal cost of EV batteries by recycling. Rahman et al. (2017) suggest a way of recycling about
47.34% of the battery active metals.

13

electricity generation.

Damage of carbon emissions from a vehicle 𝑗 is the social cost of carbon (SCC) from total

carbon emissions during the vehicle 𝑗’s lifetime. The aggregate social cost is calculated by summing

all social costs of vehicle carbon emissions.

𝑑 𝑗 (𝐾 𝑗 ) =

year
vehicle 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)
(cid:123)(cid:122)
(cid:125)
(cid:124)
𝑙𝑖 𝑓 𝑒𝑡𝑖𝑚𝑒

×

mile
year
(cid:124)(cid:123)(cid:122)(cid:125)
𝑎𝑛𝑛𝑢𝑎𝑙 𝑚𝑖𝑙𝑒𝑠

×

gallon𝑒𝑞

mile
(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)
(cid:125)
(cid:123)(cid:122)
(cid:124)
1
𝑀 𝑃𝐺 𝑗 (𝐾 𝑗 )

×

emission 𝑗
gallon𝑒𝑞
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:124)
(cid:125)
(cid:123)(cid:122)
𝑢𝑛𝑖𝑡 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛

×

cost($)
emission 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:125)
(cid:123)(cid:122)
(cid:124)
𝑢𝑛𝑖𝑡 𝑐𝑜𝑠𝑡

𝐷𝐸 (𝐾𝐾𝐾, 𝜂𝑒) =

∑︁

𝑗

𝑑 𝑗 (𝐾 𝑗 )𝑠 𝑗 (𝐾𝐾𝐾, 𝜂𝑒)𝑀

(1.8a)

(1.8b)

where 𝑑 𝑗 (𝐾 𝑗 ) is the social cost of carbon from the lifetime emission of one vehicle 𝑗 and 𝐷 (𝐾𝐾𝐾, 𝜂𝑒)

is the total social cost of carbon from all new vehicles per period. The social cost is a product of

several terms: the social cost of unit carbon emission SCC ($ per g CO2), the average mileage per

year mile (miles per year), the discounted total life span of a vehicle year (years), and the conversion

factor emit 𝑗 (g CO2 per unit fuel),3 and fuel economy mpg 𝑗 (miles per unit fuel). The miles per

gallon (MPG) for ICE equals the miles per gallon equivalent (MPGe) for EV. I assume that annual

mileage and lifetime are time-invariant, which means no rebound effect. The social cost of carbon

emission is also assumed to be time-invariant. Table 1.1 shows the above parameters and their

sources. US Environmental Protection Agency (2010) suggests that social costs of carbon will be

$52.04/ton CO2 under 3% of discount rate. Then, EVs emit 30% of carbon emissions per mile from

ICE.

The regulators’ per-period social net benefit (SNB) is the sum of consumer surplus (CS),

producer surplus (PS), minus government expenditure (GE), and social cost of carbon emission

4

1

3For ICE, the conversion factor is carbon emission per unit gasoline. For EVs, a gasoline equivalent is needed
g CO2
electricity (kWh) ·
. EPA defined both 33.7 kWh of electricity and 1 gallon of gasoline as

to reflect the carbon emissions from electricity generation.
electricity (kWh) · 33.7kWh
electricity (kWh)
gasoline (galloneq) =
generating the same heat of 115,000 BTU.

gasoline (gallons) and emit𝑔 =

emit 𝑓 =

gasolineeq

g CO2

g CO2

14

(DE). Governments’ problem and Hamilton–Jacobi–Bellman’s equation are

∫ ∞

0

max
𝜏𝑥 ∈𝜏𝜏𝜏

𝑒−𝜌𝑡 SNB(𝐾𝐾𝐾; 𝜏𝜏𝜏)𝑑𝑡

𝑠.𝑡. (cid:164)𝐾 𝑗 ,

(cid:164)𝐾− 𝑗 , 𝐾 𝑗 (0) = 𝐾0 𝑗 and 𝐾− 𝑗 (0) = 𝐾0− 𝑗

SNB(𝐾𝐾𝐾; 𝜏𝜏𝜏) = CS(𝐾𝐾𝐾; 𝜂𝑒) + PS(𝐾𝐾𝐾; 𝜏𝜏𝜏) − GE(𝐾𝐾𝐾; 𝜏𝜏𝜏) − 𝐷𝐸 (𝐾𝐾𝐾; 𝜂𝑒)

𝜌Ω(𝐾𝐾𝐾) = max
𝜏𝑥 ∈𝜏𝜏𝜏

(cid:20)

SNB(𝐾𝐾𝐾; 𝜏𝜏𝜏) +

𝜕Ω
𝜕𝐾𝑒

· (cid:164)𝐾𝑒 +

(cid:21)

· (cid:164)𝐾 𝑓

𝜕Ω
𝜕𝐾 𝑓

(1.9a)

(1.9b)

(1.9c)

where Ω(𝐾𝐾𝐾) is the net present value of social welfare. 𝜕Ω
𝜕𝐾𝑒
by capital accumulation, where 𝜕Ω

𝜕𝐾 𝑗 is the price of capital accumulation for social welfare.
A government is assumed to know market responses and information, denoted ˇ𝑝∗

𝑗 (𝐾𝐾𝐾; 𝜂𝑒),
𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏). Given this information, the optimality condition for the policy instrument

𝑗 (𝐾𝐾𝐾; 𝜂𝑒), and 𝐼∗
𝑠∗

· (cid:164)𝐾𝑒 + 𝜕Ω
𝜕𝐾 𝑓

· (cid:164)𝐾 𝑓 is the welfare improvement

is to set the marginal benefit equal to the marginal cost of the policy. The F.O.C. for policy

5

1

instrument 𝜏𝑒 ∈ 𝜏𝜏𝜏 = {𝜂𝑒, 𝜃𝑒} is

𝜕 SNB
𝜕𝜏𝑒

+

𝜕Ω
𝜕𝐾𝑒

(cid:19)

(cid:18) 𝜕𝐼𝑒
𝜕𝜏𝑒

+

𝜕Ω
𝜕𝐾 𝑓

(cid:19)

(cid:18) 𝜕𝐼 𝑓
𝜕𝜏𝑒

= 0

(1.10)

The optimal subsidy has economic implications. The first term is the marginal impact of subsidy

on the current market. It represents how the consumer and producer surplus and social cost of

carbon change due to the subsidy. The second and third terms are the change in the net present

value of social benefit by capital accumulation due to investment stimulation caused by the subsidy

on EV firms and ICE firms. I get the optimal level of subsidy as a function of capital by solving

the F.O.C. Appendix 1.C.2 describes how to get the optimal purchase subsidy. Solving for 𝜂𝑒 gives

Equation (1.11).

𝜂∗
𝑒 (𝐾𝐾𝐾) =

(cid:104)

( ˇ𝑝∗

𝑒 (𝐾𝐾𝐾, 𝜂∗

+

1 + 𝑤1
(1 − 𝑤1)𝛼𝑠𝑒 (𝐾𝐾𝐾, 𝜂∗
𝑒 (𝐾 ∗𝐾 ∗𝐾 ∗) = ( ˇ𝑝∗
𝜂∗

𝑒) − 𝑐𝑒 (𝐾𝑒) − 𝑑𝑒 (𝐾𝑒)) − ( ˇ𝑝∗
𝑓 (𝐾𝐾𝐾, 𝜂∗
(cid:19)
(cid:18) 𝜕𝐼𝑒
𝜕Ω
𝜕𝐾 𝑓
𝜕𝜂𝑒

(cid:20) 𝜕Ω
𝜕𝐾𝑒

𝑒)𝑠 𝑓 (𝐾𝐾𝐾, 𝜂∗

𝑒)𝑀

+

𝑒) − 𝑐 𝑓 (𝐾 𝑓 ) − 𝑑 𝑓 (𝐾 𝑓 ))

(cid:105)

(cid:19)

(cid:18) 𝜕𝐼 𝑓
𝜕𝜂𝑒

−

𝜕𝜓𝑒 (𝐼𝑒)
𝜕𝜂𝑒

−

(cid:21)

𝜕𝜓 𝑓 (𝐼 𝑓 )
𝜕𝜂𝑒

𝑒 (𝐾 ∗𝐾 ∗𝐾 ∗, 𝜂𝑒) − 𝑐𝑒 (𝐾 ∗

𝑒 ) − 𝑑𝑒 (𝐾 ∗

𝑒 )) − ( ˇ𝑝∗

𝑓 (𝐾 ∗𝐾 ∗𝐾 ∗, 𝜂∗

𝑒) − 𝑐 𝑓 (𝐾 ∗

𝑓 ) − 𝑑 𝑓 (𝐾 ∗

𝑓 ))

(1.11)

(1.11a)

The first part is the marginal effect of the subsidy on changing consumers’ discrete choices from

ICE to EV in the current market. This first term is markup minus damage of EV minus that of ICE:

if the markup minus damage from EV becomes larger, the subsidy increases, and if that of ICE

15

increases, the subsidy decreases. At steady state, this part is directly the optimal purchase subsidy

at the state in Equation (1.11a). The second term explains the marginal effect of the subsidy in the

future market from the change in net present social welfare by stimulating capital investment. The

bracket means a net marginal increase in social welfare by the subsidy: the welfare increase minus

investment cost. The optimal purchase subsidy is determined by the balance of marginal impact on

the current and future markets.

The optimal investment subsidy, 𝜃∗

𝑒, is calculated from Equation (1.12), and Appendix 1.C.3

describes how to get the subsidy.

(cid:19)

(cid:18) 𝜕Ω
𝜕𝐾𝑒

(cid:19) (cid:18) 𝜕𝐼𝑒
𝜕𝜃𝑒

+

(cid:18) 𝜕Ω
𝜕𝐾 𝑓

(cid:19) (cid:18) 𝜕𝐼 𝑓
𝜕𝜃𝑒

(cid:19)

= 𝜓′

𝑒 (𝐼𝑒)

(cid:19)

(cid:18) 𝜕𝐼𝑒
𝜕𝜃𝑒

+ 𝜓′

𝑓 (𝐼 𝑓 )

(cid:19)

.

(cid:18) 𝜕𝐼 𝑓
𝜕𝜃𝑒

(1.12)

The left-hand side is how much social net benefit will be improved by the investment subsidy

via both firms’ capital accumulation, and the right-hand side is how much investment cost will

be caused by the investment subsidy via both firms’ capital accumulation. It considers how much

6

1

investment in each firm will be stimulated by subsidy,
caused by capital accumulation, 𝜕Ω

𝜕𝐾 𝑗 and 𝜓′

𝑗 (𝐼 𝑗 ).

𝜕𝐼 𝑗
𝜕𝜃𝑒 , and how much benefit and cost are

The rate of return is gained by taking partial derivatives of social net benefit with respect to

𝐾 𝑗 , 𝑗 ∈ {𝑒, 𝑓 }, which is similar to the adjoint condition in a typical optimal control model.

𝜌 + 𝜇 =

𝜕𝑆𝑁 𝐵
𝜕𝐾 𝑗
𝜕Ω
𝜕𝐾 𝑗

+

(cid:164)𝐾 𝑗 +

𝜕2Ω
𝜕𝐾 2
𝑗
𝜕Ω
𝜕𝐾 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)
(cid:124)

𝜕2Ω
𝜕𝐾 𝑗 𝐾− 𝑗
𝜕Ω
𝜕𝐾 𝑗
(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)(cid:32)

(cid:164)𝐾− 𝑗

(cid:125)

𝑑 (

)/𝑑𝑡

(cid:123)(cid:122)
𝜕Ω
𝜕𝐾 𝑗
𝜕Ω
𝜕𝐾 𝑗

(1.13)

The left-hand side indicates the return adjusted for capital depreciation, 𝜇, and the rate of return,

𝜌, that the government could earn or expend elsewhere, an opportunity cost of subsidization.

Therefore, the left-hand side is the risk-adjusted rate of return that the government is required

to earn through its subsidization. The first term of the right-hand side is the government’s rate

of return before subsidization. The marginal benefit includes a rise in consumer and producer

surplus brought about by innovation through capital accumulation and a decrease in the social

16

cost of carbon through altered consumption patterns. The second term of the right-hand side is

a social welfare gain or loss, which represents proportional increases (gain) or decreases (loss)

in the marginal value of both firms’ capital. The direction and pace of capital gain or loss by
firm 𝑗’s capital accumulation is represented by 𝜕2𝑆𝑁 𝐵
𝜕𝐾 2
𝑗
capital accumulation is represented by 𝜕2𝑆𝑁 𝐵
the capital stock rises as a result of declining returns on capital at given 𝜕𝑆𝑁 𝐵
𝜕𝐾 𝑗
with 𝜕2𝑆𝑁 𝐵
𝜕𝐾 2
𝑗
no incentive to profit or lose money if 𝜕2𝑆𝑁 𝐵
𝜕𝐾 2
𝑗

> 0, investment results in a capital gain because of rising returns on capital. There is

= 0. A capital spillover impact via the market is also

, and the direction and speed by firm − 𝑗’s

𝜕𝐾 𝑗 𝐾− 𝑗 . Assuming 𝜕2𝑆𝑁 𝐵

< 0, a capital loss occurs when

> 0. Conversely,

𝜕𝐾 2
𝑗

7

1

included in the capital gain and loss term.

1.3 Calibration and Estimation

1.3.1 Calibration

This chapter has two unknown parts in its model: unknown parameters of demand and produc-

tion and unknown functional forms of value functions. Regarding unknown value functions, I use

the collocation method to approximate unknown value functions for both firms and a government.

The collocation method has been widely used in analyzing dynamic economic systems since the

late 20th Century (Miranda & Glauber, 1995), and is now routinely used in economics to solve

non-linear dynamic models (Malin et al., 2011) and to approximate continuous Bellman equations

(Homayounfar et al., 2011). The method is flexible, accurate, and numerically efficient for most

research in economics and finance (King & Lohano, 2006). The core concept of the collocation is

to approximate the unknown value function by a weighted sum of easy functions such as polyno-

mials. We approximate the value function with a polynomial. This polynomial and its derivatives

will replace the unknown value function and its derivatives in the objective functions. Objective

functions must hold for any value of the state variables. Now, a polynomial with 𝑛 terms has 𝑛

coefficients to fit. To get those 𝑛 coefficients, we hold all value functions exactly at 𝑛 different

combinations of finite points, called collocation nodes. This method replaces the optimal control

problems in non-linear programming with a problem of algebraic equations (Khamseh et al., 2021).

Increasing 𝑛 results in better fitting by having more points to hold the equations but requires more

17

computational effort. The detailed collocation process is described in Appendix 1.D.

1.3.2 Estimation

I estimate demand and production functions with real market data and use the coefficients as

parameters in the theoretical model. It is to get realistic results for dynamic optimization. For

demand estimation, I built a dataset of all 598 vehicle models sold in the U.S. from 2008 to 2019

using a dataset of global automobile marketing companies: Marklines and Wardsauto. The vehicle

models are light-duty vehicles, excluding sport, luxury, and commercialized cars, and the rule is

described in Appendix 1.B. The data is on the yearly basis of the model year4. Table 1.2 shows the

descriptive statistics of the dataset.

Prices are manufacturer-suggested retail prices (MSRP) at the beginning of the model year and

8

1

include destination charges. Then, a federal purchase subsidy or guzzler tax is added to the vehicle

model’s price, gathered from US Department of Energy (2022). All dollar values of the nominal

price are transformed into a real price in 2019 by applying the consumer price index (CPI) from

US Bureau of Labor Statistics (2022). The no-purchase option is introduced to secure the sum of

market share equal to 1. The number of no-purchases is 𝑀 (17 million) minus the total sales of

each model year. Table 1.3 shows those statistics and annual oil and electricity prices. Oil prices

are from US Energy Information Administration (2024), and electricity prices are from US Energy

Information Administration (2023), with applying CPI index for each fuel.

I take the log of the market share in Equation (1.1c) and subtract the common term as per Berry

et al. (1995). Then, I use two-way mixed effect models with controls on each vehicle model and

year. I assume the fixed effect in the year and the fixed or random effect in the vehicle model and

compare them with the Hausman test (Hausman, 1978).

𝛾𝑦𝑚,𝑡
𝛽𝑥𝑚,𝑡
𝛾𝑦𝑚,𝑡 + 𝛿𝑚𝑧𝑚 + 𝜁𝑖 + 𝜁𝑡 + 𝑒𝑖,𝑡
𝛽𝑥𝑚,𝑡 − 𝛼( 𝑝𝑚,𝑡 − 𝜂 𝑗,𝑡) + 𝛾𝑦𝑚,𝑡
ln 𝑠𝑚,𝑡 − ln 𝑠𝑛,𝑡 = 𝛽𝑥𝑚,𝑡

ln 𝑠𝑛,𝑡 = ln

∑︁

𝑘∈models

(cid:2)𝑒𝛽𝑥𝑘,𝑡
𝛾𝑦𝑘,𝑡 +𝛿𝑘 𝑧𝑘 (cid:3)
𝛾𝑦𝑘,𝑡
𝛽𝑥𝑘,𝑡
𝛽𝑥𝑘,𝑡 −𝛼( 𝑝𝑘,𝑡 −𝜂𝑘,𝑡 )+𝛾𝑦𝑘,𝑡

(1.14)

(1.14a)

4The automobile industry’s model year runs from October to September, different from its fiscal year. The 2019

model year is from October 2018 to September 2019.

18

9

1

The estimation result is in Table 1.4. The Hausman test shows 𝜒2(17) = 1.24, and 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 >

𝜒2 = 1.000, which means the hypothesis that the individual-level effects are adequately modeled

by a random-effects model cannot be rejected. Therefore, I adopt the two-way mixed effect mod-

els with random effect in the vehicle model and fixed effect in a year. According to the results,

consumers prefer cheaper, longer, and more powerful and fuel-efficient vehicles that drive longer.

$10,000 increase in price will drop the market share by 29.24%. Each 10% increase in the average

power-weight ratio (0.0057HP/lb) and the average fuel economy increase (1.01 mile/$) has the

same effect as a price decrease of $1,106 and $1,046. A 100-mile increase in the maximum driving

range has the $5,141 value of price decrease. A one-inch increase in wheelbase has the $439 value

of price discount. Then, there is a clear preference for ICE by observing 𝛿 𝑓 , which corresponds

to Jackman et al. (2023) saying that EV adopters represent a relatively narrow band of consumer

characteristics until now. From 2008 to 2019, the majority of consumers prefer ICE.

The estimation result is in Table 1.4. The Hausman test shows 𝜒2(17) = 1.24, and 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 >

𝜒2 = 1.000, which means the hypothesis that the individual-level effects are adequately modeled

by a random-effects model cannot be rejected. Therefore, I adopt the two-way mixed effect mod-

els with random effect in the vehicle model and fixed effect in a year. According to the results,

consumers prefer cheaper, longer, and more powerful and fuel-efficient vehicles that drive longer.

$10,000 increase in price will drop the market share by 29.24%. Each 10% increase in the average

power-weight ratio (0.0057HP/lb) and the average fuel economy increase (1.01 mile/$) has the

same effect as a price decrease of $1,106 and $1,046. A 100-mile increase in the maximum driving

range has the $5,141 value of price decrease. One-inch increase in wheelbase has the $439 value

of price discount. Then, there is a clear preference for ICE by observing 𝛿 𝑓 , which corresponds

to Jackman et al. (2023) saying that EV adopters represent a relatively narrow band of consumer

characteristics until now. From 2008 to 2019, the majority of consumers prefer ICE.

In the real market, it is impossible to get data for cumulative capital, investment, and unit

production costs for each of the 598 vehicle models. Therefore, I assume that the two virtual

aggregate EV and ICE firms release each representative vehicle model with the same size, 𝑦𝑦𝑦, but

19

different price, cost, and capital relevant attributes, 𝑥𝑥𝑥 from 2008 to 2019. First, I gathered SEC

filing reports and production data for Tesla and Ford, and from the reports, I define "the property,

plant and equipment, net in asset" as capital, "research and development in operating expenses"

as investment, "the total cost of revenue for automotive sales and lease" as a total cost. I define

the total production as a total production from Ward’s yearbook to get the unit production cost.

Then, considering the volume-weighted average, I convert the capital and investment of Tesla and

Ford into those of virtual firms of EV and ICE. The unit production cost is converted from Tesla

and Ford to virtual firms, applying their price ratio to other firms. Regarding specification, I get

the volume-weighted average specification of the year for both EV and ICE. Table 1.5 shows the

descriptive statistics of the dataset. Then, I use Equation (1.2) to estimate the production cost and

0

2

attribute functions, Equation (1.3c) to estimate the capital depreciation rate, and Equation (1.3d) to

estimate the investment cost functions.

The estimation result of production functions is in Table 1.6. For both EV and ICE, coefficients

for the slope of experience curves, 𝜙 𝑗 𝑐1 and 𝜙 𝑗𝑙1, are negative for production cost and positive for

attributes. This means that the unit cost decreases and attributes improve as capital accumulates.

Depreciation rate, 𝜇, is estimated as 5.1%, and the coefficient for convex investment cost, 𝜈, is

positive.

1.4 Results

The capital stream flows for both enterprises are depicted in Figure 1.2. The arrows are the

optimal movements of each inner point, which is a combination of capital. From any initial

allocation of capital, the arrows from that point describe how the system moves, and so following

these arrows maps out an optimal path from that initial allocation. Every path is an optimal one

linked to the capital combinations along that path. The movement shows the law of motion of

capital affected by investment and subsidies in Equation (1.3c) at each combination of capital. In

2024, the capital of both companies—$276.17 billion (ICE) and $52.81 billion (EV)—began to

flow red. At zero subsidy, there is an equilibrium with a high ICE capital in Table 1.2 and a corner

solution with no ICE capital, described in Figure 1.2a. At a constant $7500 subsidy, the stream

20

flow leads us to the corner solution, and it reaches $0 billion (ICE) where $449 billion (EV) in

Figure 1.2b. Figure 1.2c shows a corner solution under dynamic purchase subsidy: about $0 billion

(ICE) where $421 billion (EV). In Figure 1.2d, Dynamic investment subsidy leads us to a steady

state with $42.56 billion (ICE) where $365.59 billion (EV).

Figure 1.3 shows the optimal subsidy contour plot with the stream flow. Under the dynamic

purchase subsidy, we need a very high purchase subsidy starting from the 2024 capital level.

However, the optimal subsidy converges to zero as the state moves along with the optimal path in

Figure 1.3a. Figure 1.3b shows the optimal investment subsidy contour plot with the stream flow.

The path will arrive at a steady state where the net capital accumulation is zero.

1.5 Discussion

1

2

Table 1.7 compares four scenarios: zero subsidy, current purchase subsidy ($7.5k), dynamic

purchase subsidy, and dynamic investment subsidy. The first part describes what happens at

the beginning of 2024: EV firms have $52.81 billion, and ICE firms have $276.17 billion as

their capital. In 2024, the optimal subsidy is higher than the current subsidy: 𝜂𝑒 = $15000 and

𝜃𝑒 = $37.01𝑏𝑖𝑙𝑙𝑖𝑜𝑛. Then, these dynamic subsidies become zero during the path to equilibrium.

TSNB means the total net present value of the social net benefit from 2024 to an infinite time

horizon with a discount rate. The subsidization increases total benefit compared to zero subsidies

by 2.31% (current purchase subsidy), 3.84% (dynamic purchase subsidy), and 2.39% (dynamic

investment subsidy). Dynamic subsidies are also better than the current policy, increasing benefits

by 1.49% (dynamic purchase subsidy) and 0.08% (dynamic investment subsidy). SNB, CS, PS,

GE, and DE are per period term in 2024. The subsidization also immediately increases the current

social net benefit, consumer surplus, and producer surplus of EV firms and decreases the producer

surplus of ICE firms and the social costs of carbon. Dynamic ones have a greater impact than

constant ones. Investment subsidy has no impact on consumer surplus and social costs of carbon

in 2024 because they will affect future markets by stimulating EV investment. The SNB in 2024

is about 6.2% to 6.6% of 2023 US GDP ($27.36 trillion), and it would be about 5% to 6% of US

GDP in 2024, considering recent economic growth. This corresponds to analytical reports saying

21

that the auto industry contributes about 5% of total US GDP (Ballew & Schnorbus, 1994; Alliance

for Automotive Innovation, 2022).

I performed a sensitivity analysis of the results in terms of discount rate and unit emission to

validate the model and to see how TSNB levels respond to change in key assumptions, such as the

social cost of carbon or discount rates. I did not do sensitivity analysis related to parameter values

because I gain them from estimation of real market data, while this may be needed. The main

analysis of this paper uses $52.04/ton CO2 under 3% of discount rate and 12,993 g CO2 emission

per 33.7kWh of electricity generation in Table 1.1. First, I consider other scenarios suggested by

US Environmental Protection Agency (2010): (1) $14.87/ton CO2 under 5% of the discount rate,

and (2) $152.40/ton CO2 under 3% of the discount rate. Second, I also consider the decarbonization

2

2

in electricity generation by increasing renewable sources: (3) RE50 (Renewable Energy 50%) -

current carbon emission in electricity generation becomes 50%, and (4) RE100 (Renewable Energy

100%) - current carbon emission in electricity generation becomes 0%. The unit emission from

electricity generation will be 6,497 g CO2per 33.7kWh under (3) and 0 g CO2per 33.7kWh under

(4). Table 1.8 shows the sensitivity analysis for different discount rates: (1) and (2), and Table 1.9

shows the sensitivity analysis for different unit emissions: (3) and (4). In general, we can observe

that the percentage change of each social net benefit, consumer and producer surplus, expenditure,

and social cost of carbon are similar among scenarios. The location of equilibrium is also similar

except for scenario (1). Each scenario shows different values of social net benefit and producer

surplus. Regarding social net benefit, it decreases with the high value of the social cost of carbon in

scenario (2) and increases with decreasing unit emission from EV driving in scenarios (3) and (4).

The social net benefit is much smaller in the 5% scenario (1), which along with applying different

discount rates over infinite horizons 5. Therefore, it supports the robustness of the outcomes.

Figure 1.4 shows the path of subsidy and expenditure under each subsidy, which starts from

2024 capital levels, which are not normalized over time. The optimal dynamic purchase subsidy

5When applying a discount rate, 𝜌, over infinite horizons, the infinite geometric series is

. The ratio of the
infinite geometric series under 𝜌 = 5% to 𝜌 = 3% is 61.17%. The ratio of TSNB at zero subsidy under 𝜌 = 5% in
Table 1.8, to 𝜌 = 3% in Table 1.7 is 61.33%.

1
(1− 1
1+𝜌 )

22

path (blue solid line) starts from $15k and continuously decreases over time, while the constant

subsidy path (black dashed line) stays at $7.5k. Along with the subsidy and market share changes,

the expenditure under dynamic subsidy (blue pattern area) starts from $82.06 billion but converges

to zero. On the other hand, the expenditure under constant purchase subsidy (grey area) keeps

increasing over time. The expenditure under dynamic subsidy (black area) starts from $37.01

billion, which is 205% of EV investment (blue solid line), but it shrinks to zero very quickly.

Figure 1.5 compares the path of firms’ capital under four policies. In Figure 1.5a, EV firms’

capital grows over time in any kind of subsidy, and purchase subsidy leads us to equilibrium at

higher EV capital. Figure 1.5b shows any form of subsidy will dramatically reduce ICE capital

on a path, and purchase subsidy will make it zero. Dynamic purchase subsidy reach the zero ICE

3

2

capital much faster than constant purchase subsidy.

Table 1.7 clearly shows that dynamic subsidies improve social net welfare. Figure 1.4 indicates

dynamic purchase subsidy requires much more expenditure and leads to more welfare improvement.

This is because of their nature. This chapter focuses on the twofold impact of subsidies on the

current and future markets. Dynamic purchase subsidy intervene in the current market first, then

it will indirectly stimulate capital investment by increasing the short-term profit of EV firms. On

the other hand, dynamic investment subsidy does not intervene in the current market; instead,

it directly affects EV firms’ investment decisions, indirectly affecting future markets. Therefore,

dynamic purchase subsidy alters the market earlier and is stronger with market size, while dynamic

investment subsidy only focuses on innovation on the producer side.

The growth of the market competitiveness of EVs depends on the experience curve. This

means this result is based on the assumption that the EV production cost and attributes will be

improved at the same speed in the experience curve from the past.

If the innovation of EV

technology suddenly slows due to technological difficulty or maturity, then the investment in EV

capital becomes inefficient. If scientists and engineers find new breakthroughs in EV technology,

such as solid-state batteries, which is one of the certain future of batteries (Janek & Zeier, 2023),

then investment in EV capital is remarkably attractive.

23

1.6 Conclusion

I have demonstrated the dynamics of optimal policy on firms’ dynamic competition and con-

sumers’ purchase behavior. The government promotes EV adoptions by stimulating EV investment

using two instruments: EV retail purchase subsidy and manufacturer investment subsidy. This

chapter analyzes all agents’ behavior and choices to investigate policy intervention. This analysis

shows that the optimal path should be a very high level of intervention at the 2024 capital levels;

however, all will soon reach zero when the EV capital accumulates. This is because the policy in-

strument exerts two kinds of impact on the market: impact on the current market and impact on the

future market via investment stimulation. The earlier intervention results in an accrued impact over

time. On the other hand, as the products’ attributes improve and prices decrease, the government

4

2

may no longer need to intervene at some point – as per Archsmith et al. (2022)’s finding that, if

intrinsic demand growth is high, the higher future market share will head to no subsidies required.

This result also seems to accord well with Rapson & Muehlegger (2023). Acemoglu et al. (2012)

show that it is optimal to redirect technology innovation toward clean technologies immediately

and that delaying intervention is costly. They found that long-run growth can be achieved using

temporary intervention when the inputs are substitutable.

My finding seems contrary to Langer & Lemoine (2022)’s finding that efficient subsidies

increase over time; however, it is justifiable due to the different nature of the research topic. First,

the consumer characteristics are different for solar panels and EVs. Langer & Lemoine (2022)

analyzed solar panel adoption, which has a fixed total sale and long lifetime of a good exceeding 20

years, while the automobile market has a fixed total sale per year. Therefore, in Langer & Lemoine

(2022), early adopters install solar panels first, and they will not be in the market for a long time.

So, the result may be considered to avoid overpaying early adopters and to pay more late adopters.

If all homeowners install solar panels on their roofs, there will be no new consumers before the

installed panels are outdated after 20 years. However, this chapter has 17 million new vehicles

consumed every year, considering the recent several decades trend. Therefore, early adopters may

buy vehicles every year. Second, the objectives of government are different from each other. Langer

24

& Lemoine (2022) assume that the government dislikes spending money due to administrative costs

and budget limits, and regulators will maximize instantaneous benefit minus cost from adoption. In

this chapter, the regulators consider all stakeholders’ surplus, and the regulators have no preference

for spending money because it will be a tradeoff in society. Thus, regulators maximize consumer

and producer surplus with social cost minimization. It makes us focus on how subsidies stimulate

capital investment, which will change the social equilibrium, while Langer & Lemoine (2022)

focuses on the dynamic and heterogeneous consumer preference at given conditions.

A further implication of this study requires expanding this model. Regarding assumptions,

some damage-related parameters are assumed to be constant, even though they are not so in reality.

The unit emission from EVs will decrease as the energy source becomes increasingly renewable

5

2

(Shafique & Luo, 2022; Rapson & Muehlegger, 2023). The social cost of carbon will increase as the

carbon budget is exhausted (US Environmental Protection Agency, 2010). Rapson & Muehlegger

(2023) argued that there is an active debate about how much EVs are driven, and there may be

evidence that average traveled miles of EVs are less than ICEs. Second, future work may consider

the consumer’s ability to delay the adoption choice and induced technology together.

It will

include this chapter’s findings, how to stimulate investment via subsidies, and Langer & Lemoine

(2022)’s findings on how to use subsidies as price discrimination for consumer heterogeneity. There

are two competing trends: one to decrease subsidy over time from increasing target technology

competitiveness, and one to increase subsidy over time from considering consumers who are

unwilling to pay for the technology. Finally, we could apply this model to industries where

governments need to intervene to correct externalities, or we could expand this model to other

environmental policies such as carbon tax or emission trading schemes. This model is based on

market competition and how to promote the target product’s market share with policy intervention.

25

6

2

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31

APPENDIX 1.A: Tables and Figures

Table 1.1 Parameters for damage function

year
mile
emit 𝑓
emit𝑒

SCC
𝜌

Variable
Total lifetime of a car
Annual miles traveled per year
Emission per gallon of gasoline
Emission per gallon-equivalent
Emission per 1 kWh electricity
Social cost of carbon
discount rate

Value
11.8 year
14,263 mile/year
8,897 g CO2/gallon
12,993 g CO2/galloneq
385.55 g CO2/kWh
$52.04/ton CO2
3%

Source
US Bureau of Transportation Statistics (2021)
Book (2021)
US Environmental Protection Agency (2023)
Calculated by 33.7kWh=1 gallon
US Energy Information Administration (2021)
US Environmental Protection Agency (2010)
US Environmental Protection Agency (2010)

2

3

32

Table 1.2 The descriptive statistics of the dataset for demand estimation

Variables
Dependent

𝑝 𝑗
𝑥1
𝑥2
𝑥3
𝑦1
𝑦2
𝑦3
𝑧𝑒
𝑧 𝑓

Unit

𝑙𝑛𝑠𝑚,𝑡 − 𝑙𝑛𝑠𝑛,𝑡
%
Market Share
count
Sale
$
Price
Power weight ratio
HP/lb
Mileage per fuel of dollar value mile/$
mile
Maximum driving range
inch
Wheelbase
inch
Height
inch
Width
binary
Type of Vehicle - EV
binary
Type of Vehicle - ICE

Obs.
3,417
3,417
3,417
3,252
3,258
3,238
3,121
3,280
3,279
3,279
3,417
3,417

Mean
−4.467 (2.288)
0.300 (0.488)
50,941 (82,932)
39,220 (19,759)
0.057 (0.015)
10.103 (4.954)
415.089 (87.473)
111.461 (9.647)
63.38 (6.752)
73.547 (3.923)
0.026 (0.158)
0.835 (0.371)

Min
-15.779
5.88 × 10−6
1
12,246
0.020
4.538
58.0
73.5
53.0
60.9
0
0

Max
1.058
5.155
876,341
132,310
0.134
41.776
758.0
153.0
84.6
89.0
1
1

Note: These statistics exclude the portion of no buy options

Parentheses give the standard deviation for each coefficient

3

3

33

Table 1.3 The statistics of annual sale, no-buy options, and fuel price

No-buy options Oil Price($/gallon)

Year
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
Average
Note: Prices are real prices in 2019 by applying CPI index

Total Sale
14,116,379
9,872,487
10,906,440
12,141,424
13,680,451
14,889,435
15,637,553
16,360,077
16,661,898
16,714,252
16,553,388
16,531,617
14,505,450

2,883,621
7,127,513
6,093,560
4,858,576
3,319,549
2,110,565
1,362,447
639,923
338,102
285,748
446,612
468,383
2,494,550

2.643
2.858
2.826
2.865
2.774
2.702
2.660
2.575
2.804
2.853
2.757
2.691
2.751

Electricity Price($/kWh)
N/A
N/A
N/A
0.104
0.111
0.113
0.108
0.103
0.099
0.098
0.097
0.097
0.103

Electricity price in 2011 is gained by applying CPI for electricity index

4

3

34

Table 1.4 The demand estimation result of the OLS, FEE, and RFE models

$

𝛼

𝑝 𝑗

𝑥1

𝑦2

𝛽1

𝛽2

𝛽3

inch

Unit

mile

Price

HP/lb

Height

Variables

Power weight ratio

𝑦1 Wheelbase

𝑥3 Maximum driving range

𝑥2 Mileage per fuel of dollar value mile/$

OLS
−3.61 × 10−5****
(2.20 × 10−6)
16.068****
(3.415)
0.093****
(0.012)
9.805 × 10−3****
(5.428 × 10−4)
0.002
(0.005)
0.048****
(0.007)
-0.122****
(0.011)
1.791****
(0.382)
2.616****
(0.146)
-5.275**
(0.404)
None
None
𝑁𝑜𝑡𝑒 : ∗𝑝 < 0.1; ∗ ∗ 𝑝 < 0.05; ∗ ∗ ∗𝑝 < 0.01; ∗ ∗ ∗ ∗ 𝑝 < 0.001
Parentheses give the robust standard errors for each coefficient

Vehicle model control
Time control

Type of Vehicle - ICE

Type of Vehicle - EV

𝑦3 Width

Constant

binary

binary

inch

inch

𝛾2

𝛾1

𝛾3

𝛿 𝑓

𝛿𝑒

𝑧 𝑓

𝑧𝑒

FFE
−1.001 × 10−5***
(3.429 × 10−6)
4.539**
(1.960)
0.044***
(0.014)
1.151 × 10−3***
(3.853 × 10−4)
0.048****
(0.009)
-0.024*
(0.013)
0.013
(0.008)
N/A
N/A
N/A
N/A
-10.248****
(1.308)
Fixed
Fixed

RFE
−2.924 × 10−5****
(2.480 × 10−6)
3.236*
(1.912)
0.030***
(0.012)
1.503 × 10−3****
(3.578 × 10−4)
0.013**
0.006
-0.003
(0.008)
0.001
(0.007)
0.071
(0.389)
2.267****
(0.162)
-8.253****
(0.645)
Random
Fixed

5

3

35

Table 1.5 The descriptive statistics of the dataset for production estimation

Variables
EV
𝑐𝑒
𝑥1
𝑥2
𝑥3
𝐾𝑒
ICE
𝑐 𝑓
𝑥1
𝑥2
𝑥3
𝐾 𝑓
Both
𝐾 𝑗
𝐼 𝑗

Unit

Obs.

Mean

Min

Max

Unit production cost
Power weight ratio
Mileage per 33.7kWh
Maximum driving range
Cumulatice capital

$
HP/lb
mile/33.7kWh
mile
$ Billion

Unit production cost
Power weight ratio
Mileage per gallon
Maximum driving range
Cumulatice capital

$
HP/lb
mile/gallon
mile
$ Billion

7
9
9
9
9

9
9
9
9
9

46,866 (7,958)
0.052 (0.012)
106.29 (6.71)
145.28 (57.53)
8.12 (7.95)

28,563 (1,082)
0.057 (0.000)
25.47 (0.77)
437.44 (8.31)
218.98 (27.36)

35,373
0.032
97.98
73
0.48

27,277
0.056
23.95
419.89
173.36

59,930
0.063
116.39
243.93
19.25

30,204
0.057
26.22
446.13
248.30

Cumulatice capital
Investment

$ Billion
$ Billion

21
21

22.00 (15.64)
0.91 (0.36)

0.32
0.24

42.58
1.51

6

3

36

Table 1.6 The production estimation result

Dependent Variables
𝑐 𝑗

ln(unit production cost)

𝑥1

𝑥2

𝑥3

ln(Power weight ratio)

ln(MPG(e))

ln(Maximum driving range)

coefficient
𝜙 𝑗𝑐1
ln 𝜙 𝑗𝑐0
𝜙 𝑗11
ln 𝜙 𝑗10
𝜙 𝑗21
ln 𝜙 𝑗20
𝜙 𝑗31
ln 𝜙 𝑗30
1 − 𝜇
𝜈

EV
-0.124 (0.044)**
13.543 (0.996)****
0.166 (0.034)***
-6.663 (0.751)****
0.039 (0.001)***
3.809 (0.187)****
0.269 (0.047)***
-1.060 (1.041)

ICE
-0.185 (0.084)*
15.091 (2.187)****
0.037 (0.019)*
-3.841 (0.500)****
0.211 (0.040)***
-2.262 (1.032)*
0.111 (0.037)**
3.189 (0.961)**

0.949 (0.021)****
8.423 × 10−10 (4.337 × 10−11)****

Cumulative capital
Investment

𝐾 𝑗
𝐼 𝑗
𝑁𝑜𝑡𝑒 : ∗𝑝 < 0.1; ∗ ∗ 𝑝 < 0.05; ∗ ∗ ∗𝑝 < 0.01; ∗ ∗ ∗ ∗ 𝑝 < 0.001
Parentheses give the robust standard errors for each coefficient

7

3

37

Table 1.7 Comparison of policy instruments and their equilibrium

Unit

Zero subsidy
$0

Purchase subsidy
Current ($7500)

Purchase subsidy
Dynamic (𝜂𝑒)

Investment subsidy
Dynamic (𝜃𝑒)

$ 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$0
60.40
1700.06
554.46
91.24
1,094.69
0
40.34

In 2024
Policy level
TSNB
SNB
CS
PS (EV)
PS (ICE)
GE
DE
Equilibrium
Equlibirum
Policy level
EV capital at Eq
ICE capital at Eq
* In 2024, EV capital is $52.81 billion and ICE capital is $276.17 billion

$7500
+1.40 (+2.31%)
+68.28 (+4.02%)
+70.86 (+12.78%)
+85.55 (+93.77%)
-50.73 (-4.63%)
+38.10
-0.71 (-1.75%)

Corner solution
$7500
449
0

Steady-state
$0
147.77
665.46

$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$15026
+2.32 (+3.84%)
+122.49 (+7.21%)
+143.45 (+25.87%)
+162.34 (+177.93%)
-102.67 (-9.38%)
+82.06
-1.44 (-3.58%)

$37.01 𝑏𝑖𝑙𝑙𝑖𝑜𝑛 (206%)
+1.44 (+2.39%)
+120.31 (+7.08%)
-
+121.43 (+133.09%)
-1.11 (-0.10%)
+37.01
-

Corner solution
$0
421
0

Steady-state
$0 (0%)
365.59
42.56

8

3

38

Table 1.8 Senstivity analysis for different discount rates

Unit

$0

$7500

𝜂𝑒

𝜃𝑒

$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

Steady-state
$0
123.21
1030.22

$0
37.04
1789.66
554.46
138.10
1108.62
0
11.53

$ 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$7500
+0.72 (+1.95%)
+57.79 (+3.23%)
+70.86 (+12.78%)
+78.31 (+56.70%)
-53.48 (-4.82%)
+38.10
-0.20 (-1.75%)

(1) 𝜌=5%
In 2024
Policy level
TSNB
SNB
CS
PS (EV)
PS (ICE)
GE
DE
Equilibrium
Equlibirum
Policy level
EV capital at Eq
ICE capital at Eq
(2) 𝜌=3% and High SCC
In 2024
Policy level
TSNB
SNB
CS
PS (EV)
PS (ICE)
GE
DE
Equilibrium
Equlibirum
Policy level
EV capital at Eq
ICE capital at Eq
* In 2024, EV capital is $52.81 billion and ICE capital is $276.17 billion

$7500
+1.46 (+2.53%)
+69.64 (+4.29%)
+70.86 (+12.78%)
+85.55 (+93.77%)
-50.73 (-4.63%)
+38.10
-2.07 (-1.75%)

$ 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$0
57.59
1622.27
554.46
91.24
1094.69
0
118.13

Corner solution
$7500
450
0

Steady-state
$7500
328.08
34.61

Steady-state
$0
147.16
665.83

$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$10694
+0.93 (+2.50%)
+77.21 (+4.31%)
+101.49 (+18.30%)
+108.54 (+78.60%)
-77.08 (-6.95%)
+56.04
-0.29 (-2.52%)

Steady-state
$0
297.83
18.12

$16073
+2.55 (+4.43%)
+131.88 (+8.13%)
+153.67 (+27.71%)
+172.31 (+188.85%)
-109.97 (-10.05%)
+88.65
-4.54 (-3.84%)

$21.20 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
-0.05 (-0.14%)
+72.27 (+4.04%)
-
+83.45 (+60.42%)
-11.18 (-1.01%)
+21.20
-

Corner solution
$0 (0%)
435
0

$17.06 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
+1.17 (+2.03%)
+96.46 (+5.95%)
-
+90.52 (+99.21%)
+5.95 (0.54%)
+17.06
-

9

3

Corner solution
$0
422
0

Steady-state
$0 (0%)
370.11
40.26

39

Table 1.9 Senstivity analysis for different unit emissions

Unit

$0

$7500

𝜂𝑒

𝜃𝑒

$15091
+2.33 (+3.86%)
+123.27 (+7.24%)
+144.09 (+25.99%)
+162.97 (+178.61%)
-103.13 (-9.42%)
+82.47
-1.82 (-4.77%)

$30.55 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
+1.26 (+2.07%)
+113.66 (+6.68%)
-
+112.30 (+123.08%)
+1.36 (+0.12%)
+30.55
-

Corner solution
$0
421
0

Steady-state
$0 (0%)
363.97
40.85

$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

Steady-state
$0
146.32
663.86

$0
60.49
1702.35
554.46
91.24
1094.69
0
38.05

$ 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$7500
+1.40 (+2.31%)
+68.46 (+4.02%)
+70.86 (+12.78%)
+85.55 (+93.77%)
-50.73 (-4.63%)
+38.10
-0.88 (-2.32%)

(3) RE50
In 2024
Policy level
TSNB
SNB
CS
PS (EV)
PS (ICE)
GE
DE
Equilibrium
Equlibirum
Policy level
EV capital at Eq
ICE capital at Eq
(4) RE100
In 2024
Policy level
TSNB
SNB
CS
PS (EV)
PS (ICE)
GE
DE
Equilibrium
Equlibirum
Policy level
EV capital at Eq
ICE capital at Eq
* In 2024, EV capital is $52.81 billion and ICE capital is $276.17 billion

$7500
+1.40 (+2.31%)
+68.64 (+4.03%)
+70.86 (+12.78%)
+85.55 (+93.77%)
-50.73 (-4.63%)
+38.10
-1.06 (-2.96%)

$ 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$0
60.60
1704.64
554.46
91.24
1094.69
0
35.75

Corner solution
$7500
450
0

Corner solution
$7500
450
0

Steady-state
$0
146.57
666.45

$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
$ 𝑏𝑖𝑙𝑙𝑖𝑜𝑛

$15087
+2.33 (+3.85%)
+123.61 (+7.25%)
+144.05 (+25.98%)
+162.93 (+178.57%)
-103.10 (-9.42%)
+82.45
-2.18 (-6.09%)

$40.58 𝑏𝑖𝑙𝑙𝑖𝑜𝑛
+0.91 (+1.50%)
+123.55 (+7.25%)
-
+126.11 (+138.22%)
-2.55 (-0.23%)
+40.58
-

0

4

Corner solution
$0
418
0

Steady-state
$0 (0%)
370.11
40.26

40

1

4

Figure 1.1 A simplified diagram illustrating the model’s market dynamics and regulations

41

(a) Zero purchase subsidy

(b) Constant $7,500 purchase subsidy

2

4

(c) Dynamic purchase subsidy

(d) Dynamic investment subsidy

Figure 1.2 Flow chart under each policy

42

(a) Dynamic purchase subsidy

3

4

(b) Dynamic investment subsidy

Figure 1.3 Flow chart with each subsidy

43

Figure 1.4 The path of subsidy and expenditure under each subsidy

4

4

44

(a) Path of EV capital under four policies

5

4

(b) Path of ICE capital under four policies

Figure 1.5 Path of firms’ capital under four policies

45

APPENDIX 1.B: Demand Estimation

To estimate aggregate demand, market data are gathered from global automobile marketing
companies: Markline and Wardsauto, and filtered for relevance. First, I excluded commercial
vehicles, oversized trucks, and supercars. They have different segments in the market, and there
were no commercialized EVs of these types. The list of excluded cars is in Table 1.B.1.

Table 1.B.1 List of excluded vehicle models

Brand
All models
in this brand:

Alfa Romeo
Audi
BMW
Cadillac
Chevrolet
Chrysler
Dodge
Fiat
Ford
GMC
Honda
Hyundai
Jaguar
Mazda
Mercedes-Benz
Mitsubishi
Nissan
Pontiac
Porsche
Ram
Saturn
Subaru
Toyota
Volkswagen

Model
Aston Martin, Bentley, Ferrari, Lamborghini, Maserati, Rolls-Royce, Freightliner, Hino, International,
Isuzu, Kenworth, Lotus, Mack Trucks, Mitsubishi Fuso, Peterbilt, Sterling, UD Trucks, Volvo Trucks,
Western Star
4C
TT, RS6, R8
M3, Z4, i8, Z8
XLR
Camaro, Express cargo, City Express, Silverado médium, Corvette, Kodiak, W, C/T
Truck, Crossfire
Challenger, Viper, Sprinter
124 Spider
Truck, Mustang, F-series Medium duty, GT, Transit, Low Cab Forward
Savana Cargo, Sierra Medium duty, C/T, C/W, Truck(GM)
S2000, NSX(Acura)
Tiburon
XK, F-Type
MX-5, RX-8
SLC, SLK, CLK, AMG-GT, CL, SL, SLR, SLS, Sprinter
Eclipse, Eclipse Spyder
350Z, 370Z, GT-R, Truck, Q60(Infiniti)
Solstice, Firebird, GTO
Boxster, Cayman, Carrera, Porsche 911, Porsche 918
Medium duty, Cargo van, ProMaster
S-series, Sky
BRZ
86, Celica, MR2, Supra, FR-S(Scion), RC(Lexus), SC(Lexus), LC(Lexus), LFA(Lexus)
Eurovan

6

4

46

APPENDIX 1.C: Solving Optimal Decisions

1.C.1 Optimal Price and investment

If we solve Equation (1.3e) with respect to price, the F.O.C. of price is 𝜌 𝜕𝑉 𝑗
𝜕 𝑝 𝑗
𝜕𝑠 𝑗
= 𝛼𝑠𝑒𝑠 𝑓 .
=
𝜕 𝑝 𝑗

𝑀. We can rewrite this with

= −𝛼𝑠𝑒𝑠 𝑓 , and

= 𝜕𝑠𝑒
𝜕 𝑝 𝑓

𝜕𝑠 𝑓
𝜕 𝑝 𝑓

𝜕𝑠𝑒
𝜕 𝑝𝑒

𝜕𝑠𝑒
𝜕 𝑝 𝑓

𝑐 𝑗 )

= 0 = 𝑠 𝑗 𝑀 + ( 𝑝 𝑗 −

+

𝑝∗
𝑒 (𝑝𝑝𝑝, 𝑥𝑥𝑥; 𝜂𝑒) = 𝑐𝑒 (𝐾𝑒) +

1
𝛼 exp[𝛽𝛽𝛽(𝑥𝑒𝑥𝑒𝑥𝑒 − 𝑥 𝑓𝑥 𝑓𝑥 𝑓 ) + 𝛿𝑒 − 𝛿 𝑓 − 𝛼( 𝑝∗
1
𝛼 exp[𝛽𝛽𝛽(𝑥 𝑓𝑥 𝑓𝑥 𝑓 − 𝑥𝑒𝑥𝑒𝑥𝑒) + 𝛿 𝑓 − 𝛿𝑒 + 𝛼( 𝑝∗
To solve this exponential equation, I rearrange Equation (1.C.1.1) using the Lambert 𝑊 function,

𝑓 (𝑝𝑝𝑝, 𝑥𝑥𝑥; 𝜂𝑒) = 𝑐 𝑓 (𝐾 𝑓 ) +

𝑒 − 𝜂𝑒 − 𝑝∗

𝑒 − 𝜂𝑒 − 𝑝∗

(1.C.1.1b)

(1.C.1.1a)

1
𝛼
1
𝛼

𝑓 )]

𝑓 )]

𝑝∗

+

that 𝑤𝑒𝑤 = 𝑥 can be solved as 𝑤 = 𝑊0(𝑥) for 𝑥 ≥ 0.

𝑝∗
𝑒 ( 𝑝 𝑓 , 𝑥𝑥𝑥; 𝜂𝑒) = 𝑐𝑒 (𝐾𝑒) + 1/𝛼 + 𝑊0𝑒/𝛼

𝑊0𝑒 ≡ 𝑊0

(cid:2) exp (cid:0)𝛽𝛽𝛽(𝑥𝑒𝑥𝑒𝑥𝑒 − 𝑥 𝑓𝑥 𝑓𝑥 𝑓 ) + 𝛿𝑒 − 𝛿 𝑓 + 𝛼( 𝑝 𝑓 + 𝜂𝑒 − 𝑐𝑒 (𝐾𝑒)) − 1(cid:1)(cid:3)

𝑝∗

𝑓 ( 𝑝𝑒, 𝑥𝑥𝑥; 𝜂𝑒) = 𝑐 𝑓 (𝐾 𝑓 ) + 1/𝛼 + 𝑊0 𝑓 /𝛼

(1.C.1.2a)

(1.C.1.2b)

𝑊0 𝑓 ≡ 𝑊0

(cid:2) exp (cid:0)𝛽𝛽𝛽(𝑥 𝑓𝑥 𝑓𝑥 𝑓 − 𝑥𝑒𝑥𝑒𝑥𝑒) + 𝛿 𝑓 − 𝛿𝑒 + 𝛼( 𝑝𝑒 − 𝜂𝑒 − 𝑐 𝑓 (𝐾 𝑓 )) − 1(cid:1) (cid:3)

The range of 𝑊0 𝑗 is [0, 14] at the range of 𝑝 𝑗 ∈ [$10𝑘, $100𝑘], 𝜂𝑒 ∈ [$0, $20𝑘], and 𝐾 𝑗 ∈
[$0, $300𝑏𝑖𝑙𝑙𝑖𝑜𝑛]. In this range, we can approximate 𝑊0(𝑥) (cid:27) 𝑤1 ln(𝑥) + 𝑤0 with 𝑤1 = 0.3546,
and 𝑤0 = 0.7232 and 𝑅2 is 0.9095. If we substitute Equation (1.C.1.2) for each other, then the
optimal price is now the function of both firms’ capital only.

ˇ𝑝∗
𝑒 (𝐾𝐾𝐾; 𝜂𝑒) =

𝑐𝑒 (𝐾𝑒)
1 + 𝑤1

+

1 + 𝑤0 − 𝑤1
𝛼

+

𝑤1

(cid:2)𝛽𝛽𝛽(𝑥𝑒𝑥𝑒𝑥𝑒 (𝐾𝑒) − 𝑥 𝑓𝑥 𝑓𝑥 𝑓 (𝐾 𝑓 )) + 𝛿𝑒 − 𝛿 𝑓 + 𝛼(𝑐 𝑓 (𝐾 𝑓 ) + 𝜂𝑒)(cid:3)
𝛼(1 + 𝑤1)

(1.C.1.3a)

ˇ𝑝∗

𝑓 (𝐾𝐾𝐾; 𝜂𝑒) =

𝑐 𝑓 (𝐾 𝑓 )
1 + 𝑤1

+

1 + 𝑤0 − 𝑤1
𝛼

+

𝑤1

(cid:2)𝛽𝛽𝛽(𝑥 𝑓𝑥 𝑓𝑥 𝑓 (𝐾 𝑓 ) − 𝑥𝑒𝑥𝑒𝑥𝑒 (𝐾𝑒)) + 𝛿 𝑓 − 𝛿𝑒 + 𝛼(𝑐𝑒 (𝐾𝑒) − 𝜂𝑒)(cid:3)
𝛼(1 + 𝑤1)

(1.C.1.3b)

7

4

If we solve Equation (1.3e) with respect to investment, we have the F.O.C. of investment:

𝜌 𝜕𝑉 𝑗
𝜕𝐼 𝑗

=

𝜕𝑉 𝑗
𝜕𝐾 𝑗

− 𝜕
𝜕𝐼 𝑗

𝜓 𝑗 (𝐼 𝑗 ) = 0. The optimal investment is 𝐼∗

𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) = 1
2𝜈

𝜕𝑉 𝑗
𝜕𝐾 𝑗 .

1.C.2 Optimal Purchase Subsidy

There are two policies to be optimized: 𝜂𝑒 (purchase subsidy) and 𝜃𝑒 (investment subsidy). The
optimal subsidy is determined by solving Equation (1.9c). First, the F.O.C. of purchase subsidy is
𝜕𝑆𝑁 𝐵
𝜕𝜂𝑒
derivatives and Equation (1.1c), we get

) = 0. From Equation (1.C.1.3),
= 1−𝑤1
1+𝑤1

𝛼𝑠𝑒𝑠 𝑓 . From Equation (1.9b),

. Then, with these

= 𝑤1
1+𝑤1

) + 𝜕Ω
𝜕𝐾 𝑓

+ 𝜕Ω
𝜕𝐾𝑒

( 𝜕𝐼𝑒
𝜕𝜂𝑒

𝜕 ˇ𝑝∗
𝑓
𝜕𝜂𝑒

𝜕 ˇ𝑝∗
𝑒
𝜕𝜂𝑒

𝜕𝑠 𝑓
𝜕𝜂𝑒

𝜕𝐼 𝑓
𝜕𝜂𝑒

𝜕𝑠𝑒
𝜕𝜂𝑒

= −

= −

(

𝜕 SNB
𝜕𝜂𝑒

=

𝜕 CS(𝐾𝐾𝐾, 𝜂e)
𝜕𝜂𝑒

+

𝜕 PS(𝐾𝐾𝐾, 𝜂e)
𝜕𝜂𝑒

+

𝜕 GE(𝐾𝐾𝐾, 𝜂e)
𝜕𝜂𝑒

+

𝜕 D(𝐾𝐾𝐾, 𝜂e)
𝜕𝜂𝑒

=

1 − 𝑤1
1 + 𝑤1

[( ˇ𝑝∗

𝑒 − ˇ𝑝∗

𝑓 ) − (𝑐𝑒 − 𝑐 𝑓 ) − (𝑑𝑒 − 𝑑 𝑓 ) − 𝜂𝑒]𝛼𝑠𝑒𝑠 𝑓 𝑀 − 2𝜈𝐼𝑒

𝜕𝐼𝑒
𝜕𝜂𝑒

− 2𝜈𝐼 𝑓

𝜕𝐼 𝑓
𝜕𝜂𝑒

(1.C.2.1)

47

Then, we rewrite Equation (1.C.2.1).

𝑤1 − 1
1 + 𝑤1

𝜂𝑒 +

2𝑤1
𝛼(1 + 𝑤1)

[𝛽𝛽𝛽(𝑥𝑒𝑥𝑒𝑥𝑒 − 𝑥 𝑓𝑥 𝑓𝑥 𝑓 ) + 𝛿𝑒 − 𝛿 𝑓 − 𝛼(𝑐𝑒 − 𝑐 𝑓 )] − (𝑑𝑒 − 𝑑 𝑓 )

=

1 + 𝑤1
(1 − 𝑤1)𝛼𝑠𝑒𝑠 𝑓 𝑀

[(2𝜈𝐼𝑒 −

𝜕Ω
𝜕𝐾𝑒

)

𝜕𝐼𝑒
𝜕𝜂𝑒

+ (2𝜈𝐼 𝑓 −

𝜕Ω
𝜕𝐾 𝑓

𝜕𝐼 𝑓
𝜕𝜂𝑒

]

)

(1.C.2.2)

In the above equation, 𝐼 𝑗 is linear in 𝜂𝑒, and the inverse of the market share term is

1
𝑠𝑒𝑠 𝑓

= 2 + 𝑒 𝛽(𝑥𝑒−𝑥 𝑓 )+𝛿𝑒−𝛿 𝑓 −𝛼( 𝑝𝑒−𝑝 𝑓 −𝜂𝑒) + 𝑒−𝛽(𝑥𝑒−𝑥 𝑓 )−(𝛿𝑒−𝛿 𝑓 )+𝛼( 𝑝𝑒−𝑝 𝑓 −𝜂𝑒)

(1.C.2.3)

If we apply Taylor approximation to 𝜂𝑒, the term is approximated as,

(cid:16)

1
(cid:27) 2 + 𝑒Δ𝐾 + 𝑒−Δ𝐾 +
𝑠𝑒𝑠 𝑓
Δ𝐾 ≡ 𝛽(𝑥𝑒 − 𝑥 𝑓 ) − 𝛼 1 − 𝑤1
1 + 𝑤1

(𝑐𝑒 − 𝑐 𝑓 )

𝑒Δ𝐾 + 𝑒−Δ𝐾 + (𝑒Δ𝐾 − 𝑒−Δ𝐾)

1 − 𝑤1
1 + 𝑤1

(cid:17)

𝛼

𝜂𝑒

(1.C.2.4)

(1.C.2.4a)

8

4

If we substitute this into Equation (1.C.2.2), then we get the quadratic equation of 𝜂𝑒.

1.C.3 Optimal Investment Subsidy
𝜕𝑠 𝑗
Regarding investment subsidy,
𝜕𝜃𝑒

( 𝜕Ω
𝜕𝐾 𝑓

− 2𝜈𝐼 𝑓 )(

𝜕𝐼 𝑓
𝜕𝜃𝑒

= 0. Therefore, the first-order condition is ( 𝜕Ω
𝜕𝐾𝑒

−2𝜈𝐼𝑒) ( 𝜕𝐼𝑒
𝜕𝜃𝑒

)+

) = 0.

𝐼 𝑗 =

1
2𝜈

𝜕𝑉𝑗
𝜕𝐾 𝑗

=

1
2𝜈

(𝑍 𝑗1𝜃𝑒 + 𝑍 𝑗2) where

𝜕𝑉𝑗
𝜕𝐾 𝑗

≡ 𝑍 𝑗1𝜃𝑒 + 𝑍 𝑗2

(1.C.3.1)

and

− 𝑍𝑒1𝜃𝑒 − 𝑍𝑒2) 𝑍𝑒1

2𝜈 + ( 𝜕Ω
Then, ( 𝜕Ω
𝜕𝐾𝑒
𝜕𝐾 𝑓
𝑍 𝑓 1
𝜕𝐼 𝑓
2𝜈 . Therefore, we can get the optimal investment subsidy.
𝜕𝜃𝑒
𝑍𝑒1( 𝜕Ω
𝜕𝐾𝑒

− 𝑍 𝑓 1𝜃𝑒 − 𝑍 𝑓 2)

− 𝑍 𝑓 2)

=

𝜃∗
𝑒 =

− 𝑍𝑒2) + 𝑍 𝑓 1( 𝜕Ω
𝜕𝐾 𝑓
+ 𝑍 2
𝑓 1

𝑍 2
𝑒1

𝑍 𝑓 1
2𝜈 = 0 with the derivatives:

𝜕𝐼𝑒
𝜕𝜃𝑒

= 𝑍𝑒1
2𝜈

(1.C.3.2)

48

APPENDIX 1.D: Collocation Process

𝑉𝑗 (𝐾𝐾𝐾; 𝜏𝜏𝜏) is a function of three variables: 𝐾𝑒, 𝐾 𝑓 , and 𝜏𝑒 ∈ {𝜂𝑒, 𝜃𝑒}. I choose a polynomial
with 32 terms in three variables, allowing up to third orders for 𝐾 𝑗 and the first order for 𝜂𝑒.
This choice of dimensionality is a balance between having enough scope for good fitting versus
computation costs. There are 32 unknown coefficients, 𝜓𝑛 𝑗 ∈ 𝜓 𝑗𝜓 𝑗𝜓 𝑗 and 𝑛 ∈ {1, ..., 32}; therefore, it
should interpolate 32 points of variables for each firm 𝑗.

ˇ𝑉𝑗 (𝐾𝐾𝐾; 𝜂𝑒) ≡

32
∑︁

𝑛=1

𝜓𝑛 𝑗 𝜏𝑎

𝑥 𝐾 𝑏

𝑒 𝐾 𝑐

𝑓 , where 𝑎 ∈ {0, 1}, 𝑏, 𝑐 ∈ {0, 1, 2}

(1.D.1)

I solve both firms’ problems simultaneously to get a total of 64 unknowns: 𝜓𝑒𝜓𝑒𝜓𝑒 and 𝜓 𝑓𝜓 𝑓𝜓 𝑓 . Uniformly
distributed points of supports are widely used for determining collocation nodes. 32 nodes are
combinations of 10 uniformly distributed points of a support of 𝐾𝐾𝐾 and 𝜏𝑒. We can check the
correctness of the collocation by comparing the right-hand side of Equation (1.3e) and Equation
(1.D.1) with calibrated 𝜓 𝑗𝜓 𝑗𝜓 𝑗 . If the collocation is correct, their difference should be close to zero.
The sum of squared errors, [ 𝑉𝑒 (𝐾𝐾𝐾;𝜏𝑥)− ˇ𝑉𝑒 (𝐾𝐾𝐾;𝜏𝑥)
]2, is 1.90 × 10−5 for purchase subsidy and 8.52 × 10−7
]2 is 6.46 × 10−6 for purchase subsidy and 2.85 × 10−6 for
for investment subsidy. [
investment subsidy.

𝑉𝑒 (𝐾𝐾𝐾;𝜏𝑥)
𝑉 𝑓 (𝐾𝐾𝐾;𝜏𝑥)− ˇ𝑉 𝑓 (𝐾𝐾𝐾;𝜏𝑥)
𝑉 𝑓 (𝐾𝐾𝐾;𝜏𝑥)

The government’s unknown value function, Ω(𝐾𝐾𝐾), has two unknown variables: 𝐾𝑒 and 𝐾 𝑓 . I
assume the polynomial has 16 terms in two variables with 16 unknown coefficients, 𝜓𝑛𝑔 ∈ 𝜓𝑔𝜓𝑔𝜓𝑔,
necessitating 16 support points.

9

4

ˇΩ(𝐾𝐾𝐾) ≡

16
∑︁

𝑛=1

𝜓𝑛𝑔𝐾 𝑏

𝑒 𝐾 𝑐

𝑓 , where 𝑏, 𝑐 ∈ {0, 1, 2}

(1.D.2)

Substituting the value function and its derivatives into Equation (1.9c) generates 16 equations
with 16 unknown coefficients. I choose 16 uniformly distributed nodes as combinations of 𝐾𝐾𝐾. The
correctness of the collocation is checked in the same way for firms’ value functions. The sum of
squared errors, [ Ω(𝐾𝐾𝐾)− ˇΩ(𝐾𝐾𝐾)
]2, is 7.18 × 10−9 for purchase subsidy and 1.71 × 10−5 for investment
subsidy.

Ω(𝐾𝐾𝐾)

49

CHAPTER 2

PEER EFFECTS IN ELECTRIC VEHICLE ADOPTION

2.1

Introduction

Individuals communicate and interact with each other, and it significantly affects individual

choices and decisions. In many social science disciplines, peer effects have been widely used as an

indicator of interaction behavior. Abundant literature considers peer effects in housing (Patacchini

& Venanzoni, 2014), productivity (Falk & Ichino, 2006), employment rate (Kondo & Shoji, 2019),

sexual behavior (Ajilore, 2015), general consumption (De Giorgi et al., 2020; Agarwal et al.,

2021), product adoption (Axsen et al., 2013; Hu & Van den Bulte, 2014; Park, 2019; Simpson &

Mishra, 2021; Bailey et al., 2022; Ding et al., 2022), technology adoption (Conley & Udry, 2010;

0

5

Skevas et al., 2022; Meng et al., 2023), program participation (Dahl et al., 2014), and animation

watching (Ameri et al., 2019). In economics, there is growing evidence of whether, how, and to

what extent the peer effect affects consumer decisions. Such peer effects play an important role in

understanding consumer demand, which is specifically crucial for policymakers and entrepreneurs.

Heutel & Muehlegger (2015) find that an increase in initial adopters may positively or negatively

affect subsequent diffusions according to the quality of the product.

If positive peer effects on

product adoption exist, boosting the demand via word of mouth, the actual aggregate demand

would be larger than expected from a simple aggregation of individual demand. With negative peer

effects, the actual aggregate demand would be lower than expected. McCoy & Lyons (2014) find

that mild peer effects could result in large clusters of adopters in certain areas even if adoption is

relatively low. This relationship between peer effect and aggregate demand may affect the actual

impact of demand-boosting policies, such as purchase subsidies and firms’ demand forecasts.

The peer effect is particularly important in the early stage of business when there is no common

and widely shared understanding of the product, e.g., eco-friendly goods such as electric vehicles

(EV) or renewable energy. The growth and the spread of new technology show an S-shaped curve.

Under the initial lack of information, the market grows slowly at the beginning, and then a snowball

effect accelerates the adoption according to the Diffusion of Innovation Theory (Rogers, 1976;

50

Xiong et al., 2016; Barnes et al., 2022). The snowballing can be driven via the peer effect (Bass,

1969; McCoy & Lyons, 2014; Manca et al., 2020) explaining the initial growth in product adoption.

In the United States, the EV market grows continuously but heterogeneously. The EV market

share has sharply increased since 2010. It was 0% in 2010, increased to 1.2% in 2019, and to

about 9.8% in 2023 (Tefft, 2023). Nevertheless, EV adoption differs between states. According to

US Department of Energy (2022), last accessed July 2024, percentages of EV registrations from

total vehicle registration at the state level ranged from 0.08% (600 EVs) in North Dakota to 2.50%

(903,600 EVs) in California; the average is 0.63% (47,888) with a standard deviation of 0.51%

(127,582). There is further geographical variation within states.

In the state of Michigan, for

example, in 2019, the range of EV adoption by ZIP code ranged from zero to 1033 (in ZIP code

1

5

48033), and at the county level, it ranged from zero to 7684 (in Oakland) (Atlas EV Hub, 2023).

The average and standard deviation are 6.63 (29.32) for the ZIP code level and 271.82 (969.58)

for the county level. From 2011 until now, the US federal government provided an EV purchase

subsidy, which is capped at $7500, while Michigan has not provided incentives for purchasing an

EV. The wide variations in county and ZIP code tabulation area registrations suggest that further

factors affecting EV adoption exist that vary over the region.

Most US daily driving consists of commuting and driving in neighborhood areas. First, the

daily driving range is not far. During the second half of 2019, drivers made an average of 3.7

trips per day, of which 1.1 were for commuting and 2.6 for non-work-related purposes (Tefft et al.,

2021). Workers specifically made an average of 2.2 trips per day for commuting and 2.0 trips for

non-work purposes. In 2021, drivers made an average of 2.56 trips, covering 32.7 miles and taking

61.3 minutes per day (Tefft, 2022). Second, Speidel & Bräunl (2014) found that EVs are mostly

charged at business and home locations (55%) while charging stations are only used for 33%. Thus,

the probability of EVs being observed is high in areas near EV owners’ homes or workplaces.

In this chapter, I study whether and to what extent peer effects affect EV adoption with EV and

charging station data in Lower Michigan from 2013 to 2019. I utilized the spatial panel regression

models to address spatial dependence in the peer effect of EV adoption. First, peer effects are

51

defined as the cumulative EV adoption in the same ZIP code, considering the probability of having

EV owners among peers and/or being exposed to EVs driving and parking. Second, I include

covariates of household variables to disentangle the exogenous peer effect. Third, cumulative

installation of charging stations is included to address the correlated peer effect identified by Li

et al. (2017).

This chapter contributes mainly to the literature on peer effect in product adoption, specifically

considering the probability of observing movable products. There is substantial peer effect literature

concerning environmental goods: EV or Hybrid vehicle adoption (Narayanan & Nair, 2013; McCoy

& Lyons, 2014; Sexton & Sexton, 2014; Heutel & Muehlegger, 2015; Manca et al., 2020; Mukherjee

& Ryan, 2020), solar panel adoption (Bollinger & Gillingham, 2012; Noll et al., 2014; Graziano

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5

et al., 2019; Mundaca & Samahita, 2020; Balta-Ozkan et al., 2021; Barnes et al., 2022; Bollinger

et al., 2022; O’Shaughnessy et al., 2023; Sokołowski, 2023), low-carbon practice (Jiang et al.,

2023; Liu & Xia, 2023). In addition, peer effects have been proven to influence environmental

behavior (Bollinger et al., 2020; Wolske et al., 2020; Moncada et al., 2021; Wen et al., 2021;

Zhang et al., 2023). They mainly focus on the peer effect of group behavior on individual behavior.

Nevertheless, movable products can have additional peer effects through their exposure to nearby

residents. Bollinger et al. (2022) find that solar panel installation positively affects peers’ solar

adoption decisions at distances of at least 500 meters via visibility. That implies that visibility may

affect nearby residents. Due to their mobility, EVs’ visibility is spread wherever they travel, so they

may exert a wider visibility impact than solar panels: people who observe an EV driving on the

road and/or EVs parked while passing by will receive an additional peer effect from the EV owners

in their peer group. This chapter considers these additional effects together in the case of movable

products.

2.2 Theory

Peer effect has been widely used to study consumer behavior and how it works to form aggregate

demand. Nevertheless, there is always complexity to address all possible effects correctly. Accord-

ing to Manski (1993), there is a reflection problem when we try to infer if the average behavior

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5

of some group may affect others. Manski’s reflection problem can be classified into three effects:

endogenous, exogenous, and correlated effects. Endogenous effects capture the impact of the in-

teraction between people on their behavior. Exogenous effects mean that consumers’ exogenous

characteristics may form their behavior. Correlated effects mean that consumers in the same group

may tend to behave in a similar way because they face similar institutional surroundings. We must

carefully define and estimate each effect to avoid omitted variable problems.

Endogenous effects are the peer effects and are of primary interest to this chapter. The peer

groups should be defined in terms of households’ geographical proximity to potential adopters,

similar to applications in Bollinger et al. (2022). McCoy & Lyons (2014) defines group influence

as the proportion of adopters within each agent’s social group. I defined the basic unit of geographic

scope as ZIP Code Tabulation Areas (ZCTA).1 Then, the peer effect within the ZCTA is proportional

to the cumulative EV adoption in the same ZCTA. This is because the cumulative EV registration

in a particular ZIP code area indicates the probability of observing EV driving and parking in the

associated ZCTA, which forms the peer effect. Lower Michigan has 801 ZIP codes covering 40,162

sq mi. The average ZIP code area is 50.14 sq mi per zip code, similar to a square with a side of 7.08

miles. According to (Tefft, 2022), in 2021, drivers made an average of 2.56 trips, 32.7 miles per

day, which means 12.77 miles per trip. 2.56 trips means every 2 trips per day and 4 additional trips

per week. The mean daily traveled miles are similar to the ZIP code area. These may mean the

majority of daily trips are ranged within ZIP code or commuting. Therefore, I use the cumulative

EV adoption in the same ZCTA as the indicator for the peer effect from the same ZCTA. In the

case outside of ZCTA, I defined the EV adoption in the same year as the peer effect. The spatial

interaction will explain the influence of other ZCTAs.

Regarding the exogenous effects, I include socioeconomic variables relevant to EV adoption that

are aligned with the literature on EV adoption. I consider three types of consumer characteristics:

income, political attributes, and urbanization. First, income affects EV adoption due to the high

price of EVs. Household income level affects EV adoption decisions because of its high market

1ZIP Code Tabulation Areas are a geographic concept of the U.S. Census Bureau. It is mostly similar to the ZIP

code areas and was designed by the U.S. Census Bureau to map demographic information.

53

price compared to internal combustion engines (ICE). Households with enough income and assets

may be more likely to purchase EVs. Axsen et al. (2015, 2018); Hamamoto (2019); Manca et al.

(2020) consider income level as covariates affecting EV adoption, and Bollinger et al. (2022)

include income in studying peer effect on solar PV installation. Second, political attributes affect

buying eco-friendly goods, such as EVs.

In the US, Democrats usually support climate policy,

while Republicans doubt climate policy (Van Boven et al., 2018). Bollinger et al. (2022) use the

ratio of Democrats to Republicans as the indicator. Due to data availability, I use education level

and age as indicators for the attributes. It is common to include both variables when studying EV

adoptions: education (Axsen et al., 2015; Manca et al., 2020; Mukherjee & Ryan, 2020) and age

(Mukherjee & Ryan, 2020; Manca et al., 2020). These variables are time-variant due to the net

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5

population flow and the number of residents pursuing academic degrees. Lastly, I include the type

of land (urban or rural) to consider the urbanization factor. Kotval-K & Vojnovic (2015) shows a

distinct difference in travel behavior according to each type of area.

Regarding the correlated effect, I consider both tangible and intangible effects. Tangible effects

are caused by factors such as the number of charging stations installed in the same ZCTA. Li et al.

(2017) built an indirect network model between EV adoption and charging stations and found that

40% of EV adoption increase is explained by the feedback loops via charging station increase.

They show that EV adoption and charging station installation stimulate each other: cumulative

EV adoption increases new charging port installation, and cumulative charging station installation

increases new EV adoption. Mukherjee & Ryan (2020) also includes the average distance to the

nearest charge stations.

I include cumulative charging station installation in the same ZCTA. I

assume that the charging station is exogenously given and may affect EV adoption, but omit how

it is affected by EV adoption in order to focus on the peer effect from the EV adoption side. This

assumption is, nevertheless, quite strong because there is clear evidence that charging stations are

endogenous and, even more, EV adoption and charging stations exert mutual indirect effects (Li

et al., 2017). On the other hand, regarding intangible correlated effects, Michigan does not provide

any incentives for buying new or used EVs. Therefore, Michigan residents can get such benefits only

54

from the federal government, which means there is no heterogeneous intangible effect in Michigan.

How do peers affect their neighbors’ decisions on whether to purchase an EV? Wang et al. (2022)

found that lead users play an important role in future EV adoption, lead users being customers who

want to buy cutting-edge products ahead of typical users. According to the diffusion of innovation

theory, different adopters can be characterized by when they adopt the new product: early adopters,

the early majority, the late majority, and laggards. As adoption progresses through these four

groups, the adoption rates show an S-shaped curve, starting slowly among the early adopters,

accelerating as the early majority join in, slowing as the later majority adopt, and converging to

zero as the laggards finally come on board.

In the first stage, only early adopters or lead users will buy EVs, and their decision is based on

5

5

limited information and experience. The main influence from peers comes only from those few

adopters. The rate of sharing experience and information is too slow; therefore, most households

still have limited awareness of EV driving and ownership, making it difficult for them to decide

whether to buy an EV. Only a limited amount of EV adoption is observed, and adopters in this stage

usually have enough information about EVs from their own backgrounds or they are risk-takers.

In the second stage, early adopters have widely affected consumer decisions regarding EV

adoption, and more people have started to receive sufficient information and shared experiences.

In this stage, it is not uncommon to observe EVs on roads or parking lots, and consumers only

care about the price and specification of EVs versus ICE when they want to get a new car. This

dissemination of information, knowledge, and experience is extensive and works through multiple

channels described in Figure 2.2. First, when early adopters buy an EV, they share information

about EV driving and their experiences with peers such as family, friends, and colleagues in the

workplace. Second, non-peers can also get indirect experience with EVs by observing EVs on

roads or parking lots. They may come to think that EVs are safer than they had initially expected

or are good at accelerating, and these non-peers may share their opinions and experiences with

their own peers via word of mouth. Third, consumers may get information from experts via public

reports or social media. As more EVs are adopted, more public reports, articles, news, and posts

55

on social media about EVs become available. This information, along with the increased frequency

of having EV owners in peer groups or observing EVs on roads or parking lots near hometowns,

affects EV adoption by neutral customers. These channels form consumers’ valuation of EVs, and

they will be essential factors in vehicle adoption choice along with other information such as price,

specification, and household characteristics. As more people adopt EVs, the adoption rate becomes

faster.

In the third and final stage, the adoption rate starts to slow as the remaining drivers may be

against EVs, very risk-averse, or have high inertia that keeps them faithful to familiar technology

or special needs for which EVs are not suited. These consumers may not purchase an EV even

with full information about EVs. A higher benefit may be required to change their decision, or

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they may experience special needs that EVs cannot fulfill. According to the dataset and Michigan

context, Michigan residents have experienced only the first or second stage because, since the first

EV registration in 2013, the EV adoption rate has only gotten faster and has not yet shown any

signs of slowing, as in Table 2.1.

2.3 Data

I chose the research area of Lower Michigan from 2013 to 2019 due to several reasons. The

first EV registration was in 2013, and I consider only until 2019 to exclude the exogenous shock of

COVID-19. Then, most EVs and stations are located in Lower Michigan (Table 2.1). In addition,

Michigan has only one border with other states in the South, which minimizes the peer effect from

other states. Figure 2.1 shows the EV and charging station in Lower Michigan, 2019. It shows

the spatial distribution of EV and charging station data, and EV registration is focused on some

geographical areas.

I make the dataset a strongly balanced panel in order to use dynamic spatial panel regression,

and Table 2.2 shows the descriptive statistics. First, I combine ZIP code-level data into ZCTA using

US Census Bureau (2023b), and I have 801 ZCTAs in my dataset after excluding the 45 ZCTAs

which have no full data on all variables. I established a dataset of EV registration and charging

stations from Atlas EV Hub (2023) and other variables from US Census Bureau (2023a). The

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education level is the average duration (in years) of post-secondary education. Each type of final

education converted to the duration as the following: High school (0 years), Associate (2 years),

Bachelor (4 years), Master (4+2 years), Professional (4+4 years), Doctor (4+2+5 years). Then, I

divided the total education duration of residents by the population in the same ZCTA. I coded the

land type as 1 if urban or sub-urban area and 0 if rural area.

2.4 Empirical model

Strong spatial dependence is observed in Figure 2.1. In this case, traditional panel regression

may be biased due to correlation in error terms and variables (Narayanan & Nair, 2013). Due

to identification issues pointed out by Manski (1993) and this possible spatial dependence, I use

several spatial models: the spatial error model (SEM), the spatial autocorrelation model (SAC),

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5

the spatial autoregressive model (SAR), and the spatial Durbin model (SDM). Comparing these

four models allows us to identify spatial interactions which may occur among any of the dependent

variables, the independent variables and/or the error terms (Lozano et al., 2023). Equation (2.1) is

a general specification of spatial models, the basis for the four models considered here.

𝑦𝑖𝑡 = 𝜌𝑊𝑊𝑊 𝑖 𝑗 𝑦𝑦𝑦 𝑗𝑡 + 𝑋𝑖𝑡𝑋𝑖𝑡𝑋𝑖𝑡𝛽𝛽𝛽 + 𝑊𝑊𝑊 𝑖 𝑗 𝑋𝑋𝑋 𝑗𝑡𝜃𝜃𝜃 + 𝜉𝑖 + 𝜉𝑡 + 𝜇𝑖𝑡

𝜇𝑖𝑡 = 𝜆𝑊𝑊𝑊 𝑖 𝑗 𝜇𝜇𝜇 𝑗𝑡 + 𝜖𝑖𝑡

𝑋𝑋𝑋𝑖𝑡 = (Inc𝑖𝑡, Edu𝑖𝑡, Age𝑖𝑡, Urban𝑖𝑡) and 𝑋𝑋𝑋 𝑗𝑡 = (𝑌𝑌𝑌 𝑗𝑡−1, CS 𝑗𝑡−1)

(2.1)

(2.1a)

(2.1b)

where 𝑦𝑖𝑡 is EV adoption in ZCTA 𝑖 and year 𝑡. 𝑦𝑦𝑦 𝑗𝑡 is a matrix containing 𝑦 𝑗𝑡 for all of ZCTA 𝑗 in

Lower Michigan. 𝑊𝑊𝑊 𝑖 𝑗 is a contiguity-based spatial weights matrix. We say that there is contiguity

if two spatial units have a common border of non-zero length. 𝑊𝑊𝑊 𝑖 𝑗 contains the weight calculated

from the contiguity of ZCTAs and represents the spatial relationships through common boundaries

in the dataset. 𝑤𝑖 𝑗 is an element of 𝑊𝑊𝑊 𝑖 𝑗 , valued at 1 if ZCTAs 𝑖 and 𝑗 have a common border, and

0 if there is no common border or if 𝑖 = 𝑗. The dimensions of 𝑊𝑊𝑊 𝑖 𝑗 are 801 × 801. If a ZCTA

shares a common border with 𝑁 ZCTAs, which means (cid:205)801
𝑗=1

𝑤𝑖 𝑗 = 𝑁, then it has 𝑁 links with other

ZCTAs. The total number of links is 4582, and the average number of links per ZCTA is 5.72,

with a minimum of 1 and a maximum of 13. 𝜌 captures the endogenous effect from other ZCTAs,

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and 𝛽𝛽𝛽 captures the exogenous effect from demographic characteristics. 𝜃𝜃𝜃 captures the impact from

covariates on the EV adoption of neighbor ZCTAs. 𝜉𝑖 is a ZCTA-specific fixed effect that captures

effects of all time-invariant predictors that only differ across ZCTAs, which pick up the inter-ZCTA

differences. The time-specific fixed effect 𝜉𝑡 explains the effects of all common predictors for

all ZCTAs that only differ across years and hence pick up the time trend. 𝜖𝑖𝑡 is assumed to be

independent and identically distributed. 𝜇𝑖𝑡 is the error term specific for ZCTA 𝑖 and year 𝑡. 𝜇𝜇𝜇 𝑗𝑡 is

the error term considering spatial dependence on the error terms described in Equation (2.1a) with

the spatial influence, 𝜆.

𝑋𝑋𝑋𝑖𝑡 is a covariate matrix of exogenous effect including Inc𝑖𝑡 (median household income applying

consumer price index), Edu𝑖𝑡 (mean post-secondary education years), Age𝑖𝑡 (mean age), and Urban𝑖𝑡

(a binary variable indicating urban and sub-urban areas in ZCTA 𝑖 and year 𝑡). I consider that EV

adoption may be affected by neighbors’ cumulative EV adoption and charging stations, not by their

demographic variables.

Each model assumes that spatial dependence exists only in some part of the model: in the error

term (SEM), in the dependent variable and error term (SAC), in the dependent variable (SAR), and

in both independent and dependent variables (SDM). SAC assumes that 𝜃𝜃𝜃 = 0. SAC can be reduced

to SEM by assuming that 𝜌 = 0, and to SAR by assuming 𝜆 = 0. SDM considers that 𝜃𝜃𝜃 ≠ 0, and

it assumes that 𝜆 = 0. I define the endogenous peer effect from the same ZCTA, cumulative EV

adoption as follows.

year=𝑡
∑︁

𝑌𝑖𝑡 =

𝑦𝑖,year

year=2013

PE𝑖𝑡 = 𝑓 (𝑌𝑖𝑡−1) = 𝛼1𝑌𝑖𝑡−1 + 𝛼2𝑌𝑖𝑡−1 + 𝛼3𝑌𝑖𝑡−1 = 𝛼𝑌𝑌𝑖𝑡−1

(2.2a)

(2.2b)

where 𝑌𝑖𝑡 is cumulative EV adoption in ZCTA 𝑖 and year 𝑡. PE𝑖𝑡 is the peer effect from the same

ZCTA 𝑖 at year 𝑡, and it is a function of the cumulative EV adoption until last year. I assume that peer

effect is a linear combination of peer effects from EV owners in the same social network and ZCTA,

effects from EV driving, and effects from EV parking, but not any other sources, such as peers

from outside of Michigan and/or social media. 𝛼1 captures peer effect from having EV owners in

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the same ZCTA, which are the conventional peer effects via social networks. It only counts for EV

owners who are in the consumer’s peer group and live in the same ZCTA. I consider the peer effect

from EV owners in other ZCTAs; however, I exclude the peer effect from outside of Michigan,

even if consumers may have peers who drive EVs but live outside the state. 𝛼2 captures the peer

effect from observing EV driving on roads and thus depends on the probability of being exposed

to EV driving. This is governed by the unique transportation infrastructure because transportation

practices affect the visibility of EVs driving on the road to passengers, other drivers, and people

riding public transportation. 𝛼3 captures the peer effect from observing EV parking on lots and

hence depends on the probability of being exposed to EV parking. It is also relevant to the unique

structure of parking lots. The architecture of parking lots affects the visibility of EV parking to

passengers or other drivers who park their cars in the same lot. 𝛼𝑌 = 𝛼1 + 𝛼2 + 𝛼3, and shows the

relationship between the endogenous peer effect and cumulative EV adoption in the same ZCTA

up to the previous year.

Next, I adopt the static spatial panel regression models in Equation 2.3. SEM is Equation 2.3a,

SAC is Equation 2.3b, SAR is Equation 2.3c, and SDM is Equation 2.3d.

𝑦𝑖𝑡 = 𝛼PEPE𝑖𝑡 + 𝑋𝑋𝑋𝑖𝑡𝛽𝛽𝛽 + 𝛾CS𝑖𝑡−1 + 𝜉𝑖 + 𝜉𝑡 + 𝜇𝑖𝑡

= 𝛼𝑌𝑖𝑡−1 + 𝑋𝑋𝑋𝑖𝑡𝛽𝛽𝛽 + 𝛾CS𝑖𝑡−1 + 𝜉𝑖 + 𝜉𝑡 + 𝜇𝑖𝑡

𝑦𝑖𝑡 = 𝛼𝑌𝑖𝑡−1 + 𝜌𝑊𝑊𝑊 𝑖 𝑗 𝑦𝑦𝑦 𝑗𝑡 + 𝑋𝑋𝑋𝑖𝑡𝛽𝛽𝛽 + 𝛾CS𝑖𝑡−1 + 𝜉𝑖 + 𝜉𝑡 + 𝜇𝑖𝑡

𝑦𝑖𝑡 = 𝛼𝑌𝑖𝑡−1 + 𝜌𝑊𝑊𝑊 𝑖 𝑗 𝑦𝑦𝑦 𝑗𝑡 + 𝑋𝑋𝑋𝑖𝑡𝛽𝛽𝛽 + 𝛾CS𝑖𝑡−1 + 𝜉𝑖 + 𝜉𝑡 + 𝜖𝑖𝑡

𝑦𝑖𝑡 = 𝛼𝑌𝑖𝑡−1 + 𝜌𝑊𝑊𝑊 𝑖 𝑗 𝑦𝑦𝑦 𝑗𝑡 + 𝑋𝑋𝑋𝑖𝑡𝛽𝛽𝛽 + 𝛾CS𝑖𝑡−1 + 𝑊𝑊𝑊 𝑖 𝑗 𝑋𝑋𝑋 𝑗𝑡−1𝜃𝜃𝜃 + 𝜉𝑖 + 𝜉𝑡 + 𝜖𝑖𝑡

(2.3a)

(2.3b)

(2.3c)

(2.3d)

In Equation (2.3𝑎), 𝛼𝑝𝑒 captures the impact of peer effect on the EV adoption; therefore, 𝛼 is

𝛼𝑝𝑒𝛼𝑌 , via Equation (2.2𝑏). The only estimable coefficient is 𝛼 due to data availability. 𝛼 captures

the endogenous peer effect from the same ZCTA. CS𝑖𝑡 is cumulative charging station installation;

therefore, 𝛾 means the correlated effect from charging stations. In SDM (Equation (2.3d)), I include

the spatial impact from the cumulative EV adoption and charging stations of other ZCTAs. 𝑌𝑌𝑌 𝑗𝑡−1

and CS 𝑗𝑡−1 are matrices containing 𝑌𝑗𝑡−1 and CS 𝑗𝑡−1 for all of ZCTA 𝑗 in Lower Michigan.

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2.5 Results

In this section, I report the estimation result of Equation 2.3. Table 2.3 shows the estimation

results of each model. Measures of goodness of fit for models are at the bottom of Table 2.3:

Log-likelihood function value (LL), Akaike information criterion (AIC), and Bayesian information

criterion (BIC). I use these three scores to choose the most appropriate model (Belotti et al.,

2017). The LL value is meaningless in itself, but informative when comparing several models:

the higher the LL value, the better the model. Lower AIC and BIC scores indicate a better fit of

the model. The AIC and BIC methods punish the complexity of models by increasing their scores

as the number of parameters grows. The punishment also becomes larger in BIC with a larger

sample size. According to Burnham & Anderson (2004), AIC captures the difference between the

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probability distribution of real data and predicted data by the model. Thus, AIC is concerned about

predictability, while BIC cares about the real distribution of data. In Table 2.3, according to LL,

AIC, and BIC scores, SEM and SAC models better fit the dataset than SAR and SDM. Therefore, I

will interpret only the results of SEM and SAC. The spatial dependence in error terms in both SEM

and SAC is significant but much smaller than other coefficients.

Regarding endogenous effect, I consider the peer effect from the same ZCTA, 𝛼, and outside

the ZCTA, 𝜌. 𝛼 is consistent across the models, around [0.326, 0.352]. 𝜌 is 0.079 in the SAC

model, much lower than 𝛼. For the exogenous effects, demographic variables are considered: mean

household income, mean education level, mean age, and the type of land. Then, in both models,

income and education correlated positively with EV adoption at high significance, while age is

negatively correlated with EV adoption, and type of land is insignificant. This means that, if the

residents of ZCTA are wealthier, younger, and have more education, EV adoption will increase. A

$1000 increase in average income will lead to 0.260 to 0.313 more EV adoption, a 1-year increase

in average education will lead to 11.92 to 13.07 more EV adoption, and a 1-year increase in average

age will lead to 0.267 less EV adoption. Lastly, as correlated effects, the number of cumulative

charging stations increases EV adoption.

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2.6 Conclusions

Due to the nature of new technology, EV adoption follows an S-shaped diffusion curve, and peer

effect plays an important role in early adoption. Nevertheless, there has been little consideration of

spatial dependence on peer effect. In this chapter, I estimate the endogenous peer effect, which is

defined as cumulative EV adoption, the sum of interaction from peers and from being exposed to

EVs on roads and parking lots, using different spatial panel regression models. I use the panel data

by ZCTA in Lower Michigan from 2013 to 2019, including endogenous, exogenous, and correlated

peer effects. To consider exogenous effects, I include demographic characteristics such as median

household income, mean education level, mean age, and type of land. I also consider the correlated

effect by including the cumulative number of charging stations in the analysis.

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6

The key contributions and implications of this article are twofold. First, I estimate the en-

dogenous peer effect, including exposure to EVs on roads and parking lots, and consider spatial

dependence. To address this, I use different spatial panel regression models and gain consistent

results. One increase in cumulative EV adoption in any given ZCTA will increase the next year’s

EV adoption in the same ZCTA by 0.326 to 0.352, and one increase in one year’s EV adoption

from other ZCTAs will effect a 0.079 increase in that year’s EV adoption considering spatial depen-

dence. This effect is of reasonable magnitude when we consider there are additional interactions

from observing EV driving and parking. Bollinger et al. (2022) compares the peer effect and the

effect of price in solar panels and finds that a peer installation in some conditions increases solar

panel adoption by the same amount as a price decline of $577. In SEM and SAC, a cumulative EV

adoption increases EV adoption in the same ZCTA by the same amount of an income increase of

$1125 to $1254. This means that EV has a more endogenous effect when observed by residents in

the same ZCTA. Bollinger et al. (2022) find that solar panels fixed on roofs positively affect peers’

adoption over at least 500 meters, while EVs can affect a wider range of residents because they are

driven, so their visibility extends over a greater distance. Second, there would be unobservable

peer effects spatially dependent at ZCTA levels. SEM and SAC models, which consider spatial

dependence in error terms, are better than SAR and SDM, which do not consider them. This implies

61

that we need to address unobserved and spatially correlated variables relevant to EV adoption. It

may include accessibility of EV dealerships and charging stations. The number of EV dealerships

affects vehicle adoption choices at least before 2020, while more people have tended to purchase a

vehicle through online search after COVID-19. Charging ports installed in more crowded places

have more influence than those located in less crowded places, as they are observed by more people.

Some limitations of this chapter are raised by the nature of movable products and peer effects.

First, measuring the actual exposure to other people when driving or parking is difficult. To capture

that, we need to calculate all driving patterns of each EV and calculate the frequency of staying in a

specific area. Second, another channel exists to get information and knowledge about EVs, not from

EV owners. People can rent an EV and drive it for their vacation or trip. They also can test EVs

2

6

on the road by visiting the dealerships. They can also learn about EVs remotely, such as watching

videos of famous automobile experts and daily experience of EV driving or communicating with

their peers from different states. Nevertheless, it would be a small effect because these possible

channels only take effect when people are very close to purchasing EVs. Future research may

measure the frequency of exposure to other people as a case study or experiment.

This chapter contributes to the literature on peer effect, specifically in adopting EVs and movable

products, by quantifying the effect while considering spatial dependence. Policymakers may

intensify incentives in areas showing increased EV adoption because cumulative EV adoption will

increase EV adoption in the future. Peer effect, including observations, intensifies the aggregate

demand, increasing EV subsidization’s policy efficiency. The current status is that of the early

adopter or early majority ones in the S-shaped diffusion of innovation theory. These results imply

that incentivizing EV adoption in the early stage may have a greater impact by stimulating aggregate

demand via peer effect.

62

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APPENDIX 2.A: Tables and Figures

Table 2.1 The number of EV and charging stations in Lower and Upper Peninsula of Michigan

Year
2013
2014
2015
2016
2017
2018
2019

EVs
1
292
509
546
5,629
6,437
23,792

Lower Peninsula

Charging stations Total vehicles

Upper Peninsula
EVs Charging stations

14
20
42
85
110
147
230

3,492,280
3,536,550
3,602,120
3,665,530
3,728,410
3,787,930
3,829,965

0
2
4
4
47
49
209

1
1
1
1
2
4
10

8

6

68

Table 2.2 Descriptive statistics for variables in each ZCTA

Unit
Variable
count
New EV adoption
count
Cumulative EV adoption
count
Cumulative charging station installation
$ 1000
Median household income
year
Mean education level
year
Mean age
Urban/Rural
binary
Note: 𝑁=4,806 (801 ZCTAs over 6 years from 2014 to 2019)

Symbol
𝑦
𝑌
CS
𝐼𝑛𝑐
𝐸 𝑑𝑢
𝐴𝑔𝑒
𝑈𝑟𝑏𝑎𝑛

Mean (SD)
4.944 (21.855)
7.732 (31.536)
0.132 (0.725)
136.444 (67.054)
0.931 (0.545)
42.861 (6.515)
0.743 (0.437)

Min
−41
0
0
22.400
0.096
21.1
0

Max
748
1033
15
804.300
3.283
66.1
1

9

6

69

Table 2.3 Estimation results of each model

variable
𝑌𝑖𝑡 −1

coefficient
𝛼

𝑦 𝑗𝑡

Inc𝑖𝑡

Edu𝑖𝑡

Age𝑖𝑡

Land𝑖𝑡

CS𝑖𝑡 −1

𝑌 𝑗𝑡 −1

CS 𝑗𝑡 −1

𝜇 𝑗𝑡

𝜌

𝛽1

𝛽2

𝛽3

𝛽4

𝛾

𝜃1

𝜃2

𝜆

unit
count

count

$ 1000

year

year

binary

count

count

count

SEM
0.352****
(0.020)

0.313****
(0.090)
13.074***
(4.038)
−0.266
(0.167)
0.450
(3.165)
3.940****
(0.685)

SAC
0.326****
(0.019)
0.079****
(0.006)
0.260***
(0.085)
11.919***
(3.781)
−0.267*
(0.156)
0.742
(2.939)
3.612****
(0.643)

SAR
0.307****
(0.025)
0.302****
(0.000)
0.487****
(0.115)
11.863**
(5.201)
−0.169
(0.215)
−0.468
(4.073)
3.446****
(0.882)

SDM
0.325****
(0.025)
0.302****
(0.000)
0.429****
(0.113)
12.782**
(5.084)
−0.135
(0.210)
−0.177
(3.981)
3.467****
(0.862)
−0.136****
(0.010)
−1.797****
0.343

0

7

Control
Control
−22,243
44,512
44,597

Control
Control
−22,074
44,195
44,351

Year
ZCTA
LL
AIC
BIC
Note: * 𝑝 < 0.1; ** 𝑝 < 0.05; *** 𝑝 < 0.01; **** 𝑝 < 0.001

0.010**
(0.004)
Control
Control
−20,347
40,719
40,804

−0.089****
(0.009)
Control
Control
−20,323
40,673
40,764

and parentheses contain the robust standard errors for each coefficient.

70

(a) EV registrations in Lower Michigan, 2019

1

7

(b) Charging stations in Lower Michigan, 2019

Figure 2.1 EV registrations and charging stations in Lower Michigan, 2019

71

2

7

Figure 2.2 Descriptive diagram of how peer effect works

72

3

7

CHAPTER 3

THE IMPACT OF TRANSNATIONAL MUNICIPAL NETWORKS ON LOCAL ENERGY
CONSUMPTION

3.1

Introduction

Climate change is one of the most urgent international issues of the 21st century, and local

governments are the key to climate policies (Gordon & Johnson, 2017). Local governments know

how a policy should be designed: which areas have more priority for implementation given budget

limitations and how to lead public opinion toward less resistance by considering the geographic,

economic, and political landscape (Picavet et al., 2023). Local governments even act when a

national government hesitates. For example, U.S. local governments have moved ahead with

climate actions even after the federal government refused to promote climate policies during the

Bush and Trump administrations (Byrne et al., 2007, 2022; Kousky & Schneider, 2003; Rabe &

Mills, 2017). In Australia, local governments actively engage in renewable energy policy despite

unfavorable national political conditions in 2016 (Mey et al., 2016). Furthermore, local actions can

become a driving force for enhanced action (Kuramochi et al., 2020).

Transnational municipal networks (TMNs) support local governments by sharing policy im-

plementation experience. A TMN is an international network of local authorities with distinct

characteristics: autonomous membership, non-hierarchical structure, and network structure (Kern

& Bulkeley, 2009). There is growing evidence that members can benefit from getting to know other

members’ experiences and reducing the amount of trial and error (Bulkeley et al., 2003; Davidson

et al., 2019; Fünfgeld, 2015; Kern & Bulkeley, 2009). After the end of the Cold War in the early

1990s, there was rapid growth in TMNs; one of their main subjects is climate change (Kern &

Bulkeley, 2009). The International Council for Local Environmental Initiatives – Local Govern-

ments for Sustainability (ICLEI) is one of the main TMNs in climate actions, and it has more than

2,500 member cities that comprise 25% of the world’s population. These TMNs support internal

mobilization, formulate carbon inventory and goals, and offer project support and incentives like

certificates (Busch et al., 2018; Kern & Bulkeley, 2009).

73

Substantial prior literature shows growing evidence of the role of TMNs with some limitations:

lack of quantitative studies, incomplete data analysis, and little focus on policy outcome. First, a lot

of literature identified the role of TMNs with qualitative analyses (Bansard et al., 2017). Heikkinen

et al. (2020) argued that a lack of quantitative evidence exists regarding the actual impact of network

membership. Qualitative analyses include governance analysis (Kern & Bulkeley, 2009), using

qualitative survey data (Busch et al., 2018), network analysis (Woodruff, 2018), and comparative

analyses of member cities (Adesanya et al., 2020; van Doren et al., 2020; Emelianoff, 2014; Lee

& Painter, 2015; Picavet et al., 2023). Second, another mainstream is analysis with selective data.

Substantial case studies compare pioneer cities in climate policy (Adesanya et al., 2020; Aylett,

2013; Emelianoff, 2014; Hodson et al., 2013; Jaglin, 2014; Lee & Painter, 2015; Leffel, 2022;

4

7

Linton et al., 2022; Rocher, 2017). Several studies tried to use a large number of cities in analyses,

but only including member cities (Busch et al., 2018; Krause et al., 2016) or only including local

governments in a specific state (Pablo-Romero et al., 2016), or using cross-sectional data (Yi,

2013). Third, some literature tried to analyze the impact of TMNs on local policy; however, it

did not consider the policy outcome. Krause (2012) and Hakelberg (2014) found the impact of

TMN membership on the number of local policies, and Steffen et al. (2019) argued that TMN

membership increases solar panel investment. It did not count if the increased number of activities

really reduced carbon emissions. Yi (2013) identified that ICLEI membership increased the number

of green jobs. There is little literature on the emerging role of urban networks on urban policies

(Busch et al., 2018; Davidson et al., 2019; Steffen et al., 2019).

To the best of our knowledge, this chapter is the first quantitative analysis to answer whether

TMNs really help local authorities achieve local energy policy outcomes. In this article, we adopt

staggered difference-in-differences (DID) methods with a panel dataset to address the staggered

joins in ICLEI over time in estimating the impact of ICLEI membership. This method is better

for estimating staggered treatment, such as ICLEI memberships over time, than traditional DID.

We built a dataset that included all ICLEI and non-ICLEI members for long periods before and

after ICLEI membership. The dataset is based on South Korea from 2005 to 2019 and focuses on

74

final energy consumption per capita as the main outcome; the reasons for choosing the spatial and

time scope are as follows. First, Korean governments have built extensive, abundant local datasets

crucial to statistical analysis. Second, Korea has very active ICLEI networks with a reasonable

number of members and non-members. Korea has one of the nine regional secretariats and one

of the 12 country offices in ICLEI, and 13 of 17 states and 46 of 228 counties had joined ICLEI

by 20191. Third, the time scope is from 2005 to 2019 because the Korean dataset for all counties

starts in 2005, and COVID significantly impacted energy consumption starting in 2020 (Jang et al.,

2021; Kang et al., 2021). We define final energy consumption per capita as the local energy policy

outcome because it is the target of ICLEI. It evaluates how the ICLEI membership affects the policy

outcome, which complements Krause (2012) and Hakelberg (2014).

5

7

This study finds that Korean local governments significantly reduce energy consumption after

joining the ICLEI network, and the reduction becomes larger in the order of county, state, and both

county and state membership. We focus on the Korean ICLEI network due to its well-established

local-level dataset, active engagement in the ICLEI network at all levels of decision-making, and

substantial numbers of ICLEI members. These findings can be extended to other geographic regions

with data availability and real activities in the local ICLEI network. We first discuss the theoretical

and contextual background of the Korean ICLEI network. We then show key methodologies and

variables that explain energy consumption in Korea. Political implications are also provided in the

conclusion.

3.2 Background, Data, and Methods

3.2.1 The Role of ICLEI as a TMN in Korea

Learning mechanisms are required to promote innovation in the public sector. Learning is

indispensable for local governments, especially in challenging new areas of public policy, such

as climate change. Growing evidence emphasizes policy implementation’s role in local energy

transition (van Doren et al., 2020; Neij & Nemet, 2022). According to Zambrano-Gutiérrez &

1The Korea has one Central Government, 17 Broad Local Government (BrLG), and 226 Basic Local Government
(BaLG). We define a “state” as a BrLG and a “county” as BaLG because a BrLG is similar to a state or a province, and
a BaLG is similar to a county or a city.

75

Puppim de Oliveira (2022), the collective learning process of governments moves from internal and

external learning to governance and then innovation. There are three types of internal learning and

six types of external learning: one of the sources of external learning is from foreign organizations

or other cities. Grønnestad & Bach Nielsen (2022) and Zambrano-Gutiérrez & Puppim de Oliveira

(2022) said TMNs are key places for local governments to obtain knowledge and information

about local policy implementation. Therefore, TMNs function as one of the main external learning

mechanisms for local governments. On the TMN side, TMNs are built to support local governments’

policy implementation. There are three types of internal governing stratagies in TMNs (Kern

& Bulkeley, 2009). First, information and communication are indispensable for networks via

developing and sharing best practices. There is growing evidence that local governments recognize

6

7

this benefit of membership (Kern & Bulkeley, 2009; Zambrano-Gutiérrez & Puppim de Oliveira,

2022). Second, TMNs provide a more direct intervention with project funding and cooperation.

Lastly, TMNs use recognition, benchmarking, and certification. These strategies encourage political

leaders of members who may need outcomes to win reelection.

ICLEI is one of the most successful TMNs in climate action.

ICLEI has more than 2600

members of local governments from 130 countries, which address 20% of the world’s population.

ICLEI is one of the first TMNs in climate change since the 1990s and has become an influential

advocate for international agreements on greenhouse gas reduction (Fünfgeld, 2015). According to

Gordon and Johnson (2017), a substantial number of ICLEI members included climate change in

their core policy area. ICLEI has a multi-level governance system so member cities can participate

in decision-making.

ICLEI has a president, a board, and a general assembly, and the board

comprises the Global Executive Committee (GexCom), Regional Executive Committee (RexCom),

and Management Committee. Gexcom has six members from the RexCom for each continent

and eight from sub-networks for portfolio seats. RexCom has nine committees from the regional

secretariat.

ICLEI has one world secretariat in Germany, nine regional secretariats, and seven

country offices worldwide. ICLEI helps local governments create climate actions and set specific

targets for their climate actions. Therefore, literature considers ICLEI membership part of local

76

climate efforts (Krause, 2012; Krause et al., 2016; Yi et al., 2017; Deslatte et al., 2021). Krause

(2012) found that ICLEI membership increased the number of GHG-reducing activities. ICLEI

has a global initiative, the Global Covenant of Mayors for Climate & Energy (GCoM). Local

governments in the GCoM provide their carbon emission inventory, climate resilience analysis

reports, and climate mitigation targets within 2 years and establish a climate action plan and

sustainable energy plan within 3 years. In 2019, ICLEI and the Carbon Disclosure Project (CDP)

merged into a CDP-ICLEI unified reporting system in which local governments in CDP and ICLEI

report the targets, actions, and inventories of their climate actions.

The Korean ICLEI network has been actively engaged in all levels of decision-making in ICLEI.

The mayor of Seoul was elected as the president of ICLEI for 2015-2018 as a result of the 2015 ICLEI

7

7

assembly in Seoul. In 2023, the Korean network had two of the five members of East Asia RexCom

and one of 22 of GexCom. The Korean ICLEI network hosted one of nine regional secretariats

(the East Asia secretariat in Seoul) and one of the 12 country offices (the Korea office in Ilsan).

In 2021, the ICLEI Korea network launched the ICLEI Korea executive committee (K-ExCom)

for 2021-2023. ICLEI K-ExCom has 7 members from Korean ICLEI members representing each

policy field: climate and energy, sustainable economy, biodiversity, eco transportation, and urban

agriculture. It is unique in the ICLEI network to build a national executive committee.

In the Korean ICLEI network, there are several channels and mechanisms for how ICLEI

membership leads to decreased energy consumption: active sharing of best practices and experi-

ences among members and project funding. These are TMN’s main strategies to achieve its goal

(energy consumption reduction is one of ICLEI’s main goals), as suggested by Kern & Bulkeley

(2009). The first is information and communication. The Korean ICLEI network provides monthly

newsletters with members’ best practices and international meeting results. Then, they produce

case study reports on Korean ICLEI members’ activity in Korean and English. The network holds

an annual assembly among Korean members and shares the annual report. Public officers in local

governments that joined ICLEI have received the newsletters and reports. Then, the ICLEI Korea

office regularly educates those public officers and provides workshops and seminars to teach them

77

about climate, energy, and sustainable policies. Second, the Korean network provides project

funding and cooperation. It supports local governments’ participation in international meetings,

such as the ICLEI Congress, the United Nations, and the United Nations Framework Convention on

Climate Change. It also organizes the mutual participation of local governments in project funding

advanced by ICLEI. In 2019, the ICLEI Korean office spent 30.6% of its total expenditures on local

government projects (ICLEI Korea Office, 2020). In Korea, 21 ICLEI members joined GCoM, and

they also joined Race to Zero, which was launched in 2020 by the United Nations. They should

set a goal of 50% emission reduction by 2030 and 100% reduction by 2050. Two Korean ICLEI

members also joined the 100% RE Cities & Regions Network supported by ICLEI. Through this

information sharing and project funding, ICLEI members are able to take steps to implement energy

8

7

policy to reduce energy consumption.

Korean governments consist of one central government, 17 states, and 228 counties. Each

level of government has its own department for each policy area. Then, at the discretion of the

political leader, a new department may be launched to address the implementation of a new policy.

In the case of climate and energy policy, some local governments order existing departments of

the environment to take responsibility, and others launch new departments to implement these

new policies. Their discretion heavily depends on the budget conditions. Sometimes, wealthier

counties have more influence on policy implementation than poorer states. Nevertheless, states

usually have more power based on the budget size. In Korea, upper-level governments favor using

a match to implement a policy; therefore, they can have dominant power. To describe the policy

case propelled by local governments, One Less Nuclear Power Plant (OLNPP) by Seoul, the capital

of Korea and a state government, is a good example. Seoul joined ICLEI in 1999, and 8 of 25

counties in Seoul joined ICLEI between 2012 and 2017. OLNPP was designed in 2012 after the

Fukushima nuclear accident and national blackout, and the goal is to reduce energy consumption

to 2 million TOE, which is equivalent to energy production from one nuclear power plant (Seoul

Metropolitan Government, 2017). Subgoals are to reduce wasted energy consumption, increase

energy efficiency, and promote renewable energy production. Seoul subsidized mini solar panels

78

on balconies and solar panels on roofs supported building energy self-supporting villages (they

substituted old bulbs with LEDs and adopted a smart grid in the town) and introduced eco-mileage

(consumers get payback when reducing energy consumption). The mini solar PV was designed by

a county, Nowon, Seoul, and it was actively adopted by Seoul, and Seoul spread it to its counties

and other states (Han & Yun, 2021).

Figure 3.1 shows how the Korean ICLEI network affects its members. This internal governing

is indicated as black lines in Figure 3.1. All states and counties in ICLEI have a direct impact from

the ICLEI Korea office (thick line), and counties in an ICLEI state have an indirect impact from the

policy of the state and vice versa (dashed line). It is a hypothetical diagram of the network. State 1

and some of its counties joined in ICLEI. This includes cases in which a county and a state joined

9

7

ICLEI simultaneously. They are connected to other members via a thick line, and some non-ICLEI

counties in State 1 are indirectly affected by State 1 via a dashed line. Then, State 2 does not join

ICLEI, while only some counties join ICLEI. Only those member counties are connected to the

ICLEI network, and they indirectly affect State 2 via the dashed line. In State 3, only State 3 joins

ICLEI, with no county members. State 3 is connected to the ICLEI network and indirectly affects

its counties. State 4 has no ICLEI members, states, or counties.

The scope of our research covers almost all 226 local Korean governments from 2005 to 2019.

We have several adjustments in the data. First, Korea has 17 states and 226 counties. Two states,

Sejong and Jeju, have no counties; therefore, we define them as a state and also a county. Then,

we consider the unified counties from 2005 to 2019 as one county from 2005 to 2019. Masan,

Jinhae, and Changwon were unified into Changwon in 2010. Yeongi was changed to Sejong in

2012. Cheongwon and Cheongju were unified into Cheongju in 2014. Finally, we excluded two

counties: Geumsan and Hoengseong. According to the ICLEI Korea office, they were withdrawn

from ICLEI Geunsan in 2015 and Hoengseong in 2019. They are excluded in order to use staggered

difference-in-difference methods, which require no reverse treatment.

By 2019, 13 of 17 states and 46 of 226 counties in Korea had joined ICLEI, according to the

ICLEI Korea Office. 38 of 46 counties joined ICLEI in 2019, and their states also joined ICLEI.

79

Table 3.1 shows the number of ICLEI members in Korea by county and state from 2005 to 2019.

Among all 228 counties, only 2 counties withdrew ICLEI membership during the period. In the

other 226 counties, the number of ICLEI memberships is monotonically increasing. 180 had not

joined ICLEI by the end of the period, 13 had joined ICLEI before 2005, and many joined in

different years. Eight states joined ICLEI before 2005; 4 states had not joined ICLEI by the end

of the period; and two states joined in 2008, one in 2009, and one in 2014. This shows the robust

ICLEI network in Korea, although international ICLEI membership dropped significantly from

2010 to 2012 (Yi et al., 2017).

3.2.2 Data

We define the log of energy consumption per capita as the dependent variable and the indicator

0

8

of local energy policy outcome because it explains a substantial part of carbon emissions. It is

defined as the final energy consumption of gas, oil, and electricity per capita in the unit of TOE2 3.

According to Waheed et al. (2019), there is substantial evidence of causal relations between energy

consumption and carbon emissions. For example, Korea emitted 701 million CO2eq in 2019, and

87.2% of the emission came from energy consumption (Korean Ministry of Environment, 2021).

We exclude coal consumption because the local dataset is not built for coal in every county. In

addition, coal is usually consumed at coal power plants in Korea, which makes it difficult to separate

consumption at the county level. Electricity consumption by a county covers the coal consumption.

We defined final energy consumption as the sum of electricity, gas, and oil, and it accounts for

83.5% of total energy consumption in 2019 (Korean Ministry of Trade, Industry and Energy, 2022),

while coal accounts for 13.2%.

The final energy consumption of electricity, gas, and oil is merged into one variable using the

TOE. Conversion coefficients (Korean Energy Economics Institute, 2022) in Table 3.2. The basic

unit of the database is a barrel for oil, 𝑘 𝑀 3 for gas, and 𝑀𝑊 ℎ for electricity, and is described

2TOE is abbreviated for a ton of oil equivalent. It is a unit of energy as the amount of energy comes from burning

one ton of crude oil. It is 41.868 gigajoules.

3tCO2 would be a better unit because we can easily calculate social costs of carbon from this, and carbon emissions
are a final target. Nevertheless, we could not get the annual Korean tCO2/kWh conversion factors from 2005 to 2019
because Korean governments has not release the term annually.

80

in the column, Unit, in Table 3.2. Korea Energy Agency (2023) provides conversion coefficients

between TOE and liter for oil, kg for propane and butane, 𝑀 3 for gas, and 𝑘𝑊 ℎ for electricity,

which are in the column, KEA coefficients, in Table 3.2. We got the Conversion to TOE coefficients

in Table 3.2 that fit the database by considering that 1 barrel of oil is 158.987𝑙, 1 barrel of propane

is 80.775kg, and 1 barrel of butane is 91.912kg. We aggregate the following oil consumption of

the followings: propane, butane, gasoline, kerosene, diesel, bunker-A oil, bunker-B oil, bunker-C

oil, jet fuel, By-products I & II 4, which are usually used by combustion. Naphtha, solvent, asphalt,

and lubricant are excluded because they are irrelevant to carbon emission except for unintentional

leaks. We got electricity consumption by county from Korea Electric Power Corporation (2023),

oil consumption by county from Korea National Oil Corporation (2023), and gas consumption by

1

8

county from Korean Local Governments (2021).

The final energy consumption per capita is defined as:

𝑦𝑖𝑡 = (𝐺𝑎𝑠𝑖𝑡 + 𝑂𝑖𝑙𝑖𝑡 + 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦𝑖𝑡)/𝑃𝑖𝑡

(3.1)

where 𝑦𝑖𝑡 is the energy consumption per capita of county 𝑖 in year 𝑡; 𝐺𝑎𝑠𝑖𝑡, 𝑂𝑖𝑙𝑖𝑡, and 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦𝑖𝑡

are the gas, oil, and electricity consumptions of county 𝑖 in year 𝑡, and 𝑃𝑖𝑡 is the population of

county 𝑖 in year 𝑡.

It is difficult and infeasible to implement an expeirment on ICLEI joins that randomly assigns

local governments into a treated group which will join ICLEI and a control group which will not join

ICLEI and keep eye track on their energy consumption. Therefore, we use a quasi-experimental

design (DID), in which the assignment of governments is based on observed behavior.

ICLEI

members are classified into the treated group, and non-ICLEI members are classified into the control

group for the quasi-experimental design. In this setting, ICLEI membership is the treatment. In

4By-products I and II are byproduct gas from naphtha-related processes during oil purification. By-product I is

Hi-sene, which can replace diesel and kerosene. By-product II is C-9, and it can replace bunker oils.

81

the canonical DID setting, the estimator comes from the following regression:

𝑙𝑛(𝑦𝑖𝑡) = 𝛼0 + 𝛼1𝑐𝑡𝐼𝐶𝑖𝑡 + 𝛼2𝑌 𝑒𝑎𝑟𝑡 + 𝛼3𝑐𝑡𝐼𝐶𝑖𝑡 × 𝑌 𝑒𝑎𝑟𝑡 + 𝛼4𝑋𝑖𝑡 + 𝜖𝑖𝑡

𝑙𝑛(𝑦𝑖𝑡) = 𝛼′

𝑙𝑛(𝑦𝑖𝑡) = 𝛼′′

1

0 + 𝛼′
0 + 𝛼′′

𝑌 𝑒𝑎𝑟𝑡 + 𝛼′
𝑠𝑡𝐼𝐶𝑖𝑡 + 𝛼′
3
2
𝑌 𝑒𝑎𝑟𝑡 + 𝛼′′
𝑏𝑡𝐼𝐶𝑖𝑡 + 𝛼′′
3
2

1

𝑠𝑡𝐼𝐶𝑖𝑡 × 𝑌 𝑒𝑎𝑟𝑡 + 𝛼′
4

𝑋𝑖𝑡 + 𝜖 ′
𝑖𝑡

𝑏𝑡𝐼𝐶𝑖𝑡 × 𝑌 𝑒𝑎𝑟𝑡 + 𝛼′′
4

𝑋𝑖𝑡 + 𝜖 ′′
𝑖𝑡

𝑋𝑖𝑡 = (𝐺𝑣𝑛𝑜𝑟, 𝑀𝑎𝑦𝑜𝑟, 𝐿𝑡𝑎𝑥, 𝐿𝑡𝑎𝑥2, 𝐹 𝐼 𝑅, 𝑀𝑛𝑝𝑐, 𝐶𝑎𝑟 𝑝𝑐)

(3.2a)

(3.2b)

(3.2c)

(3.2d)

2

8

where 𝑐𝑡𝐼𝐶𝑖𝑡 is a dummy variable for ICLEI membership of county 𝑖 in year 𝑡 and 𝑠𝑡𝐼𝐶𝑖𝑡 is a dummy

variable for ICLEI membership of the state county 𝑖 belongs to in year 𝑡. 𝑏𝑡𝐼𝐶𝑖𝑡 is a dummy variable

for ICLEI membership of the county 𝑖 and the state county 𝑖 belongs to in year 𝑡. If they joined

before 2005, we consider them as having joined ICLEI in 2005. These variables are irreversible

and are 1 after they were treated. 𝑌 𝑒𝑎𝑟𝑡 is a time dummy variable, and 𝜖𝑖𝑡 and 𝜖 ′

𝑖𝑡 are independent

and identically distributed error terms with zero-mean.

We include 𝑋𝑖𝑡, covariates of energy consumption, and its mechanism is in Figure 3.2. These

attributes are classified into five groups: political, financial, industrial, and transportation. First,

political variables are the political parties of the county mayor and state governor.

In Korea,

democrats strongly support climate policies, while conservatives place a low priority on climate

actions. We coded 1 if the governor or mayor was affiliated with the democratic party; other-

wise, 0. Data were gathered from Statistics of Successful Candidates (Korean National Election

Commission, 2022). Second, financial attributes include local income tax collected and the fi-

nancial independence ratio. Local income tax indicates the county’s available budget and income

level. The energy-environmental Kuznets curve shows an inverted-U shape for the relationship

between income and energy consumption or environmental pressure. Baek & Kim (2013) found

empirical evidence of the energy-environmental Kuznets curve in Korea for income and carbon

emissions. Therefore, we include a quadratic form of local income tax to consider the inverted-U

shape relations. The financial independence ratio is the amount the local government can use for

its purposes out of the total budget. Local income tax and the financial independence ratio were

gained from Korean Local Governments (2021) and the Local Finance Integrated Open System

82

(Korean Ministry of the Interior and Safety, 2023a). Third, the industrial attribute is defined as the

gross value added per capita in manufacturing. Manufacturing is one of the most energy-intensive

sectors, and Korea has one of the world’s largest manufacturing economies, with 27.5% of its GDP

from manufacturing in 2019 (Statistics Korea, 2022a). The gross value-added dataset came from

Korean Local Governments (2021), and populations came from Resident Registration Population

Status (Korean Ministry of the Interior and Safety, 2023b). Fourth, the transportation variable is

the number of cars per capita. More cars per capita make traffic more crowded and means more

energy consumption in transportation. The number of cars per capita was obtained by dividing

total car registration numbers from Korean Local Governments (2021) by population. Local tax

and gross value added in manufacturing are nominal values each year; they were converted to the

3

8

2019 value using the Korean Consumer Price Index (Statistics Korea, 2022b).

We chose observables that may not be the result of the energy policy stimulated by TMN

membership in the Korean context. Participation in ICLEI in Korea would not affect other variables.

The main factors that decide who will win the election for Mayor/Governor are the economy and

political issues, and ICLEI membership would not significantly affect the election result. ICLEI

membership also will not significantly affect the financial independence ratio and local income tax.

ICLEI membership fee is negligible compared to the annual expenditure of local governments. It is

also the same for financial variables. ICLEI membership almost does not affect the FIR ratio or local

income tax. Then, in the Korean context, local governments do not want to prohibit manufacturing

because it supports local finance a lot. The only exception was to move the industrial complex

out of the capital due to environmental concerns in the last 20th century. From 2005 to 2019,

Korean local governments never tried to prohibit manufacturing to reduce energy consumption,

and I may not believe that there are any local governments who want to kick out manufacturing

industries only for energy reduction purposes. Nevertheless, including manufacturing may explain

the unavoidable energy consumption from economic activities. Local governments may support

green investment; however, the policy instruments for green investment are typically funded by

the central government in Korea. Transportation is also the same. Korean local governments do

83

not try to prohibit using personal vehicles with tax or other instruments. Rather than this, they

usually do increase the efficiency and accessibility of public transportation and build more roads

to decrease traffic jams. So, the number of cars can indicate the traffic and energy cunsumptions

in transportation, but not be affected by ICLEI membership. Descriptive statistics are in Table

3.3, and the mean of variance inflation factors is 1.19, which means there is almost no correlation

between ICLEI memberships and other variables.

3.2.3 Staggered DID estimator

We use a staggered DID method and compare it with a two-way fixed effect DID model to

answer the research question.

In the conventional DID format, there are 2 x 2 time and group

settings: no one is treated at Time 1, and some are treated at Time 2. Researchers want to estimate

4

8

the treatment effect of an applied policy. The treatment effect is gained by comparing the outcomes

of groups over time. The two-way fixed effect DID model considers fixed effect in group and

time together with the 2x2 DID setting. Due to its intuitive and powerful explanation, DID has

been widely used in natural and social science to estimate the impact of treatment. Specifically

in social science, many studies adopt this model even into datasets of staggered treatment because

social scientists often have to design quasi-experiments with given datasets on society, which we

cannot easily set experimental settings. However, if we have staggered intervention of policies over

time, which means more periods and groups, we need another approach because the result of a

traditional DID could be biased and may contain Type I and Type II errors when there are staggered

interventions (Baker et al., 2022).

Recently, several robust alternatives to DID under staggered treatments, called staggered DID

methods, have been suggested to remedy this staggered setting, and we have chosen the CS

estimator suggested by Callaway & Sant’Anna (2021). Baker et al. (2022) suggested a way to

evaluate staggered treatment settings using Callaway & Sant’Anna (2021), Sun & Abraham (2021),

or stacked regressions. Callaway & Sant’Anna (2021) suggested a CS estimator that estimates

the group and time-specific treatment effects (allowed to be heterogeneous) and aggregates them

to generate an overall estimator like Goodman-Bacon (2021). CS estimator means the average

84

5

8

treatment effect calculated from each DID estimator in all possible combinations. The CS estimator

under staggered treatment is close to what is under the 2 x 2 settings. In addition, the CS estimator

has more flexibility in using the not-yet treated group as a control, allows covariates, and allows

parallel trend assumptions to hold only for conditional covariates and observed anticipation. To

check the robustness of the result, we include a static DID estimator with an event study setting to

get rid of timing differences among groups.

Callaway & Sant’Anna (2021) suggested using a nonparametrically point-identified average

treatment effect with outcome regression, inverse probability weighting, or a doubly robust es-

timator; we use the latter as also proposed by Sant’Anna & Zhao (2020).

In addition, we use

not-yet-treated units as a comparison group. First, we define IC as a group that includes all treated

counties if their join years are the same. Then, 𝐼𝐶𝑖𝑐 is a dummy variable that is 1 if a county joined

ICLEI in year 𝑖𝑐. According to Callaway & Sant’Anna (2021), the average treatment effect for units

in group 𝑖𝑐 of counties joining ICLEI in year 𝑖𝑐 and year 𝑡 is defined as:

𝐴𝑇𝑇 (𝑖𝑐, 𝑡) = 𝐸 [(

𝐼𝐶𝑖𝑐
𝐸 [𝐼𝐶𝑖𝑐]

+

𝑝𝑖𝑐,𝑡 (𝑋)(1−𝐷𝑡 )
1−𝑝𝑖𝑐,𝑡 (𝑋)
𝑝𝑖𝑐,𝑡 (𝑋)(1−𝐷𝑡 )
1−𝑝𝑖𝑐,𝑡 (𝑋)

𝐸 [

)

]

× (𝑙𝑛(𝑦𝑡) − 𝑙𝑛(𝑦𝑖𝑐−1) − 𝐸 [𝑙𝑛(𝑦𝑡) − 𝑙𝑛(𝑦𝑖𝑐−1)|𝑋, 𝐷𝑡 = 0, 𝐼𝐶𝑖𝑐 = 0])]

𝑝𝑖𝑐,𝑡 (𝑋) = 𝑃𝑟𝑜𝑏(𝐼𝐶𝑖𝑐 = 1|𝑋, 𝐼𝐶𝑖𝑐 + (1 − 𝐷𝑡) (1 − 𝐼𝐶𝑖𝑐) = 1)

(3.3)

(3.3a)

where 𝐴𝑇𝑇 (𝑖𝑐, 𝑡) is the average treatment effect, and 𝐷𝑡 is a dummy variable that is 1 if a county

remains in ICLEI at year 𝑡 and otherwise 0. Therefore, 𝐷𝑡 is 𝑠𝑡𝐼𝐶𝑡 if we test the impact of state

ICLEI membership, and 𝐷𝑡 is 𝑐𝑡𝐼𝐶𝑡 if we test the impact of county ICLEI membership. 𝑝𝑖𝑐,𝑡 (𝑋)

is the generalized propensity score indicating the probability of being first treated at time 𝑖𝑐.

The main assumptions of the DID method are parallel trends and no anticipation. The parallel

trend assumption is that the treated and control groups show the same trend before treatment.

The no anticipation assumption is that there is no observed displacement right before policy

implementation. Callaway & Sant’Anna (2021) said that the CS estimator is suitable when units

can anticipate participating in the treatment and may adjust their behavior before the treatment is

implemented. Local governments should pay substantial admission fees to join ICLEI; therefore,

85

it is highly likely that they will recognize they will join ICLEI. Therefore, the no anticipation test

is unnecessary. There are two ways of testing parallel trends: statistical tests and reading graphs.

Baker et al. (2022) mentioned that static DID estimates should be accompanied by an event-

study design to identify the timing of outcome differences between treated and control groups. We

run the following regressions to evaluate parallel trend assumptions.

𝑙𝑛(𝑦𝑖𝑡) = 𝛽0 +

𝑙𝑛(𝑦𝑖𝑡) = 𝛽′

0 +

𝑙𝑛(𝑦𝑖𝑡) = 𝛽′′

0 +

−2
∑︁

𝜏=−14

−2
∑︁

𝜏=−14

−2
∑︁

𝜏=−14

𝛽𝜏 × 1[𝑐𝑡𝐽𝑜𝑖𝑛𝑖 − 𝑡 = 𝜏] +

𝛽′
𝜏 × 1[𝑠𝑡𝐽𝑜𝑖𝑛𝑖 − 𝑡 = 𝜏] +

𝛽′′
𝜏 × 1[𝑠𝑡𝐽𝑜𝑖𝑛𝑖 − 𝑡 = 𝜏] +

14
∑︁

𝜏=0

14
∑︁

𝜏=0

14
∑︁

𝜏=0

𝛽𝜏 × 1[𝑐𝑡𝐽𝑜𝑖𝑛𝑖 + 𝑡 = 𝜏]

+𝛽𝑋 𝑋𝑖𝑡 + 𝜁𝑖 + 𝜁𝑡 + 𝑢𝑖𝑡

(3.4)

𝛽′
𝜏 × 1[𝑠𝑡𝐽𝑜𝑖𝑛𝑖 + 𝑡 = 𝜏]

+𝛽′

𝑋 𝑋𝑖𝑡 + 𝜁 ′

𝑖 + 𝜁 ′

𝑡 + 𝑢′
𝑖𝑡

𝛽′′
𝜏 × 1[𝑠𝑡𝐽𝑜𝑖𝑛𝑖 + 𝑡 = 𝜏]

+𝛽′′

𝑋 𝑋𝑖𝑡 + 𝜁 ′′

𝑖 + 𝜁 ′′

𝑡 + 𝑢′′
𝑖𝑡

(3.5)

(3.6)

6

8

where 𝑐𝑡𝐽𝑜𝑖𝑛𝑖 is the year county 𝑖 joined ICLEI, 𝑠𝑡𝐽𝑜𝑖𝑛𝑖 is the year the state of county 𝑖 joined

ICLEI, and 𝑏𝑡𝐽𝑜𝑖𝑛𝑖 is the year the state of county 𝑖 and the county 𝑖 joined ICLEI. If they did not
𝑖 are county-specific, and 𝜁𝑡, 𝜁 ′
𝑡 ,

join by 2019, we define 𝑠𝑡𝐽𝑜𝑖𝑛𝑖 or 𝑐𝑡𝐽𝑜𝑖𝑛𝑖 as equal to 𝑡. 𝜁𝑖, 𝜁 ′

𝑖 , 𝜁 ′′

𝑡 are year-specific fixed effect, and 𝑢𝑖𝑡, 𝑢′
𝜁 ′′

𝑖𝑡, 𝑢′′

𝑖𝑡 are independent and identically distributed error

terms with zero-mean.

3.3 Results

We drew event study plots for CS estimators (solid line) and event study estimators of conven-

tional DID (dashed line) with and without covariates, along with 95% confidence intervals in Figure

3.3. Pre-treatment estimates of CS estimators indicate that there are almost no parallel trends. The

post-treatment estimates of CS estimators are the treatment effect. In Figure 3.3a, without covari-

ates, all pre-treatment estimates are close to zero; the average is -0.0016 (0.0048)5 with a p-value of

0.737. On the contrary, post-treatment estimates have an average of -0.0589 (0.310) and a p-value

of 0.057, which means clear energy consumption reduction after joining ICLEI. In Figure 3.3b, the

5parenthesis means the standard errors.

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average pre-treatment is -0.0053, and the average post-treatment is -0.0699 with covariates. CS

estimators and event study estimators show similar flat trends before the treatment, which means

there are no pre-trends and a sudden fall just after the treatment. The noise after the treatment is

caused by the small number of counties that joined ICLEI in the same year.

Figures 3.3c and 3.3d show CS estimators estimators on the state ICLEI membership with

and without covariates. There are no pre-trends, and there are clear treatment effects. Without

covariates, the average pre-treatment effect is -0.0152 (0.0034) with a p-value of 0.000, while the

post-treatment effect is -0.0927 (0.0257) with a p-value of 0.000. With covariates, the average

pre-treatment is 0.0013, while post-treatment is -0.0920. Although there may be a pre-trend under

event study estimators, there is no pre-trend under the CS estimator, which is enough to justify

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the result under Callaway & Sant’Anna (2021). Event study estimators with static DID show the

violation of no anticipation assumption on the plot; however, if we assume a county can anticipate

its future joining, it would be okay to use CS estimators (Callaway & Sant’Anna, 2021).

Figures 3.3e and 3.3f are CS estimation results on county and state ICLEI membership with and

without covariates. There is clearly no pre-trend and substantial decrease in post-treatment. Without

covariates, the pre-treatment average is -0.0125 (0.0056), and the post-treatment average is -0.1651

(0.0311). With covariates, the pre-treatment average is -0.0233 (0.0233), and the post-treatment

average is -0.3997 (0.0923). In each group-year 2 x 2 setting, there are almost no pre-trends.

CS estimators for each case of ICLEI memberships are in Figure 3.4. Green and triangular

ones are for county membership, red and rectangular ones are for state membership, and black and

round ones are for both memberships. Thick lines are for with covariates, and dashed lines are for

without covariates. There is no pre-trend in all cases and a clear decrease after joining ICLEI. The

magnitude becomes greater from county to state and to both memberships.

Table 3.4 shows the average treatment effect estimated using CS estimators on the impact of

county and state ICLEI membership with and without covariates. First, we compare the result

with static two-way fixed effect (TWFE) DID methods. The TWFE row shows estimates of a post-

treatment effect from TWFE DID, a conventional DID design. CS estimators in Table 3.4 mean the

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weighted average treatment effect described in Equation 3.3. Both report a significant decrease in

energy consumption after joining ICLEI. County-specific effects report average treatment effects

by the timing of joining ICLEI, and ic means the year a county joined. Year-specific effects indicate

average treatment effects in year t. The event study row of Table 3.4 reports average treatment

effects by the length of ICLEI membership years, and post-term means the number of years since

joining ICLEI. The numerical value of ATEs after year 0 is shown in Table 3.4. Without covariates,

energy consumption per capita is estimated to decrease by 4.53% after joining ICLEI. In the first

year after a county joined ICLEI, the energy consumption per capita decreased by 3.67%, and it

is estimated to decrease by 6.95% in the 4th year, 7.52% in the 5th year, 7.28% in the 7th year,

and 21.65% in the 12th year. This is similar to the estimation with covariates. There is no clear

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fortifying trend after joining ICLEI by a county.

We observe a much clearer treatment effect with a state ICLEI membership. Table 3.5 shows

a growing energy consumption reduction after joining ICLEI. Without covariates, there is no

significant decrease in energy consumption for 3 years; after 3 years, there is a 5.09% decrease

in energy consumption per capita. This keeps growing and becomes a 14.32% decrease in the

12th year of joining ICLEI. With covariates, the significant decrease shows up after 6 years, and

the magnitude keeps growing over time. The aggregated treatment effects by group and year are

also consistent with the hypothesis that ICLEI membership will decrease energy consumption on

a county level compared to non-CLEI members. The CS estimators are similar with and without

covariates.

Table 3.6 shows the treatment effect with both county and state membership. The magnitude is

bigger than the sole membership of a county or a state. Then, we can observe the growing impact

of membership over time. Without covariates, the treatment grew from a 2.68% decrease in 1st

year to a 40.64% decrease in the 12th year. With covariates, the treatment becomes significant after

4 years: 21.82% decrease in the 4th year to 84.36% decrease in the 12th year.

The parallel trend assumption needs to be justified, but we do not need to check no-anticipation

assumptions using CS methods (Callaway & Sant’Anna, 2021). The CS methods lean on the idea

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that the decision to join ICLEI is made at a county or state level, and other social, political, or

economic conditions may not affect their decisions. Counties or states may anticipate when they

will join ICLEI, and the CS methods is suitable for this case (Callaway & Sant’Anna, 2021). First,

we check the parallel trend assumption with and without covariate. Figure 3.5 shows the point

estimates and 95% confidence levels for pre- and post-treatment periods clustered at the county

level without covariates. Green points before 0 indicate the pre-treatment effects, and red ones after

0 indicate the post-treatment effects. Under the null hypothesis of parallel trends, the pre-treatment

effect should equal 0. The post-treatment effect may deviate from 0 if ICLEI membership has any

impact on energy consumption. Each group shows the set of counties that joined ICLEI each year.

In most cases, the parallel trend assumptions are justified, though Groups 2010, 2017, and 2019

9

8

have some deviations from 0. Group 2016 shows an increase in energy consumption after joining

ICLEI. Figure 3.6 shows better results with covariates, while Group 2017 still shows a violation of

the assumption. This may be because a few counties joined ICLEI in the same year. The number

of counties that joined ICLEI in the same year ranged from one to eight Table 3.3. Regarding state

ICLEI membership, we clearly identify no pre-trend and significant deviation after the treatment in

Figures 3.7. Figures 3.8 and 3.9 show that there is almost no pre-trend in estimating both county

and state membership. Some groups in 2017 and 2019 showed sudden increases before treatment;

however, this is due to the low numbers of treated groups: one in 2017 (Songpa) and two in 2019

(Icheon and Yuseong).

3.4 Discussion

Overall, the estimation had several meaningful results. First, using the CS methods, we find

evidence that ICLEI membership reduces energy consumption per capita at a county level, and

state membership has a stronger impact than county membership, and both county and state

membership have the biggest impact. The total average effect of county ICLEI membership is a

4.53% decrease in energy consumption per capita without covariates and a 6.62% decrease with

covariates. The aggregated treatment effect of state membership is a 9.00% decrease without

covariates and an 8.91% decrease with covariates. With both memberships of a county and a state,

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energy consumption is decreased by 11.8% without covariates to 21.4% with covariates. In Korea,

the average energy consumption per capita at the county level from 2005-2019 is 3.968 TOE/person,

which means the energy consumption reduction is 0.184 to 0.2420.180 to 0.263 TOE/person with

a county membership and 0.354 to 0.357 TOE/person with a state membership, and 0.467 to 0.848

TOE/person with both memberships. It may point out that multi-level governance can generate

a bigger impact on policy outcomes when each agent tends to cooperate and support the shared

goal. Second, unlike county ICLEI membership, state ICLEI membership shows a stronger and

fortifying trend in local energy consumption over time. State membership shows an increase in

energy consumption reduction over time after joining ICLEI. The reduction becomes significant

after 3 years without covariates and 6 years with covariates. Third, there is a significant difference

0

9

between the results of TWFE DID and CS methods, which means we avoid the potentially biased

result of the canonical DID setting.

The policy implementation power of local governments made greater energy consumption

reduction with state membership. In the Korean context, state governments have greater influence

and discretion in policy implementation compared to county governments. First, states can spend

much more money at their discretion. According to the Local Finance Integrated Open System

(Korean Ministry of the Interior and Safety, 2023a), the average financial independence ratio of

states is 72.7, and that of counties is 59.4. The average budget is 7,027 billion Korean won

for states and 619 billion Korean won for counties. This means that states can initiate a more

powerful drive if they want to do so. Furthermore, in Korea, higher-level governments often utilize

matches for policy implementation. Central or state governments do a project a match: i.e. if they

want to subsidize charging station installation, the central government may suggest a 5:3:2 match

(central:state:county). States also do this kind of match for their counties; however, the county has

no other lower-level governments. It makes local governments tend to accept the policies of the

higher governments (Han & Yun, 2021). Second, states have bigger political and policymaking

power than counties. They have more negotiation power against the central government and more

influential political leaders (governors are usually more popular and well-known than mayors),

90

and it is the same for the local congress. Governors and state congressmen are closer to National

congressmen than mayors and county congressmen. This makes it easier for state governments to

lead the national budget and policy favorable to them. Third, states have greater populations, which

they can affect. Korea has 17 states and 228 counties, and each state can affect all the populations

of its counties.

Policy learning is the key mechanism for explaining how ICLEI membership affects local

policy outcomes. When a local government wants to learn how to implement climate policy

effectively, the most required resources are the capacity of public officers, budget, and experience.

Grønnestad & Bach Nielsen (2022); Zambrano-Gutiérrez & Puppim de Oliveira (2022) assert that

TMNs provide knowledge and information about their policy fields. The ICLEI Korea network

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provides capacity building for local public officers, sharing knowledge and information of successful

policy implementation cases from domestic and international member cities to its members. The

network has also spent a substantial budget to support project funding for member cities. Through

these channels, ICLEI Korean members can build their capacity to implement climate policy

and sometimes can secure project funding.

In contrast to Grønnestad & Bach Nielsen (2022);

Zambrano-Gutiérrez & Puppim de Oliveira (2022), who estimate the impact of each channel, we

estimate the impact of TMN membership on the final outcome of local energy policy. Therefore,

we did not compare the external learning from TMN membership with other channels of learning

climate policy. Nevertheless, the finding shows that the impact of external learning from TMNs is

highly significant to improve the final policy outcome.

In terms of global stocktake under the Paris Agreement, this high impact of ICLEI membership is

remarkable but still not enough to achieve the overarching climate goals agreed upon in Paris, 2015,

or Glasgow, 2021. This chapter analyzes to what extent ICLEI membership decreases “Energy

Consumption,” not “Greenhouse Gas Emissions.” The 4.5% to 11% decrease in energy consumption

is the average impact of ICLEI membership. First, after joining ICLEI, local governments may

start to take care of the low-hanging fruit, such as increasing energy efficiency, installing solar

PV, subsidizing electric vehicle adoption, and advertising energy policy. However, after harvesting

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them, local authorities will face high-hanging fruit, such as energy consumption in manufacturing,

agriculture, or retailing. It is impossible to reduce energy consumption in those sectors unless we

produce goods without energy consumption. In these fields, we need to invest in new technology

to produce the same quality products with less carbon emissions or energy consumption; however,

it is out of the local government’s control. For the last, the most essential point is that the ultimate

climate goal is to reduce carbon emissions, not reduce energy consumption. At this point, they

have the same meaning because most energy comes from burning fossil fuels. However, if we

consume energy without carbon emissions, we can still have a chance to meet overarching climate

goals with substantial energy consumption. Therefore, the high impact of ICLEI membership may

support the initiation of climate policy over the nation, and it should be spread nationwide. Then,

2

9

we should follow up if further innovation is made to meet the national and global goals. Korea has

national goals for greenhouse gas emissions: reduction of up to 40% of 2018 emissions by 2030

and 100% by 2050.

Our findings of the impact of ICLEI membership on energy consumption can be transferable to

other contexts. To extend the results, researchers should consider the following factors. First, local

governments should have guaranteed local autonomy. Communication between local governments

should be safe, active, frequent, and encouraged. Assured representative democracy is one of the

parts that make it possible. Korean local governments are highly democratized, and the Korean

constitution guarantees local autonomy. Second, local governments should have a sufficient local

budget to build their capacity. Implementing climate and energy policy is difficult for beginner

cities, and both budget and knowledge are required. Only with enough capacity on both sides can

TMNs stimulate local policy implementation. Local governments should have enough budget or be

ready to utilize external resources and funds under a low level of corruption. Third, national public

opinions should be somewhat favorable for climate and energy policy. Otherwise, it is difficult to

observe meaningful numbers of ICLEI members or significant activities of ICLEI members.

Nevertheless, there are several important limitations to the finding. First, some groups of

counties may deviate from 0 in the pre-treatment periods, which may violate the parallel trend

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assumption. It may be close to 0 if we include covariates, while some groups remain deviated from

0. This is inevitably caused by the small number of counties that joined ICLEI in the same year. The

total number of counties in South Korea is 228, and it is not easy to observe more than 20 counties

joining ICLEI in the same year. Second, we treat the impact of joining ICLEI as the same for

every county, although there is some heterogeneity among ICLEI members in their actual efforts to

pursue the goal of ICLEI. Thus, the estimated impact of ICLEI membership should be interpreted

as the average treatment effect. The main reason we include political factors as covariates is to

address this concern.

3.5 Conclusion

This chapter has identified the impact of TMN membership on local energy policy outcomes.

3

9

It adopted a staggered DID to address the potential bias from using a canonical DID on staggered

interventions. Some local governments persistently implement climate policies despite the central

government’s neglect. Some of the external learning for their successful policy implementation

comes from TMNs. TMNs offer members the best strategies, success cases, and communication

opportunities. Therefore, they are informative and valuable places for beginners to learn new

climate policies. This study is the first attempt to estimate the impact of TMN membership on local

policy outcomes. Using a database of all 228 local governments in Korea between 2005 and 2019,

this chapter identified the impact of ICLEI membership on local energy consumption.

The primary contribution of this chapter is to identify the significant role of ICLEI, one of the

TMNs in climate actions, on local climate policy in Korea. This chapter shows that member cities

actually drive the policy outcome alongside the goal of ICLEI. This is the first chapter to identify the

impact of TMN membership on the final policy outcome. It means local governments have tried to

meet the goal via multiple channels, and it achieves remarkable differences. If central governments

want to implement climate policies under budget limits, they should seriously consider selectively

supporting ICLEI members, which have better policy performance than non-ICLEI members, as

European countries have done (Kern & Bulkeley, 2009). This suggests the possibility of global

urban governance from the international urban network. Gordon & Johnson (2017) state that

93

cities can substantially contribute to meeting global climate goals and suggest the orchestration

framework to analyze politics and power dynamics in global urban governance. They pointed

out that cities were remarkably moving beyond simple symbolic pledges and consolidating urban

climate governance in the 2010s, while TMNs showed low levels of activation at first in the 1990s.

Acuto & Leffel (2021) also argued that urban networks lead to further internationalization of city

leadership. They said that institutionalized boundaries of networks would be a stretch for a bigger

picture of global urban governance.

Second, this chapter sheds light on the impact of ICLEI on local climate policy through

quantitative analysis, given that previous literature was mainly qualitative. We systematically

compared the impact of ICLEI membership on local energy consumption for all members and

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9

non-members of TMNs in Korea. The results reveal that county and state ICLEI membership

has significantly decreased local energy consumption. Specifically, if a county becomes an ICLEI

member, there is a 4.53% to 6.62% decrease; if a state becomes an ICLEI member, there is an

8.91% to 9.00% decrease; and if both county and state become an ICLEI member, there is an

11.8% to 21.4% decrease in energy consumption per capita. These findings show a statistically

significant effect of TMN membership, which fortifies qualitative findings in previous literature.

We also found a growing impact of ICLEI membership over time. When a state joins ICLEI, it

shows significant energy consumption reduction after 3 to 6 years of membership. This means

energy consumption is reduced more if a state maintains membership longer.

Third, to the best of our knowledge, this study is the first to adopt staggered DID for staggered

intervention at the county level using all the county data in a nation. There is growing evidence

that traditional DID results may be biased if there is staggered treatment timing. The CS estimator

shows robust results, and the required assumptions are justified. The results are similar with

or without covariates, which means the impact of ICLEI membership significantly affects local

energy consumption reduction. Those results significantly differ from the TWFE and event study

estimators. We can avoid this bias in canonical DID under staggered treatment by using staggered

DID.

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Our findings lead researchers to further studies. First, researchers may use carbon emission

reduction as the target with TMN membership if they can build a carbon inventory database by

county. We use energy consumption rather than carbon emissions because of data feasibility at a

county level. Korea has started to build a carbon inventory by county; in 2022, the Greenhouse Gas

Inventory & Research Center of Korea (2022) published tentative carbon emissions by county for

2016-2019. Second, researchers may apply these approaches to other studies of local policies across

a broader geographical scale. Extending these findings to other TMN areas or other geographic

regions requires careful consideration of data availability. Our theoretical background was based on

robust evidence from previous literature on the role of TMNs in climate change. When a researcher

tries to expand this to other TMNs, robust evidence of the relationship between target TMNs and

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9

local governments should be identified. Third, Callaway & Sant’Anna (2021) is one part of the

rapidly growing literature on staggered DID settings. We chose this method based on its fit with

our research. A researcher can get knowledge about this staggered DID method from Baker et al.

(2022).

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100

APPENDIX 3.A: Tables and Figures

Table 3.1 The number of counties or states that joined ICLEI

Year
Joined
before 2005

2007
2008
2009
2010
2011
2012
2013

2014

2015

2016
2017
2019
Non-Members
(as of 2019)
Total in data
Excluded

County
Ansan, Bucheon, Damyang,
Gimpo, Gumi, Jeju, Jeongseon,
Jeonju, Pyeongchang,
Suncheon, Suwon, Wonju
Changwon, Gwacheon
Hadong, Seongnam
Gapyeong, Namyangju
Yeosu
Seocheon
Buyeo, Cheongyang, Seongbuk
Anyang, Gangneung, Osan,
Seodaemun, Taean, Yeongju
Cheongju, Gangdong, Inje
Jongno, Sejong, Uiwang
Asan, Dangjin, Dobong, Nowon
Pohang, Siheung, Yuseong
Eunpyeong, Namgu (Incheon)
Songpa
Icheon
180 counties

226 counties
Geumsan, Hoengseong

State (# of its counties)
Busan (16), Chungnam (15),
Gangwon (18), Gwangju (5),
Gyeonggi (36), Jeju (1)
Seoul (25), Ulsan (5)

Daegu (8), Gyeongnam (18)
Incheon (10)

Sejong (1)

Daejeon (5)
Chungbuk (11), Gyeongbuk (23)
Jeonbuk (14), Jeonnam (22)
17 states (226 counties)

County and State
Ansan, Bucheon,
Gimpo, Jeju,
Jeongseon, Pyeongchang,
Suwon, Wonju
Gwacheon
Changwon, Hadong, Seongnam
Gapyeong, Namyangju

Seocheon
Buyeo, Cheongyang, Seongbuk
Anyang, Gangneung, Osan,
Seodaemun, Taean
Gangdong, Inje
Jongno, Sejong, Uiwang
Asan, Dangjin, Dobong,
Nowon, Siheung
Eunpyeong, Namgu (Incheon)
Songpa
Icheon, Yuseong
188 counties

226 counties

1

0

1

101

Table 3.2 Conversion factors for energy unit conversion

TypeTypeType

Oil

Gas
Electricity

Sources
Sources
Sources
Gasoline
Kerosene
Diesel
Bunker-A
Bunker-B
Bunker-C
Jet fuel
By-products I
By-products II
Propane
Butane
Natural Gas
Electricity

UnitUnitUnit
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑏𝑏𝑙
𝑘 𝑀3
𝑀𝑊 ℎ

KEA coefficients
KEA coefficients
KEA coefficients
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑙
𝑡𝑜𝑒/𝑘𝑔
𝑡𝑜𝑒/𝑘𝑔
𝑀3
𝑡𝑜𝑒/𝑘𝑊 ℎ

0.000781
0.000877
0.000903
0.000931
0.000967
0.000996
0.000872
0.000886
0.000953
0.001204
0.001182
0.001043
0.000211

Conversion to TOE
Conversion to TOE
Conversion to TOE
𝑡𝑜𝑒/𝑏𝑏𝑙
0.124
𝑡𝑜𝑒/𝑏𝑏𝑙
0.139
𝑡𝑜𝑒/𝑏𝑏𝑙
0.144
𝑡𝑜𝑒/𝑏𝑏𝑙
0.148
𝑡𝑜𝑒/𝑏𝑏𝑙
0.154
𝑡𝑜𝑒/𝑏𝑏𝑙
0.158
𝑡𝑜𝑒/𝑏𝑏𝑙
0.139
𝑡𝑜𝑒/𝑏𝑏𝑙
0.141
𝑡𝑜𝑒/𝑏𝑏𝑙
0.152
𝑡𝑜𝑒/𝑏𝑏𝑙
0.097
𝑡𝑜𝑒/𝑏𝑏𝑙
0.109
𝑡𝑜𝑒/𝑘 𝑀3
1.043
𝑡𝑜𝑒/𝑀𝑊 ℎ
0.211

2

0

1

102

Table 3.3 Descriptive statistics for variables

UnitUnitUnit

Symbol
Symbol
Symbol
Ln(Enpc)

Variable
Variable
Variable
Ln (Energy Consumption per capita)
Energy Consumption per capita
Energy Consumption
ICLEI membership of a state
ICLEI membership of a county
ICLEI membership of both
a party of a Governor
a party of a Mayor
Local Income Tax
Financial Independence Ratio
Gross Value Added per capita
in Manufacturing
The Number of Cars per Capita
Note: N=3,390 (226 counties over 15 years from 2005 to 2019)

ST
CT
BT
Gvnor
Mayor
Ltax
FIR
Mnpc ₩1 million/person

TOE/person
TOE
Binary
Binary
Binary
Binary
Binary
₩1 million
%

Car/person

Carpc

Mean (SD)
Mean (SD)
Mean (SD)
1.177(0.572)
3.960(3.405)
767,854(943,786)
0.632(0.482)
0.124(0.330)
0.096(0.295)
0.442(0.497)
0.367(0.482)
50,610(101,218)
62.969(11.299)
7.605(11.871)

MinMinMin
0.119
1.127
21,645
0
0
0
0
0
480.610
28.280
0.022

MaxMaxMax
3.511
33.473
9,208,969
1
1
1
1
1
1,257,906
93.900
90.373

0.404(0.108)

0.191

2.011

3

0

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103

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108

Figure 3.1 Korean ICLEI network

9

0

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109

Figure 3.2 Main variables affecting local energy consumption

0

1

1

110

(a) ATE of county membership without covari-
ates

(b) ATE of county membership with covariates

1

1

1

(c) ATE of state membership without covariates

(d) ATE of state membership with covariates

(e) ATE of both memberships without covariates

(f) ATE of both memberships with covariates

Figure 3.3 CS estimators on county and state ICLEI membership w/ and w/o covariates

111

Figure 3.4 ATE of ICLEI memberships by CS estimators

2

1

1

112

Figure 3.5 county-time ATE of county ICLEI membership - unconditional parallel trends

3

1

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113

Figure 3.6 county-time ATE of county ICLEI membership - conditional parallel trends

4

1

1

114

(a) Unconditional parallel trends

5

1

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Figure 3.7 County-time ATE of state ICLEI membership

115

Figure 3.8 county-time ATE of both ICLEI membership - unconditional parallel trends

6

1

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116

Figure 3.9 county-time ATE of both ICLEI membership - conditional parallel trends

7

1

1

117