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Essays on the implementation of environmental regulations in Canada Eckert, Heather 2001

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E S S A Y S O N T H E I M P L E M E N T A T I O N O F E N V I R O N M E N T A L R E G U L A T I O N S IN C A N A D A by H E A T H E R E C K E R T B . A . , University of Alberta, 1995 M . A . , University of British Columbia, 1996 A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E STUDIES (Department of Economics) We accept this thesis as conforming To the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A August 2001 ©Heather Eckert, 2001 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of E c £ W OWl) C \ The University of British Columbia Vancouver, Canada Date QoJt- 1 ) ; 2QQ DE-6 (2/88) Abstract This thesis examines two important issues concerning the implementation of environmental regulation, with an emphasis on Canada. The first essay presents an empirical examination of inspection and warnings used to enforce inventory regulation for petroleum storage sites in Manitoba. Between 1983 and 1998, Manitoba Environment responded to 97% of inventory violations with a warning. The typical model used to study the enforcement of environmental regulations provides no role for warnings to reduce noncompliance. I develop a two stage probit model based on state dependent enforcement. In the first stage, the probability of an inspection is estimated as a function of site characteristics and violation history. The probability of a violation is then estimated as a function of site characteristics, violation history, and the estimated inspection probability. I find that the probability of a violation is decreasing in the inspection probability, suggesting that inspections and warnings may be effective even if few prosecutions result. The second and third essays examine the possibility that the distribution of regulatory powers between federal and regional governments in countries such as Canada can provide a strategic advantage in international environmental negotiations. I develop a model in which two countries negotiate an agreement on the abatement of a global pollutant. Each country is a federation and its exogenous constitution determines whether the federal or regional governments have jurisdiction over negotiating and enforcing international agreements. The regional governments place less weight on the global benefits of abatement, and therefore display a relative aversion to abatement. The second essay shows that the domestic region's relative aversion to abatement can provide the country with a strategic advantage when the region holds regulatory powers if the region is sufficiently large and the foreign country's regulatory powers lay with either the federal government or a larger ) region. If equal sized regions hold regulatory powers, both countries are worse off relative to federal control in both countries. In the third essay I show hat the federal government can enjoy a similar strategic advantage when the region enforces agreements negotiated by the federal government. ii Contents Abstract i i List of Tables v i List of Figures v i i 1 Introduction 1 2 Inspections, Warnings, and Compliance: The Case of Petroleum Storage Regulation 5 2.1 Introduction 5 2.2 Petroleum Storage Regulation 8 2.3 A Theory of Enforcement and Compliance ... 11 2.4 Empirical Model and Data 17 2.4.1 Estimating Equations 18 2.4.2 The Data 21 2.4.3 Explanatory Variables 25 2.5 Empirical Results 33 2.5.1 The Probability of a Inspection 33 2.5.2 The Probability of a Violation 35 2.6 Predictions and Examples 37 2.7 Conclusions 40 iii 3 International Environmental Agreements and The Level of Domestic Regulatory Power 42 3.1 Introduction 42 3.2 The M o d e l 46 3.3 Solutions and Comparisons 48 3.3.1 Noncooperative E q u i l i b r i a 48 3.3.2 Cooperative E q u i l i b r i a 54 3.4 A n Example 62 3.4.1 F-F Agreement 63 3.4.2 R-F Agreement 63 3.4.3 R-R Agreement 64 3.5 Conclusions 66 4 International Environmental Agreements and Domestic Divisions of Regulatory Power 68 4.1 Introduction 68 4.2 The M o d e l 72 4.2.1 The Players 72 4.2.2 The T i m i n g 73 4.2.3 T h e Payoffs 76 4.3 Solutions and Comparisons 79 4.3.1 Noncooperative Equ i l i b r i a 79 4.3.2 Cooperative E q u i l b r i a 81 4.4 A n Example 96 4.4.1 F-F Agreement 96 4.4.2 R-F Agreement 97 4.4.3 R-R Agreement 99 4.5 Conclusions 101 iv 5 Concluding Remarks 103 6 References 107 7 Appendices 115 7.1 Append ix A 115 7.2 Appendix B 122 v List of Tables Table 2.1: Summary Statistics 135 Table 2.2: Site Ownership 136 Table 2.3: Outlet Type 136 Table 2.4: Region 137 Table 2.5a: Inspections Probit Results 138 Table 2.5b: Inspections Probit Results Continued .... 139 Table 2.6a: Violations Probit Results 140 Table 2.6b: Violations Probit Results Continued 141 vi List of Figures Figure 2.1: Yearly Inventory Inspections 142 Figure 2.2: Yearly Violations per Inspections 142 Figure 3.1: Federal-Federal Threat Point 143 Figure 3.2: Regional-Federal Threat Point 144 Figure 3.3: Regional-Federal Agreement 145 Figure 3.4: Symmetric Regional Threat Point 146 Figure 3.5: Symmetric Regional Agreement 147 Figure 3.6: Regional-Federal and Federal-Federal Threat Points 148 Figure 3.7: Regional-Federal and Federal-Federal Agreements 148 Figure 3.8: Symmetric Regional-Regional and Federal-Federal Threat Points 149 Figure 3.9: Symmetric Regional-Regional and Federal-Federal Agreements 149 Figure 3.10: Asymmetric Regional-Regional and Federal-Federal Threat Points 150 Figure 3.11: Asymmetric Regional-Regional and Federal-Federal Agreements 150 Figure 4.1: Federal-Federal Threat Point 151 Figure 4.2: Regional-Federal Threat Point 152 vii Figure 4.3: R-F Regional Net Benefits With No Transfers ... 153 Figure 4.4 Regional-Federal Agreement (Zero Transfer) 154 Figure 4.4: Regional-Federal Agreement (Positive Transfer) 155 Figure 4.5: Symmetric Regional-Regional Agreement 156 Figure 4.6: Regional-Federal and Federal-Federal Agreements . 157 Figure 4.7: Symmetric Regional-Regional Agreements 157 Figure 4.8: Asymmetric Regional-Regional and Federal-Federal Agreements af=0.5 158 Figure 4.9: Asymmetric Regional-Regional and Federal-Federal Agreements af=0.9 158 viii Chapter 1 Introduction Environmental regulations are becoming increasingly important in countries around the world. This thesis examines two important issues concerning the implementation of environmental regulations, with an emphasis on Canada. Chapter 2 examines the use of warnings to enforce environmental regulations while Chapters 3 and 4 examine the strategic effect that different distributions of regulatory power within a country can have on international environmental agreements. In Chapter 2, we present an empirical examination of the use of inspections and warn-ings to enforce environmental regulations. Regardless of how well environmental policies are designed, if enforcement is lacking, regulation will be ineffective at improving envi-ronmental quality. In Canada, as well as the United States and a number of European countries, violators of environmental regulations are often issued a warning rather than prosecuted. The theoretical model typically used to study the enforcement of environ-1 mental regulations is static and provides no role for warnings to reduce noncompliance. Therefore, the empirical effectiveness of warnings is an interesting question. Chapter 2 provides a study of the use of warnings and inspections to enforce inven-tory regulations for petroleum storage sites in Manitoba between 1983 and 1998. These regulations focus on ensuring the early detection of leaks from storage tanks. In the sample period, Manitoba Environment responded to 97% of violations with a warning. We develop a two stage probit model based on a state dependent enforcement model. According to the model, warnings can increase the future probability of an inspection and expected fines, which can in turn reduce the probability of a violation. We estimate the probability of an inspection at a specific site in a given time period as a function of site characteristics and violation history. The probability of a violation is then estimated as a function of site characteristics, violation history and the estimated probability of an inspection. We find that the probability of an inspection is an increasing function of past violations and that the probability of a violation is decreasing in the probability of an inspection. This provides evidence that, even in the absence of frequent prosecutions, inspections and warnings may be effective at increasing compliance with environmental regulations. In Chapters 3 and 4, we examine the possibility that the distribution of domestic regulatory powers between the federal and regional governments in federations such as Canada and the United States can provide a strategic advantage in the negotiation of international environmental agreements. Chapter 3 asks the specific question of whether 2 a country can be better off when a regional government negotiates and enforces inter-national environmental agreements instead of the federal government. We develop a model in which two countries cooperatively negotiate an agreement on the abatement of a global pollutant. Each country is a federation and its constitution places the power to both negotiate and enforce agreements with either the federal or regional government. We suppose that the federal governments maximize the net benefits of the entire country while regional governments maximize the net benefits of their region. In our model, this has the effect that regional governments display an aversion to abatement relative to the federal governments. It is shown that the relative aversion to abatement of the region can give the country a strategic advantage in the international negotiations. In fact, the country can enjoy the same type of advantage as if it were able to delegate negotiation authority. Specifically, a country is better off when the domestic regional government holds the regulatory power as long as the region is sufficiently large and the foreign country's regulatory powers lie with either the federal government or a larger region. In these cases, there is a substitution of foreign abatement for domestic abatement relative to the agreement signed by both federal governments. As long as the regions preferences are not too far from those of the federal government, the domestic country is better off. On the other hand, when regions of the same size hold regulatory power, both countries are worse off relative to federal control. In this case, neither country enjoys a strategic advantage, and abatement in both countries is lower than if the federal governments hold regulatory power. 3 In Chapter 4, we extend the model of Chapter 3 to examine whether a country can be better off when regional governments enforce agreements negotiated by the federal gov-ernment rather than having both powers lie with the federal government. This question is of particular interest to Canada since the Canadian constitution places the power to ne-gotiate internationally with the federal government while the jurisdiction over enforcing the terms of the agreement often lies with provincial governments. In our model, when enforcement powers lie with regions, the federal government negotiates international agreements subject to the constraint that its region may need to be compensated to ensure enforcement of the agreement. It is assumed that such compensation takes the form of costly lump sum transfers and that transfers are only undertaken if an agreement is reached. It is shown that the regional government's relative aversion to abatement can again give the country a strategic advantage in international negotiations. Here, the making of costly transfers has the effect of committing the federal government to a greater aversion to abatement and the country again enjoys a strategic advantage of the same form as if it were able to hire a negotiator. We show that when the opposing country's federal government holds all regulatory powers, the domestic country is better off having the enforcement power lie with its region as long as the region is sufficiently large. On the other hand, if regions of the same size in both countries hold the enforcement power, neither country can be better off than when the two federal governments hold regulatory powers. 4 Chapter 2 Inspections, Warnings, and Compliance: The Case of Petroleum Storage Regulation 2.1 Introduction In Canada and the United States it is common for environmental regulators to respond to a detected violation by issuing a warning rather than prosecuting the violator. At the same time, there is evidence of relatively high compliance rates.1 According to the traditional static regulatory framework used to study environmental regulation, based on Polinsky and Shavell (1979), if sites face a zero penalty, all sites will violate the regulation. 1See Russell, Harrington, and Vaughn (1986) for a summary of American case studies. 5 In this way, the traditional framework does not provide an active role for warnings. Therefore, it is important to determine whether warnings are empirically effective at reducing noncompliance and examine the mechanism through which warnings work. This chapter empirically examines the use of inspections and warnings to enforce environmental regulations. Although a number of recent studies have examined the interaction between enforcement and compliance, there has been no explicit study of warnings. In fact, most existing studies are based on a regulatory model which does not provide an active role for warnings. Magat and Viscusi (1990) and Laplante and Rilstone (1996) examine the effect of inspections in the American and Canadian pulp and paper industries respectively. The result of the inspections is either not known or not formally examined. Deily and Gray (1991, 1996) examine the interaction of both compliance and plant closings with an aggregate enforcement measure which includes letters, legal orders, and phone calls. Nadeau (1997) considers the separate effects of monitoring actions (inspections) and general enforcement actions (orders and penalties) on the duration of noncompliant spells. In contrast, Helland (1998) is based on a state dependent regulatory model which allows for warnings to be effective but the author examines the role of previous violations on self reporting. Therefore, little is understood about the role and effectiveness of warnings. In this chapter, we use data on monitoring regulations at petroleum storage sites in the province of Manitoba to investigate the use of inspections and warnings. Leaks and spills from petroleum storage sites threaten the environment and human health through 6 fires, explosions, and groundwater contamination. According to a Manitoba Environment information bulletin, "the biggest threat to our ground water supply is from leaking stor-age tanks - 1 litre of gasoline can make 1 million litres of water undrinkable" (Manitoba Environment, 1995). Monitoring regulations ensure the early detection of spills by requir-ing sites to regularly reconcile their product inventory with deliveries and withdrawals. If a site complies, the expected damage from a leak is small since a loss of product is detected immediately by the firm. If the site fails to reconcile inventories, a leak may not be detected until much later when the damage is greater. Manitoba Environment enforces inventory regulations with inspections conducted by environment officers. A key stylized fact is that, between 1983 and 1998, 97% of inventory violations led to the issuing of a warning. Discussions with Manitoba Environment suggest that, in general, warnings are meant to indicate stronger future enforcement. Therefore, we develop an econometric model based on the state dependent enforcement theory of Landsberger and Meilijson (1982) and Harrington (1988). According to this model, a regulator uses an agent's violation history to classify it as "good" or "bad" and sets inspection probabilities and fines for the two groups. That is, Manitoba Environment uses warnings to move sites to the bad group, where they will face stronger enforcement. A two stage probit model of the probability of an inspection and the probability of a violation is estimated for the sample of quarterly observations between 1983 to 1998. The probability that a site is inspected is estimated as a function of its characteristics and violation history. The probability of a violation is estimated as a function of site 7 characteristics, violation history, and the estimated probability of an inspection. Our results suggest that, even in the absence of frequent prosecutions, the probability of an inspection substantially decreases the probability of a violation. As well, although past violations do increase the probability of an inspection, there is evidence that increased enforcement is not the only way in which warnings affect the probability of a violation. The chapter proceeds as follows. Section 2.2 outlines the petroleum storage moni-toring regulations in Manitoba. In section 2.3, the state dependent regulatory model is discussed in the context of petroleum storage regulation. Section 2.4 presents the empir-ical model, the data to be used, and the choice of explanatory variables. The estimation results are outlined in Section 2.5 while section 2.6 presents examples and predictions based on the estimation results. Finally, Section 2.7 concludes. 2.2 Petroleum Storage Regulation This section briefly discusses the history and present state of petroleum storage monitor-ing regulations in Manitoba. The storage of petroleum products has been regulated by the provincial government of Manitoba since 1976. Until 1987, the regulation of petroleum storage was enabled by the Clean Environment Act of 1972 (M.R. 148/76 and C .C .S .M. C130). Although each regulation enabled by the Act set out unique rules and guidelines, the Clean Environment Act stipulated the maximum penalties for noncompliance as five hundred dollars for an individual and five thousand dollars for a corporation. The original version of the Storage and Handling of Gasoline and Associated Products 8 Regulation was passed in 1976 (M.R. 148/76). This regulation governed all storage tanks except aboveground and underground tanks holding less than 4545 litres or 1000 gallons. A key aspect of the 1976 regulation was the requirements regarding the monitoring of tank volumes.2 Above and underground tanks required the following monitoring or inventory procedure.3 A l l tanks except those at bulk plants were to be gauged or dipped daily and these measurements were to be reconciled with receipt and withdrawal records either daily or weekly. The Department was to be informed of any above normal losses recorded in two consecutive reconciliations for aboveground tanks, and four consecutive reconciliations for underground tanks. Normal losses are those of less than 2^% of the capacity of the tank or volume of product for aboveground and less than | of 1% of the capacity or volume for underground tanks. A l l records were to be maintained for 2 years. Therefore, a violation of the monitoring regulations is a failure to undertake reconciliations according to schedule, a failure to keep adequate records, or a failure to report above normal losses. Revisions were made to the regulations in 1980 (M.R. 156/80). The monitoring re-quirements were extended to bulk plants so that daily gauging and weekly reconciliations were now required. As well, operators of above and underground tanks were required to record cumulative apparent losses on a semi annual basis and inform the department if the loss exceeded \ of 1% of throughput for the corresponding period. The remainder of the 1976 regulations were continued. 2The regulation also specifies registration, construction, testing, and supervision requirements. In the case of a large spill or leak, the department could close the site and turn over the case to remediation. 3Specific types of storage facilities, such as heating oil facilities, were exempt from the regulation. 9 In 1987, the government of Manitoba replaced the Clean Environment Act with the Environment Act (C.C.S.M. E125), which significantly increased the maximum penalties for a violation. According to the Environment Act, first time individual offenders are liable to a fine of no more than fifty thousand dollars or to imprisonment for not more than six months, or to both. The maximum penalty for a subsequent offence is one hundred thousand dollars, or imprisonment for not more than one year, or both. A n offending corporation is liable to a fine of no more than five hundred thousand dollars for a first offense and one million dollars for each subsequent offense. At the end of 1990 the regulatory budget was greatly increased and there was a sig-nificant change in enforcement. Prior to 1991, all inspections were performed by a single environment officer based in Winnipeg. At the beginning of 1991, the enforcement of in-ventory regulations was regionalized and more environmental officers began performing site inspections. The province was divided into five regions with at least two environment offices in each region.4 There was not only an increase in the number of inspectors, but the officers are closer to the sites they inspect. However, the regional officers are respon-sible for the enforcement of a number of different environmental regulations whereas the provincial officer focused on the enforcement of petroleum storage regulations prior to 1991. A n important feature of Manitoba's petroleum storage regulation is the use of in-spections and warnings as enforcement tools. Both the Clean Environment Act and the 4 There axe 5 offices in Winnipeg, 3 offices in the Eastern-Interlake region, 2 offices in the South-Central region, 4 offices in the Park-West region, and 3 offices in the North region. 10 Environment Act allow for inspections to enforce regulations. These inspections involve an environment officer visiting a storage site and determining if the inventory reconcilia-tions are performed correctly and if the records are in compliance with the regulations. If a site is found to be in violation, the officer can issue a warning, a legal order, or initiate a prosecution of the owner and/or operator of the site. In reality, the response to most violations of inventory regulations is a warning. Discussions with Manitoba Environment suggest that, although it is at the discretion of the environment officers, warnings are meant to indicate that more serious legal action will result from future violations. There-fore, warnings separate sites into two groups: those that will face prosecution for their next violation, and those that will not face prosecution. 2.3 A Theory of Enforcement and Compliance The traditional approach taken in the environmental enforcement literature derives from Becker (1968) and Polinsky and Shavell (1979).5 In these models, the regulator chooses penalty functions and detection probabilities for the current period. Since the detection probability represents the resource constraint of the regulator, this static model generates a static probability of detection. Therefore, the probability of a detection is constant for all agents. A site will comply if c < pF, where c is the site's cost of compliance, p is the detection (inspection) probability, and F is the fine. As such, increasing the compliance 5 See Heyes (1998) for a discussion of the standard enforcement model and a survey of various extensions. 11 level requires an increase in either the probability of an inspection or the fine. For our purposes, there are two important features of the static model. First, unless past violations provide the regulator information as to the current probability of a viola-tion, past compliance choices of sites do not directly enter the regulator's decision. That is, the only role for past violations is if compliance is lag dependent and the probability of compliance in t is higher if the site was in compliance in the past. The second salient feature of the static model is that there is no role for warnings in reducing violations. If a regulator responds to violations with a warning, then F — 0, and any site with positive compliance costs will violate.6 The typical static model is in sharp contrast to what is observed for petroleum storage regulation in Manitoba. In fact, 97% of detected violations between 1983 and 1998 were issued a warning by Manitoba Environment. The average compliance rate at inspections over the same period was 50% and yearly violations per inspections fell throughout the 1990's (see Figure 2.2). Discussions with Manitoba Environment suggest that, although it is at the discretion of the environment officer, warnings are issued to indicate that a future violation will be prosecuted. Landsberger and Meilijson (1982) propose a model that can explain why warnings, when used to indicate future enforcement, may reduce noncompliance. The model is 6In fact, there are plausible explanations for warnings in this type of model, but they are unsatisfactory for our purposes. First, if sites learn about the regulations and compliance through inspections, sites need not be fined in order to increase compliance. However, in this case, it would not be warnings that reduce violations but the actual inspection. The possibility of learning through inspections is discussed further in the context of our empirical model. Secondly, if there is a positive cost of prosecution, warnings can offer a "cheap" alternative. However, without some threat of future enforcement, the warnings still have no effect on compliance rates. 12 developed for the problem of tax evasion. It is argued that when a single agent may-generate an externality repeatedly, a static detection probability may not be the most efficient use of resources. The authors develop a model in which the enforcement system is state dependent. States are the regulator's classifications of people according to their recent violation record and transitions between states are governed by detected violations. The authors specify the following simple structure to the state dependence. The regulator separates taxpayers into two groups such that pi < p2. Initially, taxpayers are arbitrarily assigned between the two groups. If a person in group 1 is found to be in violation she is transferred to state 2. Individuals in group 2 are transferred into group 1 only if they are detected to be in compliance. In the first stage, the regulator chooses inspection probabilities to maximize govern-ment revenue subject to a resource constraint on the level of inspections and an upper bound on penalties. The regulator is able to commit to her strategy and makes no further decisions. In each subsequent period, individuals choose whether to comply by reporting their income truthfully. In equilibrium, taxpayers choose one of three strategies: comply in both groups, violate in both groups, or violate in group 1 and comply in group 2. 7 By allowing people to make transitions between the two groups, the state dependent system creates the incentive for individuals who violate under static enforcement to violate in group 1 and comply in group 2. Intuitively, people may prefer to comply in group 2 because the probability of being audited is higher than under static enforcement and if 7The strategy of complying in group 1 and violating in group 2 is dominated. 13 audited, they will be moved into group 1 where they face a low audit probability and will violate. The authors show that state dependent enforcement system offers larger feasible expected revenues than the state independent system. Harrington (1988) adapts Landsberger and Meilijson's model to explain the coexis-tence of low enforcement and high compliance with respect to environmental regulations in the U.S. 8 Harrington considers a system in which both inspection probabilities and fines are state dependent with states defined by a site's violation history. The regulator is assumed to know the compliance costs of individual sites.9 Again, sites move between groups according to their compliance status, although Harrington allows for rigidity in the movement from group 2 to group 1. The author assumes that the regulator separates sites into two groups such that pi < p2 and Fx < F2. In the first stage, the regulator chooses pi,p2, Fi, F2 to minimize the resources ex-pended to implement a given compliance rate subject to a maximum fine.10 The regulator commits to her strategy and in each subsequent period, sites decide whether to comply. Again, in the long run stationary equilibrium, sites will either comply in both groups, violate in both groups, or violate in group 1 and comply in group 2. Which strategy 8 Other models which offer alternative explanations for high compliance rates with little enforcement seem less applicable to the case of petroleum storage. For example, Harford (1991a) considers the effect of measurement error in monitoring which is reasonable if the regulator is measuring emissions, but is less important when officers simply inspect inventory records and perform reconciliations. Livernois and McKenna (1999) develop a model in which sites self report emissions, but inventory violations are not self reported. Finally, Heyes and Rickman (1999) consider a model of regulatory dealing in which the regulator uses tolerance in some regulations to increase compliance with other regulations. 9 Raymond (1999) examines the robustness of Harrington's results to the introduction of asymmetric information. 10Harford and Harrington (1991) reconsider the state dependent penalty system when the regulator takes into account the social cost of enforcement. 14 is chosen will depend on the site's compliance cost. Intuitively, sites with intermediate compliance costs will choose to avoid paying for compliance when they face little enforce-ment (pi,Fi) but will comply in group 2 to avoid paying F2. Sites with low compliance costs will comply in both groups and sites with high compliance costs will violate in both groups. The regulator's choice of the two probabilities and two fines determines the number of sites playing each strategy and therefore the number of sites that comply in the two states. Again, the state dependent penalty system induces compliance from sites that would not comply in a static model and the regulator can meet the compliance target at a lower cost than with state independent enforcement. To see why the regulator prefers to set pi < p2 over a single inspection probability p, consider the case when pi = P2 = P- Recall that, for a given site, the regulator is minimizing the expected probability of an inspection subject to site behaviour, a maxi-mum fine, and meeting a compliance rate target. When the probability of an inspection is constant, sites with c < pF will comply and all others will violate. Suppose the reg-ulator decreases pi and increases p2 in such a way that the expected probability of an inspection remains unchanged. When px < p2 and sites can move between groups, a third strategy is introduced: to violate in group 1 and comply in group 2. Depending on the distribution of compliance costs across sites, the number of sites that begin complying in group 2 is larger than the number of sites that begin violating in group 1, and the expected compliance rate increases.11 For example, this is true when compliance costs are 1 1 See Raymond (1999). 15 distributed according to any symmetric distribution. Since it is possible to slacken the compliance target constraint while leaving the value of the objective function unchanged, the regulator prefers to set pi <p2. Similarly, it can be demonstrated that the regulator prefers F i < F2 by considering the effect of decreasing F1 (for a constant F2). When Fi falls, some sites that violate in both groups will begin complying when they are in group 2 because the benefits of being moved into group 1 are higher. On the other hand, some sites which comply in both groups begin violating in group 1 since the costs of violating are now smaller. Again, for some distributions of compliance costs, the shift in the threshold between violating in both groups and violating only in group 1 is larger than the shift in the threshold between complying in both groups and complying only in group 2. A state dependent penalty system offers a possible explanation for Manitoba Envi-ronment's use of warnings. Specifically, warnings can be seen as a way to transfer sites from state 1 to state 2. If a site in group 1 is inspected and found to be in violation of the inventory regulations, it is given a warning and moves into group 2. The site now faces a higher probability of being inspected, and if another violation is found, it will face prosecution. Overall, the general ideas we take from the state dependent models to our empirical model of inventory regulations are as follows. First, the functions defining inspection probabilities and fines are assumed to be chosen at the beginning of the game and remain the same over the sample period. Secondly, the regulator faces a resource constraint that 16 places an upper bound on the expected number of inspections. Thirdly, as opposed to Harrington's model, in which sites are defined by their compliance cost alone, petroleum storage sites are defined by a number of site characteristics that together determine its compliance cost (c), the probability of a spill (q), and the damage from a potential spill (d). We therefore suppose that Manitoba Environment chooses a high and low inspection probability for every (q, d, c) combination. As such, the inspection probability facing a site will be a function of not only general site characteristics and the resource constraint, but also the site's violation history. Notice that there are two types of sites that violate. If a site violates in group 1 and complies in group 2, a past violation will decrease the probability of observing a violation. However, if a site violates in both groups, a past violation increases the probability of observing a violation. Therefore, the model makes no prediction as to the relationship between past violations and the current probability of a violation. Finally, if warnings are an effective enforcement tool, we expect that the probability of a violation will be falling in the probability of an inspection. That is, if warnings indicate a higher inspection probability in the future, and the probability of a violation is falling in the inspection probability, warnings reduce the probability of a violation. 2.4 Empirical Model and Data This section presents the empirical model to be estimated and discusses the data to be used. The model is based on the state dependent model discussed in Section 2.3. The 17 goal of the estimation is to examine both the effectiveness of Mani toba Environment 's use of inspections and the way in which warnings affect the future probability of a violation. Note that our estimation does not provide a test of the state dependent model against other regulatory models. Rather, we wish to examine whether the data are consistent w i th the state dependent model since the model provides an explanation for why warnings may be an effective enforcement tool. We propose a two stage probit model of the probabili ty of an inspection and the probability of a violation. In theory, a thi rd equation representing the regulator's decision to prosecute a site rather than issue a warning could be estimated. However, the small number of prosecutions in our data set implies that there is insufficient variation i n the subsample of violations. 2.4.1 Estimating Equations We suppose that the regulator ini t ial ly chooses two inspection probability functions (high and low) to minimize the expected environmental damage from spills subject to a resource constraint. 1 2 The regulator w i l l inspect site % i n time t i f Ylit = s l a f t + elit > 0, (2.1) which represents the decision made by the regulator i n the first stage of the game. A s such, xut w i l l include the regulator's first stage expectation of the probability of a spi l l , 1 2That is, the mandate of the environment ministry is to minimize damages subject to the budget it receives from the provincial government. As such, social welfare and compliance cost considerations enter only the provincial government's objective function. 18 the damage from a spill, compliance costs, and inspection costs. xUt will also reflect the regulator's resource constraint and the site's violation history. e l i t will pick up any unobserved site or time period variables and we assume that em ~ ^(0,1) . We also assume that -E[eijt|x l i t] = 0 so that the unobserved variables are independent of the included explanatory variables. This assumption is made for feasibility, although our estimation controls for a large number of site characteristics, and single period shocks such as extreme weather are likely independent of xm. In each period, site i decides whether to reconcile its inventories in compliance with the regulations. A site will violate if the benefits of violating are greater than the costs of violating. We suppose that site i will violate in time t if *2« = xlitfa + e 2« > 0. (2.2) x2u includes compliance costs, potential fines, the probability of an inspection, and other site characteristics. We assume that e2it ~ ^(0,1) and E[e2it\xnt\ = 0. Again, e2u will pick up any unobservable time and site variables that influence the probability of a spill. Since x2it includes the predicted probability of an inspection and a large number and variety of site characteristics, we assume that -E[e2ii|e l i t] = 0. That is, once we have controlled for the probability of an inspection and numerous site characteristics, there is no other important variation that is simultaneously determining the two decisions.13 1 3 In general, since the outcome of the violation equation is only observed when Y\a > 0, there is endogenous selection. If E[e2it\€\it) ^ 0, the probit estimates will be biased. The typical approach to endogenous selection is to include the Inverse Mills Ratio for the inspections equation, IMRm = 19 Yin and Ynt are latent variables whereas our observations relate to whether inspections or violations actually take place. Therefore, we estimate the following two stage probit model. In the first stage, we estimate the probability of an inspection as P(Ym > 0) = P (e l i t > -x\M = *(xlM, (2.3) where $(•) is the standard normal cumulative distribution function. The probability of an inspection is estimated on the entire sample. In the second stage, the probability of a violation is estimated on the subsample of inspections. Since E[ e2it|eizt] = 0, P(X2it > 0\Yut > 0) = P(Y2it > 0) and we estimate the unconditional probability of a violation as P(Y2it > 0) = *(xTM- (2-4) Before discussing the data, we will briefly address econometric issues which arise in our model. First, our model is identified in two ways. Including the predicted inspec-tion probability, 7 l i t = ^ ( a ; ^^ ) , as a regressor in the violations equation identifies the deterrent effect of inspections by the functional form of the standard normal cumulative distribution function. However, identification by functional form is problematic for a ^(j^ff1)' ^ a r e g r e s s o r m the violations equation. However, using the Inverse Mills Ratio to correct for selection bias is only valid when the second stage equation is linear. The two equations are not estimated as a system for two reasons. First, identification of the correlation coefficient would rely entirely on the functional form of the error distribution. Secondly, it seems reasonable that the inclusion of the estimated inspection probability ( $ ( 3 ^ / ^ ) ) and the depth of site characteristics controls for possible correlation. 20 number of reasons. Therefore, our model is also identified by a natural exclusion re-striction. As will be discussed below, there is an explanatory variable (LATE) that is expected to shift the probability of an inspection but does not directly affect the proba-bility of a violation. Since this variable is included in the first stage but is not directly included in the second stage estimation, we can identify the deterrent effect of inspections. Secondly, our model does not include site fixed effects. Site fixed effects would be included if we wished to control for a known unobservable variation in inspection and violation probabilities across sites. However, because our data set includes numerous site characteristics and we attempt to control for the possibility of a relationship between the site and the regulator, we do not expect that important unobservable site characteristics remain. As well, fixed effects estimation in a probit model requires defining a dummy variable for each site and estimating the inspection and violation probabilities as a func-tion of our time series variables and the 3818 dummy variables. Not only would this be impractical, it would remove many explanatory variables of interest and likely lead to explanatory variables perfectly predicting inspections or violations (see Baltagi (1995) for a discussion). 2.4.2 The Data This subsection describes the data to be used in our estimation. Our data set tracks all 4471 sites registered to be petroleum storage sites at some time between 1976 and 1998, and was obtained from Manitoba Environment. We focus on the period between 1983 21 and 1998. Although the enforcement mechanism was in place in 1976, the resources were not in place, and there was little or no enforcement, until the last quarter of 1982. This also allows us to calculate relatively long lags of violations and inspections and avoids the regulatory amendments of 1980. The data set includes site specific characteristics and a record of each inspection made by Manitoba Environment, giving the date of inspection, the reason for the inspection, and the result of the inspection. Therefore, for each time period, we know whether a site was inspected, if it was found to be in violation of the regulations, whether a prosecution ensued, and descriptive statistics for the site. Other demographic and geographic data was obtained from Statistics Canada or constructed by the author. As of March 1999, there were 1958 active storage sites, 452 proposed, 222 inactive, and 1838 dismantled sites. Figure 2.1 shows the yearly inventory inspections beginning in 1983.14 Yearly inspections were relatively low during the 1980's, increased during the early 1990's, and fell over the last three years of the sample. Figure 2.2 shows yearly violations per inventory inspection, which were relatively stable and high over the 1980's but fell throughout the 1990's. Our estimation sample consists of 175 947 quarterly observations on the 3818 sites that stored petroleum for at least one quarter, and is an unbalanced panel.15 There are 3142 inventory inspections and 1561 violations during the 16 years. Table 2.1 pro-14One feature of figure 2.1 is the one time increase in the number of inspections in 1995. The most likely explanation is that there was a review of the petroleum storage regulation in Manitoba, and the increased attention paid to the regulation temporarily led to more inspections. 1 5 Sites were removed from the sample either because they were exempt from the inventory regulations or because site characteristic and census data were incomplete. 22 vides summary statistics for noteworthy site characteristics as well as inspections and violations. Our data set includes the following physical characteristics of the tanks at each site. UNDER is a dummy variable which is equal to 1 when at least one tank at the site is located underground. From table 2.1, 75% of observations are at sites with some underground tanks. The data set also includes the number of tanks and total capacity of each site. The largest number of tanks at any one site is 72 while capacity ranges from 225L to over 2 million litres. On average, there are 3 tanks and a total capacity of 33482L. The dummy variables for the level of leak protection indicate how many tanks at the site have some sort of leak protection, typically cathodic protection. Just over one half of the observations are at sites with no protected tanks. Finally, our data set includes the age (in quarters) of the oldest tank at the site. Our data set also includes information regarding the ownership structure and outlet type of each site. Sites are either independently owned, or owned by an oil company, an institution, a municipal government, the Manitoba government, or the federal gov-ernment. Table 2.2 outlines the breakdown of ownership structures for the 4471 sites in March 1999. 65% of sites are independently owned while 19% are owned by an oil company. There are seven different outlet types representing the primary purpose of the site. Sites are either retail petroleum sites, bulk storage sites, fleet sites, used oil sites, aviation and marina fuel sites, industrial sites, or miscellaneous sites.1 6 Table 2.3 1 6 Miscellaneous sites are those which have storage tanks for any other purpose. 23 provides the breakdown of outlet types in March 1999. Just over one half of sites are retail petroleum stations. Notice that, while only 9% of sites are bulk storage sites, these sites will account for a much larger proportion of tanks and capacity. Thirdly, the data set includes location characteristics of each storage site. WINNIPEG is a dummy variable equalling one if a site is located in the capital city of Winnipeg. Ac-cording to table 2.4, in March, 1999, 28% of all sites were located in Winnipeg. As well, we know the population density and real average income of the census subdivision of each site. Finally, we construct a dummy variable, NO ROAD, which is equal to one if there is no major road leading to the site. A major road is taken as that found on a 1988 road map. According to table 2.1, 7% of observations are for sites with no road access. Fourthly, our data set includes variables capturing time series variation. LATE is a dummy variable that is equal to one for all observations after 1990. LATE corresponds to the large change in the regulator's resource constraint at the end of 1990. LEG is a dummy variable which equals 1 for all quarters after 1987 and controls for the legislative increase in fines. There are also dummy variables corresponding to the second, third, and fourth quarters of each year. Lastly, our data set includes information on the violation history of each site. We know whether the site has been inspected before, the total number of past violations, and whether there was a violation at the site's most recent inspection. From table 1, the maximum number of past violations for any one site is seven. 24 2.4.3 Explanatory Variables In this subsection we outline the explanatory variables included in the inspections and violations equations. The probability of an inspection Recall that the probability of an inspection is estimated by P(Yiit > 0) = ^(x^P^ where xut includes the variables determining the regulator's expectation of the spill probability and damages at site i, and the cost of compliance. As well, xnt includes the cost of inspecting i, the resource constraint, the level of fines, and the violation history of site i. We assume that the probability of a spill from a given tank is exogenous and deter-mined by technology alone.17 As such, the probability of a spill depends on the level of leak protection and the number of tanks at the site. In addition, older tanks are more likely to leak, and we include the age of the oldest tank. The expected environmental damage from a spill will depend on the site capacity because the size of a spill is increasing in the capacity. Underground tanks pose a larger environmental threat since leaks are more difficult to visibly detect and seepage is imme-diate. Finally, greater external damage is done when the site is located closer to other people and property, and we include the population density of the surrounding area. 1 7In reality, the tank technology is chosen by the site owner/operator when the tank is installed. However, for the purposes of inventory regulations, this is taken as exogenous. It is possible that owners/operators are either cooperative or not cooperative in that those that choose safe technology will also comply with inventory regulations and those that install high risk technology will not reconcile inventories. We control for this possibility in our estimation. 25 To control for compliance costs, we include variables that determine the frequency of deliveries and withdrawals at the site as well as the frequency of required inventory reconciliations. The number and frequency of deliveries and withdrawals depend on the level of demand for the stored product, and we include local population density, local real average income, and quarterly dummies. We also include the site's outlet type since it will affect the frequency of both shipments and required reconciliations. The cost of inspecting a site will depend on whether there is a major road leading to the site and the quarter.18 Road access is important because many sites are located at remote fishing lodges which are only accessible by plane. Three quarterly dummies are included to control for travel difficulties due to weather and possible seasonality in the other duties of environmental officers. The largest variation in the resource constraint of the regulator is the budgetary increase of 1990 and the subsequent regionalization of enforcement. Following regional-ization, there were more environmental officers and officers were closer to the sites. On the other hand, each officer was responsible for more types of environmental inspections. The change in the budget constraint is captured by LATE, which is equal to 1 for all quarters after 1990. We assume that the form of the inspection probability functions is the same for the entire sample. That is, although the performing of inspections was regionalized in 1991, 1 8 A measure of the travelling distance from the nearest regulator was constructed but was not statis-tically significant in any specification. Since other qualitative results were unchanged, the specification presented here does not include distance. 26 the decision rule governing which sites are inspected remains the same. A n alternative approach would assume that there was a single provincial inspection rule between 1983 and 1990 inclusive, and beginning in 1991, each region decided on it's own inspection rule for the rest of the sample. This possibility was examined by allowing all explanatory variables to have different effects before and after regionalization. However, there were insufficient observations in the subperiods to identify the model. Therefore, due to data limitations, we are restricted to allowing regionalization to shift the intercept of the inspection probability function.1 9 The probability of an inspection is also a function of the fine structure. As in most regulatory models, we expect that inspections and fines are substitutes. That is, if the regulator increases the expected fines, a given level of compliance can be maintained with fewer inspections. In 1987, the maximum fine for all violations was increased substan-tially. Therefore, we include a dummy variable, LEG, which is one for all quarters after 1987. Our dataset does not include information on the fines issued for individual cases. However, discussions with Manitoba Environment suggest that there is little variation in the fines for inventory violations since they are not tied to specific environmental damages. The violation history of a site will reflect which state the site is in at time t and deter-mines whether the site faces the low or high inspection probability. A strict interpretation 1 9We also assume an equal shift variable for all regions. It seems reasonable to assume that Manitoba distributed the regional offices and funding such that the change in the time and budget constraints was equal across regions. As well, interacting LATE with regional dummies but not with other variables seems ad hoc. Since we can not allow for a full regime shift, we assume a single shift parameter. 27 of the state dependent model is that sites move between the high and low risk groups ac-cording to their compliance status at the last inventory inspection. If so, the outcome at the site's last inventory inspection completely determines to which group the site belongs. In reality, there may be rigidities in the movement between the high and low groups as it may take repeated violations to move to the high risk group. Therefore, we also estimate specifications which include cumulative past violations. 2 0 We also include the dummy variable indicating whether a site has ever been inspected, PREVINSP. It is likely that sites which have never been inspected are treated differently and PREVINSP may also reflect any learning that is done at a site's first inspection. Specifically, if sites are edu-cated about the regulation and compliance when they are inspected, the probability of an inspection will be smaller for sites that have a previous inspection. Finally, we include two other variables expected to determine the probability of an inspection. First, a dummy variable WINNIPEG which is equal to one for all sites located in Winnipeg is included for a number of reasons. We expect that sites located in the capital city have greater access to information about the regulations and the potential environmental damages. As well, over 50% of the population of Manitoba and 28% of all storage sites are located in Winnipeg. It seems reasonable that the behavior of sites in Winnipeg may be different than those located in more rural settings. Thirdly, it is possible that the regulator develops a relationship with some site owners or operators. 2 0 Rigidity in the opposite direction was examined by including a dummy variable indicating if the site was ever in violation. These specifications add little to the general results of the paper, and are not presented. 28 Until 1991, the only environment officer was located in Winnipeg, and in light of the large number of sites and their diffuse locations throughout the province, such relationships are most likely for sites in Winnipeg. Finally, WINNIPEG may also pick up differences in the frequency of deliveries and withdrawals at sites since the demand for petroleum products is likely higher in Winnipeg. We also allow for the inspection probability to depend on the site's ownership structure. Sites owned by the federal government also face safety regulations from within the government. As well, it is possible that large oil companies also have internal discipline for individual sites. If so, Manitoba Environment will inspect these sites less often. In sum, the probability of an inspection at site % is P(Ylit> 0) = *{xlMt (2.5) where x\u includes the number of tanks, the ownership and outlet type, the inspection and violation history variables, dummies corresponding to the increase in fines in 1987 and regionalization in 1990, the position and protection of the tanks, the age of the oldest tank, a road accessibility dummy and quarterly dummy variables.21 2 1 It is likely that the variables explaining the probability of an inspection do so nonlinearly. For example, since the regulator is minimizing expected damage, the probability of a spill and the damage from a spill should enter multiplicatively. However, the theory is not sufficient to give specific predictions on how all of the variables will enter and we assume that the variables enter linearly. 29 The probability of a violation Recall that, each period, the operator of site i decides whether to reconcile its inventories in compliance with the regulation and that the probability of a violation is P(Y2it > 0) = $(x2it[32). x2it includes variables which determine the expected benefits and costs of a violations, as well as other site characteristics expected to determine whether a site violates the inventory regulations. The expected benefits from a violation are the cost savings enjoyed by site i, which are simply the negative of the site's compliance costs. Compliance costs depend on the regularity of deliveries and withdrawals and the frequency with which inventories must be measured and reconciled. Therefore, as in the inspections equation, we include outlet type, population density, real average income, quarterly dummies, and WINNIPEG. The latter four variables control for variation in the demand for the stored product. The demographic characteristics are also expected to pick up the fact that some site owners and operators may care about damages to local citizens, and its community reputation. To better control for the solitude of many northern and eastern sites, we also include the accessibility dummy variable. In particular, the population density measures are for census subdivisions, which, for the north and eastern regions on Manitoba, are large areas with a small number of towns and vast areas of wilderness. These measures deflate the population density for sites in the towns and inflate the population density for sites located in remote areas. We would expect owners and operators of sites in the towns to be more sensitive to environmental damages than sites that have no close 30 neighbors. On the other hand, many of the remote sites are tourist destinations which rely on environmental quality to attract customers. The expected cost of a violation depends on the expected fine in t, the expected future fine, the expected increase in clean up costs if a spill is not detected immediately,2 2 and any owner discipline. The expected fines depend on the fine structure and we include LEG. The expected fine also depends on the site's expectation of the probability that it will face an inspection. Therefore, the predicted inspection probability from the first stage estimation of the inspections equation, Iut = ^(x\itPi), is included as a regressor. If inspections are effective at enforcing the regulation, a higher probability of an inspection will imply a lower probability of a violation. To determine whether warnings are working only through the threat of increased enforcement, we include the violation history variables as separate regressors. If the only role for warnings is through the probability of an inspection, the coefficients on these variables should be zero. Again, we consider specifications with a violation at the last inspection and cumulative violations. Notice that PREVINSP will pick up any learning done by sites at their first inspection and previous violations may reflect lag dependency of violations. The expected increase in clean up costs due to the failure to reconcile inventories depends on the size of a spill and the probability of a spill. Therefore we include the number and position of the tanks, the level of leak protection at the site, and the age of 2 2 In the event of a spill, injured parties have the right to sue the facility owners or operators for damages. However, such action has been rare in Manitoba. 31 the oldest tank. As with the probability of an inspection, we include WINNIPEG and ownership dummy variables. The access to information and the general situation faced by sites located in Winnipeg is expected to differ from that of other sites in the province. Own-ership may affect the expected costs of a violation if large companies and government agencies have internal monitors and controls for inventory controls. As well, corporations face higher maximum penalties. Overall, the probability of a violation can be written as P(Y2U>0) = $(xlitP2 + T!it7), (2.6) where x\it are all of the variables in x\it except LATE, and (32 are the corresponding elements of /32- Recall that LATE corresponds to an increase in the resource constraint of the regulator. It seems reasonable that the budget change only affects the probability of a violation through changes in the probability of an inspection. As such, our model is identified by the exclusion of LATE from the violation equation. 32 2.5 Empirical Results 2.5.1 The probability of an inspection The results from the probit estimation of the probability of an inventory inspection are presented in Tables 2.5a and 2.5b.2 3 Model A includes only cumulative violations, Model B includes only a violation at the last inspection, and Model C includes both violation history variables. The results of the three specifications are similar. 2 4 For all specifications, F-tests reject the null hypotheses that the coefficients on the relevant violation history variable are jointly zero. This supports the idea that inspec-tions are state dependent. As expected, the probability of an inspection is increasing in cumulative violations. On the other hand, the coefficient on a violation at the last inspection is not statistically different from zero in any specification, suggesting that Manitoba Environment bases its site classification on cumulative violations rather than the outcome at the last inspection. Finally, our results indicate that thie actual impact of cumulative violations is small. At the mean, the derivative of the inspection probability with respect to cumulative violations is approximately 0.002, with an elasticity of 0.056. 2 3For all results, * indicates significance at 1%, ** at 5%, and * at 10%. Standard errors are given in brackets. 2 4It is possible that the probability of an inspection is correlated with an inspection at the site last period, implying serial correlation of the errors. We test for first order serial correlation using the generalized residuals as estimates of the errors (see Pagan and Vella (1989) for a discussion of tests using generalized residuals). The null hypotheses of no correlation were rejected at the 5% level. To examine whether the inclusion of lagged dependent variables and serial correlation biased our coefficients, we re-estimated the models with the lagged value of the inspection dummy as a regressor. This is similar to controlling for heterogeneity by including a dummy variable indicating whether a person worked last period in the estimation of their decision to work this period (see Nakamura and Nakamura (1985) for an application to labour decisions of married women). We do not report the specifications including the first lag of inspections because the other qualitative results are the same. 33 As such, the probability of an inspection when the site is in the high risk group is not substantially different than when it is in the low risk group. 2 5 Finally, we find that a previous inspection only significantly increases the probability of an inspection in Model B . The remainder of the qualitative results are the same in all three specifications, and we will discuss the results in the context of Model C. In accordance with the idea that inspections and fines are substitutes in enforcement, the coefficient on the legislative dummy is negative. As expected, the probability of an inspection is significantly higher after regionalization. In fact, at the mean, an inspection is more than twice as likely after 1990. Other noteworthy results include the following. As expected, both population density and the real average income of the surrounding census subdivision are found to have small positive effects on the probability of an inspection. This supports the idea that the regulator responds to the greater risk from leaks at sites in densely populated areas and perhaps to political incentives to inspect wealthier regions. Controlling for the difference in population density, a site located in Winnipeg is less likely to be inspected than a similar site located elsewhere in the province. The significant negative coefficient on the age of the oldest tank may be capturing a tendency for Manitoba Environment to build 2 5 Notice that our results for past violations are also consistent with an alternative notion of regulatory behaviour. Suppose that, each period, the regulator chooses an inspection probability for each site given an expectation of the probability the site will be in violation. If the probability of a violation is a function of past performance, the regulator's choice of inspection probability would be an increasing function of past violations. However, this type of model would predict that, controlling for probability of an inspection, cumulative violations increase the probability of a violation. This is not consistent with our second stage results. 34 a relationship with site owners or operators over time. As expected, sites with either underground tanks or more tanks face a higher proba-bility of being inspected. The coefficients on the quarterly dummies indicate that a site is most likely to be inspected in the first quarter of the year. This may reflect seasonality in the other duties of officers, the need to use up the inspections budget before year end, or seasonality in violation probabilities. The coefficients on ownership and outlet type suggest that oil companies are not treated differently than independently owned sites and that bulk sites are the only outlet type more likely to be inspected than retail sites. Surprisingly, our results indicate that partially and fully protected sites are more likely to be inspected that unprotected sites. This may reflect the fact that tanks installed in later years were required to be protected and inspections were increasing over the sample. However, both the inclusion of a time trend and interacting protection and year dummies do not change the sign of the protection coefficients. 2.5.2 T h e probab i l i ty of a v io la t ion Tables 2.6a and 2.6b present the results for the estimation of the probability of a violation. Recall that we estimate the probability of a violation on the subsample of inspections. As well, the predicted value from the corresponding inspections equation is included as a regressor while LATE is excluded. To account for the inclusion of an estimated explanatory variable, we correct the standard errors according to the method outlined in 35 Murphy and Topel (1985). As expected, we find that the estimated probability of an inspection reduces the probability of a violation. For the mean site, the derivative of the violation probability with respect to the estimated probability of an inspection is -3.1 and the elasticity is -0.09. Although this elasticity appears small, examples presented in the next section indicate that the effect of inspections at specific sites can be large. Abstracting from the costs of the program, these results suggest that Manitoba Environment's use of inspections and warnings is effective at encouraging proper inventory reconciliation and therefore reducing expected environmental harm. In all specifications, F-tests reject the null hypothesis that the effect of the violation history are jointly equal to zero. This suggests that past violations influence the cur-rent violation probability by more than changing the probability of an inspection. The insignificant coefficient on cumulative violations in Model A suggests that cumulative violations only affect present violations through an increased probability of an inspec-tion. When both history variables are included, the coefficient on cumulative violations is negative and significantly different from zero at the 10% level. We find that a viola-tion at the last inspection increases the probability of a violation, suggesting a short run lagged dependency in violations. Moreover, a previous inspection is found to have a di-rect negative effect on the probability of a violation. One possible explanation confirmed by discussion with Manitoba Environment is that sites learn about inventory controls and environmental regulations when they are inspected for a first time and will be less 36 likely to violate in the future. Controlling for the probability of an inspection, the increase in fines at the end of 1987 is has a significant deterrent effect. In fact, calculated at the mean, the probability of a violation was 18% lower following the regulatory change. Our results also suggest that, besides municipally owned sites, independently owned sites are the most likely to violate and that there is little difference between outlet types. Finally, sites appear to be more likely to violate in the first quarter of the year. 2.6 Predictions and Examples To better understand the implications of our results, we present examples and predictions based on the estimated coefficients. Our predictions are conditional on the assumption that the estimated model is the correct model. Since the results of the three specifications are similar, we base our calculations on Model C. First we calculate the deterrent effect of an increase in the inspection probability for different sites in the data set. Suppose that the allocation of funding or time was altered such that the probability of every site being inspected is doubled. This may involve hiring more environmental officers or increasing the inspections budget. Notice that, at the mean, this increase is a smaller change than that following the 1987 regulatory change or the 1991 regionalization. First we consider Si, an independently owned retail gas station located outside of Winnipeg. The site has one unprotected underground storage tank. The tank was 37 installed in the first quarter of 1977 and has a capacity of 2270 litres. The site is located in a census subdivision with a population density of 1.99 and a real average income of $27 466. In the first quarter of 1993, the site has no previous inspections, and our model predicts that it will violate with a probability of 0.81. If the inspection probability is doubled, the probability that this site will violate falls to 0.74, a reduction of 9.1%. Next we consider S2, an independently owned retail gas station which is located in Winnipeg. The site has one unprotected underground tank with a capacity of 4545 litres. The tank was installed in the first quarter of 1976. The local population density is 1182.84 and the real average income is $39 064. The site had no inspections prior to 1993. Our model predicts that, in the first quarter of 1993, the probability that S2 is in violation of the inventory regulations is 0.46. If the inspection probability is doubled, the model predicts that the violation probability is 23.7% lower. Thirdly, consider site 53, an independently owned retail gas station located outside of Winnipeg. The site has one aboveground tank that was installed in the first quarter of 1962. The capacity of the tank is 9090 litres and the site is located in a census subdivision with a population density of 519.96 and a real average income of $23 829. Prior to 1993, £3 had one previous inspection at which it was found to be in violation. Our model predicts that, in the first quarter of 1993, S3 is in violation with probability 0.6. A doubling of the inspection probability is predicted to decrease the probability that the site is in violation by 4.7%. Finally, consider site 64, a bulk storage facility located outside of Winnipeg and owned 38 by an oil company. The site stores 6 unprotected aboveground tanks with a total capacity of 354 600 litres. The oldest tank was installed in the first quarter of 1974. The site is located in a census subdivision with a population density of 639.38 and a real average income of $33 203. In the first quarter of 1993, the site had no previous inspections and our model predicts the site's violation probability is 0.66. If the probability of an inspection had been twice as large, the probability of a violation by S4 would have been 0.6, or 8.2% lower. Overall, the predicted changes in the violation probabilities indicate that the effect of an increase in inspections differs according to site characteristics, with the largest effect being at sites with relatively low violation probabilities. In fact, the deterrent effect of inspections has a minimum range of 4.7% to 23.7% of the original violation probability, indicating that inspections are effective at increasing compliance. To better understand the magnitude of the deterrent effect, we calculate the effect of a budgetary change on the predicted number of violations at a group of sites. Specifically, we calculate the change in the predicted number of violations at sites in Winnipeg in the first quarter of 1993 when the probability of an inspection is doubled. 2 6 First, we assume that a violation is predicted whenever the predicted probability of a violation is greater than or equal to 0.5. Our model predicts that, in the first quarter of 1993, 244 sites in Winnipeg were violating the inventory regulations. If the probability of an inspection is doubled at each site, our model predicts 63 fewer violations. That is, a 2 6 The same calculation performed for other years give similar percentage changes in predicted violations. 39 doubling of the inspection probability faced by these sites reduces predicted violations by 26%. Secondly, we calculate the expected number of violations as the sum of the probability of a violation over sites in Winnipeg in the first quarter of 1993. According to our model, 305 violations are expected. If the probability of an inspection doubles, the expected number of violations falls to 231, a reduction of 24%. 2.7 Conclusions This chapter examines the role of inspections and warnings in the enforcement of environ-mental regulations. A n empirical model that allows for past violations to directly enter into the probability of an inspection is estimated for the case of inventory reconciliation regulations for petroleum storage sites in the province of Manitoba between 1983 and 1998. Our results suggest that, even in the absence of frequent prosecutions, the probability of an inspection has a significant deterrent effect. At the mean, the derivative of the probability of a violation with respect to the estimated inspection probability is —3.1, implying an elasticity of —0.09. Moreover, for representative sites, a general doubling of the inspection probability reduces the violation probability by between 4.7% and 23.7%. Therefore, abstracting from the cost of enforcement, inspections and warnings appear to be effective at increasing compliance with inventory regulations. To the extent that compliance reduces the amount of petroleum leaked into the environment, environmen-tal damage is reduced. However, our study does not allow us to compare the use of 40 inspections and warnings to other types of enforcement, such as fines for every violation. As well, we find support for the idea that warnings are used to group sites according to their history, as past violations increase the probability of an inspection. Moreover, this classification appears to be based on cumulative violations rather than the outcome of the last inspection. There is also evidence that warnings play another role in enforcement. For example, it may be that the regulator uses inspections to educate sites as to the regulations, and therefore does not prosecute sites for their first violations. Finally, we find that the Environment Act of 1987 was followed by a period of fewer inspections. Controlling for the change in the inspection probability, the increase in fines reduced the conditional probability of a violation by 18%. Therefore, although sites are rarely prosecuted, the threat of higher maximum fines deters violations. 41 Chapter 3 International Environmental Agreements and the Level of Domestic Regulatory Power 3.1 Introduction M a n y environmental concerns arise from transboundary pollutants that adversely effect other countries. In the extreme, some pollutants have the same environmental impact in al l countries regardless of their origin. For example, the impact that emissions of green-house gases have on the atmosphere and global mean temperature is independent of their country of origin. Since no individual country takes into account the full benefits of their domestic abatement, i n the absence of an international agreement, emissions abatement 42 of transboundary pollutants is under-provided. Therefore, countries often enter into in-ternational agreements to reduce emissions. For example, the Framework Convention on Climate Change of 1992 and the Kyoto Protocol of 1997 set out greenhouse gas abate-ment targets, while the Canada-U.S. Acid Rain Agreement of 1991 concerned emissions reductions of pollutants such as sulphur dioxide in Eastern Canada and Northeastern America. The domestic distribution of regulatory powers between the federal and regional gov-ernments in federations such as Canada and the United States can affect the international environmental agreements they negotiate. The distribution of regulatory power is also an issue in the European Union as the European Commission can negotiate on behalf of the member countries, or the countries can negotiate individually.1 The purpose of this chapter is to examine the possible strategic effect that the domestic distribution of pow-ers can have on international environmental agreements. Specifically, we show that the differences in regional and federal preferences over abatement can make a country better off when a regional government negotiates agreements instead of the federal government. We develop a model in which two countries cooperatively bargain over the abatement of a transboundary pollutant. Each country is a federation with at least two regional governments. The federal governments maximize the domestic benefits from global abate-ment less the costs of domestic abatement. The regional governments maximize the net benefits of their regions. To capture the fact that emissions are often localized in specific 1See Meunier and Nicolal'dis (1999) for a discussion of international negotiations and the EU. 43 regions, we assume that one region produces all domestic emissions. As such, one region receives a share of the domestic benefits equal to the region's share of the population but faces costs equal to the country's costs. Therefore, all else equal, the regional government undertakes less abatement than the federal government. In our model, the exogenous constitution of each country places the power to both negotiate and enforce international agreements with either the federal or regional govern-ment.2 We show that a country can be better off when the domestic regional government holds the regulatory power as long as the region is sufficiently large and the foreign country's regulatory powers lie with either the federal government or a larger region. At both the threat point and Nash bargaining solutions with regional jurisdiction, global abatement is smaller than when the federal government holds regulatory power and there is a substitution of foreign abatement for domestic abatement. As long as the region's preferences are not too far from those of the federal government, the domestic country is better off with regional authority. On the other hand, both countries are worse off rela-tive to federal control when regions of the same size hold regulatory power. In this case, neither country enjoys a strategic advantage and both domestic and foreign abatement fall relative to the agreement negotiated by the two federal governments. Although there is no explicit delegation in our model, this chapter represents a new application of the literature on delegation in bargaining. The existing literature has shown that, in a variety of bargaining situations, a principal will choose an agent with 2 In Chap te r 4, we consider the case when regional governments enforce agreements that are negotiated by the federal government rather than the federal government negotiating and enforcing agreements. 44 preferences different than their own to negotiate on their behalf.3 For example, Jones (1989a) considers union-firm negotiations, Burtraw (1992) examines bargaining over a general surplus, Fershtman et al (1991) discuss their results in the context of a Cournot duopoly, and Segendorff (1998) considers principals (mean voters) in each of two countries delegating the authority to negotiate internationally to agents (governments). In general, choosing a negotiator with more extreme preferences can offer a principal a strategic advantage in negotiations and make the principal better off. On the other hand, if the other principals also choose to delegate, the strategic advantage may be lost, and both principals may be worse off when they delegate. Our model differs from the delegation literature in two ways. First, in all existing studies except Segendorff (1998), the principal retains authority if negotiations break down. In our model, if negotiations break down, the power to choose abatement lies with the level of government holding regulatory power. Secondly, there is no explicit delegation in our model. In fact, our analysis demonstrates that exogenous domestic institutions can offer a strategic advantage analogous to that found in a model of delegation. The chapter proceeds as follows. Section 3.2 presents the model while section 3.3 presents comparisons of different regulatory frameworks. Section 3.4 presents an example of the model with a specific functional form and section 3.5 concludes. 3 A number of papers examine delegation in non-cooperative frameworks, for example, delegation within a firm and delegation in international monetary games (see Dolado, Griffiths and Padilla (1994) and Vickers (1984)). 45 3.2 The Model There are two countries, Home (H) and Foreign (F), each governed by a federal gov-ernment. Within each country, there are at least two regions with individual regional governments. We assume that one region in each country is responsible for all of the emissions in its country. Therefore, all abatement accomplished by the country is under-taken in the polluting region. This assumption captures the fact that emissions are often localized in specific regions within a country. For example, the majority of the cost of greenhouse gas reductions would be borne by the energy industry, located primarily in Alberta.4 We suppose that the polluting region represents a proportion o^  of the total population of country i. Furthermore, we assume that a region of size receives an ojj share of country i's benefits from abatement. There are four potential players in the game: Home's federal government, Home's regional government, Foreign's federal government, and Foreign's regional government. Al l players are assumed to have the same complete information set. The timing of the game is as follows. Before the game begins, the exogenous con-stitution of each country establishes which level of government has jurisdiction over the negotiation and enforcement of international environmental agreements. For the pur-poses of this paper, we assume that both negotiation and enforcement powers lie either 4 Similar results would hold if a relatively large share of the abatement costs were borne by the region. This assumption enables us to focus on the effect of divisions of power without addressing issues such as multi-party bargaining within countries. These issues are an interesting area for future research. 46 with the regional government or the federal government.5 The granting of both powers to regional governments is observed in the United States. For example, the states of Washington, Alaska and Oregon negotiated and enforced the Pacific Salmon Treaty with the federal government of Canada. The international negotiation is a one stage game in which the governments hold-ing the regulatory powers cooperatively bargain over abatement levels.6 If the negotia-tions are successful, the agreement is the Nash bargaining solution with equal bargaining strengths. If negotiation break down, the same two governments play a noncoopera-tive game in abatement levels. The Nash equilibrium represents the threat point of the bargaining game. The net benefits of the federal government in country i are given by NB[(Q, Qi) = B(Q) - c( f t ) , i = H,F (3.1) and correspond to the country's net benefits. The countries are assumed to be identical. qi denotes abatement in country i and Q = qn + qF is global abatement. Since emissions reductions are a global public good, the countries receive benefits from global abatement, but only face the costs of domestic abatement. B(Q) is assumed to be increasing and 5 Chapter 4 examines the change in net benefits when regional governments enforce agreements that are negotiated by the federal government rather than the federal government negotiating and enforcing agreements. 6 A cooperative game approach is taken to isolate the effect of the distribution of domestic jurisdic-tion, given that an agreement is signed and upheld. This approach does not address the interesting enforcement issues involved with international environmental agreements in the absence of an interna-tional enforcement mechanism. See Carraro and Siniscalco (1993) and Barrett (1994) for non-cooperative models of international environmental agreements and Chandler and Tulkens (1992) for a core-theoretic approach. 47 strictly concave while c(g,) is increasing and strictly convex. This implies that net benefits are increasing and concave. The net benefits of the regional government in country i are given by NB?(Q, ft) = atB(Q) - cfo), a, e (0,1), i = H, F. (3.2) The region receives proportion CKJ of the country's benefits from global abatement but faces all of the domestic abatement costs.7 Overall, the international environmental agreement corresponds to the Nash bargain-ing solution of the game between the two governments holding regulatory power: max (NBjH(Q,qH) - NBjH(Q,qH)) (NBF{Q,qF) - NBkF(Q,qF)) . (3.3) Here j and k equal F if the federal government holds the regulatory power and R if the regulatory powers are held by the regional government, qn and qF are the threat point abatement levels defined by the Nash equilibrium between the same two governments. 3.3 Solutions and Comparisons 3.3.1 Noncooperative Equilibria 7There are two externalities in this model. In the absence of an agreement, each country will not take into account the full international benefits from its domestic abatement. In addition, regional governments will not take into account the benefits from global abatement accruing to other regions of the country. 48 If negotiations break down, the noncooperative Nash equilibrium between the two gov-ernments holding regulatory power results. This subsection presents the possible Nash equilibria. The Federal-Federal (F-F) Threat Point The benchmark to which the other regulatory regimes wi l l be compared is the case i n which both federal governments hold negotiation and enforcement powers. In this regime, if negotiations break down, the resulting Nash equilibrium abatement levels are defined by: 0 0. Since the countries are symmetric, the threat point abatement levels are equal. Figure 3.1 shows the threat points graphically as the intersection of the reaction functions of the two federal governments, R^qp) and Rp(qn)-The Regional-Federal (R-F) Threat Point Suppose that regulatory powers lie wi th Home's regional government and Foreign's federal government. The Nash equilibrium abatement levels, q^F and q^F, are defined by: aHB>(QRF)-c>(q«F) = 0 B'{QFF)-c\r/) = B\QFF) - c\r/) = 49 B'(QRF) - c'(q*F) = 0. These equations define Home's regional and Foreign's federal reaction functions, RFf(qp) and Rff(qp) and the threat point of the bargaining game is represented at the intersec-tion of these curves (see Figure 3.2). Since the reaction function of Home's region lies everywhere below that of Home's federal government, Home's abatement decreases in relation to the F-F threat point and Foreign's increases in relation to the F-F threat point. In fact, the slope of Rp{qH) is less than one in absolute value implying that global abatement is smaller at the R-F threat point. Therefore, as aH falls, there is a trade-off for Home between cost savings from less domestic abatement and a reduction in benefits from lower global abatement. To examine this trade-off, notice that when aH = 1, Home's regional and federal governments have the same net benefits. If OJ# now falls by a small amount, the effect on Home's net benefits can be given by the derivative of Home's net benefits with respect to a evaluated at an = 1 and the Nash equilibrium. In general, When an — 1> the first term on the right hand side is zero by the first order conditions of the Nash equilibrium. Since Foreign abatement is decreasing in an ,when an is near one, Home is better off at the R-F threat point.8 This is analogous to results common in the industrial organization literature, that firms in Cournot 50 Intuitively, when an is close to one, the regional government values global abatement almost as much as the federal government, and the fall in B(Q) is smaller than the fall in c(qn). Since B(Q) is concave and c(qn) is convex, when an becomes sufficiently small, the cost savings from switching abatement to the other country may not compensate for the reduction in global abatement. Finally, as OLH falls, global abatement continues to fall but Foreign undertakes in-creasing levels of abatement. Therefore, Foreign is worse off at the R-F threat point for all a These results are formalized in Proposition 1. The formal proofs for all propositions are provided in Appendix A . Proposition 1 (a)For an sufficiently large, Home's payoffs are higher at the R-F threat point than at the F -F threat point. (b)For all a^, Foreign is better off at the F -F threat point than at the R-F threat point. The Regional-Regional (R-R) Threat Point Suppose the regulatory powers are held by the regional governments of both countries. We first consider the case when the regions constitute the same proportion of their respective countries. We then consider the case of asymmetric regions. competition can be made better off through strategic commitments (see Chapter 12 in Pepall et al. (1999) for a discussion). 51 Symmetric Regions Suppose the sizes of the regions relative to their countries' pop-ulations are the same and an = cxF — a. If negotiations break down, the resulting Nash equilibrium abatement levels, q^R and q^R are defined by aB'(QRR)-c'(qfR) = 0, i = H,F. By inspection, the threat point abatement levels of the two regions are equal. Since the regional reaction functions lie below the federal reaction functions, the symmetric R-R abatement levels are less than those at the F-F threat point (see figure 3.3). It is straightforward to verify that Home's indifference curves are vertical along its reaction function while Foreign's indifference curves are horizontal along its reaction function. As such, Home's federal indifference curve for F-F threat point net benefits is vertical at the F-F threat point and Foreign's indifference curve for F-F threat point net benefits is horizontal at the F-F threat point. Home must be worse off whenever Foreign abatement falls from 5fiF and Foreign must be worse off whenever Home abatement falls from qFrF. Therefore, both are worse off at the R-R threat point. Intuitively, the strategic advantage enjoyed by Home at the R-F threat point is lost when equal sized regions hold regulatory powers in the two countries. The R-R threat point will involve less Home and Foreign abatement than the F-F agreement. Since abate-ment in the opposing country no longer increases in response to reductions in domestic abatement, both countries are worse off. 52 This result is formalized in Proposition 2. Proposition 2 For all an = aF = a, both countries are worse off at the R-R threat point relative to the F-F threat point. Asymmetric Regions Now suppose aH ^ aF and without loss of generality, let &H < aF, so that Home's region is smaller relative to the size of its country. Denoting the asymmetric R-R threat point abatement levels as q§R and gf?R,the Nash first order conditions require that aiB'(QRR)-c'(qRR) = 0, i = H,F. By inspection, since Home's region is smaller, Home will undertake less abatement. Again, Foreign's federal indifference curve for F-F threat point net benefits is hori-zontal the F-F threat point and the country is worse off for all g# < '. Since Home's regional reaction function is closer to the origin than Foreign's regional reaction function, the asymmetric R-R threat point is below the 45° line. Therefore, g f P < q^F and Foreign is worse off at the asymmetric R-R threat point for all aH < aF. To determine whether Home can be better off at the asymmetric R-R threat point, suppose ap = 1. Proposition 1 states that for aH sufficiently close to 1, Home strictly prefers the R-F Nash equilibrium to the F-F equilibrium. By continuity of Home's net benefits, Home must still prefer the regional equilibrium when aF marginally falls from 1 such that Q J J < ap. 53 These results are formalized in Corollary 1, which follows from Proposition 1 and continuity of Home's net benefits. Coro l l a ry 1 When an < ctp, (a) for an and ap sufficiently large, Home is better off at the asymmetric R-R threat point than at the F -F threat point, and (b)for all a^ and aF, Foreign is worse off at the R-R threat point. In sum, this section has characterized and compared the possible Nash equilibria which will be reached if international negotiations break down. We considered three reg-ulatory regimes: both federal governments holding regulatory power, one regional and one federal government holding power, and both regional governments having jurisdic-tion over negotiation and enforcement of the agreement. It was shown that if Foreign's regulatory powers lie with the federal government, as long as Home's region is sufficiently large, Home prefers domestic powers to lie with regions. On the other hand, when both regional governments negotiate and enforce agreements, a country can only be better off relative to the F-F Nash equilibrium if the domestic region is smaller than the Foreign region but sufficiently large relative to the domestic country. 3.3.2 Cooperative Equilibria T h e Federal-Federal (F--F)Agreement This subsection presents the international environmental agreement reached when the regulatory powers lie with both federal governments. This will represent the benchmark outcome to which other agreements will be compared. 5 4 The F-F equilibrium agreement (q^\qFF) solves max (B(Q) - c(qH) - B ( Q F F ) + cffif)) (B(Q) - c(qF) - B ( Q F F ) + cffiF)) , (3.5) where qF[F and <jpF are the threat point abatement levels. On figure 3.1, the gains from international cooperation are represented by the lens shaped area formed by the indifference curves passing through the threat point. The Nash Bargaining solution simply chooses the point in the lens shaped area which corresponds to the solution to (3.5). Given an interior solution, the first order conditions for the bargaining problem are [B\Q) ~ c'(qH)][B(Q) - c(qF) - B ( Q F F ) + c($H] = -B'(Q)[B(Q) - c(qH) - B ( Q F F ) + c{?/)\ \B\Q) - c(qF))[B(Q) - c(qH) - B{QFF) + c^/)] = -B'(Q)[B(Q) - c(qF) - B ( Q F F ) + c ( 5 T ) ] . Taking a ratio of the first order conditions implies that the solution lies on the contract curve, implicitly defined by: B'(Q) - c'(qH) B'(Q) B'(Q) B'(Q)-d(qFy V-0) The contract curve is a locus of points along which the indifference curves of the two 55 federal governments are tangent. It is straightforward to show that in (qF, qH) space, the contract curve is downward sloping with a slope of — 1 at the 45° line. Rearranging the first order conditions implies that the solution also lies on the "agree-ment locus", implicitly defined by: c'{qH) = B{Q) - c(qH) - B{QFF) + c ( ^ ) CM B(Q) - c(qF) - B(QFF) + c(qJF)' The agreement locus determines which point along the contract curve will represent the international agreement and reflects the choice of the Nash bargaining solution concept. Intuitively, the agreement locus determines the division of the bargaining surplus, as the right hand side of (3.7) is the ratio of the countries' gains to cooperation. In {qF,QH) space, the agreement locus is an upward sloping line that connects the endpoints of the bargaining lens. The F-F agreement locus coincides with the 45° line and the Nash bargaining abatement levels are equal. The Regional-Federal (R-F) Agreement Suppose that Home's regulatory powers lie at the regional level while Foreign's regulatory powers are held by the federal government. The R-F Nash bargaining international agree-ment signed by Home's regional government and Foreign's federal government, ( g § F , g ^ F ) is the solution to max (aHB(Q) - c{qH) - aHB(QRF) + c(q*F)) 56 (KB(Q)-c(qF)-B(QRF)+c(qfF)). (3.8) Recall that q^F and qf.F are the abatement levels at the Nash non-cooperative equilibrium between Home's region and Foreign's federal government. The first order conditions defining the R-F agreement imply that the solution is the intersection of the contract curve, implicitly defined by: aHB'(Q) - c'(gH) = B'(Q) aHB'(Q) B'{Q) - c>(qF) and the agreement locus, implicitly defined by: c'(qH) _ aHB(Q) - c(gF) - aHB(QRF) + cjq™) C(qF) B(Q)-c(qF)-B(QRF) + c(qRF) (3.10) A comparison of the F-F and R-F contract curves indicates that the R-F contract curve lies everywhere closer to the origin, although both have a slope of —1 at the 45° line. Since Home's threat point abatement is less than Foreign's, the R-F agreement locus lies everywhere below the 45° line (see figure 3.3). To compare the net benefits under the R-F and F-F negotiations, notice that when aH = 1, Home's regional and federal governments have the same net benefits. As such, the effect of aH falling marginally from unity can be given by the derivative of Home's Nash bargaining net benefits with respect to aH, evaluated at aH = 1. 57 From Home's federal net benefit function, we know dNBZr {Q,qH) [B'{Q) ~ c'(qH)} dqH dqF dan + B'(Q) (3.11) It is straightforward to show that, when an = 1, the contract curve can not be satisfied unless B'(Q) — c'(g#) < 0. As well, imposing aH = 1, it can be shown that Home's Nash bargaining abatement is increasing in aH and Foreign's Nash bargaining abatement is decreasing in aH- Therefore, both terms on the right hand side of (3.11) are negative. As long as a n is close to 1, Home is strictly better off at the R-F international agreement. Intuitively, moving from the F-F agreement switches the burden of abatement from Home to Foreign. In fact, Home's abatement falls by more than Foreign's increases, and global abatement also falls. Therefore, Home receives fewer benefits from global abatement but enjoys a cost savings from undertaking less domestic abatement. When aH is close to one, the regional government values global abatement almost as much as the federal government, and the fall in B{Q) is smaller than the fall in c(qH). On the other hand, by the definition of the F-F contract curve, Foreign's indifference curve for F-F agreement net benefits is tangent to the 45° line at the F-F agreement. As such, Foreign is better off at the F-F agreement than any point below the 45° line. Since the R-F agreement involves less Home abatement and more Foreign abatement than the F-F agreement, Foreign is always worse off at the R-F agreement. The results of this subsection are formalized in Proposition 3. 58 Propos i t ion 3 (a) For aH sufficiently large, Home's net benefits are higher under the R-F international environmental agreement than the agreement reached by the two federal governments, (b) Foreign is always worse off under the R-F agreement relative to the F-F agreement. Regional-Regional (R-R) Agreements Suppose that the regulatory powers lie with the regional governments in both countries. an is the proportion of Home's population in its polluting region and aF is the corre-sponding value for Foreign. We first consider the case when the regional governments constitute the same proportion of their countries, then the case of asymmetric regions. Symmet r ic Regions Suppose that = aF = ct, so that the size of the regions relative to their countries is the same. The symmetric R-R Nash bargaining abatement levels, Ijjj1 and qRR are the solutions to The first order conditions imply that the Nash bargaining solution is the intersection of the symmetric R-R contract curve, implicitly defined by: (3.12) (aB(Q) - c(qF) - aB{QRR) + c($*)) . aB' (Q) ~ c'(qH) aB'(Q) aB'(Q) aB'(Q) - d(qF) (3.13) 59 and the symmetric R-R agreement locus, implicitly defined by: c'(qH) = aB(Q)~c(qH)~aB(QRR) + c(gRR) c'M aB(Q) ~ c(qF) - aB(QRR) + c ( ^ ) ' 1 ' ' It is straightforward to show that the R-R contract curve lies everywhere closer to the origin than the F-F contract curve. Since the threat point abatement levels are equal, the agreement locus coincides with the 4 5 ° line. Therefore, the symmetric R-R agreement lies at a point on the 4 5 ° line closer to the origin than the F-F agreement. Recall that the indifference curves of both federal governments for the net benefits at the F-F agreement are tangent to the 4 5 ° line at (qFF\qFf). Therefore, both countries are worse off at the symmetric R-R agreement (see figure 3 . 5 ) . Intuitively, the strategic advantage enjoyed by Home when its regional government negotiates with Foreign's federal government is lost when the region negotiates with an equal sized Foreign region. In fact, the R-R agreement will involve less global, Home and Foreign abatement than the F-F agreement. Since the opposing country's abatement does not increase in response to the reduction in domestic abatement, both countries are worse off.9 This result is formalized in Proposition 4 . Propos i t i on 4 For all = aF = a, both countries are worse off under the R-R international environmental agreement relative to the F-F agreement. 9 This result corresponds to that in Jones (1989b) which shows that when both principals can choose a negotiator in the first stage to bargain on their behalf in the second stage, both will be worse off than if they had to negotiate for themselves. 60 Asymmetric Regions Now suppose that the two polluting regions are of different sizes, aF ~£ aH. Without loss of generality, let aH < aF, so that Home's region consti-tutes a smaller proportion of Home than Foreign's region. This subsection determines whether a country can be better off when asymmetric regions hold regulatory power. The asymmetric R-R agreement is the solution to: max 1H ax (a„B(Q) - c(qH) - aHB(QRR) + c(<^R)) (3.15) (aFB(Q) - c(qF) - aFB(QRR) + c ($* ) ) , where q§R and q^R are the asymmetric R-R threat point abatement levels. The Nash bargaining first order conditions imply that the international agreement lies on the asym-metric R-R contract curve, implicitly defined by: aHB'{Q) - c'(qH) aFB'(Q) (3.16) otHB'(Q) aFB'(Q) - c'(qF) and the asymmetric R-R agreement locus, implicitly defined by: C V ) = <*HB{Q) - c(qH) - aHB{QRR) + c(<%R) cfM aFB(Q) - c{qF) - aFB(QRR) + c (g^ ) ' [ ' ' It is straightforward to show that when the opposing country's abatement is held constant, domestic abatement is smaller on the R-R contract curve than on the F-F contract curve. Therefore, the R-R contract curve lies closer to the origin. Since Home's 61 threat point abatement is lower than Foreign's threat point abatement, the asymmetric R-R agreement locus lies everywhere below the 45° line. Recall that Foreign prefers the F-F agreement to all points below the 45° line. There-fore, Foreign is always worse off at the asymmetric R-R agreement than at the F-F bargaining solution. To compare Home's net benefits at the F-F and asymmetric R-R agreements, suppose ap = 1- Proposition 3 states that when an is sufficiently large, Home strictly prefers the R-F Nash bargaining equilibrium to the F-F agreement. Since Home's Nash bargaining net benefits are continuous, Home must also prefer the agreement signed when ap falls marginally from 1 such that aH is still smaller than ap. Therefore, by continuity, we can state the following corollary to Proposition 3. Corollary 2 When an < ap,(a)for aH and ap sufficiently large, Home prefers the asymmetric R-R agreement to the F-F agreement, and (b)Foreign is worse off under the asymmetric R-R agreement. 3.4 An Example To better illustrate the results and intuition of the paper, this section presents an example of the bargaining model for specific functional forms. Suppose that federal benefits from global abatement are given by B(Q) = \n(Q) and the costs of domestic abatement are 2 2 c ( ? t ) — \- Therefore, the country and federal net benefits are NB[(Q) = ln(Q) — 62 2 % — H,F and the regional net benefits are NBR(Q) — a* ln(Q) - i = H,F. For the purposes of this example, aH takes on values between 0.05 and 1 with increments of 0.05. 3.4.1 F-F Agreement Suppose that the powers to negotiate and enforce the agreement lie with the federal gov-ernments. The Nash noncooperative threat point between the two federal governments is given by W+W) =q"  = qp ' and q%F = q^F = \\f2. At the F-F threat point, the home country receives net benefits of NBFT(Qff\q^F) = 0.096574. The F-F Nash bargaining international agreement is given by max (in(qH + qF) - - 0 . 0 9 6 5 7 4 ) (\n(qH+qF) - ^ £ - 0 . 0 9 6 5 7 4 ) . \ I J \ 1 J The solution to this optimization is q^ = qFF = 1 and Home's net benefits are NBF(QFF,qFF) = 0.19315. 3.4.2 R-F Agreement Now suppose that Home's regional government negotiates with Foreign's federal govern-ment. If negotiations breakdown, the domestic and foreign abatement levels are defined 63 by the first order conditions 1 and q*F = . and F = , 1 . The net benefits of Home are NBF(QRF, qRF) = In ( , a « + . 1 ) - i - ^ - . Figure 3.6 plots Home's net benefits at the F-F and i?-F threat points as functions of Home is better off when the jurisdiction lies with the region as long as aH > 0.3. The R-F agreement is the solution to max I \n(qH+qF)-lq2H-\n ( . a H + , 1 J +1- °& Figure 3.7 shows Home's payoffs under the F-F and R-F agreements as functions of For this example, Home is better off under the agreement signed by its region for all aH. 3.4.3 R-R Agreement Consider the constitutional framework under which the regions of both countries hold the power to negotiate and enforce international agreements. First let a# = ap = CY. 64 The threat point abatement levels solve a tflR _ ^RR £RR , £RR HH — HF > HH Hp and q§R =qRR == The non-cooperative payoffs to the two countries are NBf(QRR, l n ( v l + v f ) ~ 22> * ~ • T n e symmetric R-R agreement is the solution to m a x ( l n ( t e + g p ) - i , | , - l „ ^ + J) + Figures 3.8 and 3.9 plot Home's payoffs under the R-R and F - F threat points and agree-ments as functions of a. Clearly Home and Foreign are worse off under R-R for all a. Finally, consider the case when aH ^ a F . The threat point abatement levels are given by £RR i ^RR HH — u HH "T" HF £RR , £RR HF u> HH ' 9> and <r£R = , a f I , while = , " F We compare Home's net benefits at the V ( a H + a f ) \J(aH+aF) asymmetric R-R and F - F threat points as functions of aH holding constant a F . Figure 3.10 shows the net benefits of the home country at the F - F and R-R threat points when 65 aF = 0.5 and aF = 0.9. As the size of the foreign region increases, Home's net benefits are higher for all aH. However, even when aF = 0.9, the net benefit function for R-R lies everywhere below that at the F-F threat point. In fact, only when aF > 0.98 can Home be better off at the R-R threat point if a# is in a range between zero and aF. Figure 3.11 plots Home's net benefits under the F-F and the asymmetric R-R Nash bargaining agreements for aF — 0.5 and aF — 0.9. Again, when Foreign's region is small, Home prefers the F-F agreement for all values of However, in comparison to the threat point, Foreign's region need not be as large in order for Home to prefer the R-R agreement. For example, when aF = 0.9, Home prefers the R-R agreement to the F-F agreement for some values of an but prefers the F-F threat point for all aH. 3.5 Conclusions This chapter examines the strategic advantage that may be created when regulatory powers within a federation lie with regional governments rather than federal governments. A n international agreement for the abatement of a public good is modeled as a cooperative game between two countries. It is assumed that one region within a federation preforms all of the abatement for the country and that an exogenous constitution assigns both the power to negotiate and enforce international agreements to either the federal or regional government. It is shown that, although domestic welfare is maximized by the federal government, a country can be better off when the regional government has jurisdiction over the enforce-66 merit and signing of international agreements. Specifically, when the opposing country's regulatory powers lie at the federal level, the domestic country is better off having powers lie with its region as long as the region's preferences are not too far away from that of the federal government. On the other hand, a country can only be better off when regulatory powers lie with both regions if the domestic region is smaller than the foreign region and if the domestic region is sufficiently large. Intuitively, the region's relative aversion to abatement gives the country a strategic advantage when its region negotiates international agreements. This advantage is anal-ogous to that enjoyed if the country were able to choose a negotiator. That is, relative to the federally negotiated agreement, domestic abatement falls but foreign abatement increases in response. As long as the domestic region is sufficiently large, the increase in net benefits from the substitution away from domestic abatement outweighs any losses from reduced global abatement. However, this strategic advantage is lost when two re-gions of equal size hold both regulatory powers. In this case, both countries are worse off when the regions negotiate and enforce the international agreement. Therefore, the paper shows that exogenous political institutions can offer a strategic advantage in international negotiations analogous to that enjoyed by a principal that can delegate negotiation au-thority. 67 Chapter 4 International Environmental Agreements and Domestic Divisions of Regulatory Power 4.1 Introduction There is significant academic and political attention being paid to transboundary pollu-tion concerns such as greenhouse gas emissions. In the absence of international agree-ments, abatement of such emissions will be underprovided. Therefore, international agreements such as the Kyoto Protocol of 1997 and the Canada-U.S. Acid Rain Agree-ment of 1991 are being established. One issue of interest is whether domestic political institutions influence the outcomes of these negotiations. 68 In Chapter 3, it was shown that the distribution of regulatory powers between the federal and regional governments, or between the E U and member states, can influence international environmental agreements in the same way as the ability of countries to delegate negotiation powers. However, the analysis in Chapter 3 was limited to agree-ments signed when the power to both negotiate and enforce international agreements lies with either the federal or regional governments. In reality, the powers to negotiate and enforce international agreements can lie with different levels of government, typically with regional governments enforcing agreements signed by the federal government. As well, such divisions of power between levels of government are often seen as a hindrance to a country's ability to sign and enforce agreements.1 The purpose of this chapter is to examine the possible strategic advantage created when a domestic regional government enforces abatement levels agreed to by the federal government. The strategic effect examined arises because federal governments may have to convince their regional government to enforce the agreement and doing so may provide the federal government with preferences that are relatively averse to abatement. Again, the distribution of domestic regulatory powers may create a strategic advantage similar to that offered by the ability to delegate negotiation authority. As in Chapter 3, we suppose two countries cooperatively bargain over abatement levels of a transboundary pollutant. Each country has a federal government that maximizes domestic net benefits and at least two regional governments maximizing the net benefits x See Meune i r and Nicolai 'dis (1999) for a discussion of this argument being used by the E u r o p e a n C o m m i s s i o n i n i ts fight for the author i ty to negotiate a l l in ternat ional agreements. 69 of their region. We maintain the assumption that one region produces all of the country's emissions and the regional government prefers less abatement than the country. We suppose that when enforcement powers lie with regions, the federal government negotiates international agreements subject to the constraint that the region may need to be compensated to ensure enforcement of the agreement. Wi th perfect information, the opposing country will not agree to any transfer from the federal to the regional government except the lump sum transfer that compensates the region just enough to induce enforcement. Transfers are costly for the federal government and we assume that transfers take place only if an agreement is reached. We show that when the opposing country's federal government holds all regulatory powers, the domestic country prefers to have the enforcement power lie with its region as long as the region is sufficiently large. In fact, the federal government's commitment to costly transfers has the effect of increasing its aversion to domestic abatement. As long as the region's preferences are not too different from its own, the strategic advantage provided by making the transfer implies that the country is better off when powers are divided. On the other hand, if regions of the same size in both countries hold the enforcement power, both countries can be no better off than when the two federal governments hold all powers. In addition to the delegation literature, the question addressed in this chapter is also related to the political science literature examining a negotiator's simultaneous interac-tion with other countries and a domestic political player. In general, this literature focuses 70 on arms negotiations and sometimes provides brief comments on trade and environmental agreements. A number of papers examine the role of regional veto power or legislative voting (see Putnam (1988), Mayer (1992), Mo (1994) and Milner and Rosendorff (1997)) while Iida (1993) and Dupont (1994) investigate domestic political constraints in situ-ations with uncertainty and asymmetric information. The authors find that domestic constraints can alter the non-cooperative international bargaining outcome. Our model differs from this literature in the following ways. First, the existing papers do not provide the negotiator with the ability to convince domestic parties to accept the agreement. Secondly, although the models do not always explicitly discuss the outcome if bargaining breaks down, they suggest that the federal governments make decisions in the absence of an agreement. The existing models correspond well to the division of powers implied in the required ratification of international agreements in the United States but do not correspond closely to the structure of federalism in Canada. In Canada, the federal government has the ability to make transfers to the regions, although such transfers are likely costly. As well, the federal government does not have the jurisdiction to enforce abatement targets, and in the event that negotiations break down, the regional governments make abatement decisions. The chapter proceeds as follows. Section 4.2 presents the general model, section 4.3 presents solutions and comparisons and section 4.4 presents a specific example. Section 4.5 concludes. 71 4.2 The Model 4.2.1 The players There are two countries, Home (H) and Foreign (F), each governed by a federal gov-ernment. Within each country, there are at least two regions with individual regional governments. We assume that one region in each country is responsible for all of the emissions in their country. Therefore, abatement accomplished by the country will be undertaken in the polluting region. This assumption captures the fact that emissions are often localized in specific regions within a country. For example, much of the cost of greenhouse gas reductions in Canada would be borne by the energy industry, located primarily in Alberta. 2 We suppose that the polluting region represents proportion a* of country i's total population. Furthermore, we assume that a region of size QJJ receives an c*i share of country i's benefits from abatement. There are four potential players in the game: Home's federal government, Home's regional government, Foreign's federal government, and Foreign's regional government. A l l players are assumed to have the same complete information set. 2 Similar results would hold if a relatively large share of domestic pollution originated in a specific region. The assumption is made in order to isolate the effect of divisions of power without addressing issues such as multi-party bargaining within countries. These issues are an interesting area for future research. 72 4.2.2 T i m i n g Before the game begins, the exogenous constitution of each country establishes which level of government has jurisdiction over the negotiation of international agreements and the enforcement of the agreements. In accordance wi th the Canadian constitution, we assume that the negotiation power always lies wi th the federal government. However, the jurisdiction over enforcement may lie wi th the federal government or regional gov-ernments. 3 The t iming of the game depends on which level of government holds enforcement power. We use as our benchmark the regime in which both negotiation and enforcement powers lie wi th the federal governments (F-F). In this case, the game is a one stage coop-erative bargaining game between the two federal governments. The federal governments negotiate over abatement levels and the agreement is the Nash bargaining solution. If negotiations break down, the federal governments play a noncooperative game in abate-ment levels. The Nash equilibrium is assumed to be the result and represents the threat point i n the bargaining game. W h e n enforcement and negotiation powers are divided across levels of government, the game is comprised of two stages and we use backwards induction to solve for the equilibrium. There are two possible regimes: the region i n only one country holds en-forcement power, or both regions have jurisdiction over enforcement. Suppose the power to enforce agreements lies wi th Home's regional government but 3 Chapter 3 examines the effect of having both the enforcement and negotiation powers lie with the region rather than the federal government. 73 Foreign's federal government. In the first stage, the two federal governments coopera-tively bargain over abatement levels subject to inducing Home's region to enforce the agreement. The constraint reflects the fact that Home's federal government may have to make a costly transfer to ensure that the region will enforce the agreement. If ne-gotiations breakdown in the first stage, the enforcing governments (Home's region and Foreign's federal government) play a noncooperative game in abatement levels and the Nash equilibrium obtains. This is the threat point in the first stage bargaining game. We assume that in all noncooperative games the cost of transfers is sufficiently high that no transfers are made.4 If a first stage agreement is reached, in the second stage, Home's regional government decides whether to enforce the first stage agreement. We assume that the region has two choices. The region can undertake the agreed upon abatement level or it can play a noncooperative game in abatement levels with Foreign's federal government. Intuitively, we suppose that Foreign's federal government signs the agreement subject to the region enforcing the agreement. If the region fails to comply, Foreign reverts to its best response behaviour and the Nash equilibrium between the two enforcing governments results. If the region adheres to the agreement, the Nash bargaining solution obtains. When the enforcement powers in both countries are held by regional governments, the game is as follows. In the first stage, the two federal governments cooperatively bargain 4 T h i s assumpt ion is made for s impl i c i ty and reflects the idea tha t the p o l i t i c a l costs o f transfers necessary to commi t to an internat ional agreement are lower than for a transfer i n the absence of an agreement. T h e general nature of our results are not expected to depend on this assumpt ion. 74 over abatement levels subject to inducing both regions to enforce the agreement. If first stage negotiations break down, the two regions play a noncooperative game in abatement levels, and the Nash equilibrium results. This is the threat point of the bargaining game and again, no transfers are made. If an agreement is reached, in the second stage, the two regions individually choose whether to enforce the agreement or play a noncooperative game in abatement levels. Notice that there are multiple equilibria in the second stage game. If both regions enforce the agreement, they receive transfers which make them indifferent between the agreement and the Nash noncooperative equilibrium. If a region believes the opposing region will not enforce the agreement, it is indifferent between enforcing and not enforcing the agreement. As such, there are two pure strategy Nash equilibria: both regions enforce the agreement and both regions fail to enforce the agreement.5 We suppose that, if the equilibrium involving enforcement of the agreement exists, it will be obtained. If the regions enforce the agreement, the Nash bargaining solution results. If at least one region fails to enforce the agreement, the Nash noncooperative equilibrium between the two regions obtains and no transfers are made. 5 There will also be a mixed strategy equilibrium, but we restrict our discussion to pure strategy equilibria. 75 4.2.3 Payoffs The federal government of country i has net benefits of NBf(Q, Qi) = B{Q) - c(gi) - \6U i = H,F, (4.1) which are assumed to correspond to the net benefits of country i. The countries are assumed to be identical, denotes abatement by country i, and Q = qn + qF is global abatement. Since emissions reductions is a global public good, the countries receive benefits from global abatement, but only face the costs of domestic abatement. B(Q) is assumed to be continuous, increasing and strictly concave while c(qi) is continuous, increasing and strictly convex. This implies that net benefits are continuous, increasing and concave. Qi is the lump sum transfer required to induce the region in country % to enforce the agreement.6 Qi must give the region the same payoffs from enforcing the agreement and receiving the transfer as it receives in the noncooperative Nash equilibrium between the enforcing governments. If, in the absence of a transfer, the region prefers the international agreement to the Nash equilibrium, no transfer is made (Qi = 0). The country can not make a larger transfer since the opposing country can observe the payoffs of the region 6 An alternative approach would be to assume that the transfer has a typical linear contract structure (9 +Pqi). Since /3 moves the federal government's reaction function, this would allow the federal govern-ment to choose (3 strategically to alter the international agreement. However, since all that is required to induce a region to undertake the agreed level of abatement is a lump sum transfer, this supposes that the foreign federal government accepts the agreement conditional on a positive (5 knowing that only a lump sum transfer is required. We choose to concentrate on the effect of the division of powers when the federal government can not use the transfer in a purely strategic manner. 76 and knows that such a transfer is not necessary to ensure enforcement of the agreement. That is, in the first stage, the opposing country will only agree to a transfer that just satisfies the region's participation constraint. Finally, A is the marginal cost of making the transfer to the region, so that transferring one dollar from the federal to the regional government costs (1 +A) dollars. The marginal cost of a transfer reflects both the possible social costs of distortionary taxation used to collect the funds for the transfer7 and political costs of making transfers between regions. The regional government of country i has net benefits of NB*{Q,qi) = atB{Q) - c($) + 0U on e (0,1), i = H,F. (4.2) Again, q i is abatement by country i, and Q = g# + qp is global abatement. The region is assumed to receive a proportion a* of its domestic benefits but face all domestic abatement costs, di is the transfer received from the federal government. Overall, the international environmental agreement corresponds to the Nash bargain-ing solution between the two federal governments subject to the individual rationality constraint of the enforcing regional governments. The bargaining strengths of the two federal governments are assumed equal, and in the event that negotiations break down, the Nash non-cooperative equilibrium between the two enforcing governments will result. 7 This is the standard argument for a positive cost of spending public funds used in numerous liter-atures such as regulation under asymmetric information (see Laffont and Tirole (1989)). See Atkinson and Stiglitz (1980) and Snow and Warren (1996) for discussions of the marginal cost of public funds. 77 The international environmental agreement is defined by max (NBFH{Q,qH) - XBH - NB*(Q,qH)) ^NBp(Q,qF) - X6F - 7V£?f ( Q , g » ) where max max {0,NB*(Q,qH) {0,NB*(Q,qF) 0 0 NBR(Q,qF)\, if Foreign's region enforces NBR(Q,qH)}, if not if not if Home's region enforces (4.3) where qn and qF are Home and Foreign's threat point abatement levels. Again, if enforcement powers lie with the federal governments no transfers are made. If the enforcement powers he with the regions, either the region enforces the agreement or the enforcing agents play a noncooperative game. If the region prefers the Nash bar-gaining agreement to the noncooperative equilibrium, it does not require compensation in order to enforce the agreement and the transfer is 0. If the region prefers the nonco-operative equilibrium, the federal government transfers just enough money to ensure the enforcement of the agreement. Therefore, the transfer is equal to the difference between the region's net benefits at the noncooperative equilibrium and those at the bargaining solution. 78 4.3 Solutions and Comparisons 4.3.1 Noncoopera t ive Equ i l i b r i a If negotiations break down in the first stage, or if regions fail to enforce agreements in the second stage, the noncooperative Nash equilibrium between the two enforcing governments results. This subsection presents the possible Nash equilibria.8 Notice that concavity of B(Q) and convexity of c(qi) imply that the second order conditions for the Nash equilibria are satisfied. In our benchmark case, both federal governments hold enforcement power and there is no second stage. If negotiations break down, the federal governments noncooperatively choose abatement levels. The resulting Nash equilibrium abatement levels, q%F and q§.F are defined by: B'&^-^r/) = o B\QFF)-c'{rFF) = 0. Since the countries are symmetric, the threat point abatement levels and net benefits are equal. Figure 4.1 shows the threat points graphically as the intersection of the reaction functions of the two federal governments, RFT(qF)and RF(qH). Suppose the enforcement powers lie with Home's regional government and Foreign's federal government. The noncooperative equilibrium represents the first stage threat 8 Comparisons of the net benefits at the different Nash equilibria are presented in Chapter 3. 79 point as well as the result if Home's region fails to enforce the agreement in the second stage. The Nash equilibrium abatement levels, q^f and gp F , are the solution to the first order conditions: 0 0. These equations define Home's regional and Foreign's federal reaction functions as shown in figure 4.2. The threat point is represented as the intersection of these curves. Since the reaction function of Home's region lies everywhere below that of Home's federal government, Home's threat point abatement level is less than that of Foreign. Finally, if enforcement powers lie with both regions, the first stage threat point and the result if a region fails to enforce the agreement in the second stage is the equilibrium defined by: CLiB'iQ™) - c'(qfR) = 0, i = H,F. If an = cup, the abatement levels are symmetric but smaller than those in the benchmark threat point. If aH ^ aF, the smaller region will undertake less abatement at the Nash equilibrium. B'(QRF)-c'(q*F) = 80 4.3.2 Coopera t i ve E q u i l i b r i a The Federal-Federal (F-F) Agreement This subsection presents the international environmental agreement reached when the both federal governments hold negotiation and enforcement powers. This case is the benchmark to which other agreements will be compared. Wi th federal control, 6H — Bp = 0, and the F-F equilibrium agreement (qFrF,qFF) solves max (B(Q) - c(qH) - B ( Q F F ) + c ( ^ F ) ) (B(Q) - c(qF) - B ( Q F F ) + c ^ ) ) , (4.4) where q%F and qF,F are the threat point abatement levels. On figure 4.1, the gains from international cooperation are represented by the lens shaped area formed by the indifference curves passing through the threat point. The Nash Bargaining solution simply chooses the point in the lens shaped area which corresponds to the solution to (4.4). Given an interior solution, the first order conditions9 for this problem are [B'(Q) ~ c(qH)][B(Q) - c(qF) - B ( Q F F ) + c(qtF)] = -B'(Q)[B(Q) - c(qH) - B ( Q F F ) + c(tHF)} and 9 The second order conditions for the Nash bargaining solutions are discussed within the proofs of the propositions provided in Appendix B. 81 [B\Q) - c(qF)][B(Q) ~ c(qH) - B(QFF) + c ( ^ ) ] = -B'(Q)[B(Q) - c(qF) - B(QFF) + c^)). Taking a ratio of the first order conditions implies that the solution lies on the contract curve defined implicitly by B'(Q) = B'{Q) - d{gH) B'(Q)-c'(qF) B'(Q) • The contract curve is the locus of points at which the indifference curves of the two federal governments are tangent. It is straightforward to show that, in (qF,qn) space, the contract curve is downward sloping and has a slope of —1 when crossing the 45° line. As well, the contract curve can not be satisfied unless B'(Q) — c'(qi) < 0, i = if, F, which characterizes the region outside the federal reaction functions. Rearranging the first order conditions implies that the solution also lies on the "agree-ment locus", defined implicitly by c'(gH) _ B(Q) - c(gH) - B(QFF) + c{r/) U Q ) CM B(Q) - cM ~ B(QFF) + c ( $ F ) ' 1 ' ' The agreement locus determines which point along the contract curve will represent the agreement and reflects the choice of the Nash bargaining solution concept. Intuitively, 82 the agreement locus determines the division of the bargaining surplus, as the right hand side of (4.6) is the ratio of gains to cooperation of each country. It is straightforward to show that the agreement locus is upward sloping and passes through the endpoints of the bargaining lens. The Nash bargaining solution corresponds to the intersection of the contract curve and agreement locus. For the F-F regime, the agreement locus corresponds to the 45° line and Nash bargaining abatement levels are equal. The Regional-Federal (R-F) Agreement Suppose that the enforcement power lies with Home's regional government and Foreign's federal government. The R-F Nash bargaining international agreement signed by the federal governments, (qRF, qRF) is the solution to max (B(Q) - c(gH) - X6H-B(QRF) + c^)) (B(Q) - c(qF) - B(QRF) + c ( $ F ) ) where (4.7' 6H = max {o, aHB(QRF) + c ( § £ F ) - aHB(Q) + c(qH)} . Recall that q^F and qpF correspond to the abatement levels at the Nash non-cooperative equilibrium between Home's regional and Foreign's federal government. Intuitively, the two federal governments negotiate over abatement levels subject to the constraint that if Home's region is worse off under the agreement relative to the 83 threat point the federal government must make a transfer to the region. This transfer ensures that the region receives the same net benefits when it enforces the agreement and receives the transfer as it would at the non-cooperative Nash equilibrium between itself and Foreign's federal government. The transfer is equal to zero if the region prefers the agreement to the noncooperative equilibrium, or aHB(QRF) — c(q^jF) —aHB(Q ) + c(qRF) < 0. We now determine for what values of aH the transfer is positive. When aH = 1, the regional net benefits correspond to the federal net benefits and the region prefers the agreement to the threat point. Therefore, when aH = 1, the transfer is zero. At the other extreme, when aH — 0, the transfer is positive by the following reasoning. First, because the region receives no benefits from global abatement, no domestic abatement is undertaken at the threat point, and the region's threat point net benefits are equal to zero. Secondly, when a.n — 0, Home's federal government enjoys benefits from global abatement and the Nash bargaining abatement level is positive ( ? § F > 0). If the region is forced to uphold the agreement with no transfers, it receives negative net benefits, and the transfer must be positive. Therefore, there must be is at least one an € (0,1) for which the region receives the same benefits at the agreement and the threat point. If the region must enforce the agreement in the absence of transfers, its net benefits at the R-F threat point and corresponding Nash bargaining agreement for the functional form considered in Section 4.4 are shown in figure 4.3 as functions of a/ / . 1 0 For this WB{Q) = ln(Q) and c ( % ) = &,i = H,F. 84 example, there is a unique value of OLH for which the payoffs are equal. If aH is larger than this value, there is no transfer and for all smaller an there is a positive transfer. In general, there may be more than one value of aH at which the payoff functions cross. If we define an to be the highest aH such that the region's threat point and agreement payoffs are equal, the transfer is zero for all aH > aH. As well, by continuity of regional net benefits, the threat point payoffs lie above the Nash bargaining payoffs for aH just less than aH, and the transfer is positive. Therefore, the following is true. 1 1 Lemma 1 When Home's region and Foreign's federal governments hold enforcement power, there exists a unique 5# < 1 such that, for all an > 5#, OH = 0, and for an less than but sufficiently close to an, OH > 0. OLH is the highest value of an such that aHB(QRF(aH)) - c{q*F{aH)) - a H B ( Q R F (aH)) + c(qRF(aH)) = 0. When aH > an, 0H — 0 and the R-F Nash bargaining agreement is the solution to max (B(Q) - c(qH) - B ( Q R F ) + c ^ ) ) (B(Q) - c(qF) - B ( Q R F ) + c ^ ) ) . (4.8) Note that this does not correspond to the benchmark F-F agreement since the threat point is the non-cooperative equilibrium between Home's regional and Foreign's federal government rather than the two federal governments. The corresponding first order conditions imply that the agreement satisfies the R-F contract curve implicitly defined n The proofs of Lemma 1, and all other results, are provided in Appendix B. 85 by: [B'(Q) - c'(qH)) B'(Q) B'{Q) [B>(Q)-c>(qF)Y W and the R-F agreement locus implici t ly defined by: c'(to) = B(Q)-c(qH)-B(QRF) + c(q*F) c'M B(Q)-c(qF)-B(Q^) + c(q§F)' B y inspection, the solution lies on the same contract curve as the F-F agreement i n (4.5). This is because the negotiators have the same preferences i n the two regimes. O n the other hand, the R-F agreement locus lies everywhere below the 45° line, and therefore below the F-F agreement locus (see Figure 4.4). Since the threat point involves more Foreign abatement and less Home abatement, the endpoints of the bargaining lens have shifted down. In this region, as aH falls, the agreement locus shifts downward while the contract curve remains unchanged. A s long as marginal costs are not too convex i n abatement, 1 2 as Home's abatement falls, Foreign's abatement increases enough to ensure that global abatement is nondecreasing. Since Home's net benefits are increasing i n global abatement and decreasing i n domestic abatement, Home is better off at the R-F agreement (see Figure 4.4). Final ly, notice that Foreign's indifference curve for the net benefits at the F-F agree-ment is tangent to the 45° line at the F-F agreement. A s such, Foreign is worse off 12 T h e specific condi t ion imposed on the marg ina l costs of abatement is discussed i n A p p e n d i x B . 86 at any agreement below the 45° line. When aH > aH, the R-F agreement locus lies below the 45° line, and Foreign prefers Home's enforcement powers to lie with the federal government. When OLU is less than but sufficiently close to aH, 9H = aHB(QRF) — c(qjf) — aHB(Q) + c(qu) > 0, and the Nash bargaining objective function can be written as max ((1 + Xag)B(Q) - (1 + \)c(qH) - (1 + XaH)B(QRF) + (1 + A ) c ( ^ ) ) (B(Q) - c(qF) - B(QRF) + c ^ ) . ) (4.11) The first order conditions again imply that the Nash Bargaining solution lie on the R-F contract curve, implicitly defined by (1 + XaH)B'(Q) - (1 + X)c'(gH) B'(Q) (1 + XaH)B'(Q) B'(Q) - c>(qF)' ^ L Z ) and the R-F agreement locus, implicitly defined by (1 + A ) c / ( ^ ) _ ( 1 + XaH)B(Q) - (1 + X)c(gH) - (1 + XaH)B(QRF) + (1 + A)c(gg f) C ' (?F) B(Q) - c(qF) - B(QRF) + c ( $ n (4.13) Comparing (4.12) to the F-F contract curve, it can be shown that the 8H > 0 contract curve lies everywhere closer to the origin. Intuitively, since Home's indifference curves with a positive transfer are everywhere flatter than when On = 0, the locus of tangency points of the negotiators's indifference curves must be closer to the origin. The new 87 contract curve still has a slope of —1 at the 45° line and as long as marginal abatement costs are not too convex, the contract curve is convex. Since the threat point has moved further down along Foreign's reaction function, it is straightforward to show that the 6H > 0 agreement locus lies nowhere above the On — 0 agreement locus (see Figure 4.5). Intuitively, making a costly transfer to the region has the effect of Home's negotiator committing to a lower weight on the benefits of global abatement. As aH falls in this region, Home abatement falls and Foreign abatement increases. As long as an is suffi-ciently close to 5/f, the potential losses from decreasing global abatement and making the transfer are smaller than the cost savings from a reduction in domestic abatement. Therefore, Home prefers the R-F agreement. Again, since the R-F agreement still requires Foreign abatement to be higher than Home abatement, the Foreign country prefers the F-F Nash bargaining solution. The general results of this section can be formalized in Proposition 5. Proposition 5 If Foreign's enforcement powers lie with its federal government and as long as marginal abatement costs are not to convex whenever B'(Q) — c'(qi) < 0, i = H,F, the following are true, (i) For all an > aH and for an less than but sufficiently close to an, Home is better off when enforcement powers lie with its regional government instead of the federal government, (ii) For all an, Foreign is worse off when Home's domestic regulatory powers are divided. In sum, this subsection has shown that when only the Home region has enforcement power, the division of domestic regulatory powers can offer a country a strategic advan-88 tage in international environmental negotiations. This advantage is borne out in two ways. First, since the region has jurisdiction over enforcement, the domestic threat point is stronger in the sense that it involves less domestic abatement and more foreign abate-ment relative to the F-F threat point. Secondly, when powers are divided, the federal government may have to make a costly transfer to the region, which effectively reduces the weight the federal government places on the benefits of global abatement. Regional-Regional (R-R) Agreements Suppose that the enforcement powers of both countries lie with the regional governments. Recall that an is the proportion of Home's population living in its polluting region and ap is the corresponding value for Foreign. We will first consider the case when the regions constitute the same proportion of their respective countries, and then consider the case of asymmetric regions. Throughout, we assume that the marginal cost of public funds is the same in both countries. Symmetric Regions Suppose that the size of the regions relative to their countries is the same, so that an = aF = a. The Nash bargaining agreement abatement levels (qHR,~q~FR) are the solutions to max (B(Q) c(qH)-\eH-B{QRR) + c(q*R)) (4.14) where 89 6H = max {o, aB(QRR) + c(g**) - aB(Q) + c(qH)} 9F = max {0,aB(QRR) + c(gPR) -aB(Q) + c(gF)} . Recall, g|P and are the threat point abatement levels. Here, each federal government makes a transfer just large enough for its region to be indifferent between the international agreement and the threat point. If the regions are better off under the agreement than the threat point, no transfer is made. Since the regions are symmetric, 9H = 6F. Following the same arguments used in the R-F case, when a = 1 both regions prefer the Nash bargaining agreement to the threat point, and the transfer is zero. At the other extreme, when a = 0, both regions prefer the threat point to the Nash bargaining agreement. Therefore, there is at least one value of a at which aB(QRR) — c(q^R) — aB(Q ) + c^f7*) = 0. Defining 5 to be the highest value for which the regional threat point and Nash bargaining payoffs are equal, we know that there is a zero transfer for all a > a and a positive transfer when a is less than but sufficiently close to 5, which we state in Lemma 2. L e m m a 2 When symmetric regions hold the enforcement powers, there exists a < 1 such that, for a > 5, 6JJ = 9F = 0, and for a less than but sufficiently close to a, 6i > 0, i = H,F. a is the largest value of a such that aB(QRR(a)) - c(g£») - aB(QRR(a)) + c(qRR(a)) = 0, i = H, F. 90 When a > a, 9H = 9F = Oand the international agreement is the solution to max (B(Q) -c(qH) - B ( Q R R ) + c(g**)) (B(Q) - c(qF) - B ( Q R R ) + C($**)) . The first order conditions imply that the solution is the intersection of the symmetric R-R contract curve implicitly defined by: B'(Q) _B>(Q)-c>(qH) B'(Q) - c'(qF) B>(Q) and the symmetric R-R agreement locus implicitly defined by: (4.15) O'(1H) = B(Q) - c(qH) - B(QRR) + C(gg*) c'M B(Q) - c(qF) - B(QRR) + c ( ^ ) ' [ ' ' Since the negotiators have the same preferences as in the F-F bargaining game, the contract curve corresponds to the F-F contract curve. As well, the threat point abate-ment levels are equal and the agreement locus coincides with the 45° line. Therefore, for this range of a, the divided powers agreement corresponds to the F-F Nash bargaining solution. Intuitively, when 9H = 6F = 0, the bargaining lens with no division of powers (F-F) is a subset of that when symmetric regions hold enforcement powers but require no compensation. Therefore, the same solution obtains and Home is indifferent between the two agreements (see Figure 4.6). When a is less than but sufficiently close to 5, 6H = 9F > 0, and the international 91 agreement corresponds to max ((1 + Xa)B(Q) - (1 + X)c(qH) - (1 + Xa)B(QRR) + (1 + A)c(g**)) ((1 + \a)B(Q) - (1 + A)c(gF) - (1 + A a )£(Q*«) + (1 + A ) c ( ^ ) ) . (4.17) The first order conditions imply that the solution lies on the symmetric R-R contract curve implicitly defined by: and the symmetric R-R agreement locus implicitly defined by: C(gg) = (1 + Xa)B(Q) - (1 + X)c(qH) - (1 + Xa)B(QRR) + (1 + A)c($gR) C (?F ) (l + A a ) B ( Q ) - ( l + A ) c ( t o ) - ( l + Aa)B(Q««)-r-(l + A)c(§««)" Comparing the contract curves when 0, > 0 and 6i = 0, it is straightforward to show that the Oi > 0 contract curve lies everywhere closer to the origin. Since the threat point abatement levels are still symmetric, the agreement locus still corresponds to the 45° line. Therefore, the new agreement lies at a point on the 45° line closer to the origin than the F-F agreement. In the absence of a transfer, the net benefits of the countries are larger at the F-F agreement than at the symmetric R-R agreement and B(QFF) - c(q%F) > B(QRR) - c(q~HR). By construction, Oi > 0, and the net benefits at the F-F agreement are higher than the net benefits at the R-R agreement less the (l + Xa)B'(Q)-(l + X)c'(qH) (1 + Xa)B'(Q) (1 + Xa)B'(Q) - (1 + X)c'(qF) (1 + Xa)B'(Q) (4.18) 92 transfer. Finally, if for some a < a, 9H = 6F = 0, regional and federal enforcement again lead to the same agreement and the countries receive the same net benefits at the R-R and F-F agreements. Furthermore, for all a < a such that 0H = 6F > 0, the agreement will again lie on the 45° line closer to the origin than the F-F agreement, and the countries will prefer the F-F agreement. The results of this subsection are formalized in the following proposition. Proposition 6 When regions of equal size hold the enforcement power in both countries, both countries are no better off having regulatory powers divided than when both federal governments hold regulatory power. Intuitively, the strategic advantage enjoyed by Home when only its regional govern-ment enforces the agreement is lost when a Foreign region of the same size also enforces the agreement. Since foreign abatement no longer increases in response to the reduc-tion in domestic abatement, both countries are worse off with regional enforcement. In Chapter 3, it was shown that when symmetric regions enforce and negotiate international agreements, both countries are strictly worse off than at the F-F agreement. The differ-ence is that here, since the federal governments always negotiate the agreement, if there are no transfers, the Nash bargaining outcome is unchanged. In fact, countries are only made worse off when they must make a positive transfer to the region since this commits the federal government to a stronger bargaining position. 93 Asymmetric Regions Now suppose that the two polluting regions are of different sizes, aF ^ a H . Without loss of generality, suppose aF > aH, so that Home's region constitutes a smaller proportion of Home than does Foreign's region. In this subsection, we determine whether the countries can be better off when both regions hold enforcement power relative to the case when both federal governments hold enforcement power. By construction, the net benefits of Foreign's region react to a change in aF the same way as the Home region's net benefits react to a change in a^. Therefore, as shown in Lemma 1 for a#, there exists an aF such that the transfer to Foreign's region is zero for all aF >aF and positive for aF less than but sufficiently close to aF. First, because aF > OCH, at any Nash bargaining solution, Home undertakes less abatement than Foreign. Since Foreign prefers the F-F agreement to any point under the 45° line in (qF, qH) space, Foreign can never be better off when both regions hold the enforcement power. To determine whether Home can be better off at the asymmetric R-R agreement, suppose aF = land aH € [5#,1). By Lemma 1, there are no transfers made at the bargaining solution. By Proposition 5, Home is strictly better off at the R-F agreement than the F-F agreement. Since the Foreign federal and regional net benefits coincide when aF = 1 ,we know that Foreign's region strictly prefers the agreement to the threat point. Therefore, if aF falls marginally from 1, there are still no transfers made at the bargaining solution. Since Home's net benefits are continuous, Home must still prefer the new asymmetric R-R agreement to the F-F agreement. 94 Now suppose ap = l and aH is slightly below aH. By Lemma 1, there is a posi-tive transfer made by Home's federal government but Foreign's region strictly prefers the agreement to the threat point (Op = 0). By Proposition 5, we know that if a# is sufficiently close to Home strictly prefers the R-F agreement to the F - F agreement. Again, suppose ap falls marginally from 1. By continuity of the region's net benefits, if the reduction in ap is sufficiently small, there is still no Foreign transfer (6p — 0). Since Home's net benefits are continuous, Home must still prefer the new asymmetric R-R agreement to the F - F agreement. Therefore, the following corollary is true by continuity and Proposition 5. Corollary 3 Let an be defined as in Lemma 1. Assuming that marginal abatement costs are not too convex when B'(Q) — c'(</,) < 0, i = H, F, the following is true, (i) For any an < &p, an not too far below an, and ap is sufficiently close to 1, Home prefers the asymmetric R-R agreement to the F-F agreement, (ii) For all an < ap, Foreign is always better off at the F-F agreement than at the asymmetric R-R agreement. In sum, this subsection has examined the effect of having both regions enforce interna-tional agreements relative to the case when both federal governments hold enforcement power. It was shown that the two countries can be no better off when regions of the same size hold enforcement powers in both countries relative to the federal governments holding all regulatory powers. Intuitively, regional enforcement provides no strategic ad-vantage if a region of the same size enforces agreements in the other country. However if regions of different sizes hold enforcement powers in both countries, it is possible for 95 a country to be better off with divided powers if its region is smaller than the opposing region, although further conditions on the size of the two regions is needed. Finally, a country is always worse off with regional enforcement in both countries if the domestic region is larger than the opposing region. 4.4 A n Example To gain intuition about the general results of the paper, this section presents an example of the bargaining model for a specific functional form for net benefits. As in Chapter 3, suppose that federal benefits from global abatement are given by B(Q) = ln(Q)and 2 the costs of domestic abatement are c(qi) = -|--Therefore, the country and federal net 2 benefits are NB[(Q) = ln(Q) — \,i = H,F and the regional net benefits are NBR(Q) = 2 ai\n(Q) — \ , i = H,F. Finally, let the marginal cost of a transfer (A) be 0.2. For the purposes of this example, we assume that a; takes on values between 0.05 and 1 at increments of 0.05. 4.4.1 F - F Agreement Suppose that the powers to negotiate and enforce the agreement lie with the federal governments. Let qFlF and qpF be the Nash noncooperative threat point between the two federal governments, so that f ^FF "FF •ZFF I ^FF\ ~ QH ~ AF J 96 and q\Y = qJF = \y/2. At the F-F threat point, Home receives net benefits of NBF(QFF, q\Y) 0.096574. Therefore, the F-F Nash bargaining international agreement is given by max (hx(qH + qF) - ^q2H - 0.09 6574^ ^ln (qH + qF) - ^q2F - 0.09 6574j . (4. 20) The solution to this system of equations is qHF = q^F = 1 and Home's net benefits are NBF(Q ,qFF) = 0.19315. 4.4.2 R - F Agreement Now suppose that Home's regional government and Foreign's federal government have jurisdiction over the enforcement of the international agreement (R-F). If negotiations breakdown, the domestic and foreign abatement levels are defined by the Nash non-cooperative equilibrium between Home's regional and Foreign's federal governments, de-fined by the first order conditions a H $RF _ n £RF , C f l F HH — u HH + \ rjRF _ f) £RF I -ZRF HF — u -HH "T HF Therefore, q^f = , a H and q§F = 1 .The non-cooperative net benefits of Home's region are NB§(QRF, q*F) = aHln ( s + , 1 ^ - A - ^ and the Nash 97 bargaining R-F agreement solves where (4.21) 9H= max < aH In y/{*H+l) y/(aH+l) J 2aH+l aHB(Q)+c(qH),0 Figure 4.7 shows Home's net benefits under the F-F and R-F agreements as functions of aH. In this example, 9H > 0 for aH < 0.65. That is, when the region's population is smaller than approximately 65% of the national population, the region prefers the non-cooperative Nash equilibrium to the international agreement and Home's federal government must compensate the region in order for the agreed upon abatement level to be enforced. As increases, the region places enough weight on the benefits of global abatement to give it higher net benefits under the international agreement than at the threat point and no compensation is needed (9H — 0) when aH > 0.65, approximately. Figure 4.7 also indicates that for this functional form, Home is better off under the agreement signed by its region for all a# between 0.05 and 1. Moreover, Home's payoffs are monotonically decreasing in the size of the size of the region, so that the smaller the region, the better off is the country. Therefore, as aH falls, the strategic advantage gained by Home outweighs the loss from making a larger transfer to the region. 98 4.4.3 R - R Agreement Now consider the constitutional framework under which the regions of both countries have jurisdiction over the enforcement of abatement policies. First, let aH = aF = a. The threat point abatement levels are given by " fiRR _ n £RR 4- ^RR q H ~~ HH "•" HF •pfRR , Cflfi HF — u> HH "t- qF and q§R = qpR = The regions in both countries require compensation (0H = OF > 0) whenever a < 0.55. When the size of the regions become sufficiently large (a > 0.55), the regions place enough weight on the benefits of global abatement to prefer the agreement to the threat point. Figure 4.8 shows the net benefits of the home country at the F-F and R-R agreements as functions of a . 1 3 As noted in the general model, when QH = 0F = 0, the F-F agreement is attained. When 0H = 9F > 0, both countries are worse off when the regions hold enforcement power relative to the agreement negotiated when both federal governments hold enforcement power. Moreover, as a falls, the net benefits of the countries fall monotonically. Finally, consider the case when the regions in both countries hold enforcement power, but the regions are of different sizes. To briefly examine the possible outcomes, we 13jf we were interested in the incentives for Home to move to regional enforcement given Foreign regional enforcement, a natural comparison would be the R-R agreement to the signed by Home's federal government and Foreign's region. However, we are interested in whether the countries can be better off relative to the case when both federal governments hold all powers. 99 plot Home's payoffs as a function of aH holding aF constant. Figure 4.9 plots Home's payoffs under the R-R agreement when aF = 0.5 and under the F-F agreement. For this example, Home makes a positive transfer to its region when aH < 0.5 while Foreign makes a positive transfer to its region when aH > 0.45. Therefore, 6H > 0 and 6p = 0 when aH G (0,0.4] eH > 0 a n d # F > 0 when aH e [0.45,0.5] 6H = 0 and 8F > 0 when an £ (0.55,1). Notice that when ap is this small, there are no values of an such that both countries have transfers equal to zero. Relative to the F-F agreement, Home prefers to have enforcement power lie w i th the regions only when the domestic region is strictly smaller than Foreign's region. O n the other hand, figure 4.10 depicts the payoffs when aF = 0.9. In this case, Home's federal government makes a positive transfer whenever an < 0.65 and Foreign's federal government never makes a positive transfer. In fact, 6H > 0and6> F = 0 when aH e (0,0.65) 9H = 0 a n d # F = 0 when an 6 [0.65,1). A s in the case when aF = 0.5, relative to the F-F agreement, Home is better off having enforcement power lie wi th the regions only if its region is strictly smaller than the Foreign 100 region. 4.5 Conclusions This chapter examines the role that the distribution of regulatory power within a fed-eration plays in international environmental agreements. Specifically, we consider the welfare effects of having enforcement powers held by the regional governments rather than the federal governments. A n international agreement for the abatement of a global pollutant is modeled as a cooperative game between two countries. It is assumed that one region within a federation performs all of the abatement for the country. A n exogenous constitution assigns the power to negotiate international agreements with the federal government but the power to enforce the agreements may lie with regional governments. If necessary, federal governments use costly lump sum transfers to compensate the region and ensure that the region will enforce the agreement. When the opposing federal government negotiates and enforces international agree-ments, a country prefers to have its domestic regulatory powers divided, provided that its region is sufficiently large. However, the two countries can be no better off when regions of the same size hold enforcement powers in both countries relative to the fed-eral governments holding all regulatory powers. Finally, if regions of different sizes hold enforcement powers in both countries, a country can be better off with divided powers if its region is smaller than the foreign region but sufficiently large relative to the size of the domestic country. 101 Overall, the chapter suggests that the division of regulatory powers within a federation can not only affect the international negotiations of the country but that the country may benefit from having the powers to negotiate and enforce international agreements divided between domestic levels of government. Even when the federal government is restricted to lump sum transfers to induce a region to enforce an agreement, the cost of making the transfer decreases the weight placed on the benefits of abatement and provides a strategic advantage in international negotiations. This strategic advantage is analogous to that enjoyed by a principal that hires an agent to negotiate on her behalf. 102 Chapter 5 Concluding Remarks This thesis presents an examination of two issues concerning the implementation of en-vironmental regulations in Canada. In Chapter 2 we examine the effectiveness of in-spections and warnings in enforcing environmental regulations. We focus on inventory regulations for petroleum storage sites in Manitoba. Between 1982 and 1998, Manitoba Environment responded to 97% of inventory violations with warnings. We develop a two stage probit model of the probability of an inspection and the probability of a violation based on a state dependent model of enforcement. In our model, warnings are effective if they reduce future violations by increasing the probability of an inspection in the future. Our estimation results suggest that the probability of an inspection is increasing in past violations and that the probability of a violation is decreasing in the probability of an inspection. Therefore, Chapter 2 provides evidence that, even in the absence of frequent prosecutions, inspections and warnings may be effective at increasing compliance with 103 environmental regulations. Chapter 2 leads to a number of interesting avenues for future research. In general, environmental regulations are wide ranging and complex. Empirically examining the effectiveness of the various enforcement tools currently employed would provide insight into directions for policy reform. As well, there remain interesting questions concerning the use of warnings to enforce inventory regulations. Our results in Chapter 2 indicate that inspections and warnings increased compliance with inventory regulations, but say nothing about the effectiveness of warnings relative to other forms of enforcement. One possible approach to this question is to study the enforcement of inventory regulations in different jurisdictions within or outside of Canada. If the jurisdictions rely on warnings to different degrees, a study would provide insight into the relative effectiveness of warnings. Chapters 3 and 4 of this thesis examine the strategic effect that the distribution of regulatory powers within a country can have on international environmental agreements. In Chapter 3, we consider whether a country can be better off when regional governments negotiate and enforce agreements instead of the federal government. A model in which two countries cooperatively negotiate over the abatement of a transboundary pollutant is developed. We find that, although the net benefits of the country are maximized by the federal government, the country can be better off when regional governments hold regulatory powers. This is true when the preferences of the region are not too far away from those of the federal government and the foreign country's regulatory powers are held either by the federal government or by a region larger than the domestic region. In 104 these cases, the domestic region's relative aversion to abatement provides the country with a strategic advantage borne out in lower domestic abatement and higher foreign abatement. This advantage is the analogous to that enjoyed when a country is able to delegate negotiation power. In Chapter 4, we extend the model in Chapter 3 to examine whether a country can be better off when international agreements negotiated by the federal government are enforced by the regional government rather than the federal government. If regions have jurisdiction over enforcement, a two stage game is played. In the first stage, the federal governments negotiate an international agreement subject to the constraint that the regions may require compensation to enforce the agreement. In the second stage, the regions decide whether to accept the compensation and enforce the agreement or play a non-cooperative game in abatement with the enforcing government in the foreign country. Compensation is assumed to take the form of costly lump sum transfers and we assume that transfers are only made if an agreement is reached. We show that, even though only lump sum transfers are available, the relative aversion to abatement of the region can again provide the country with a strategic advantage in international negotiations. If the foreign federal government enforces the agreements and the domestic region is sufficiently large, the domestic country prefers to have its regulatory powers divided. On the other hand, if the foreign regional government enforces the agreements, the domestic country can only prefer divided powers if the domestic region is smaller than the foreign region, but still sufficiently large. 105 One limitation of the models in Chapters 3 and 4 is that they do not consider how the distribution of powers may change the number of players involved in the bargain-ing process. In fact, a common argument supporting a centralization of power at the federal level rests on potential for coordination problems if many regions must negotiate either internationally or with the federal government. This argument has been used by the European Commission in its attempt to gain authority over the negotiation of all international negotiations (see Meunier and Nicolai'dis, 1999). 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Statistics Canada (1999), Profile of Census Divisions and Subdivisions in Manitoba, Part B, Ottawa. 56 (1994), Profile of Census Divisions and Subdivisions in Manitoba, Part B, Ottawa. 113 57 (1988), Profile of Census Divisions and Subdivisions in Manitoba, Part 2, Ottawa. 58 (1984), Profile of Census Divisions and Subdivisions in Manitoba. 59. Vickers, J . (1985), "Delegation and the theory of the firm", Economic Journal 95, 138-147. 114 Chapter 7 Appendices 7.1 Appendix A This appendix provides proofs of the propositions stated in the text of Chapter 3. Proposition 1: (a)For an sufficiently large, Home's payoffs are higher at the R-F threat point than at the F-F threat point. (b)For all an, Foreign is better off at the F-F threat point than at the R-F threat point. Proof: First, notice that the second order conditions for the Nash equilibrium require that, holding qF constant, B"(Q) - c"(qH) < 0 and holding qn constant, B"(Q) - c"(qF) < 0. As such, concavity of B(Q) and convexity of c(qi) ensure that the second order conditions are satisfied. Part (a): 115 The net benefit functions of Home's regional and federal governments are the same when aH = 1. Therefore, if we consider a marginal fall in aH from 1, the change in Home's net benefits can be given by 9NBQ^'qH^ evaluated when aH = 1 and imposing the Nash noncooperative first order conditions. In general, dNB%(Q,qH) da = [B'(Q)-c\qH)]^ + B'(Q)dqF 'dqH da H (7.1) and the Nash first order conditions are aHB'(Q)-c'(qH) = 0 B'{Q)-d{qF) = 0. When aH = 1, the first term on the right hand side of (7.1) is zero by Home's first order condition. Totally differentiating the first order conditions of the R-F threat point implies that B"(Q) - d'(qB) B"(Q) dqH ~B'(Q) B"(Q) B"{Q) - c"(qF) dqF 0 da H B'(Q)B"(Q) Since the denominator is Using Cramer's rule, g | = [ B» ( Q )_ c» ( g f j ) 1 [ B„ ( Q )_ c, ( 9 F ) ]_B, ( Q ) 2. nonnegative by the second order conditions and B(Q) is concave, ^ < 0. Therefore, dNBf dcxr. a H = l < 0 and Home is better off at the R-F threat point. 116 Part (b) : Since the R-F threat point must lie on Rp(qn) and the regional government's reaction function is below that of Home's federal government, the R-F threat point equil ibrium involves a more Foreign and less Home abatement than the F-F threat point. A long For-eign's reaction function, B'(Q) — c'(qF) = 0 and Foreign's net benefits are independent of domestic abatement. However, Foreign's net benefits are increasing in Home abatement. Since Home abatement is lower at the R-F threat point, Foreign is worse off at the R-F threat point for a l l • Proposition 2: For all an — aF — a, both countries are worse off at the R-R threat point relative to the F-F threat point. Proof: A s i n Proposit ion 1, it is straightforward to verify that strict concavity of B(Q) and strict convexity of c(qi) ensure that the second order conditions for the Nash equil ibrium are satisfied. The effect that a fall in a w i l l have on the countries' net benefits is given by = mQ) -c<W]|f + for „ -H,F,i+ i, (7.2) evaluated at the Nash equilibrium. Since the regions are always the same size, = , and g a =(M-(0)-rfta)). 117 The Nash noncooperative first order conditions require that aB'(Q) — d(qi) = 0. Since a < 1, 2B'(Q) — c'(g,) > 0 at the threat point. As a falls, the reaction functions of both countries shift toward the origin, and |& > 0. Therefore, dNBijQ>qi) > n and both countries are worse off at the symmetric R-R threat point than at the F-F Nash equilibrium. • Proposit ion 3:fa) For sufficiently large, Home's welfare is higher under the R-F international environmental agreement than the agreement reached by the two federal governments, (b) Foreign is always worse off under the R-F agreement relative to the F-F agreement. Proof: The Hessian matrix for the Nash bargaining optimization is complicated and will not be presented here. However, it can be shown that the Nash bargaining objective function has a unique maximum within the bargaining lens. The bargaining lens is characterized by two conditions. First, the bargaining lens lies on or outside of the reaction functions, implying that B'(Q) — c'(g#) < Oand B'(Q) — c'(qF) < 0. Second, at all points in the bargaining lens each country receives at least as many net benefits as at the threat point, implying that aHB(Q) - c(qF) - aHB(QRF) + c{q%?) > 0 and B(Q) - c(qF) - B(QRF) + c(qFF) > 0. When these conditions are imposed on the Hessian matrix, strict concavity of B(Q) and strict convexity of c(qi) imply that the first determinant is negative and the second determinant is positive. Therefore, the second order conditions are satisfied. 118 The choice set must be constrained to the bargaining lens since the Nash bargaining objective function is not globally concave. For example, consider reducing qn and qF below the threat point by equal amounts. In this region, aHB(Q) — c(qp) — aHB(QRF) + C(QHF) < 0 and B(Q) - c(qF) - B(QRF) + c(q^F) < 0, and as the abatement levels fall, each of these becomes further from 0. Therefore, the Nash bargaining objective function is increasing as abatement levels fall toward zero, and has a local maximum at qH = qF = 0. Part (a): In general, Since Home's regional and federal governments have the same net benefits when aH = I, evaluating d N B $ £ ' q r t ) at aH = 1 and imposing the Nash bargaining first order conditions will indicate if Home prefers the R-F agreement for sufficiently large aH. By the Nash bargaining first order conditions, we know the agreement lies on the contract curve, implicitly defined by: aHB'(Q) - c'(gH) _ B'(Q) aHB'(Q) B'(Q)-c'(qF) ^ ' A ) 119 and the agreement locus, implicitly defined by: c'(te) = <*HB{Q) - c(qF) - aHB(QRF) + c(q*F) d{qF) B(Q) - c(qF) - B(QRF) + c($fF) ' ( ' } Rearranging the contract curve implies that at the bargaining solution, (aHB'(Q) - c'(qH))c'(qF) = —B'(Q)c'(qH). (7.6) If aHB'{Q) - c'{qH) = B'(Q) - c'{qF) = 0, the left hand side of (7.4) is 0 and the right hand side is oo. If OLHB'(Q) — c'(qH) > 0, (7.6) can not be true since the right hand side is negative. Therefore, aHB'(Q) — c'(qn) < 0 along the contract curve, and when an — 1, B'(Q)-c'(qH)<0. Totally differentiating the Nash bargaining first order conditions and imposing an — 1, Cramer's rule implies that > 0 and < 0 at the Nash bargaining solution. Therefore, dNBf dan Part (b): < 0 and Home is better off at the R-F agreement. aH=l The Foreign indifference curve for the level of net benefits at the F-F agreement is tangent to the 4 5 ° line at the F-F agreement. As such, Foreign prefers the F-F agreement to all points below the 45° line. It is straightforward to show that both endpoints of the bargaining lens involve less Home abatement so that as aH falls, the agreement locus shifts down. As such, the R-F agreement is below the 45° line for all aH and Foreign is always worse off when Home's region holds regulatory power. • 120 Proposition 4: For all a.H = aF = a, both countries are worse off under the R-R international environmental agreement relative to the F-F agreement. Proof: Again, the Hessian matrix for the Nash bargaining optimization is not presented here. However, as in Proposition 3, it can be shown that there is a unique maximum for points within and on the boundary of the bargaining lens. Within this region, concavity of B(Q) and convexity of c(g*) imply that the second order conditions are satisfied. The change in country i's net benefits from a move to the R-R agreement are dNB^Q^) = m Q ) _ d { q i ) ] d « + for i t j = H > F a n d i j ) ( 7 . 7 ) evaluated at the Nash bargaining solution. Since the regions are always the same size, "-t = ^ d dNB?(QAi) d q i Y a = (2B(Q)-c(qi)) — . The first order conditions of the symmetric R-R agreement imply that the agreement corresponds to the intersection between the contract curve implicitly denned by: aB'(Q) - c'(gH) _ aB'(Q) aB'(Q) aB'(Q) - c'(qF) 121 and the agreement locus, implicitly defined by: c'(qH) _ aB(Q) - c(qH) - cxB(QRR) + c(q*R) c'(qF) aB(Q) - c(qF) - aB(QRR) + c ( g f « ) ' 1 ' Since the threat points are symmetric, the agreement locus coincides with the 45° line and the Nash bargaining abatement levels are symmetric. Rearranging the contract curve and imposing symmetry implies that 2aB'(Q) = c%) at the symmetric R-R agreement. Therefore, 2B'(Q) > c'(qi) at the Nash bargaining solution. Examining the symmetric R-R contract curve indicates that as a falls from 1, the Nash bargaining contract curve moves toward the origin. Therefore, g > 0 and d N B ? ^ > 0. Both countries are worse off under the symmetric R-R agreement. • 7 . 2 A p p e n d i x B This appendix presents the proofs to the propositions and lemmas found in the text of Chapter 4. L e m m a 1: When Home's region and Foreign's federal governments hold enforcement power, there exists an < 1 such that, for all an > 3#, OJJ = 0,and for an less than but 122 sufficiently close to OLH,9H > 0. OLH is the largest value of ct# such that aHB(QRF(aH)) - c{q*F(aH)) - aHB(QRF(aH)) + c{qRF{aH)) = 0. Proof: When Of/ = 1, the net benefits of Home's regional and federal government are the same. Since both countries are better off at the Nash bargaining solution than at the corresponding threat point, when aH = 1, NB§(QRF ,q^F)-NB§(QRF ,qHF) < 0. When aH = 0, the regional government receives no benefits from global abatement. Therefore, q§F = 0 and NBH(QRF, q§F) = B(i?£(0)) > 0. Since Home's federal government receives benefits from global abatement, qRF > 0 and NB§(Q ,qHF) = —c(qHF) < 0, implying NBR(QRF,q§F) - NBR(QRF,qRF) > 0. Therefore, N BR{QRF ,q%F) - NBR(QRF,qRF) = 0 for at least one aH E [0,1]. If we define aH to be the largest OLH for which the region is indifferent between the threat point and the agreement, it must be the case that for aH > OLH, NBH(QRF, Q^F) ~ NBH[Q ,~q~HF) < 0 a n d @H = 0. By continuity of the regions net benefits, there must also be a set of aH less than but sufficiently close to OLH such that NBH(QRF,q^F) — NBH(Q ,qRrF) > 0, and 9H > 0. Therefore the lemma is true.B Proposition 5: If Foreign's enforcement powers lie with its federal government and as long as marginal abatement costs are not to convex whenever B'(Q) — c'(qi) < 0, i = H, F, the following are true, (i) For all OLH >&H and for an less than but sufficiently close to 123 aH, Home is better off when enforcement powers lie with its regional government instead of the federal government, (ii) For all aH, Foreign is worse off when Home's domestic regulatory powers are divided. (i) From Lemma 1, we know that there exists aH < 1 such that, for a f f > aH, no transfer is made and for a# less than but sufficiently close to aH, Home's federal government makes a positive transfer to the region. In this proof, we first show that Home prefers the R-F agreement to the F-F agreement when aH > aH. Then we show that this is still true as falls just below aH. (a) Suppose an > 5H-The R-F Nash bargaining solution is between the two federal governments with threat points at the Nash non-cooperative equilibrium between Home's region and Foreign's federal government. The agreement solves where qn and q~p are defined by the intersection of Home's regional reaction function and Foreign's federal reaction function. The first order conditions imply that the agreement is the intersection between the i?-.Fcontract curve P r o o f : max iH,qF (B(Q) - c(qH) - B(QRF) + c ( ^ ) ) (B(Q) - c(qF) - B(QRF) + c ( ^ ) ) [B'(Q) - c'(qH)} B'(Q) [B'(Q)-d(qp)Y B'(Q) (7.10) 124 and the R-F agreement locus, = B(Q)-c(qH)-B(QRF)+c(qY) , 11) CM B(Q)-cM-B(QRF) + c(qRF)' The Hessian matrix for the bargaining problem is complicated and not presented here. However, the second order conditions for the maximization are satisfied when the choice set is constrained to points within and on the boundary of the bargaining lens. That is, the Nash bargaining objective function has a unique maximum within the bargaining lens. The bargaining lens is characterized by two conditions. First, the lens lies on or outside of the reaction functions implying that B'(Q) — c'(^) < 0, i = H, F. Secondly, within the bargaining lens, both players are at least as well of as they are at the threat point implying that B(Q) — c(qi) — B(QRF) + c(qRF) > 0. When these conditions are imposed on the Hessian matrix, concavity of B(Q) and convexity of c(qi) imply that the first determinant is positive and the second determinant is negative. The choice set must be constrained to the bargaining lens because the Nash bargaining objective function is not globally concave. For example, consider reducing qHaad qF below the threat point by equal amounts. In this region, aHB(Q) — c(qF) — affB(QRF) + c(qHF) < 0 a n d B(Q) - cM - B(QRF) + c(q%F) < 0, and as the abatement levels fall, each of these becomes further from 0. Therefore, the Nash bargaining objective function is increasing as abatement levels fall toward zero, and has a local maximum at qH z=qF = 0. Since the federal governments negotiate the agreement and have the same net benefit 125 functions as in the F-F negotiation, the R-F contract curve corresponds to the F -F contract curve. Notice that the contract curve can only be satisfied if B'(Q) — c'(qi) < 0 so that the contract curve is everywhere outside of Home and Foreign's reaction functions. Specifically, if B'(Q) — c'(^) = 0, the left hand side of (7.10) is 0 and the right hand side is co. On the other hand, B'(Q) — d(qi) ^ 0,since the contract curve can be rewritten as d(qH)[B'(Q) - d{qF)\ = -B'(Q)d(qF), which can not be satisfied if B'(Q) - c'(qi) > 0. Taking a total derivative of the contract curve implies that, along the contract curve, dqH _ -B"(Q)[c'(qF) + d{qH)} - c"(qF)[B'(Q) - d{qH)} ac. B"(Q)[d{qF) + d(qH)} + d'(qH)[B'{Q) - d{qF)] < ^ dq By inspection, when qH — qF, = —1. As well, if we assume that, for qH < qF, ^ ml\-ZHA w h e n e v ^ B'(Q) - d(qi) < 0, i = H, F , we know that ^ > - 1 when qH < qF. Notice that, since abatement costs are increasing, [B'(g)-^(gpj| > ^ when qu < qF. Therefore, this assumption simply states that, in the region outside the countries' reaction functions, the marginal cost of abatement is not too convex. Intuitively, for the contract curve to have a slope greater than —1 when qu < qF, qF must be sufficiently responsive to a reduction in qn- If the marginal costs of abatement rise rapidly, Foreign will find it too expensive to sufficiently increase their abatement in response to a reduction in qH. Finally, since the R-F threat point involves less Home abatement and more Foreign abatement than the F-F threat point, the R-F agreement locus lies nowhere above the F-F agreement locus. Taking a total derivative of the agreement locus indicates that it is 126 upward sloping between the endpoints of the bargaining lens. Therefore, the R-F Nash bargaining solution lies along the contract curve at a point where qn < qF-In fact, as aH falls in this region, the Nash bargaining solution simply moves along the contract curve in the direction of less Home abatement and more Foreign abatement. Given that the slope of the contract curve is greater than —1 when q^ < qF, as the agreement moves down along the contract curve below the 45° line, qH falls by no more than qF increases, so that Q is nondecreasing. Since Home's net benefits are increasing in Q and decreasing in qH, as aH falls in this region, Home is strictly better off. ^Suppose an < 3#, but that an is sufficiently close to Tin and a positive transfer is made under the agreement. First notice that Home's net benefit function changes discretely at aH- That is when aH > &H, NB§(Q,qH) = Biff) — c(qn) and when aH < aH, NBF(Q,qH) = (1 + XaH)B(Q) - (1 + X)c(qH) -XaHB(Q) + Xc{qH). Therefore, Home's net benefit function is not differentiable with respect to a# at this point. However, we now show that Home's net benefit function is everywhere continuous. Clearly, the only point at which there may be a discontinuity is at aH — aH. To see why the level of Home's net benefits at the Nash bargaining solution does not discretely jump at aH, suppose aH = aH. If Home's net benefits are given by NB^(Q,qH) = B(Q) — c(qn), the Nash bargaining agreement solves max (B(Q) - c(qH) - B(QRF) + c^)) (B(Q) - c(qF) - B(QRF) + c ( ^ ) ) . 127 The bargaining solution is the intersection of [B'(Q) - c'(gH)} _ B'(Q) B'(Q) [B'(Q)-d(qF)Y [ L i Z ) and c'(qH) _ B(Q) - c(qH) - B(QRF) + c(ggF) c'M B(Q) - c(qF) - B(QRF) + c(g*F) ' On the other hand, if we suppose that Home has net benefits are given by NB^(Q, qH) = (1 + XaH)B(Q) - (1 + X)c(qH) -XaHB(Q) + Xc(qHj, the Nash bargaining agreement solves max ((1 + XaH)B(Q) - (1 + X)c(qH) - (1 + XaH)B{QRF) + (1 + A ) c ( ^ ) ) (B(Q) - c(qF) - B ( Q R F ) + c ( $ F ) . ) (7.13) By definition, when aH = aH, a H B ( Q R F ) - c(q\Y) - aHB(Q) + c(qH) at the Nash bargaining agreement. Substituting this into the bargaining problem in (7.13) implies that the agreement solves max (B(Q) - c(qH) - B ( Q R F ) + c ^ ) ) (B(Q) - c{qF) - B ( Q R F ) + c ^ ) ) , which will result in the same abatement levels as the OJ# > 3#net benefit function. Therefore, the Nash bargaining net benefits derived from the two functions must be equal at S#, and Home's net benefits are continuous in aH. The first part of this proposition showed that Home strictly prefers the R - F agreement 128 to the F-F agreement when aH = OLH. By continuity of Home's net benefits, it must be true that Home strictly prefers the R-F agreement to the F-F agreement when an falls marginally below aHM L e m m a 2: When symmetric regions in Home and Foreign hold enforcement powers, there exists a < 1 such that, for a >a, OH = Op = 0, and for a less than but sufficiently close to a, Oi > 0 . a is the largest value of a such that *B{QRR{a)) - c{q**(a)) - aB(QRR(a)) + c(qRR(a)) =0,i = H,F. P r o o f : The proof of Lemma 2 is analogous to Lemma 1. When an — 1, the net benefits of Home's regional and federal government are the same and both regions will be better off at the Nash bargaining solution than at the corresponding threat point. That is, when a = 1, NBR(QRR,qfR) - NBR(QRR,qRR) < 0,i = H,F. When a = 0, the regional governments receive no benefits from global abatement. Therefore, gf R = 0 and NBR(QRR,qRR) — B(0) = 0. Since the federal governments receive benefits from global abatement, qfR > 0 and NBR(QRR,qRR) = -c(qRR) < 0, implying NBR(QRR, qfR) -NBR(QRR,q™)>0,i = H,F. Therefore, there must be at least one a for which OLB(<2* H (a))-c(g^(a))-aB(<2 (<*))+ c(qRR(a)) = 0, i = H, F. If we let 5 be the highest a for which the regions are indifferent between the threat point and the Nash bargaining solution, when a > a, 0H = 0F — 0. By continuity of the net benefit functions, when a is less than but sufficiently close to 5 , 129 6H = 6F > 0. Therefore the lemma is true.B Proposition 6: When regions of equal size hold the enforcement power in both coun-tries and assumption 1 holds, both countries are no better off having regulatory powers divided compared to when both federal governments hold regulatory power. Proof: As in the R-F bargaining solution, the Hessian matrix is not presented here. Again, it can be verified that the Nash bargaining objective function has a unique maximum within the bargaining lens. Specifically, when the choice set is constrained to points within and on the boundary of the bargaining lens, concavity of B(Q) and convexity of c(qi) imply that the first determinant of the Hessian is positive and the second determi-nant is negative. From Lemma 2, we know that there exists an 5 < 1 such that, for a > 5, no transfers take place (#i = 0, i = H, F) and that for a less than but sufficiently close to 5, both regional governments receive a transfer. Notice as well that since the regions and countries are symmetric, it will always be the case that 6H = 6F. (a) Suppose a > a. We will show that the R-R and F-F agreements are the same in this region. When 6H = 6F — 0, the Nash bargaining agreement is the solution to max (B(Q) - c(qH) - B ( Q R R ) + c(gg*)) (B{Q) - c(qF) - B ( Q R R ) + c($*)) . The first order conditions of this optimization imply that the solution is the intersection 130 of the contract curve B'(Q) B'(Q) - c'(qH) B'(Q) - d(qF) B'(Q) and the agreement locus, (7.14) c ' M = B(Q) - c(qH) - B(QRR) + c(gg") c'(qF) B(Q) - c(qF) - B(QRR) + c(g*«) ' 1 ' ' Note that q§R — <jpR and the agreement locus corresponds to the 45° line since (7.15) is violated whenever qH ^ qF. As well, the contract curve clearly corresponds to the F-F contract curve. Therefore, for this range of a, the divided powers agreement corresponds to the F-F Nash bargaining solution and the countries are no better off with divided powers. Intuitively, when no transfers are made, the bargaining lens with no division of powers is a subset of that when there are symmetric regions but zero transfers. (b) Suppose a < 5, but that a is sufficiently close to 5 to positive transfer is re-quired. We now show that both countries are worse off at the R-R agreement than the F-F agreement. Define the F-F agreement (no division of powers) as (qjf, qFF), the sym-metric R-R agreement as ( ? B f l , ? F f l ) , and the symmetric R-R threat point as {q^R,qFR)-We want to show that B(Q**) - c(qFHF) > B(Q ) - c(qRR) - \[aHB(QRR) - c ( ^ ) - aHB{QRR) + c(qRR)}. (7.16) 131 The (qHR, qRR) R-R agreement is the solution to max ((1 + \a)B{Q) - (1 + \)c(qH) - (1 + Xa)B(QRR) + (1 + A)c($f^)) ((1 + Xa)B(Q) - (1 + X)c(qF) - (1 + Xa)B(QRR) + (1 + A)c(g^) . ) (7.17) The first order conditions for the Nash bargaining solution imply that the agreement is the intersection of the contract curve, (1 + Xa)B'{Q) - (1 + X)c\qH) (1 + Xa)B'(Q) (1 + Xa)B'(Q) (1 + Xa)B'{Q) - (1 + X)d(qF) ( 7 - 1 8 ) and the agreement locus, <S(QH) = (1 + Xa)B(Q) - (1 + X)c{q„) - (1 + Xa)B{QRR) + (1 + A)c(gg f l) c ' ( ^ ) (1 + Xa)B(Q) - (1 + A ) C ( t e ) - (1 + \a)B(QR*) + (1 + A ) c ( i ^ ) ' ( ' j Since q^R — q§R, the agreement locus again corresponds to the 45° line. Rearranging and simplifying the R-R contract curve leaves (1 + Xa)B'(Q)c'(qH) + (1 + Xa)B'(Q)c'(qF) = (1 + X)c'(qH)c'(qF) whereas, along the F-F contract curve B'(Q)c'(qH) + B'(Q)c'(qF) = c'(qH)c'(qF). 132 Since (1 4- Xa) < (1 + A), it is straightforward to show that if qH (qF) is held constant, lF{qH)i is smaller along the R-R contract curve than along the F - F contract curve. Therefore, the R-R contract curve is everywhere closer to the origin than the F - F contract curve, and the R-R agreement lies at a point on the 45° line but closer to the origin than the F - F agreement. We know that Home's no transfer indifference curve through the F - F bargaining solution is tangent to the 45° line at the F - F agreement. Therefore, Bi^q^) — c(qFrF) > B(QRR) - cQqff1). By construction, when a < a, 9H = 9F > 0 and aHB(QRR) - c{q§R) -aHB(QRR) + c(qRR) > 0. Therefore B(qFHF) - c(qFHF) + X[*HB(QRR) - c(Sg*) - aHB{QRR) + c(qRR)} > B(QRR) + C ( ^ ) , and rearranging implies that - c(g£ F ) > B(QRR) - c ( g j P ) - X[aHB(QRR) -c(q3R)-aHB(QRR)+c(qRR)}. Therefore, both countries can be no better off than at the F-F agreement. (c)Finally, if the regions are indifferent between the threat point and the Nash bar-gaining agreement for only one value of a, the proof in (b) holds for all a < a. If the regions are indifferent between the threat point and the Nash bargaining equilibrium for more than one level of a, the reasoning in (a) implies that regional and federal enforce-ment lead to the same agreement for every a such that 0, = 0, i = H, F. Therefore, for these values of cv, the country receives the same net benefits under federal and re-gional enforcement. Likewise, following the reasoning in (b), for all a such that Qi > 0, 133 i = H,F, the agreement will lie on the 45° line at a point closer to the origin than the F-F bargaining solution, and the countries will be worse off relative to the F-F agreement. Therefore, the proposition is true.B 134 Table 2.1: Summary Statistics Variable N Mean Std. Dev. Minimum Maximum Inspection 175 947 0.0178 0.1324 0 1 Violation 175 947 0.0088 0.0938 0 1 Underground Tanks 175 947 0.7527 0.4315 0 1 Number of Tanks 175 947 3.199 3.416 1 72 Total Capacity 175 947 335861.5 5916410 225 223000000 Some protected 175 947 0.0884 0.2839 0 1 A l l protected 175 947 0.3925 0.4883 0 1 Age of Oldest Tank 175 947 63.048 44.602 0 343 Population Density 175 947 457.4785 471.7754 0.0006 1460.7 Real Average Income 175 947 32939.01 7382.134 7892.8 69203.5 No Road Access 175 947 0.065 0.2463 0 1 Previous Inspection 175 947 0.2173 0.412 0 1 Cumulative Violations 3818 0.2476 0.581 0. 7 Violation at Last Inspection 3142 0.1327 0.3393 0 1 135 Table 2.2: Site Ownership Ownership Number of Sites Independent 2917 Oil Company 831 Institution 166 Municipal Govt 173 Manitoba Govt 288 Canadian Govt 96 Table 2.3: Outlet Type Outlet Type Number of Sites Retail 2267 Bulk 403 Fleet 890 Industrial 218 Used Oil 272 Aviation/Marine 67 Miscellaneous 50 136 Table 2.4: Region Region Number of Sites Winnipeg 1273 Eastern-Interlake 941 South-Central 518 Park West (Brandon) 1055 Northern Region 684 137 Table 2.5a: Inspections Probit Results Variables (N=175 947) Model A Model B Model C Winnipeg -0.1419* (0.0277) -0.1633* (0.0275) -0.1425 * (0.0277) No Road - 0.3437 * (0.0682) -0.3445 * (0.0682) -0.3416 * (0.0682) Population Density 0.00009 * (0.00002) 0.00009 * (0.00002) 0.00009 * (0.00002) Real Avg. Income 7.88e-06 * (1.42e-06) 8.79e-06 * (1.41e-06) 7.82e-06 * (1.42e-06) Late (after 1990) 0.7132 * (0.0309) 0.7293 * (0.0308) 0.7101* (0.031) Legislation (after 1987) -0.3833 * (0.0333) -0.3839 * (0.0333) -0.3822 * (0.0333) Previous Inspection -0.0033 (0.02) 0.0389t (0.023) 0.0133 (0.0237) Violation Last Insp. 0.0277 (0.0259) -0.0358 (0.0276) Cumulative Violations 0.078 * (0.0119) 0.0833 * (0.0126) Underground Tanks 0.5351 * (0.0353) 0.548 * (0.0351) 0.535 * (0.0353) Number of Tanks 0.018 * (0.0035) 0.0185 * (0.0035) 0.018 * (0.0035) Capacity -1.8e-09 (1.96e-09) -2.0e-09 (1.97e-09) -1.78e-09 (1.97e-09) Quarter 2 -0.262 * (0.021) -0.2607 * (0.0209) -0.2622* (0.021) Quarter 3 -0.3887 * (0.0225) -0.3863 * (0.0224) -0.3889 * (0.0225) Quarter 4 -0.2661* (0.021) -0.2641* (0.021) -0.2666 * (0.0211) Age of the Oldest Tank -0.0008* (0.0002) -0.0008* (0.0002) -0.0008* (0.0002) 138 Table 2.5b. Inspections Probit Results Continued Variables (N=175 947) Model A Model B Model C Oil Company 0.0234 (0.212) 0.0182 (0.0216) 0.0225 (0.0212) Institution 0.1061 f (0.0606) 0.1053 t (0.0606) 0.1052 t (0.0606) Municipal Gov 0.0743 (0.0457) 0.077 t (0.0456) 0.0752 (0.046) Manitoba Govt -0.1708 * (0.0581) -0.1728* (0.058) -0.171 * (0.0581) Canada Govt -0.383 * (0.1378) -0.4031 * (0.1383) -0.3837 * (0.1379) Bulk 0.086 ** (0.042) 0.079 * (0.0419) 0.0871** (0.042) Fleet -0.1805* (0.028) -0.1812* (0.028) -0.1795* (0.028) Used Oil -0.9886 * (0.0775) -0.9936 * (0.0774) -0.9857 * (0.0775) Aviation/Marina -0.3207** (0.1298) -0.3303** (0.13) -0.3203** (0.1299) Industrial -0.789* (0.0804) -0.8065 * (0.0805) -0.7872 * (0.0803) Miscellaneous -0.8843 * (0.2156) -0.8905 * (0.2153) -0.8814 * (0.2154) Partial Protection 0.3131 * (0.0275) 0.3309 * (0.0273) 0.312 * (0.0275) Full Protection 0.2962* (0.024) 0.3066* (0.024) 0.2944* (0.024) Constant -2.895 * (0.0598) -2.936 * (0.0595) -2.89 * (0.0599) Log Likelihood -13780.279 -13800.416 -13779.439 Pseudo R 2 0.1257 0.1244 0.1257 139 ±aDie z.oa: violation rrooit nesi Variables (N=3142) uts Model A Model B Model C Winnipeg -0.8262* (0.127) -0.81 * (0.131) -0.8231* (0.119) No Road 0.4382 (0.377) 0.3683 (0.383) 0.3821 (0.35) Population Density -0.0002** (0.0001) -0.0002 ** (0.0001) -0.0002 ** (0.0001) Real Average Income 8.59e-06 (6.47e-06) 7.65e-06 (6.59e-06) 9.91e-06 (6.07e-09) Legislation -0.2306** (0.103) -0.2273** (0.105) -0.2205** (0.096) Previous Inspection -0.4364* (0.083) -0.7819* (0.111) -0.7846* (0.1) Violation at Last Inspection 0.5919* (0.117) 0.6732 * (0.113) Cumulative Violations -0.0013 (0.051) -0.1013** (0.051) Estimated Prob. of an Inspection -9.1265* (2.17) -9.4759* (2.23) -7.789* (2.1) Underground Tanks 0.4472 ** (0.183) 0.4424** (0.187) 0.3969** (0.175) Number of Tanks 0.016 (0.016) 0.0138 (0.16) 0.0142 (0.015) Capacity -4.81e-09 (8.06-09) -3.68e-09 (9.0e-09) -4.12e-09 (8.06-09) Quarter 2 -0.2357** (0.109) -0.2494** (0.11) -0.2023** (0.102) Quarter 3 -0.4226* (0.126) -0.4532* (0.128) -0.3856* (0.119) Quarter 4 -0.3686* (0.111) -0.37 * (0.113) -0.3223* (0.105) Age of Oldest Tank -0.0011 (0.001) -0.0012 (0.001) -0.001 (0.001) 140 Table 2.6b: Violation Probit Results Continued Variables (N=3142) Model A Model B Model C Oil Company -0.2372* (0.092) -0.2151* (0.094) -0.2348* (0.086) Institution -0.3232 (0.264) -0.3358 (0.266) -0.3618 (0.245) Municipal Govt 0.2038 (0.216) 0.1968 (0.217) 0.1839 (0.199) Manitoba Govt -0.5238t (0.269) -0.5085f (0.273) -0.4589* (0.257) Canada Govt -0.361 (0.827) -0.2555 (0.902) -0.2717 (0.83) Bulk 0.0559 (0.199) 0.0792 (0.2) 0.0438 (0.187) Fleet 0.1736 (0.136) 0.1457 (0.137) 0.1638 (.127) Used Oil 0.1451 (0.419) 0.1114 (0.423) 0.1732 (0.399) Aviation/Marine -0.3176 (0.767) -0.2945 (0.771) -0.2895 (0.722) Industrial -0.5843 (0.426) -0.6347 (0.422) -0.6707* (0.396) Miscellaneous 0.3406 (1.139) 0.2595 (1.139) 0.2952 (1.075) Partial Protection 0.0207 (0.128) 0.0399 (0.131) 0.0398 (0.119) Full Protection -0.1794 (0.1157) -0.1524 (0.118) -0.1791t (0.108) Constant 0.7992 * (0.2796) 0.8156* (0.285) 0.7454* (0.263) Log Likelihood -1828.277 -1803.288 -1790.2622 Pseudo R 2 0.1605 0.1720 0.1780 141 Figure 2.1: Yearly Inventory Inspections 600 500 400 300 200 100 II Inspections cs O N O N co O N O N •3-ON ON in O N O N O N O N O N O N 0 0 ON Year Figure 2.2: Yearly Violations per Inspections 0.9 0.8 0.7 0.6 H 0.5 0.4 IB Violations 0.3 0.2 0.1 CO 0 0 O N oo O N in oo O N oo Oi 0 0 O N 0 0 0 0 O N O N oo O N o O N O N O N O N CM O N O N co O N O N •3" O N O N in O N ON NO ON ON ON O N oo O N O N Year 142 Figure 3.1: Federal-Federal Threat Point R F H (q F ) : Home's federal reaction function R F F (q H ) : Foreign's federal reaction function N B F H : Home's federal indifference curve (F-F threat point) N B F F : Foreign's federal indifference curve (F-F threat point) q H F F : Home's F -F threat point abatement q F F F : Foreign's F -F threat point abatement 143 Figure 3.2: Regional-Federal Threat Point R"F(qH) R F H (q F ) : Home's federal reaction function R R H (q F ) : Home's regional reaction function R F F (q H ) : Foreign's federal reaction function q H F F : Home's F - F threat point abatement q F F F : Foreign's F -F threat point abatement q H R F : Home's R-F threat point abatement q F R F : Foreign's R-F threat point abatement 144 Figure 3.3: Symmetric Regional Threat Point Home's federal reaction function Home's regional reaction function Foreign's federal reaction function Foreign's regional reaction function N P / H : Home's federal indifference curve (R-R and F-F threat points) N B F F : Foreign's federal indifference curve (R-R and F -F threat points) qu F F : Home's F -F threat point abatement qp F F : Foreign's F -F threat point abatement q H R R : Home's R-R symmetric threat point abatement q F R R : Foreign's R-R symmetric threat point abatement R F H(qp) : RR H(qp) : RFF(qn) : R \ ( q H ) : 145 Figure 3.4: Regional-Federal Agreement R F H(qp) : Home's federal reaction function R R H (q H ) : Home's regional reaction function R F F (q H ) : Foreign's federal reaction function N B R H : Home's regional indifference curve (R-F threat point) N B F F : Foreign's federal indifference curve (R-F threat point) q H F F : Home's F -F agreement abatement % F F : Foreign's F-F agreement abatement q H R F : Home's R-F agreement abatement q F R F : Foreign's R-F agreement abatement c c : R-F contract curve a.l. : R-F agreement locus 146 Figure 3.5: Symmetric Regional Agreement Home's federal reaction function Home's regional reaction function Foreign's federal reaction function Foreign's regional reaction function N B F H : Home's federal indifference curve (F-F agreement) N B F F : Foreign's federal indifference curve (F-F agreement) qjj F F : Home's F -F agreement abatement q F F F : Foreign's F -F agreement abatement qjj R R : Home's R -R symmetic agreement abatement q F R R : Foreign's R -R symmetric agreement abatement cc . : contract curves (F-F and symmetric R-R agreements) R F H (q F ) : R \ ( q F ) : 147 Figure 3.6: Regional-Federal and Federal-Federal Threat Points 0.14 T ~ _ _ _ _ _ _ alpha H Figure 3.7: Regional-Federal and Federal-Federal Agreements 0.4 1 alpha H 148 Figure 3.8: Symmetric Regional-Regional and Federal-Federal Threat Points 0.2 T — , alpha Figure 3.9: Symmetric Regional-Regional and Federal-Federal Agreements 0.4 ~i _ _ _ _ _ _ _ -1 J alpha 149 Figure 3.10: Asymmetric Regional-Regional and Federal-Federal Threat Points 0.15 -0.35 J alpha H Figure 3.11: Asymmetric Regional-Regional and Federal-Federal Agreements - • — R - R 0.5 R-R 0.9 alpha H 150 Figure 4.1: Federal-Federal Threat Point R F H (q F ) : Home's federal reaction function R F F (q H ) : Foreign's federal reaction function N B F H : Home's federal indifference curve (F-F threat point) N B F F : Foreign's federal indifference curve (F-F threat point) q H F F : Home's F - F agreement abatement q F F F : Foreign's F - F agreement abatement c c : F - F contract curve 151 Figure 4.2: Regional-Federal Threat Points R F H (q F ) : Home's federal reaction function R R H(qp) : Home's regional reaction function R F F (q H ) : Foreign's federal reaction function q H F F : Home's F - F threat point abatement qp F F : Foreign's F -F threat point abatement q^lp : Home's R - F threat point abatement qp.RF : Foreign's R-F threat point abatement 152 153 Figure 4.4: Regional-Federal Agreement (Zero Transfer) R F H (q F ) : Home's federal reaction function R R H (%) : Home's regional reaction function R F F (q H ) : Foreign's federal reaction function N B F H : Home's federal indifference curve (R-F threat point) N B F F : Foreign's federal indifference curve (R-F threat point) q H F F : Home's F - F agreement abatement q F F F : Foreign's F -F agreement abatement q H R F : Home's R - F agreement abatement q F R F : Foreign's R-F agreement abatement cc . : F -F contract curve a.l. : R-F agreement locus 154 Figure 4.5: Regional-Federal Agreement (Positive Transfer) R F H (q F ) : Home's federal reaction function R R H (q F ) : Home's regional reaction function R F F (q H ) : Foreign's federal reaction function N B F H : Home's federal indifference curve (R-F threat point) N B F F : Foreign's federal indifference curve (R-F threat point) q H F F : Home's F -F agreement abatement qj. F F : Foreign's F-F agreement abatement q H R F : Home's R-F agreement abatement q F R F : Foreign's R-F agreement abatement cc . : R-F contract curve a.l. : R-F agreement locus 155 Figure 4.6: Symmetric Regional-Regional Agreement (Zero Transfers) R F H ( q F ) : Home's federal reaction function R R H(qp) : Home's regional reaction function R F F ( q H ) : Foreign's federal reaction function N B F H : Home's federal indifference curve ( R - F and F - F threat points) N B F F : Foreign's federal indifference curve ( R - F and F - F threat points) q H F F : Home's F - F agreement abatement q/F : Foreign 's F - F agreement abatement q H R : Home's R - R symmetric agreement abatement q F R : Foreign's R - R symmetric agreement abatement c c : F - F contract curve 156 Figure 4.6: Regional -Federa l a n d Federa l -Federa l Agreements 157 Figure 4.8: Asymmetric Regional-Regional and Federal-Federal Agreement Of=0.5 Figure 4.9: Asymmetr ic Regional-Regional and Federal-Federal Agreement a.fO.9 0.35 alpha H 158 

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