Interstate pollution spillover and setting environmental standards

Accepted Manuscript Interstate pollution spillover and setting environmental standards Ce Huang, Ernesto D.R. Santibanez-Gonzalez, Malin Song PII:

S0959-6526(17)32216-3

DOI:

10.1016/j.jclepro.2017.09.264

Reference:

JCLP 10769

To appear in:

Journal of Cleaner Production

Received Date: 24 April 2017 Revised Date:

23 September 2017

Accepted Date: 23 September 2017

Please cite this article as: Huang C, Santibanez-Gonzalez EDR, Song M, Interstate pollution spillover and setting environmental standards, Journal of Cleaner Production (2017), doi: 10.1016/ j.jclepro.2017.09.264. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Interstate pollution spillover and setting environmental

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standards

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Ce Huang a, Ernesto D.R. Santibanez-Gonzalez b and Malin Song c,∗

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a

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Economics, Chengdu 611130, China

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b

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em Ciências Ambientais, UFSB - Porto Seguro – BA, Brazil

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c

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Economics, Bengbu 233030, China

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School of Public Finance and Taxation, Southwestern University of Finance and

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Depto. Ingenieria Industrial, Universidad de Talca, Chile and Centro de Formação

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School of Statistics and Applied Mathematics, Anhui University of Finance and

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Highlights

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This paper studies emission standard for pollutants with interstate spillover.

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The study investigates how the federal government sets emission standards.

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Federal government communicates with state governments on local conditions.

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The paper compares total welfare under different degrees of pollution spillover.

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Standard setting at federal level may be inferior to decentralized standard setting.

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Abstract: This paper investigates in a multi-level government system, how the federal

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government sets environmental standards for different states after communicating

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with state governments regarding the cost of pollution abatement to local economies.

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Here, the term “federal government” refers to the level of government in a federation

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responsible for the whole country, while “state governments” are responsible for

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individual states. We adopt a game-theoretical analysis under asymmetric information

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where state governments, which know the pollution abatement cost, report to the

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∗

Corresponding author. E-mail: [email protected], Tel: +86 15805521822. 1

ACCEPTED MANUSCRIPT federal government, which is initially uninformed about the true cost level. We argue

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that interstate spillover of pollution causes a bias for state governments towards lax

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environmental standards and gives state governments an incentive to exaggerate the

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economic cost of pollution abatement. In equilibrium, state governments partition the

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set of possible costs into disjoint subsets and report the same cost to the federal

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government under different costs within each partition. After receiving reports, the

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federal government only knows the partition to which the local cost belongs and sets

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environmental standards that are not appropriate for the state. On the other hand,

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when state governments have the authority of setting local standards, the standards are

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inefficiently lax from a total welfare perspective. The paper compares total welfare

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levels of all states under the environmental standards set by the federal and state

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governments. The result indicates that if the degree of spillover is small, the welfare

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level in the centralized system is less than that in the decentralized system.

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Keywords: Interstate pollution; environmental standards; communication; total

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welfare.

1. Introduction

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Environmental standards are a set of quality conditions that are adhered to or

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maintained for a particular environmental component and function. There are three

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types of environmental standards, i.e., ambient, emission, and technological standards.

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This paper focuses on the emission standard, which specifies the maximum amount of

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pollutants legally allowed (Field and Field, 2006)1. To meet the standards, local 1

The reason why we focus on the emission standard rather than ambient standard is because emission

standard is a better tool to control individual polluting sources compared to ambient standard. This is because ambient standard focuses on the ambient environmental quality, which is influenced by many 2

ACCEPTED MANUSCRIPT polluting firms often have to reduce the amount of emitted pollutants by treating the

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pollutants or by switching to a cleaner but usually more expensive production

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technology. This in turn leads to higher production costs and prices, together with

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lower employment and investment of polluting firms (Greenstone, 2002; Walker,

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2013). In addition, workers working in polluting firms also bear the cost from

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environmental regulation in terms of lost employment and lower compensation

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(Walker, 2013). Together, these amount to a huge amount of cost on local economies.

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For example, Greenstone et al. (2012) find that stricter air pollution regulation in the

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United States led to an annual economic cost of 21 billion U.S. dollars during the

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period from 1972 to 1993.

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On the other hand, environmental regulation leads to a benefit of cleaner

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environment, which is also huge (Chay and Greenstone, 2003 and 2005;

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Lleras-Muney,

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environmental standard balances the benefits from a cleaner environment with the

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costs to the local economy.

Deschenes et

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an appropriate

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In addition, many pollutants cross the boundaries of states, for instance, by air,

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water or through production chains (Feng et al., 2014). With inter-jurisdictional

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spillovers, state governments who are interested in the welfare of their own states

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often fail to take into account the benefit of pollution abatement on the environments

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of other states (Helland and Whitford 2003; Sigman 2005). Thus, the environmental

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standards set by state governments are often inefficiently lax (Sigman, 2005).

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factors other than the amount of pollutants emitted by polluting firms, such as weather conditions (see Hamilton and Requate, 2012). On the other hand, technological standard specifies the procedure that polluting firms adopt to reduce their emission (Field and Olewiler, 2011). This kind of standard does not provide polluting firms with incentive to look for better ways to reduce their emission. Therefore, we do not discuss this standard in our paper. 3

ACCEPTED MANUSCRIPT In order to correct this inefficient situation due to interstate spillover, many

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countries such as the United States and the European Union have assigned the federal

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government the authority of setting environmental standards (Oates, 2002). For

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example, under the Clean Air Act passed by the U.S. Congress in 1970, the U.S.

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Environmental Protection Agency was given the authority to set standards for ambient

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air quality across all states. However, researchers have found that inefficiencies may

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also emerge in the decision-making process at the federal level, such as lack of

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information on local conditions (Crémer et al., 1996), diminished accountability

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(Seabright, 1996), uniform standard for different states (Dinan et al., 1999) and

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conflict of interest among representatives of different states (Lockwood, 2002; Besley

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and Coate, 2003).

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While previous studies have examined various aspects of inefficiencies at the

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federal level, lack of information about local condition has not been studied in details.

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Previous research usually sees lack of information as a justification for the federal

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government to set uniform environmental standards for different states. However, in

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reality, the federal government often actively engages in information sharing with the

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state governments before setting standards for different states (Kessler, 2014).

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Therefore, the possibility that the federal government acquires information by

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communicating with state governments should be considered. Can the federal

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government obtain all information from state governments by communicating with

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them? If not, how much information will the federal government get? How inefficient

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will its decision be after obtaining this amount of information? Are the environmental

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standards set by the federal government less efficient than those set by the state

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governments?

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ACCEPTED MANUSCRIPT This article aims to tackle these questions by studying communications between

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the federal and state governments. We employ a game-theoretical analysis of the

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communication process between two levels of government. During communication,

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each state government first chooses a report about local conditions to be sent to the

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federal government. Based on the state government’s report, the federal government

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then forms an estimate about state conditions and chooses an emission standard for

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the state (See Kessler, 2014 for a similar analysis). In the analysis, both state and

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federal governments are rational in the sense that they choose decisions to achieve

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their respective objectives. In addition, they reason strategically by taking account

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their knowledge of the other’s behavior. As pointed out by Osborne and Rubinstein

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(1994), game-theoretical analysis is particularly well suited for such strategic

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interaction between rational decision makers.

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As we show below, when pollution spills over into other states, the

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environmental standards optimal for state governments are laxer relative to those

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preferred by the federal government. Therefore, in the communication with the federal

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government, state governments have an incentive to exaggerate the cost that pollution

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regulation imposes on local economies, in order to induce the federal government to

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set a standard that is closer to the optimal level of state governments. Knowing state

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governments’ incentive to exaggerate, the federal government does not believe the

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report of state governments at face value. As a result, the federal government cannot

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obtain all of the information from state governments, and the standards set by the

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federal government based on inadequate information will fail to maximize the total

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welfare of all states. With a greater degree of interstate spillover, the distance between

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optimal levels of standards of the two levels of governments is greater, so state

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governments have a stronger incentive to exaggerate the true cost. The quality of

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communication between two government levels becomes worse and the federal

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government can get less information from the state counterparts. As a result, the total

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welfare level under the environmental standards set by the federal government

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decreases. We characterize the levels of total welfare attained under the environmental

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standards set by the federal government and study whether the environmental

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standards set by the federal government can achieve a greater total welfare than those

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set by state governments. We find that when the degree of pollution spillover is less

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than a threshold value, the total welfare under federal planning is less than that under

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the decentralized standard setting of state governments. The result is that

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decentralized state governance is better than federal planning when the interstate

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spillover is small. Otherwise, when the degree of pollution spillover is greater than the

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threshold, federal planning is better than decentralized decision making.

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Our analysis sheds light on the information exchange process across different

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levels of government in the setting of environmental standards and identifies factors

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that affect the quality of communication. This issue receives scant attention in the

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literature and our paper fills an important gap. In addition, we contribute to the debate

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on whether environmental standards should be governed at the federal or state level.

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Previous literature argues that the degree of spillover only affects the efficiency level

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of standards set by the state governments. However, we find that it also influences the

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efficiency level of standards at the federal level, through changing the interest

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divergence between the federal and state governments and quality of their

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communication. Therefore, our analysis enriches the existing research and policy

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debate on the relevant issue. At last, our paper shows the usefulness of

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game-theoretical

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decision-making authority of controlling interstate pollutions. Our research may

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inspire other scholars to take similar approaches to study environmental problems. Previous literature on interstate spillover mainly focuses on the inefficiency

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caused by the spillover and measures to reduce the inefficiency. However, we find

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that the spillover causes an interest divergence between different levels of government.

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This finding enriches our understanding about implications of interstate spillovers.

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Also, most research on the decision making process of government usually sees the

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government as a unified entity therefore does not discuss the relationship between

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different levels of governments in the decision making process. We focus on the

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interaction between different levels of governments therefore provide a more detailed

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study on the government’s decision making process. We find that the interest

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divergence across different levels of governments, caused by interstate spillover,

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affects the quality of communication between them and the efficiency level of

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decision making by the government. As last, among those researches who study

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relationship between different levels of government in the decision making process,

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they usually focus on information exchange accompanied by monetary transfer across

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different governments. However, we study the communication without any transfer,

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which we believe are more relevant for the reality.

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The rest of the paper is organized as follows. Section 2 reviews previous research

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related to the current paper. Section 3 establishes a model with two states where

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pollution produced in one state affects the other. It also studies the communication

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process between federal and state governments regarding local conditions. Section 4

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compares the welfare attained by the centralized and decentralized setting of

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environmental standards. Section 5 provides further discussions about the paper’s

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results and concludes the paper. 7

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2. Literature Review The question whether environmental standards should be regulated by state or

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federal governments, in cases of interstate pollution, is currently receiving much

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research attention (Besley and Coate, 2003; Loeper, 2011; Oates, 2002, 2005;

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Seabright, 1996). In order to compare the relative performance of environmental

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standards setting at the state and federal levels, researchers make different

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assumptions about decision-making processes at the federal and state levels.

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In a series of seminal papers, Oates (2002, 2005) assumes that the federal

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government, who wishes to maximize the total welfare of all states, must set the same

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environmental standard for different states. The reason for this assumption is that

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either states are ex ante identical and the federal government lacks information about

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local conditions or it is not politically feasible to treat states differently. On the other

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hand, state governments can choose the appropriate standards for their own state but

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since there is interstate spillover, their standards are overly lax. It is found that when

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the degree of spillover is large, the federal government achieves a higher level of total

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welfare than the state governments do, while the reverse is true when the

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heterogeneity among states is large enough2.

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Other scholars extend the results in Oates (2002, 2005) by relaxing the

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assumption that the federal government must set a uniform standard for different

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states and studying how the federal government is formed and how it makes decisions.

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In Seabright (1996), the federal government is formed by nation-wide election (See

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also Aidt and Dutta, 2017). Therefore, the government is accountable to the majority

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of voters in the whole country. Compared to any regional government, the federal

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government is less accountable to voters in the region. In Besley and Coate (2003),

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Loeper (2011) proposes a different externality that is not from spillover, but from the cost of

inconsistent standards across states. 8

ACCEPTED MANUSCRIPT the federal government is composed of a legislature of representatives elected from

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different states. The authors consider several different specifications of the

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decision-making process of the legislature and find that the decision may be

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inefficient due to conflicts of interest among representatives of different states.

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Lockwood (2002) takes a similar approach in describing the federal government as a

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legislature of elected representatives. The decision-making process of the legislature

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is assumed to follow a bargaining game. In our model, as with the previous three

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papers, the federal government is not constrained to set uniform standards for

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different states. However, we do not discuss how the federal government reaches its

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final decision among its members, since our focus is on communication between

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different levels of governments. Instead, we simply assume that the federal

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government takes a decision to maximize the welfare of all states.

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Crémer et al. (1996) explain the reason why the federal government possesses

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less information about local conditions than state governments do. They argue that for

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the federal government, the value of information about local conditions is often less

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than that of the information for state governments. Therefore, the former acquires less

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information and is less informed about local conditions. We provide another

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explanation for the federal government being less informed. This is the pollution

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spillover and the resulting interest divergence, which hinders effective communication

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between state and federal governments. Therefore, our study complements the

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research of Crémer et al. (1996).

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Ulph (2000) studies an environment similar to ours in that state governments

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have more information about the costs of local pollution abatement than the federal

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government does. Unlike in our model, which considers interstate pollution spillover,

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he considers a situation where individual states will engage in environmental dumping 9

ACCEPTED MANUSCRIPT when standards are set at the state level. Another difference is that in his model, the

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federal government commits to a rule of choosing environmental standards and a

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monetary transfer to (or from) state governments as functions of state governments’

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reports about local costs. However, in our model, there is no transfer between two

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levels of governments, and the federal government cannot commit to a rule specifying

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how the environmental standard depends on report from the state governments. Thus,

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our paper is more about communication and information exchange between different

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levels of governments.

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Kessler (2014) analyzes a similar communication problem between the federal

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and state governments where the federal government cannot commit to the rule

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specifying how the decision depends on report from the state governments. However,

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Kessler (2014) focuses on whether or not a public project should be constructed in

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one state when the project can bring positive benefit for other states. Therefore, the

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federal government’s choice is binary, while the choice of environmental standards in

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our model can be any positive real number.

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In an abstract and theoretical model, Dessein (2002) studies communication

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between an advisor and a decision maker who needs to choose a real number from a

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closed interval. This model is suited to analyze our problem, which is about

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communication between state and federal governments where the federal government

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needs to choose an environmental standard from a continuous interval. Our paper can

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be seen as an application of Dessein’s (2002) finding to the issue of dividing the

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environmental standard-setting authority between different levels of government. We

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find that the federal government in the current paper can be seen as the decision

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maker in Dessein (2002) and the state government is the advisor. Centralized

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governance is equivalent to communication in Dessein (2002), and decentralized

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governance corresponds to delegation in Dessein’s model. Our contribution here is the finding that the problem of setting an appropriate

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environmental standard to control pollutant emissions can be formulated as a problem

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of minimizing a loss function, which is a quadratic function of the deviation of the

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chosen standard from the optimal standard. In addition, we also find that the interstate

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spillover of pollution leads to a disagreement between the federal and state

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governments regarding the ideal environmental standards. With greater pollution

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spillover, the divergence between the federal and state governments is also greater.

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These findings suggest a possible application of the abstract and mathematical model

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of communication, such as the Dessein (2002) model, in solving practical problems

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such as setting environmental standards.

There exists a literature that uses empirical methods to investigate whether

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emission standards set by state governments are lax when there are interstate

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spillovers. Sigman (2005) finds more pollution in interstate rivers than rivers within

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states in the United States. In a cross-country study, Sigman (2014) finds long-lived

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water pollutants, which have great spillover effect, are lower in nations with more

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centralized governments.

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Several papers also use empirical methods to compare the efficiency levels of

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environmental standards set by the federal and state governments. Banzhaf and Chupp

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(2012) empirically find that for the air pollution in the United States, the total welfare

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under environmental standards set by state governments is about 31.5% lower than

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that under efficient environmental standards, while that under the uniform standard set

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by the federal government is only 0.2% lower than the efficient standards. The authors

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argue that air pollution can easily spillover to other regions, thus the authority of 11

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standards setting should be assigned to the federal government. See Muller and

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Mendelsohn (2009) for a similar study. In conclusion, the existing research that considers situations where the federal

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government sets environmental standards for different states has not considered

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communication between state and federal governments. It has not considered the

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impact of the divergence of state interests on communication, either. Since the federal

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government lacks information, communication with the state governments plays a key

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role in the federal government’s determination of environmental standards. Therefore,

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the communication process should be studied more carefully.

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3. Material and Methods: A Model of Environmental Standards and

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Communication between Governments

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In this section, we use a theoretical model to demonstrate the communication process

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between state and federal governments in setting emission standards, when the

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pollutant emitted in one state spills over to other states. In order to do this, we first

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analyze the benefit and cost faced by governments when they set standards to reduce

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pollution emissions. Then, we consider the case where information about the cost of

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emission control on state economies is asymmetrically distributed between state and

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federal governments. In this case of asymmetric information, we analyze how state

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government communicates with the federal government.

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3.1 A Model of Controlling Emission by Setting Emission Standards

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Based on the theoretical model of Barrett (1994) and Ulph (1996) 3 , we

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investigate the government’s choice of state environmental standards when pollutants

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Barrett (1994) and Ulph (1996) discuss environmental governance in international trade. Every

country has the motivation to set a loose environmental standard to give domestic firms a competitive 12

ACCEPTED MANUSCRIPT spill into other regions. We choose this model because of its several advantages. First,

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the model considers all parties affected by the pollution, including the polluting firms,

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consumers of the products by these firms, residents other than consumers and the

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government. Second, the model adopts widely accepted measures of well-being such

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as consumer surplus and firms’ profit. Finally, the model is simple and can be easily

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adapted to study information asymmetry and communication between different levels

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of government.

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There are two states A and B , in each of which a firm is located. The

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production process of each firm generates pollution that harms the local environment

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and spills over into the other state. Every state has a state government. Above the two

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state governments, there is a federal government. The government (either the state or

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the federal government) can control the pollution discharge of firms by setting an

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upper limit of pollutant emission allowed in each state.

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The output level of the firm in state i is denoted as q i , where i denotes the

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state under consideration and is either A or B . Suppose that the firm’s marginal

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cost of production is constant, which is normalized to zero. The production of the firm

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generates pollution. Following the literature, we assume that the production of a unit

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of output generates one unit of pollutant (See also Ulph, 2000).

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The government (the state or federal government) sets the emission limit for the

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firm in state i , denoted as ei . We assume that demand for the product of the firm in

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each state is large enough so that the emission limit set by the government is strictly

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less than the amount of pollutant generated by the firm’s production. In other words,

advantage in international trade. This paper applies their model to discuss the relations between regions under the federal government. In this paper, we assume that firms in each region only sell to consumers in that state, and we do not discuss the competition between firms. We then add the assumption of interstate spillover of pollutants. 13

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the emission limit is restrictive. To meet the limit, the firm must reduce its emission of

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pollutant by q i − ei units. In general, reducing pollutant emission brings additional costs to the firm (in

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addition to the production cost), because the firm needs to switch to a cleaner but

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usually more expensive way of production or to purchase additional equipment to

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treat pollutant. Typically, the cost increases in the units of reduced emission. In

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addition, the incremental cost of reducing an additional unit of emission increases in

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the amount of emission reduced. We assume that for the firm in state i , the cost of

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reducing q i − ei units of emission is equal to (qi − ei ) 2 2 , which is the simplest

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form that satisfies aforementioned properties.

The firm in each state sells its output to consumers in the state. Suppose that in

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state i , consumers’ demand for output by the firm is Di ( pi ) = X i − pi , where

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Di ( pi ) denotes the amount of output that consumers are willing to buy when the

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price of the output is pi . Notice that this amount of demanded output is also the

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highest amount that the firm are able to sell under price pi . In the demand function,

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X i is a parameter reflecting the magnitude of consumers’ demand: under a greater

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X i , consumers are willing to buy a greater amount of output at each price level. The

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firm knows the demand function of consumers and chooses a price of its output to

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maximize its profit, which is equal to the firm’s revenue minus the total cost that the

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firm has to pay during production and emission reduction.

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We assume that the government first decides the upper limit of emission allowed

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in state i and makes the decision public. Then, after knowing the limit set by the

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government, the firm in state i chooses its price level to maximize its profit. It is

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straightforward to see that under the emission limit ei set by the government, the 14

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profit-maximizing price level of the firm in state i is pi (ei ) = (2 X i - ei ) 3 . Under this

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price, the profit of the firm is π i (ei ) = (−2ei + 2 X i ei + X i ) 6 and the well-being of

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consumers in state i , reflected by consumer surplus, is CS i (ei ) = ( X i + ei ) 2 18 . The

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sum of consumer surplus and profit of the firm in the state represents the economic

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benefit that residents in state i receive from the firm’s production and is equal to

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+ 8 X i ei + 4 X i2 18 .

The above economic benefit of state i decreases as the emission limit in the state

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becomes stricter ( ei decreases). This is because a stricter emission limit forces the

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firm to reduce more emission, which increases its cost. A greater cost implies a higher

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price, a lower production level and a lower profit. In addition, the higher price reduces

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the consumer surplus in the state. This relationship between emission standards and

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economic benefit is consistent with empirical findings in Greenstone (2002) and

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Greenstone et al. (2012).

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In particular, when the emission standard decreases by one unit, the economic

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benefit of the state drops by (− 5ei + 4 X i ) 9 . Notice that the loss in economic benefit

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associated with one unit decrease in the emission standard increases in the magnitude

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of consumers’ demand X i : when consumers have a higher demand for the firm’s

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product, the loss in the economic benefit is greater. So we sometimes denote X i as

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the cost of emission control on the state economy.

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Pollutants emitted by the firm in one state damage both the environment of home

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state and that of the other state. Typically, a larger amount of emission causes a

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greater environmental damage. For the reason of tractability of the following analysis,

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we assume that the damage on environments of home and the other states increases in

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a linear fashion as the amount of emission increases. In particular, when the firm’s 15

ACCEPTED MANUSCRIPT emission is ei in state i, the damage on the environment of home state is ei and the

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damage on the environment of the other state is κei . Here, the parameter κ ≥ 0

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represents the degree of interstate spillover. Therefore, the total damage on the

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environment of state i by discharged pollutants is ei + κe j , where e j represents the

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emission of the firm in the other state. The table that summarizes notations of the

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model can be found in the appendix.

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minus the damage of state environment, which is

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8

The welfare of state i is equal to the economic benefit of residents in the state

) 18 − e − κe . i

j

M AN U

7

RI PT

1

The above state welfare demonstrates a trade-off between economic benefit (the

11

first term in the above expression) and environment protection (the second term)

12

when the government sets emission limit ei . A stricter emission limit (a lower ei )

13

implies a lower economic benefit of the residents in the state but a smaller

14

environmental. Therefore, an appropriate emission standard involves a balance

15

between economic benefit and environment protection.

16

3.2 Government’s Choice in Emission Standards

EP

TE D

10

In this subsection, we analyze government’s decision in setting emission

18

standards. We discuss two distinct institutional arrangements for setting state emission

19

standards. The first one is the decentralized model where the permitted level of

20

emissions in each state is determined by the respective state government. The second

21

is the centralized model in which the federal government determines the limits of

22

emission in the two states. We assume that the goal of each state government is to

23

maximize the welfare of the respective state, while the federal government maximizes

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17

16

ACCEPTED MANUSCRIPT 1

the total welfare of two states. The main objective of our paper is to compare the total

2

welfare of the two models. In the decentralized model, state government in state i chooses the discharge

4

standard ei to maximize the welfare of the state, given the discharge limit in the

5

other state, e j . In other words, the state government’s problem is:

6

Max ei

RI PT

3

SSi (ei , e j ) .

Thus, the optimal emission standard for the state government is

8

ei ( X i ) = (4 X i − 9) 5 .

9

On the other hand, in the centralized model, if the federal government has

10

information about local conditions, the government chooses emission standards in two

11

states to solve the following problem:

Max ei , e j

13 14

∑ SS (e , e ).

i∈{A, B }, j ≠ i

i

i

j

M AN U

d

Hence, from the perspective of the federal government, the optimal emission standard in state i is

TE D

12

SC

7

15

ei ( X i ) = (4 X i - 9 - 9κ ) 5 .

16

The optimal standards for the federal government represent the efficient standards,

17

i.e., the standards that achieve the highest possible total welfare level. Notice that

18

when κ > 0 , ei ( X i ) > ei ( X i ) . This is because state governments are interested in

19

the welfare of their own state and ignore the benefit of emission control on the

20

environment of the other state. Therefore, state governments set standards that are too

21

lax from the perspective of the federal government, who takes the benefit of pollution

22

control on the other state into consideration.

AC C

EP

*

d

*

17

ACCEPTED MANUSCRIPT Up to now, information is symmetrically distributed across different levels of

2

governments: both state and federal governments perfectly know everything about the

3

firm and consumers in each state. In the next subsection, we will relax this assumption

4

and study a situation in which state governments are better informed about situations

5

in the state than the federal government is. Our aim is to study communication

6

between two levels of governments.

7

3.3 Information Asymmetry and Communication between federal and state

8

governments

SC

RI PT

1

In reality, state governments usually possess more information than the federal

10

government does about situations in the state. The reason is that it is usually less

11

costly for state governments to acquire information about the firm and consumers than

12

it is for the federal government. This is because state governments have already

13

possessed some preliminary information about the firm and consumers during

14

day-to-day interaction with them.

TE D

M AN U

9

In this subsection, we explicitly impose the asymmetry of information across

16

different levels of governments. Our aim is to investigate how the federal government,

17

who possesses less information, communicates with state governments, who

18

possessed more information. In addition, we study how the federal government

19

determines the emission standards of pollutants after exchanging relevant information

20

with state governments.

AC C

21

EP

15

In particular, we assume that the federal government is uninformed about the

22

magnitude of consumer demands in each state (or the cost of emission control on state

23

economies) while state governments know this information. Formally, the magnitudes

24

of consumer demand in the two states, X A and X B , are assumed to be two

25

independent random variables, both of which follow uniform distribution on interval 18

ACCEPTED MANUSCRIPT 1

[1,2] .4 Each state government observes the realization of demand magnitude in the

2

respective state but the federal government is uninformed about the realization. Due to

3

lack of information, the federal government communicates with state governments

4

before choosing emission standards. Following Crawford and Sobel (1982), a seminal paper on strategic

6

communication, we model the communication between two levels of governments as

7

the following process. First, each state government, knowing the magnitude of

8

consumer demand in the respective state, reports that information to the federal

9

government. The reported magnitude can be any number between 1 and 2 and may

10

not be equal to the true demand magnitude. After getting reports from two state

11

governments, the federal government estimates demand magnitudes in two states.

12

Finally, based on that estimation, the federal government determines environmental

13

standards for the two states.

M AN U

SC

RI PT

5

We denote the reporting strategy of state government in state i by ri ( X i ) ,

15

which means that the state government sends report ri ( X i ) to the federal

16

government when the demand magnitude in the state is X i . Given the report ri of

17

state government, the federal government estimates the demand magnitude in state i ,

18

denoted by conditional expectation Ei ( X i ri ) . Based on the report ri of state

19

government and the federal government’s estimate about the demand magnitude in

20

state i, the federal government sets environmental standards for the state, denoted by

21

ei (ri ) .

AC C

EP

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14

c

22

We focus on Perfect Bayesian Equilibrium (the “equilibrium”) of the

23

communication game between governments. The equilibrium requires the following 4

The assumption of uniform distribution is made for convenience for the following calculation, while interval

[1,2] can be extended to any closed interval. 19

ACCEPTED MANUSCRIPT 1

conditions to hold: (a) given the way that the emission standards set by the federal

2

government depend on the report of state government, ei (ri ) , the report chosen by

3

each state government maximizes the welfare of the respective state; (b) given the

4

way that the federal government’s estimate depends on the report of state government,

5

the environmental standards set by the federal government for the two states

6

maximize the total welfare of two states; and (c) the estimates of the federal

7

government can be derived from the reporting strategies of state governments by

8

using Bayes’ Law.

SC

RI PT

c

In the next subsection, we prove a preliminary result that in equilibrium, the two

10

levels of governments cannot communicate with each other truthfully and completely.

11

3.4 State and Federal Governments cannot Communicate Completely and

12

Truthfully

M AN U

9

According to condition (b) in the previous subsection, after receiving reports rA

14

and rB from state governments, the discharge standards chosen by the federal

15

government, eA (rA )，eB (rB ) , solves the following problem:

Max e A ,eB

18

19 20

c

)

  E X A , X B  ∑ SSi (ei , e j ) rA , rB  . i∈{A, B}, j ≠ i 

The solution to the above problem implies that

AC C

17

c

EP

16

(

TE D

13

eic (ri ) =

4 E ( X i | ri ) − 9 − 9κ . 5

(1)

Given the environmental standard set by the federal government as shown in

equation (1), the expected welfare of state i equals

20

ACCEPTED MANUSCRIPT

[

E X j SSi (eic (ri ), e cj (rj )) X i

{[

]

] 18 − κe (r ) X } ] 18 - κE [e (r )]

= E X j − 5ei (ri ) + (8 X i − 18)ei (ri ) + 4 X i 1

[

c

2

c

= − 5ei (ri ) + (8 X i − 18)ei (ri ) + 4 X i c

2

c

2

2

c

j

j

i

(2)

c

Xj

j

j

  4E( X i | ri ) − 9 − 9κ  2  4E( X i | ri ) − 9 − 9κ 2 c = − 5 + (8 X i − 18) + 4 X i  18 - κE X j e j (rj ) .  5 5    

[

]

The state government in state i chooses a report to maximize (2).

3

We prove that there cannot be complete and truthful communication between

4

state and federal governments when pollutant emission has interstate spillover. To

5

prove this result, suppose by contradiction that the communication is complete and

6

truthful. For this to be the case, state governments must report demand magnitude

7

completely and truthfully. In other words, the reporting strategy of state government

8

i is ri ( X i ) = X i . According to equilibrium condition (c), the estimate of the federal

9

government about demand magnitude in state i is equal to that reported by the state

10

government, i.e., E ( X i ri ) = ri . This implies that the federal government sets an

11

emission limit eic (ri ) = (ri − 9 − 9κ ) 5 for the state, and the welfare of state i under

12

the emission limit is

(

) [

TE D

M AN U

SC

RI PT

2

]

[

]

13

SSi ei (ri ), e j = − (4ri - 9 - 9κ ) 5 + (8 X i − 18)(4ri - 9 - 9κ ) 5 + 4 X i 18 − κE X j e j (rj ) .

14

The report of state government i that maximizes the above state welfare is

15

ri ( X i ) = X i + 9κ 4 .

2

c

EP

2

AC C

16

c

When pollution emission spills over into the other state, i.e., when κ > 0 , the

17

optimal report for state government i, ri ( X i ) = X i + 9κ 4 , is strictly greater than the

18

true demand magnitude X i . This contradicts with our hypothesis that state

19

governments report information completely and truthfully. Thus, we prove that there

20

cannot be complete and truthful communication between state and federal

21

governments in equilibrium. 21

ACCEPTED MANUSCRIPT The underlying reason why the two levels of governments cannot fully

2

communicate with each other is that they disagree on the optimal emission standards

3

when there is interstate pollution spillover: the emission standards optimal for state

4

governments are laxer relative to those optimal for the federal government. Therefore,

5

state governments have an incentive to choose a report of demand magnitude higher

6

than the true level, in order to induce the federal government to set a laxer emission

7

standard. Knowing state government’s incentive to exaggerate the demand magnitude,

8

the federal government does not take the report from state government at face value.

9

3.5 Communication Between Governments in Equilibrium

SC

RI PT

1

In this subsection, we characterize how state governments communicate with the

11

federal government in equilibrium and how much information can be exchanged

12

during communication between governments. Suppose that state government in state

13

i needs to choose between two reports, denoted by ri and ri′ , to be sent to the

14

federal government. Also suppose that the federal government’s estimate about

15

demand magnitude in state i when receiving report ri is lower than that when

16

receiving report ri′ . In other words, Ei ( X i ri ) < Ei ( X i ri′) .

TE D

M AN U

10

From equation (2), when Ei ( X i ri ) < Ei ( X i ri′) , the welfare of state i when

18

reporting ri is strictly greater than that when reporting ri′ , if and only if the true

19

demand magnitude of state i , X i , is greater than a threshold value. This implies that

20

the state government strictly prefers reporting ri to ri′ when X i is greater than the

21

threshold value. More generally, the optimal reporting strategy of the state

22

government takes the following form. The interval of demand magnitudes, [1,2], is

23

divided into several subintervals. Under demand magnitudes that fall into the same

AC C

EP

17

22

ACCEPTED MANUSCRIPT 1

subinterval, the state government sends the same report. Under magnitudes that fall in

2

different subintervals, the state government sends different reports. We denote the number of subintervals by N and the l -th subinterval by

4

[ X i , l −1 , X i ,l ] for l=1,2,…,N. Notice that X i , 0 = 1 and X i , N = 2 . Also, denote by ri ,l

5

the report sent by state government i when X i falls in subinterval [ X i , l −1 , X i ,l ] .

6

When the demand magnitude in state i is just at the boundary point X i ,l between

7

subintervals [ X i , l −1 , X i ,l ] and [ X i ,l , X i , l +1 ] , state government in state i is indifferent

8

between sending reports ri , l and ri ,l +1 . In other words,

SC

  4 E (X i | ri ,l ) − 9 − 9κ  2  4 E (X i | ri ,l ) − 9 − 9κ 2 c + 4 X i ,l  18 - κE X j e j (r j ) = − 5   + (8 X i ,l − 18) 5 5    

M AN U

9

RI PT

3

[

]

  4 E (X i | ri ,l +1 ) − 9 − 9κ  2  4 E (X i | ri ,l +1 ) − 9 − 9κ 2 c + − + ( 8 X 18 ) 4 X − 5  i ,l i ,l  18 - κE X j e j (r j ) .  5 5    

[

]

The above expression can be simplified as

11

E (X i | ri ,l ) + E ( X i | ri ,l +1 ) - 9κ 2 = 2 X i ,l .

12

Knowing that state government i sends report ri , l whenever the demand

13

magnitude of state i falls in subinterval [ X i , l −1 , X i ,l ] , by Bayes’ law, the federal

14

government believes that X i is uniformly distributed in the subinterval [ X i , l −1 , X i ,l ]

15

when receiving report ri , l . Therefore, the federal government’s estimate of demand

16

magnitude in state i is E ( X i ri ,l ) = ( X i ,l −1 + X i ,l ) 2 . Substituting this into equation (3),

17

we have that

(3)

AC C

EP

TE D

10

18

X i , l +1 = 2 X i ,l − X i ,l −1 + 9κ .

19

According to the results in Crawford and Sobel (1982), an equilibrium exists in

20

the communication game between federal and state governments. In equilibrium, state

21

government i partitions [1,2] into N subintervals. The boundary points of the

(4)

23

ACCEPTED MANUSCRIPT 1

partition are given by first-order difference equation (4), initial value condition

2

X i , 0 = 1 , and end value condition X i , N = 2 .

4 5 6

We in addition establish that the number of subintervals, N, cannot be too large. By iteratively repeating equation (4), we have that

X i , l +1 = (l + 1) X i ,1 − lX i , 0 + 9l (l + 1)κ 2 , which, evaluated at l = N − 1 , is

RI PT

3

X i , N = NX i ,1 − ( N − 1)X i , 0 + 9 N ( N − 1)κ 2 .

8

Substituting X i , 0 = 1 and X i , N = 2 into the above expression, we have

9

X i ,1 = 1 + 1 N - 9( N − 1)κ 2 .

11

M AN U

10

SC

7

From the fact that X i ,1 must be strictly greater than X i , 0 , which is equal to 1, we have that

N ( N − 1) ≤ 2 (9κ ) .

13

We denote the greatest integer N that satisfies the above inequality by N (κ ) .

TE D

12

Notice that N (κ ) is finite for any positive degree of spillover κ > 0 . This implies

15

that after receiving the report from state government, the federal government only

16

knows the subinterval that the demand magnitude of the state belongs to, but not the

17

exact position in the subinterval. In this sense, the federal government cannot fully

18

communicate with state governments.

AC C

19

EP

14

When κ ≤ 1 / 9 , N (κ ) ≥ 2 and the federal government can exchange partial

20

information with state governments: from the report of state government, the federal

21

government has a finer knowledge about demand magnitude in the state, compared to

22

the federal’s initial knowledge before the communication. Also, notice that N (κ )

23

decreases in the degree of spillover, κ . This means that with a greater spillover, there

24

ACCEPTED MANUSCRIPT 1

is greater information loss in the communication between the federal and state

2

governments. When spillover is large enough, in particular when κ ≥ 1 / 9 , N (κ ) = 1

3

and interval [1,2] is the only subinterval. In this case, no information can be

4

exchanged between state and federal governments. In the next section, we characterize the level of expected total welfare of two

6

states under the emission standards set by the federal government, who choose the

7

standards after communicating with state governments regarding local conditions.

8

4. Welfare Comparison between Centralized and Decentralized

9

Standard Settings

M AN U

SC

RI PT

5

Based on the equilibrium reporting strategies of state governments characterized

11

in the previous section, we discuss the total welfare level of two states under the

12

environmental standards set by the federal government in the centralized model. Then,

13

we calculate the total welfare in the decentralized model. Lastly, we compare the total

14

welfare in the centralized model with that in the decentralized model, under different

15

degrees of interstate spillover.

In the centralized model, the expected total welfare equals

EP

16

TE D

10

[

]

  E X A , X B  ∑ SS i eic (ri ), e cj (r j )   i∈{A , B }, j ≠ i 

[

AC C

17

=

E {[- 5 e (r ) + (8 X ∑ { }

i∈ A , B

18 19

]

  2 = E X A , X B  ∑ - 5 eic (ri ) + (8 X i − 18 )eic (ri ) + 4 X i2 18 − κ e cj (r j )  i∈{A , B }, j ≠ i  Xi

c i

2

i

i

] }

− 18 − 18 κ )eic (ri ) + 4 X i2 18 .

According to the reporting strategies of state governments characterized in the previous section, the above equation can be written as

25

ACCEPTED MANUSCRIPT  X i , l  c 2 c 2  ∫ − 5ei (ri ,l ) + (8 X i − 18 − 18κ )ei (ri ,l ) + 4 X i dX i 18  ∑ ∑ i∈{A , B } l =1  X i , l −1   X X 2 i ,l  4 X i − 9 − 9κ  1 N (κ ) 1 i ,l  c 2 2 dX i + 36 X i − 72 (1 + κ )X i + 81(1 + κ ) dX i  = ∑  − 5 ∫ e i (ri ,l ) ∫  9 l =1  X i , l −1  5 5 X i , l −1    X i ,l  16 N (κ )  (X i ,l − X i ,l −1 ) ∫ [E (X i ri ,l ) − X i ]2 dX i −  ∑ X i ,l − X i ,l −1 1  5 l =1  X i , l −1 =   9  3 N (κ )  3 3 2 2 2  + 5 ∑ 4 X i ,l − X i ,l −1 − 12 (1 + κ ) X i ,l − X i ,l −1 + 27 (1 + κ ) ( X i ,l − X i ,l −1 )  l =1   N (κ ) 1  16  1 3 2 = ∑  − ( X i ,l − X i ,l −1 )Var ( X i ri ,l ) + × 28 − 36 (1 + κ ) + 27 (1 + κ ) 9 l =1  5 9 5  N (κ )

[

]

[

)

(

]

)

RI PT

[(

]

[

2 3

=−

[

[

]

4 N (κ ) 1 3 2 ∑ (X i ,l − X i ,l −1 ) + 15 28 − 36(1 + κ ) + 27 (1 + κ ) . 15 × 9 l =1

]

According to (4) and (5), we have that

(6)

M AN U

1

(X i ,l − X i ,l −1 )2  1 1 N (κ ) 16 2 ( ) X X 28 − 36 (1 + κ ) + 27 (1 + κ ) − −  + ∑ i ,l i , l −1 9 l =1  5 12 15 

SC

=

]

X i ,l +1 = 1 + (l + 1) N (κ ) − 9(l + 1)[N (κ ) − 1 − l ]κ 2 ,

4

which implies that X i , l − X i ,l −1 = 1 N (κ ) − 9[N (κ ) + 1]κ 2 + 9κl . Substituting this into

5

(6), the expected total welfare in the centralized model is

[

]

6

18κ + 19 3 4 2 . + 4 - N (κ ) κ 2 − 2 15 5 135 N (κ )

7

Next, we characterize the total welfare in the decentralized model. The expected

TE D

total welfare equals

EP

8

[

10

]

  E X A , X B  ∑ SS i eid ( X i ), e dj (X j )  i∈{A, B}, j ≠i 

AC C

9

(7)

[

]

  2 = E X A , X B  ∑ - 5eid ( X i ) + (8 X i − 18)eid ( X i ) + 4 X i2 18 − κe dj (X j ). i∈{A, B}, j ≠i  Substituting the environmental standard set by the state government,

11

eid ( X i ) = (4 X i − 9) 5 , into the above equation, the total welfare in the decentralized

12

model is

26

ACCEPTED MANUSCRIPT

1

  5  4 X i − 9 2 4 2 4 X j − 9   E X A ,X B  ∑    + Xi −κ  5   i∈{A,B}, j ≠i 18  5  18  4 9(1 + 2κ ) 2 = 2 E X i  X i2 − (1 + κ )X i + 5 10  5 18κ + 19 . = 15

( )

(8)

where we have used the facts that E X i X i2 = 7 3 and E X i ( X i ) = 3 2 when X i is

3

uniformly distributed on interval [1,2].

RI PT

2

Comparing (7) and (8), we find that when N (κ ) ≥ 2 or equivalently, when

5

κ ≤ 1 9 , the expected total welfare in the centralized model is lower than that in the

6

decentralized model. This finding replicates the result in Dessein (2002) that

7

communication is inferior to delegation whenever communication is informative. On

8

the other hand, when κ > 1 9 , the communication between state and federal

9

governments is completely uninformative and the comparison of expected total

10

welfare depends on the value of κ . When 1 9 < κ ≤ 2 9 3 , the expected total

11

welfare level in the centralized model is lower than that in decentralized governance.

12

When κ > 2 9 3 , the expected total welfare in the centralized model is higher.

13

Figure 1 illustrates the comparison of expected total welfares between the centralized

14

and decentralized models.

AC C

EP

( )

TE D

M AN U

SC

4

27

( )

ACCEPTED MANUSCRIPT 1.6 Centralized Standard Setting Decentralized Standard Setting 1.55

1.45

RI PT

Expected Social Welfare

1.5

1.4

1.35

0

0.02

0.04

1 2

0.06

0.08 0.1 0.12 Degree of Spillover, k

0.14

0.16

0.18

0.2

M AN U

1.25

SC

1.3

Figure 1. Total Welfare Comparison between Centralized and Decentralized Models

3

The comparison of expected total welfares between centralized and decentralized

5

models is an application of the result of Dessein (2002). When the spillover is small

6

enough, the environmental standards optimal for state environments are also

7

arbitrarily close to the efficient standards preferred by the federal government.

8

Therefore, with a sufficiently small degree of spillover, the federal government can

9

communicate almost all information with state governments in the centralized model.

10

The result is that the environmental standards set by the federal government are

11

arbitrarily close to those efficient standards that the federal government would choose

12

when it has full information. On the other hand, the emission standards chosen by

13

state governments are also arbitrarily close to the efficient ones when the pollution

14

spillover becomes sufficiently small.

AC C

EP

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4

15

However, the speed that the standards approach the efficient ones is different in

16

the decentralized and centralized models. As the degree of spillover approaches zero, 28

ACCEPTED MANUSCRIPT 1

the standards in the decentralized model approach the efficient ones at a higher rate

2

than that in the centralized model. Therefore, when the spillover is small enough, the

3

total welfare in the decentralized model is greater than that in the centralized model.

4

5. Discussion and Conclusion Our model involves several simplifying assumptions, including uniform

6

distribution of consumer demand and linearity of environmental damage in the

7

amount of emitted pollutants. These assumptions simplify the theoretical calculation

8

and lead to a successful characterization of the equilibrium strategy for state and

9

federal governments.

SC

RI PT

5

For example, under linear damage of emitted pollutants, the welfare level of each

11

state takes a quadratic form in the deviation of the actual emission limit from the

12

optimal limit. The quadratic form of welfare implies whether an emission limit is

13

better for a state government than another one depends on whether the former one is

14

closer to the optimal limit than the latter is. In other words, given any two emission

15

limits, state governments with optimal limits lower than the average of the two limits

16

prefer the lower limit. This implies that the strategies of state governments in

17

communicating with the federal government take a simple form. That is, given several

18

limits chosen by the federal government, the interval of possible consumer demands is

19

partitioned into several subintervals. State governments whose optimal limit lies in a

20

subinterval prefers one emission limit to all the others. In addition, quadratic forms of

21

welfare, together with the assumption of uniform distribution of consumer demand,

22

allow an easy calculation of the expected total welfare. Although the above

23

assumptions are not always satisfied in real life, they allow an analytical expression of

24

total welfare under different assignments of the decision-making authority and an

25

accurate characterization of the better assignment.

AC C

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10

29

ACCEPTED MANUSCRIPT In conclusion, the insufficient investment in interregional pollution governance

2

has been one of the main factors that influence sustainable economic growth and

3

quality of life of residents. This paper applies a game-theoretical analysis under

4

asymmetric information to analyze the feasibility of centralized governance of

5

interregional pollution by the federal government. We focus on investigating interest

6

divergence and information communication between state and federal governments.

7

We also explore the magnitude of the total welfare of all states achieved when

8

interregional pollution regulation is centralized by the federal government. We discuss

9

the assignment of decision-making authority across different levels of government

SC

that best addresses interregional pollution.

M AN U

10

RI PT

1

Due to the interstate spillover of pollution, the optimal emission limit in the state

12

for the state government is higher than that for the federal government since the state

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government ignores the benefit of emission control on other states. Because of this

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difference in the most preferable emission limits, state governments would want to

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report a higher cost than the true level to induce the federal government to set a higher

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emission limit. This incentive hinders effective communication between governments

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and makes the environmental standards set by the federal government inefficient.

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Our research indicates that both centralized governance by the federal

19

government and decentralized governance by state governments have their own

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benefits and drawbacks in the regulation of interregional pollution. When the

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interstate spillover of pollutants is less than some specific critical value, decentralized

22

setting of environmental standards by state governments achieves a greater total

23

welfare than the centralized governance. However, when the spillover is greater than

24

the critical value, centralized setting of environmental standards by the federal

25

government achieves a greater total welfare.

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ACCEPTED MANUSCRIPT Although this result is similar to the previous finding of the literature, the reason

2

is quite different. Previous research also finds that when the interstate spillover is

3

large enough, environmental setting at the federal level is better than that at the state

4

level. However, in previous literature, the spillover only affects the efficiency of

5

standard setting at the state level, but not that at the federal level. This is not true

6

when the federal government sets environmental standards after communicating with

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state governments about local conditions, because spillover also affects the interest

8

divergence between governments and affect the quality of their communication. In a

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wider sense, our results indicate the importance of recognizing information

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asymmetry and communication between different levels of government and the

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impact of interest divergence between different governments on the quality of

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communication.

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The predictions of the model can be tested empirically. For example, in our

14

theoretical model, when the degree of pollutant spillover is sufficiently large, the

15

federal government cannot communicate with state governments about local

16

conditions and therefore, the federal government sets the same standard for different

17

states. Thus, our model predicts a positive relationship between the degree of spillover

18

and uniformity of environmental standards set by the federal government. We can

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empirically test this relationship by investigating whether for pollutants with greater

20

spillover, the emission standards set by the federal government is more uniform across

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different states.

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This paper analyzes an extreme case where the federal government cannot make

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any ex ante commitment regarding the setting of standards according to the reports of

24

states. However, for some pollutants with interstate spillover, such a commitment is

25

feasible to the federal government. Future research will focus on the communication 31

ACCEPTED MANUSCRIPT 1

between federal and state governments when the federal government has the ability to

2

commit to a standard ex ante.

3

Acknowledgments

5

This work was supported by the Major Basic Theory of Fundamental Research Funds

6

for the Central Universities (grant number JBK151123) and the Major Projects in

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Philosophy and Social Science Research of the Ministry of Education of China (grant

8

number 14JZD031).

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References

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Appendix.

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contracts model. Eur. Econ. Rev. 40, 61-89.

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Seabright, P., 1996. Accountability and decentralization in government: an incomplete

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For the ease of reading, we summarize the notations of our model in the following table.

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Table 1. Summary of the model’s notations

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Decision variables and parameters

Descriptions and assumptions Output level and amount of pollutants

qi

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produced by the firm in state i Parameter showing the magnitude of

Xi

consumers’ demand in state i Upper limit on the pollutant emitted by

ei

the firm in state i, chosen by government q i − ei

Amount of emission reduced by the firm in state i

πi(ei)

Profit of the firm in state i

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ACCEPTED MANUSCRIPT κ

Degree of emission spillover

CSi (ei)

Consumer surplus in state i

SSi (ei,ej)

Welfare of state i Emission standard optimal for state

eid(Xi)

X i in state i

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government i, given consumer demand

Emission standard in state i optimal for

ei*(Xi)

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the federal government, given consumer demand X i in state i ri ( X i )

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Report of state government i, given consumer demand X i in state i

ei (ri ) c

Emission standard set by the federal government for state i, after receiving

report ri from state government Consumer demand of state i, expected by

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Ei ( X i ri )

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N (κ )

report ri from state government Maximum number of subintervals that interval [1,2] can be partitioned, given the

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degree κ of spillover Boundary point between different

X i ,l

1

the federal government after receiving

subintervals in the partition of [1,2]

36