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Opportunity Institution LIBRARY Michigan State University _ _.g..-.a.-.-.-.---—--~-------.--—-—.p - -.-.- —---5---5----.—-.-.-.—.—-— .- PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 2/05 p:lClRC/DateDue.indd-p.1 THREE ESSAYS ON UTILITY REGULATION By Vladimir Hlasny A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Economics 2006 ABSTRACT THREE ESSAYS ON UTILITY REGULATION By Vladimir Hlasny To induce utilities in the gas distribution market to operate efficiently, US states have deployed consumer-choice programs, price caps, and variations of sliding-scale plans. My first essay studies the impact of these restructuring and deregulation efforts on consumer rates, using panel data from a custom survey of state commissions and the Department of Energy. I estimate the residential, small commercial and industrial price. equations jointly, and use instrumental variables to control for the potentially endogenous demand and status of deregulation. Consumer-choice programs lower the prices by 2.2—20.1% compared to the rate-of- return regulation, benefiting industrial consumers the most and households the least. These effects appear even one to two years prior to the programs’ implementation, and become stronger over time. Price caps lower all prices by 0.0—20.0%, with the same ranking. The impacts of the sliding-scale plans are close to zero, between -2.6% and +4.0%. The second paper evaluates the health damages caused by air concentrations of sulfur dioxide (5'02), under three alternative environmental policies leading to identical ag- gregate emissions: emission caps, a nationwide emission tax, and a system of tradable emission allowances such as the one currently used in the US. The numerical model of the industry finds generators’ output, participation in energy trade and $02 abatement ef- fort under each policy. The resulting 5'02 concentrations are used to derive the aggregate health damages, using point estimates in the medical literature. I find that regional 302 concentrations vary across policies, even when the aggre- gate emissions are the same. These variations in S 02 concentrations can translate into substantially different losses for any individual state, and, nationwide, to hundreds of mil- lions of dollars of difference in aggregate damages. Emission caps are estimated to lead to the lowest aggregate damages, outperforming the currently used system of allowances by $452 million. A uniform emission tax leads to very similar damages as the system of tradable allowances, in agreement with the theory. These results are consistent with the prior academic studies, that emission allowances and uniform taxes may lead to higher damages than regulatory instruments that control regional emissions more closely. In terms of the 502 concentrations and the health impacts, emission caps are shown to favor the southwestern, south-central and southeastern states, where they deliver $840 million lower damages than under the system of allowances or an emission tax, while they deliver damages $390 million higher in the northern and northeastern states. In the third essay I compute health damages from $02 under different assumptions on the relationship between the concentration levels and their marginal health impacts. I evaluate 502 concentration profiles resulting under the three policies in the previous chapter. Using slopes consistent with the ranges of marginal damage estimates in medical literature, emission caps are shown to lead to the lowest aggregate damages under all considered parameters, although their benefit over the system of tradable allowances falls as the slope of the marginal damage function increases. With marginal damages rising at the maximum rate consistent with the current medical data, the savings in damages under the emission caps in the southern states fall to $670 million, compared the system of allowances, while the excess in damages they cause in the north and the northeast rises to $600 million. ACKNOWLEDGMENTS I would like to thank my friends Artem, Irina and Monika for making my experience at MSU an enjoyable journey. Special thanks go to Maros for forcing me into unexplored grounds of new software, and for technical assistance once there. Without his support, this work would not get half done. I also appreciate the unending support of Kristin and her patience with my returns home at 3 am. My utmost respect and gratefulness go to my academic committee, John Hoehn, Jay Wilson and Jeff Wooldridge, and particularly my advisor Ken Boyer, who greatly chal- _ lenged me, but was always available in times of need. Dr. Boyer patiently read too many drafts of my dissertation, and offered constructive criticism even in times when nothing seemed salvageable. Finally, I must thank my sister Daniela and my mom for ensuring that I was dressed, combed and well fed all these years. iv TABLE OF CONTENTS LIST OF TABLES .................................... viii LIST OF FIGURES ................................... x CHAPTER 1. THE IMPACT OF STATE RESTRUCTURING AND DEREGU- LATION ON GAS RATES .............................. 1 1.1 Natural Gas Industry Background ....................... 3 1.1.1 Options for Regulating Gas Utilities ................. 4 1.1.2 Regulatory Literature .......................... 7 1.2 Empirical Model of the Determination of Natural Gas Prices ........ 9 1.2.1 Estimation Strategy .......................... 12 1.2.2 Modeling of the Regulatory Policies .................. 17 1.2.3 Natural Gas Industry Data ....................... 19 1.2.4 Expectations from the Policy Comparisons .............. 21 1.3 Estimation Results ............................... 28 1.3.1 Seemingly-Unrelated Price Regressions ................ 31 1.3.2 Price Growth under Deregulation ................... 34 1.3.3 Instrumenting for the Endogenous Policy Implementation ...... 39 1.3.4 Testing for the Endogeneity of Mechanism Implementation ..... 44 1.3.5 Limitations of the Results ....................... 52 1.4 Conclusions ................................... 53 CHAPTER 2. THE IMPACT OF ENVIRONMENTAL REGULATION ON 502 CONCENTRATIONS AND DAMAGES ...................... 55 2.1 Motivation .................................... 56 2.2 Literature .................................... 61 2.3 Energy Industry Model ............................. 65 2.3.1 Energy Generators ........................... 70 2.3.2 Energy Consumers ........................... 73 2.3.3 Independent System Operators .................... 74 2.3.4 Generators’ Profits ........................... 76 2.3.5 Energy Industry Model Behavior ................... 77 2.3.6 Properties of the Market Solution ................... 80 2.4 Phnctional Forms Used in the Energy Industry Model ............ 81 2.4.1 Generators ................................ 82 2.4.2 Generators’ Profits ........................... 87 2.4.3 Consumers ................................ 88 2.4.4 Independent System Operators .................... 89 2.4.5 Energy Industry Model Behavior ................... 90 2.5 Numerical Approach to Modeling Energy Industry .............. 92 2.5.1 Modeling of Environmental Policies .................. 101 2.5.2 Energy 'Ii‘ading Rules ......................... 103 2.6 Energy Industry Data ............................. 105 2.6.1 Demand for Energy Data ........................ 107 2.6.2 Generators’ Emission—Abatement Data ................ 108 2.6.3 302 Concentrations and Health Damages Data ........... 108 2.7 Energy Industry Model Calibration ...................... 111 2.8 Energy Industry Model Results ........................ 117 2.8.1 Emission Tax Scenario Results ..................... 118 2.8.2 Allowance Market Scenario Results .................. 120 2.8.3 Emission Cap Scenario Results .................... 122 2.8.4 Comparison of 302 Concentrations .................. 124 2.8.5 Comparison of 802 Emission Damages ................ 127 2.9 Conclusions ................................... 132 CHAPTER 3. THE IMPACT OF RISING MARGINAL RESPONSES TO 302 ON HEALTH DAMAGES .............................. 135 3.1 Damages from 802 Concentrations ...................... 139 3.2 Literature .................................... 140 3.3 Compared Environmental Policies ....................... 143 vi 3.3.1 Expectations from the Policies ..................... 145 3.4 Emission Damages Model ........................... 146 3.5 Numerical Calculation Using Available Data ................. 151 3.5.1 Calculation of Damages ........................ 152 3.6 Results of the Emission Damages Model ................... 158 3.6.1 Results with Constant Marginal Damages .............. 159 3.6.2 Results with Marginal Damages Rising at a Constant Rate ..... 162 3.6.3 Analysis ................................. 171 3.7 Conclusions ................................... 173 APPENDIX A. APPENDIX ............................... 175 A.1 Structural Change Test ............................. 175 A2 Selection of Weights in the Calibration Objective .............. 176 A21 Model Calibration Results ....................... 180 A3 Energy Industry Model Set of Equations and Unknowns .......... 186 A31 Functional Form Representations ................... 188 A.4 Computational Issues .............................. 190 A5 Energy Industry Data—Historic Statistics .................. 193 A6 Energy Industry Data Sources ......................... 195 A.7 Detailed Results of the Health Damage Estimation ............. 201 A8 Other Forms of the Marginal Damage Function ............... 208 A81 Aggregate Damages Estimated under Additional Parameters . . . . 211 BIBLIOGRAPHY .................................... 216 vii 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.2 3.3 LIST OF TABLES Description and Sources of Variables ..................... 20 Inventory of Deregulatory Programs in the Sample ............. 22 Expectations of plausible impacts of the mechanisms on prices ....... 25 Panel Regressions with Fixed Effects ..................... 29 Seemingly-Unrelated Regressions with Instruments for Endogenous Demand 35 Differences between Before- and After-Implementation Coefficients ..... 36 ‘Phase of Implementation’ Regressions .................... 41 Regressions with Instruments for Endogenous Demand and Regulatory Policies ...................................... 45 Pooled OLS Regressions of the Year of Implementation ........... 48 Regressions of the Probability of Implementation .............. 49 Energy Industry Model Variables ....................... 71 Energy Industry Model Parameters ...................... 85 Aggregate Statistics: Emission Tax Scenario (Tax of $90/ Ton) ....... 119 502 Emissions (Pounds per Sq. Mile) and Concentrations (pg/m3) by State: Emission Tax Scenario (Tax of $90/ Ton) ............... 120 Aggregate Statistics: Tradable Allowance Scenario (9.2 Million Allowances with Equilibrium Price $89.35) ........................ 121 302 Emissions (Pounds per Sq. Mile) and Concentrations (pg/m3) by State: Tradable Allowance Scenario (9.2 Million Allowances with Equilib- rium Price $89.35) ............................... 121 Aggregate Statistics: Emission Cap Scenario (Caps of 72% of Historic Emis- sion Levels) ................................... 123 502 Emissions (Pounds per Sq. Mile) and Concentrations (pg/m3) by State: Emission Cap Scenario (Caps of 72% of Historic Emission Levels) . 123 502 Health Impacts under Alternative Policies ............... 127 Original Data Sources for Health Damage Estimates (1) ........... 155 Original Data Sources for Health Damage Estimates (2) ........... 156 502 Health Impacts under Alternative Policies: Constant Marginal Dam- ages (b = 1) ................................... 159 viii 3.4 S 02 Health Impacts under Alternative Policies: Marginal Damages Rising Linearly at Maximum Slope (b = 0) ...................... 162 A.1 Free Parameters and Their Ranges Used in Calibration ........... 177 A2 Parameter Variation under Weights 2 & Weights 3 Compared to Parameters under Weights 1 (‘70 Mean Deviations) .................... 179 A.3 Fme Parameters & Their Calibrated Means .................. 181 A.4 Criteria for Selection of Model Generators .................. 194 A.5 Aggregate Statistics: Historic 1996 Observations ............... 194 A6 Historic 1996 502 Emissions (Pounds per Sq. Mile) and Concentrations (pg/m3) by State ................................ 195 A.7 Various Simulation Data Sources ....................... 197 A8 Data Sources for Model Calibration ...................... 198 A9 Spatial Distribution of Observations by NERC Region ............ 199 A.10 Total Transmission Capabilities among N ERC Regions ........... 200 A.11 Status of Restructuring of US States ..................... 201 A.12 NERC Regions—Margin Reserve Requirements (‘76) ............. 201 A.13 302 Health Impacts under Alternative Policies: Constant Marginal Damages205 A.14 502 Health Impacts under Alternative Policies: Marginal Damages Lin- early Rising ................................... 206 A.15 Historic 1996 8'02 Health Impacts: Constant vs. Linearly Rising Marginal Damages ..................................... 207 A.16 Maximum Slopes of the Marginal Concentration Response Functions (Per Capita Incidents in Affected Population per 113%) .............. 208 m A.17 Differences in Damages against Those under the Emission Allowance Sce- nario, across Different a and b ($ million) ................... 212 ix 1.1 1.2 1.3 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 A.1 A.2 A.3 A.4 A.5 LIST OF FIGURES Number of Policies Present in the Sample ................... 22 Price Trends after Deregulation ........................ 37 Prices by Phase of Implementation of Deregulation ............. 40 Marginal Damages from 502 for Generators in Different States (lg?)— States Ordered by Concentrations under System of Allowances ....... 112 502 Concentrations under the System of Tradable Allowances ( )— 1 States Ordered by Concentrations ....................... 125 3 Differences in S 02 Concentrations against Those under the System of Trad- able Allowances (fi%)—States Ordered by Concentrations under System m of Allowances .................................. 126 Health Damages under the System of Tradable Allowances ($ million)— States Ordered by Concentrations under System of Allowances ....... 130 Differences in Health Damages against Those under the System of Tradable Allowances ($ million)—States Ordered by Concentrations under System of Allowances .................................. 131 Marginal Damages under the System of Tradable Allowances with Rising Marginal Damages ($)——States Ordered by Concentrations under System of Allowances .................................. 166 Differences in Marginal Damages against Those under the System of Tfad- able Allowances with Rising Marginal Damages (3)—States Ordered by Concentrations under System of Allowances ................. 167 Health Damages under the System of Tradable Allowances with Rising Marginal Damages ($ million)——States Ordered by Concentrations under System of Allowances .............................. 169 Differences in Damages against Those under the System of Tradable Al- lowances with Rising Marginal Damages (S million)—States Ordered by Concentrations under System of Allowances ................. 170 Relative Deviations of Model Variables from Historic Values (1) ...... 182 Relative Deviations of Model Variables from Historic Values (2) ...... 183 Relative Deviations of Model Variables from Historic Values (3) ...... 184 Distribution of 502 Concentrations under Alternative Policies (pg / m3) . . 185 Tangent Representations of Step Functions in the Model .......... 192 A.6 Differences in Damages against Those under the System of Tradable Al- lowances with Constant Marginal Damages (%)—States Ordered by Con- centrations under System of Allowances .................... 202 A.7 Differences in Damages against Those under the System of Tradable Al- lowanees with Rising Marginal Damages (%)—States Ordered by Concen- trations under System of Allowances ..................... 203 A8 Illustration of the Modeled Realizations of the Damage Function ...... 210 A9 Differences in Damages against Those under the Emission Allowance Sce- nario across Different Slopes b (a = 1) ($ million) .............. 214 A.10 Differences in Damages against Those under the Emission Allowance Sce- nario across Different Curvatures a (b = 0) ($ million) ............ 215 THE IMPACT OF STATE RESTRUCTURING AND DEREGULATION ON GAS RATES The fixed rate-of-return regulation has traditionally been prescribed in industries with significant natural barriers to entry, falling average costs, and low elasticity of demand (for instance Stigler 1971, and Posner 1974). These criteria fit the gas industry, which is often regarded as a classic natural monopoly requiring oversight by the states’ public service commissions. In the 19708, the rate-of-return regulation encountered criticism by economists because of its low power in inducing cost—minimizing efforts at utilities. Theorists started advancing price caps as the means of promoting efficiency. In the United Kingdom, regulators in the telecommunication and energy industries started adopting price caps methodically, reporting success at setting the caps at reasonable levels. In the US and particularly in the gas industry, regulators have been reluctant to delegate to utilities full responsibility and authority over procurement. Price caps have been used rarely and non-systematically [Armstrong et al., 1994, Crew and Kleindorfer, 1996]. In the 19908, a number of state public service commissions in the US departed from the rate-of—return regulation to give local distribution companies (utilities) stronger eco- nomic incentives via retaining some profits, or so—callcd sliding-scale plans. The first steps at deregulation, the capacity release and off-system sale plans, allowed utilities to share benefits from exceptional performance in marginal operations (first adopted in North Car- olina in 1993). Some states introduced monetary rewards for superb customer service. When these programs were deemed successful, new incentive programs were authorized to give utilities a wider space for decision-making, such as in signing-up of new off-system industrial customers (earnings-sharing mechanisms), and purchasing the commodity from various sources (gas-cost incentive mechanisms). By the end of the 19903, following the Federal Energy Regulatory Commission’s (FERC) Order 636, the states started impla menting retail restructuring (consumer-choice programs), rebutting the belief that the gas industry was naturally monopolistic. Under consumer-choice programs utilities’ functions were unbundled, and customers were allowed to choose from a group of firms competing to provide these individual services. Today, utilities, state commissioners and consumer advocates have had a decade to evaluate the first adopted incentive mechanisms. However, different stakeholders attribute different outcomes to the programs, based on different benchmarks and assumptions. The states examine the performance of individual mechanisms discretely, not taking into ac- count the simultaneous existence of other incentive programs at the utility, programs at other utilities, or trends in the market. There are no studies evaluating the state deregula- tion programs across all US states. A handful of academic studies have also estimated the performance of rate-of—return regulation, price caps and sliding-scale programs in terms of prices and innovation incentives in other industries. In this paper I evaluate how the deregulation and restructuring have fared in the gas distribution industry. I study whether price caps have outperformed the consumer-choice programs in lowering utilities’ residential, small commercial and industrial prices, and how sliding-scale plans—gas—cost incentive, earnings-sharing, and margin-sharing plans— compare to either of them. The mechanisms are evaluated jointly in order to distinguish between their effects and avoid biasing the results when other plans are used at the utility or elsewhere in the state. This paper compares the performance of the competing dereg- ulatory efforts to the benchmark rate-of-return regulation. The qualitative results of the policy comparison extend to similar industries—those with slow technological innovation, decreasing costs, and traditionally a small number of firms providing a homogeneous necessity—in particular water, and electricity transmission and distribution. 1 find that consumer-choice programs lower all prices by 2.2—20.1% from the levels before deregulation, benefiting industrial customers the most and residential customers the least. Price caps also lower all prices, by 0.0—20.0%, again benefiting the larger consumers more. The impacts of sliding-scale plans are small (between -2.6% and +40%) and difficult to rank across individual consumer classes. Consumer-choice programs have a beneficial impact on all prices even before the programs are fully implemented, as utilities bid for customers or fight off competitors. This impact further grows over time as the utilities learn to operate under the programs, and competition becomes more established. 1.1 Natural Gas Industry Background Prior to the 1870s, federal government oversaw the natural gas industry from the wellheads to the city gates, and individual municipalities oversaw distribution companies. There was no state-level regulation. Starting in the 18705 and throughout the first half of the 20th century, state commissions emerged in most states, and today they are the most influential body responsible for supervision of individual utilities [Priest, 1993]. The primary objective of the establishment of the commissions was to protect residential con- sumers from being abused to the benefit of larger consumers and the utilities themselves, but the evidence of whether these agendas were successful is mixed [Hollas and Stansell, 1988, Stigler and Friedland, 1962]. In the 19703, economists started pondering introduction of competition in the gas supply chain [Shepherd, 1972]. The first step was to unify the industry vertically to end the bottlenecks and the market power that had been common until then. In 1978, the National Energy Act unified the intrastate and interstate gas transmission markets, and in 1985, through Orders 380 and 436, gas providers gained open access to transmission companies’ pipelines. Through the 1978 Natural Gas Policy Act and the 1989 Wellhead Decontrol Act, wellhead prices became competitive. The 1992 F ERC Order 636 unbundled transportation and sales services entirely, and mandated open access and simplified price structure in transmission [Gorak and Ray, 1995, Mariner-Volpe, 2000, Sickles and Streitwieser, 1998]. Through the 19908, utilities started receiving the right to purchase gas in traditionally restricted venues, through hedging with futures trades and financial options [Hakam 1998]. Although still passing costs to consumers dollar for dollar, regulators signaled to utilities that efficiency was important to ratepayers. In the late 19908 unregulated interstate mar- keters entered the gas market. Without restrictions on risk-taking, and with operations in multiple states, marketers facilitated access to new sources of gas, undercutting the tradi- tionally vertical regional supply chains, and further unifying the market [Jess, 1996]. By 2000, states started implementing customer choice programs allowing consumers to select their gas provider, not only from among local utilities but also among the independent marketers approved in those states [DOE—EIA, f]. In addition to creating external competitive pressure, many commissions gave utilities incentives in particular areas of operation by allowing them to retain a portion of the dif- ference between actual and benchmark costs. These mechanisms achieve some efficiency improvements compared to the rate-of—return regulation, as under price caps, while pro- viding better equity and reliability safeguards than price caps [Comnes et al., 1995, Small, 1999]. By 2004, so—called performance—based regulation had spread to more than half of the US states. 1.1.1 Options for Regulating Gas Utilities Rate-of-return regulation is the traditional method of regulation practiced in the US [Prie8t, 1993]. Through periodic rate cases, state regulators evaluate all costs incurred by utilities and allow them to recoup from customers all reasonable expenses, plus a fixed rate of return on prudently invested capital. Since utilities pass all costs to consumers, they have lesser incentives to economize (for instance, [Crew and Kleindorfer, 1986, Leibenstein, 1966]). Since utilities are earning a rate of return on their capital and no return on the other inputs, this regulation may result in strategic overcapitalization [Averch and Johnson, 1962]. Since the commissions must judge whether all incurred expenses were prudent, utilities may also pass up long-term cost-reducing opportunities when they fear that the state commission will deny the reasonableness of their investment. In fact, regulators may punish failures more severely than rewarding successful endeavors [Hollas, 1999, Lyon, 1996]. An alternative to the fair-return regulation is price—cap regulation. Price caps give utilities the full reward for efficiency in capital investment and in risk-taking in gas pro— curement and infrastructure management. The assumption is that the utility can make better-informed procurement decisions and is no more risk-averse than the regulator. Oth- erwise some sharing of risks and savings with ratepayers may be advisable [Lyon, 1996, Lyon and Toman, 1991]. Price caps can promote technological progress and lower prices in the long run [Beesley and Littlechild, 1989]. Price regulation however requires regulators to use correct predictions of future costs and technology to set the cap. Otherwise the utility would default on its commitments, or have to charge prices above the competitive or regulated levels [Bernstein and Sappington, 1998, Braeutigam and Panzar, 1993]. Consumer-choice programs are a recent step in the restructuring of the gas distri- bution market. The rate—of-return regulation was long defended as the only possible regulation of natural monopolies beside public ownership (for instance, Demsetz 1968). The competition has become possible through the unbundling of distribution services into portions in which individual providers compete [DOE—EIA, g]. In comparison to price caps and sliding-scale plans, customer choice programs do not treat individual utilities in isolation, and take advantage of the competitive pressures among utilities even under the rate-of-return regulation of prices. Since the choice programs can be restricted to certain geographies, providers or consumer classes, the states still have the space to use other performance-based mechanisms on services not covered [DOE—EIA, g]. Because states require individual providers and marketers to register with the state commission, there is also control over the amount of competition. With the emergence of sliding-scale programs (also called the performance-based regu- lation) in the mid-19908, utilities started influencing their rates of return, and commissions rid themselves of their duty to oversee the utilities’ performance in detail. Some regulators took advantage of this shift from ‘optimal to practical’ regulation [Vogelsang, 2002] and used these programs as a temporary solution before full restructuring became politically feasible in their state [Comnes et al., 1995]. Under the sliding-scale programs, utilities are more able to make investment decisions that are best for consumers rather than do what the imperfectly informed regulator dictates [Braeutigam and Panzar, 1993]. The incen- tive mechanisms described below represent the major types of sliding—scale programs that state commissions currently use to promote performance in particular areas of utilities’ services. Margin-sharing plans promote efficient divestiture of resources on the margin. Off- system sales and pipeline capacity release plans reward utilities for selling off excess gas or capacity in their pipelines [Myers and Strain, 2000, Navajas, 1998]. The 2000 FERC’S Order 637 allows all transmission companies to lease capacity in their pipelines. Gas-cost incentive mechanisms offer utilities more options and incentives for efficient gas procurement than the rate—of—return regulation has historically offered. By having stake in finding lower cost gas, the utility’s interests are more aligned with those of the ratepayers [Myers and Strain, 2000]. The utility may take advantage of arbitrage opportunities in financial derivative markets or select the length of its contracts more I efficiently. Earnings-sharing mechanisms allow utilities to earn a higher return if they manage to make profits in areas outside of their core service. These mechanisms encourage the negotiation of special contracts with new industrial customers to make the utility more competitive with other fuels, and do not touch on the core services that the utilities offer [Bagnell, 2002]. They give the utility incentive to “take greater risks in deepening and extending its markets by providing a limited safety net in case new efforts result in failure. They can reduce business and regulatory risk and serve as an automatic means of keeping earnings within acceptable bounds” (Kentucky PSC, pp. 43—45). Service-quality plans offer explicit rewards for the utility’s score on a consumer sat- isfaction index or other performance measures, such as the average response time to consumer complaints or the average level of gas reserves (indicating the risk of defaulting on consumer demand). Service—quality plans impact providers’ costs through the induced changes in the infrastructure investment and the use of variable inputs. They also have a beneficial effect on long-term costs by lowering the number of maintenance emergencies and consumer complaints. The above policies are often used in conjunction with one another in a state or at a utility. Price caps are often combined with service-quality plans, and consumer-choice programs can be implemented on top of existing sliding—scale programs or price caps. These policies should therefore be studied jointly. 1.1.2 Regulatory Literature Most research on public utilities focuses on electric and telecommunication industries, but has implications for the gas market. Many studies have criticized the overcapital- ization of utilities [Averch and Johnson, 1962, Bailey, 1973, Shepherd, 1972] and the non-optimal usage of all inputs [Comnes et al., 1995, Crew and Kleindorfer, 1986] under the rate-of-return regulation, and studied the effects of the forms of regulation on techni- cal and allocative efficiency [Crew and Kleindorfer, 2002, 1996], as well as social welfare [Brown and Sibley, 1986]. Beesley and Littlechild [1989] compare the appropriateness of price caps, rate-of—return regulation, and competition-enhancing programs in different industries. They conclude that in industries with slow technological progress and with a single undifferentiated product, performance under a price cap may not differ greatly from that under the rate- ' of-return regulation. Promoting competition may be a more effective strategy for these industries. Several studies have studied the effects of transmission restructuring following the 1992 federal Order 636 on the companies’ cost structure and financial performance. Finnoff et a1. [2004] investigate the evidence of competitive or market-power behavior, and find evidence that transmission companies operate more efficiently and competitively under restructuring, but the market continues to be divided into vertical supply chains, which limit achievable competition. Mathios and Rogers [1989], in a cross-sectional study, estimate that price caps lead to lower effective consumer prices in the telecommunications industry than rate-of-return regulation. Majumdar [1997] and Greenstein et a1. [1995] report that price caps out- perform sliding-scale programs in inducing technical efficiency at electric plants, and in inducing efficient deployment of new technologies in the telecommunications industry, re- spectively. Hlasny [2006] finds no effect of the presence of gas-cost incentive mechanisms on consumer prices, compared to the rate-of-return regulation, even after controlling for other regulatory policies used elsewhere in the industry. Hollas [1994, 1999] estimates that federal acts deregulating the gas production and transportation markets helped decrease prices for all consumers, but the greatest benefits went to industrial customers, and the smallest—to residential customers. This paper strives to extend the empirical evidence on the performance of deregulatory programs implemented in the US, as compared to the traditional rate-of-return regulation. Given the lack of empirical literature on the natural gas industry, this paper evaluates all major deregulatory programs that have been implemented in this industry in the US. As in Mathios and Rogers [1989] and Hollas [1994, 1999], here I focus on the effects on consumer prices. Compared to Mathios and Rogers [1989], I use larger, panel data on all natural gas utilities in the US, and I control for several econometric issues, including the endogeneity of consumers’ demands and of the implementation of the deregulatory programs. Compared to Hollas [1994, 1999], I focus on the deregulation of utilities delivering gas to consumers, which occurred after the transmission network was deregulated in the late 19808 and early 19908. I also use a nationwide database of natural gas utilities, and include all major forms of deregulation that have been used in the industry. Finally, I treat the endogeneity of consumers’ demands and of the implementation of the deregulatory programs. 1.2 Empirical Model of the Determination of Natural Gas Prices The following model estimates the impacts of the three deregulatory regimes on prices of the three consumer classes against rate-of-return regulation. Section 1.3.5 and 1.4 compare the estimates to my prior expectations, discussed in Section 1.2.4 Table 1.3. Since my data include observations of average annual gas prices on the utility level, the model focuses on price determination in the time frame of several months to a couple of years. In this time, utilities comply with their reserve requirements, procure gas in different markets including multiple-year contracts, route gas and maintain the network of pipelines and storages in ways to ensure uninterrupted service. Their pipeline capacity is assumed non-binding. Short-term demand shocks can, however, make spot-market gas prices very responsive to regional shortages, and these costs enter the annual average costs of gas. Section 1.2.3 describes the data used in the analysis. Consumer demand for gas is modeled as a function of its price Pz-j—where 2' is an individual utility and j is a class of consumers—and a set of demand shifters specific to consumer class j in utility i’s market, Xij’ or similar for all consumer classes, Yz [Wade, 2003]. On the demand side, subscript 2' refers to consumers of utility 2'. Time subscripts are omitted here, since all endogenous and exogenous variables come from the same time period. It is assumed here that controlling for the same-period variables makes any lagged or future variables redundant in explaining present prices and output levels. This is a reasonable assumption in this year—to—year time frame, with variables that are not significantly correlated over time. Qij = Qij [P233 Xij. Y1] (1-1) Natural gas is a normal good, with substitutes available to each consumer class. Con- sumers are able to adjust the source of their heating and cooling energy. The demands considered in this study are of intermediate-term span when consumers have some ability to substitute gas as an input into production and as a consumable good [Dahl, 1993, Taylor, 1975]. Their ability to switch fuels, and adjust the technologies of their gas con- sumption are however limited by the size of the required innovations and by the constraints on the delivery of substitute fuels [Baker et al., 1989, Berndt and Watkins, 1977]. Factors determining consumers’ ability and willingness to pay for gas vary across consumer classes and are modeled as part of Xz'j» or are similar in distribution for all consumer classes as part of Yi- The regulated price of gas, Pz-j, is the sum of average commodity, transmission and 10 distribution costs, including a fixed rate of return on capital, and any transfers (such as the sharing of savings and rewards) that utilities are entitled to under their regulation. Competitive price under consumer-choice programs is a function of the utilities’ marginal costs of all services subject to competition (generally, the commodity acquisition, trans- mission and distribution portions), and the average costs of services inherently subject to profit regulation (such as the construction of pipelines and other fixed costs), which must be recovered through consumer prices. To what extent prices reflect the marginal costs of service depends on the amount of competition in each regional market and on regulatory oversight. Pij = Pij [Qija Vija W2] (12) Some costs affect prices of all consumer classes identically (for instance, as a function of the volume of gas sold to all consumer classes), and are modeled as part of Wi. Other costs are specific to consumer class j or the volume of gas purchased by consumer j from the utility (for instance, Crew and Kleindorfer 1979, pp.161—166), and are modeled as part of sz. Information on the determinants of all costs comes mainly from the DOE—EIA [h] and from a custom survey of all state public service commissions conducted for this study (refer to the description of data in Section 1.2.3). The price of gas covers three kinds of utilities’ costs: commodity, transmission and distribution [Mariner—Volpe, 2000]. Commodity cost is the most erratic of these three. In the intermediate term, it is a function of the rate of extraction and transmission from the wells to the trading hubs, as well as the regional demands for gas from all consumer classes. Since gas supply in the short run is constrained by the capacity of all pipelines, seasonal supply and demand shocks in any region may influence the commodity costs even in other regions. In the span of several years, the capacity and operating costs of gas wells 11 and various import, transmission and storage channels undergo changes. This variation in short-term and long-term costs is reflected in the average annual costs. Commodity cost is common to all consumer classes in a region. Ti‘ansmission and distribution portions of the consumer price are stable costs that depend on the cost of maintaining a stock of pipelines, storages and other facilities, as well as the amount of maintenance and general administration (monitoring, billing) required to serve representative customers in each consumer class [DOE—EIA, c, Mariner-Volpe, 2000]. Transmission and distribution costs thus differ across consumer classes, and are modeled as part of Vij- The regulatory policy used at each utility is modeled as entering V,j, since policies can have differing effects on individual consumer classes. This difference may not be the same under each policy. The coefficients on the corresponding elements of V, j’ for each policy and for each consumer class j , are the focus of this paper. 1.2.1 Estimation Strategy The market price of gas is a function of shifters of both the market supply as well as demand in the intermediate term. It is modeled as a function of: 1) the regulatory policy; 2) local and national supply shifters common to all utilities (such as federal deregulation efforts, projected state gas reserves and their adjustments, and the capacity of state gas-storage facilities); and 3) resources available to individual utilities (such as different management types and infrastructure). Since I have a number of annual observations for each utility, I build a panel data set in which I control for changes in important characteristics of utilities over time, and unobserved time—constant factors (proxying for inherent operational standards and infrastructure). Demand for gas Q,- j is modeled as a function of the consumers’ ability to pay, proxied 12 by the measures of their incomes (gross earnings, income tax rates, and unemployment and bankruptcy rates), and the need for heating and power-generation (proxied by heating and cooling degree-days that year, average high and low temperatures, and unobserved time-constant regional factors). The volume of gas purchased by consumer class 3', Q,j, is endogenous in the own price equation. If I include Q,- j in the regression of P, j directly, coefficients on all regressors correlated with 62,-]- (in both V,j and W,) may be biased, because they will include some elements from Equation 1.1. Excluding Q,- j altogether will not solve the bias, due to the correlation of other regressors with Q,,-. Some variables proxy well for the excluded volume demanded, and are not endogenous in the price equation. For identification of Equation 1.2 using proxy variables, I need a set of variables Z, j that are exogenous in the price equation and are individually or jointly highly correlated with Qij' I can write Qlj =13]: - Zij + €1,°j 131° 5&9 0 (1.3) where (lij is a measurement error in the proxies. [ij and (1,]: may be vectors if Z,- j is itself a vector of several variables. Panel regressions with proxies for Q,,, a set of exogenous supply shifters, and fixed effects are used as the benchmark model in Section 1.3: Pij = Pij [Vijv W2" Zij]+“12‘j Here I control for factors that determine P,- j as well as selected factors that determine (2,, while omitting Qij itself. Using such proxies Z,,-, the coefficients of interest on V,j may be unbiased, provided that V, j are uncorrelated with (lijv and that Z,,- are 13 uncorrelated with the residual in Equation 1.2. The coefficients on V, j may nevertheless be inefficient due to the imperfect relationship between Q,- j and Z,j. Coeflicients on the proxies may also differ from coefficients on Q,- j in Equation 1.2, because of the impact of ,Bj, which may not equal unity. Since Equation 1.3 omits Pi)" however, covariance(P,-j, Clij) yé 0. In this case our conditions for the unbiasedness of coeflicients on V, j are not satisfied, unless covariance( V, j: 61,-j) = 0, i.e., the case when controlling for volume demanded is irrelevant for the estimation of the coefficients on V, j' To deal with the endogeneity of 62,, properly, Equations 1.1 and 1.2 must either be estimated jointly, or exogenous variables from Equation 1.1, X,,- and Y,, must be used as instruments for Q,,- in Equation 1.2. The latter method is a part of the joint estimation method, but requires fewer assumptions on relationships among explanatory variables. It does not allow us to estimate coefficients in Equation 1.1, and on Qij in Equation 1.2, but since we are only interested in the coefficients on V, 3" this method suffices. In order to identify Equation 1.2 using instrumental variables for Qij’ we need some elements from the exogenous variables in Equation 1.1 to be excluded from the exogenous variables in Equation 1.2.1 We also need the instruments Xij and Y,- to be uncorrelated with the residual in Equation 1.2. To implement the instrumental variable approach, in the first stage we obtain a fitted value of the volume demanded, using all available exogenous variables. 913' = Qij [Xijv Y1] + 622') (1-4) 1Generally, some elements of Xij and V, 3" or Y,- and W,, may be identical and may directly determine both the volumes demanded by consumers and the prices. 14 In the second stage, we use the fitted value, Q, j = E (Q, j), in Equation 1.2: Provided that (X,j, Y,) were indeed highly correlated with Qij’ and uncorrelated themselves with P- - ZJ’ all coefficients in this regression are unbiased. Specifically, in the first stage, demand is modeled as a function of consumer incomes, climate shocks and prices of substitute fuels [Berndt and Watkins, 1977, Hollas, 1999]. Residential demand is modeled as a function of day and night temperatures, gross per capita earnings and personal income tax rates, unemployment and personal bankruptcy rates, and the residential price of electricity. Commercial and industrial consumers’ de- mands depend on temperatures during working hours, business incomes and income tax rates, business bankruptcy rates and the prices of electricity and coal. In the second stage, I regress the prices on the deregulatory policies, characteristics of individual util- ities, shocks to the local gas resources and input markets, aggregate commodity-supply shocks, and the fitted values of the volumes demanded from the first stage. Differences in consumer-specific exogenous variables and endogenous demands may not be the only factors distinguishing prices of individual consumer classes. Price of one con- sumer class may depend in absolute or relative terms directly on prices of other consumer classes. If a portion of common costs W,- enters the prices of individual consumer classes based on their respective price elasticities of demand—as under a third-degree price- discriminating monopoly, for instance in Ramsey [1927] and Joskow and Rose [1989]—the coefficients on P,,- in Equation 1.1 determine coefficients on some elements of W,- in Equa- tion 1.2. If this is true, coefficients on all variables correlated with Pij and the elements of W,- will be biased and inefficient. The errors in the three price equations may be cor- 15 related, giving rise to the possibility to alleviate some of the inefficiency by treating all price equations as a system of seemingly-unrelated regressions [Zellner, 1962]. To correct the bias, I would need to treat the price and the demand equations for all consumer classes as a model of simultaneous equations, using information on sector- specific supply and demand determinants and on the process determining relative prices. In this paper, however, I lack the instruments that could identify the strategic interdepen- dence among price equations. I assume that the regulator successfully bars utilities from exerting power over relative prices. While this may be a strong assumption, it may be ac- ceptable to assume that state regulators limit this ability significantly [Hollas, 1989], and that the process of setting relative prices stays unchanged over time and across different regimes of regulation. Appendix A.1 tests for a structural change occurring in the setting of relative prices at the time when the policies were implemented. If the setting of the relative prices underwent a change at the time of implementation of a policy, the relation- ship between residuals in my three regressions would change. Appendix A.1 reports that the test failed to reject the null hypothesis of no regime change at any reasonable level of significance. That implies that the alleged third-degree price-discrimination is expected to bias the coefficients on the policy variables V,j only through its bias on coefficients on W,, but not directly or through other pathways. While it is possible that strategic considerations do affect the relative price setting between individual consumer classes— as the ranking of coefficients on consumer-choice programs and price caps indicates—this relationship does not appear to change at the time of implementation of any deregulatory policy, or over time. As long as the expected changes in prices due to deregulation are small as a portion of the prices (as Section 1.2.4 confirms), the remaining bias is likely to be trivial. 16 1.2.2 Modeling of the Regulatory Policies Since deregulatory policies at the utility do not directly affect demand for gas, they are modeled as part of V, 3" They affect individual portions of consumer prices by giv- ing utilities incentives to seek lower-cost inputs, and more efficient absolute and relative amounts of inputs [Majumdar, 1997]. Sliding-scale programs also affect prices via the sharing of rewards between utilities’ shareholders and ratepayers. I have assumed that X - zj’ Y,, V, j and W, are exogenously given outside of my model. If elements of V, j: such as the deregulatory policies, are themselves determined by P,- j or variables correlated with P,,-, coefficients on these V, j as well as coefficients on all correlated variables will be biased. In that case I must instrument for these elements of V,- j the way I did with endogenous demands 62,-, The process determining deregulation at utility 2’ may look like this: Vi =Vz'j [X Y2» W23 Uij] (1.6) 1 ij’ where U,,- are exogenous variables determining deregulation efforts in the gas industry, without affecting gas prices through other venues other than through V, j“ U, j can be used to instrument for V, j in Equation 1.2. There are no clear candidates for U,,, but lagged deregulation efforts in energy and telecommunication industries, and even deregulation efforts in the gas industry in other states could perform well. These instruments are arguably exogenous in the deregulation process, and do not affect gas prices directly or 2 in other channels once their effect on V, j is accounted for. Since deregulatory policies are the focus of my paper, the following sections investigate 2Other literature assumes that simply including information on economic trends in the state [Greenstein et al., 1995], or lags of gas prices [Mathios and Rogers, 1989], can help us control for any feedback from prices on deregulation. In this paper I find, however, that policies can influence prices even in the years preceding their implementation, putting the use of lagged prices as instruments into question. 17 several models of the determination of consumer prices of gas, with different treatments of the potential endogeneity of deregulatory policies. Policies are first assumed exogenous under the regressions using panel methods (Section 1.3) and the system of seemingly- unrelated regressions of individual consumer classes (Section 1.3.1). Using some rea- sonable assumptions on how policies are implemented at individual utilities, I then use difference-in—difference regressions to control for unobserved utility-specific factors (Sec- tion 1.3.2). Finally, I use two-stage least-squares regressions using exogenous instruments for the implementation of deregulatory policies at individual utilities and in individual states (Section 1.3.3). Section 1.3.4 reports on several tests of the processes determining policy implementation. In the specifications estimated in Section 1.3, deregulatory policies are modeled as entering gas prices linearly. If the incentive power of a policy can be doubled, such a policy would have twice the impact on prices as the original policy. This is relevant for sliding-scale programs, which allow utilities to keep a certain share of any cost savings.3 I also implicitly assume that there is no interaction of coexisting policies at a utility, so the effect on prices of two policies is simply the sum of the individual effects. While these assumptions are strong, without structural estimation of the policy impacts (e.g., by individual cost component, by timing, etc), I cannot tell whether another set of assumptions would lead to more or less accurate estimates. Since different assumptions could strengthen or weaken my results, I use linearity and independence of the policies as default assumptions. To empirically evaluate the sensitivity of my results to these assumptions, I have run similar specifications modeling the impact of the policies on prices under competing assumptions (i.e., nonlinearity of the impacts of the sharing provision under the sliding-scale programs, and nonzero interactions of the policies). These results 3Thus, sliding-scale program allowing a utility to keep 10% of all its savings is expected to result in half the price reduction as a program allowing the utility to keep 20%. This is arguably locally plausible. 18 were not significantly different from the benchmark results, due to the small portion of cases when multiple policies are used at a utility, and a small variation in utilities’ allowed savings. These results are also sensitive to the accuracy of my data on all policies used at a utility and on the exact share of any rewards that the utility retains, to which the default specification is more robust. Results of these additional specifications are not reported here. As a final note, since I use imperfect proxies for several latent variables in my es- timation, residuals in Equations 1.1 and 1.2 absorb any uncontrolled variation due to measurement errors and omitted variables. The prices and volumes of gas may be re- ported imprecisely [Taylor, 1975]. These problems may cause heteroskedasticity in the residuals and correlation of the residuals for individual utilities across years. To correct the standard errors, I thus control for arbitrary heteroskedasticity, and cluster the residu- als for each utility to obtain utility-specific variance terms. Since some regressors appear in the price equations of all three consumer classes, or are highly correlated with regressors in the other price equations, residuals across these equations may also be correlated. I improve efficiency by estimating the price equations jointly, using the seemingly-unrelated regressions model. 1.2.3 Natural Gas Industry Data The background information and data come from several public sources, most impor- tantly the Department of Energy’s Energr Information Administration and the Bureau of Labor Statistics, and a custom survey of the state public service commissions. The sample includes data for all investor-owned utilities in the US, provided that they filed the EIA-176 form on their prices and volumes of gas sold in years 1996—2002. Table 1.1 reports the source and description of each variable. 19 Variable Data Source Units in the Model Choice—implemented DOE, EnergySource Dummy for full implem. Choice—pilot DOE-BIA Dummy for state pilot program Choice—considered DOE-EIA Dummy for legisl. passed in a state, but no program implem. Price cap Survey of PSCs Dummy GCIM Survey of PSCs Share of savings that utility re- Earnings-sharing Margin-sharing Survey of PSCs Survey of PSCs tains (in 10%) Dummy Share of savings that utility re- tains (in 10%), for one or both of capac. release & off-system sales Service-quality plan Survey of PSCS Dummy Pers. income BEA Log ($) Proprietors’ income Small Bus. Adm. Log of proprietors’ income per Pers. income tax rate Small bus. income tax rate Corp. income tax rate Heat., cool. deg. day Avg. day, night temp. El. price by cons. class Ind. price of coal Bus. bankruptcy rate Res. bankruptcy rate Unempl. rate Avg. salary in util. ind. Volume of gas (excl. own cons. class) Storage capacity Reserve adjust. of wet gas Fed. of Tax Adm. FTA FTA N CDC NCDC DOE-EIA DOE-EIA US Bankr. Courts US Bankr. Courts BLS BLS DOE, Form 176 DOE-EIA, Platts DOE-EIA commercial estab. in a state Log (%) Log of the lower bound on the corp. income tax (%) Log of the upper bound on the corp. income tax (%) Log (#) Degree F Log (53) 1,000 cubic feet (Mcf) sold to other consumer classes Million cubic feet (MMcf) MMcf added to state reserves, lagged one year El. ind. restructuring [Myers and Strain, Dummy 2000], [DOE—EIA, g] Telecom restructuring [Myers and Strain, Dummy 2000], [Sappington, 2002] Table 1.1 Description and Sources of Variables 2O In Table 1.1, policy variables indicate the phase of implementation of the policies at a utility where ever this information is available. The rest of policy variables are in a binary form. Gas-cost incentive mechanisms (GCIMs), capacity release plans and off-system sale plans are represented by the ten-percent units of the share of their rewards that goes to the shareholders. So a mechanism allowing utility shareholders to keep 50% of the savings enters as 5. Their coefficients are interpreted as the percent effect on price of a 10% change in the shareholders’ share. Consumer-choice programs are represented by two indicators: whether the appropriate legislation has been filed or whether they are fully in place (including pilot programs).4 Table 1.2 and Figure 1.1 report on the presence of individual deregulatory programs in the sample. Several programs are represented lightly in the sample. With a small portion of the sample under policy treatment, individual price observations can greatly influence my conclusions about the mechanisms’ performance. In much of the following estimation, due to the small number of individual occurrences, the earnings-sharing, margin-sharing, and gas—cost incentive plans are studied jointly as the sliding-scale programs. 1.2.4 Expectations from the Policy Comparisons Before performing the regression analysis, I obtained some quantitative expectations of the impacts of individual policies on the residential, small commercial and industrial prices of natural gas, to compare the regression results to some benchmark. First of all, the impacts of individual policies are bounded by the portion of the firm’s 4In addition to these specifications, I ran my regressions using the portion of consumers participating in the consumer-choice programs and the portion eligible, and the number of independent marketers registered in a state. I also distinguished choice programs considered, piloted, partially implemented, and fully implemented; and I analyzed changes in the status of restructuring for states that broadened, narrowed, or abandoned their programs during 1996—2002. I considered various interaction terms for the simultaneous presence of multiple policies. Due to the small number of selected policies and years in my sample, these alternative specifications distorted my results. 21 Program States Utilities Observations Consumer choice 24 unknown* unknown“ Price cap 5 18 41 GCIM 20 43** 229** Earnings-sharing 5 16 44 Margin-sharing 12 28 154 Service quality 6 15 58 * 357 investor-owned utilities (with 879 observations) operate in states with the consumer-choice program, but it is unclear which utilities actually participate in it or are affected by it. ** This includes all 17 utilities (102 observations) in Wyoming where all utili- ties automatically receive 10% of their savings compared to a commodity cost benchmark. Table 1.2 Inventory of Deregulatory Programs in the Sample -— Consu'ner choice - implemented (States) Consuner choice - considered (States) - - - - Pn'ce caps (Utilities - A - Gas cost plan (Utiities) -:a - Earnings sharing ( tiities) Margin sharing (Utilities) - -x- - Service quaity (Utiities) 2001 2002 Figure 1.1. Number of Policies Present in the Sample 22 price that the policies can affect. The US Department of Energy’s Energy Information Administration (EIA) reports the breakdown of the residential price of gas as 34% com- modity, 47% distribution, and 19% transmission cost portions [DOE-EIA, c]. The EIA does not report the breakdowns of the commercial and industrial rates, but I conjecture that the small commercial (and industrial) rates are composed of 41% (50%) commodity, 36% (27%) distribution and 23% (23%) transmission costs. The small-commercial price breakdown assumes that the commodity and transmission costs amount to the same ab- solute charge as in the residential price, and only change as a fraction of total costs. In the industrial price I assume the transmission cost to amount to the same portion as in the commercial price, and that 50% of the price consists of the commodity cost (using anecdotal evidence from the public service commissions). Consumer-choice programs affect all costs that utilities incur. To form a belief about the maximum achievable impact on prices, I use the conjecture that utilities in a restruc- tured state succeed in procuring gas at one standard deviation below the mean market price throughout the year.5 The utility may also shave 10% off its transmission and distribution costs. These savings enter the consumer price in their entirety and are not shared with the shareholders, under the assumption of perfect competition. Since larger commercial and industrial consumers had some choice over their provider even before the restructuring of the late 19908, and even today some residential consumers are ineligi- ble, I conjecture that only 75%, 50%, and 25% of residential, commercial, and industrial customers are affected by the new deregulation. In addition, I allow the utility to price-discriminate between the three consumer classes, giving each class of consumers a part of the savings proportional to their relative price 5The gas index daily closing price on the American Mercantile Exchange had a mean of $174 per thousand terms and a standard deviation of $35.91 during 1996—2002 (in January 1996 dollars). The standard deviation thus represented 20.6% of the price. 23 elasticity of demand. I use the elasticities (-0.22, -0.23 and -0.30, respectively) compiled by Dahl [1993] as reported in Paul and Burtraw [2002]. For sliding-scale mechanisms I assume only half the differences in relative elasticities of demand (as a mean-preserving spread of the elasticities), in effect assuming that the utility has a limited ability to price-discriminate under regulatory supervision [Hollas and Stansell, 1988]. Under price caps, I assume the effective sharing of savings of 50% between the utility and the ratepayers. In essence, I assume that the adjustments for inflation (X-factor), technological progress and risk sharing (Z—factor) in the price cap are agreed on mutually between the utility and the regulator [Bernstein and Sappington, 1998, Sappington, 2002, Sappington and Sibley, 1992], resulting in 50% sharing. The gas-cost incentive mecha- nisms affect only the commodity portion of the price and are typically limited to the core consumer classes. The residential and commercial ratepayers generally receive 50% of any cost savings (with no dead band), and the utility reallocates these savings across the two consumer classes based on their relative price elasticities of demand. Formulating my expectations about the earnings-sharing plans is more arbitrary since these mechanisms reward utilities for attracting new customers, under competitive con- ditions, rather than for cost savings. Using anecdotal evidence from the public service commissioners, I guess that a utility can increase its industrial consumer base by 5% and earn 15% return on the new contracts. The utility returns 70% of the receipts to consumers, and manages to reallocate them across the consumer classes according to the relative price elasticities of demand. I use the conjecture that 5% of the industrial con- sumers receive a lower competitive rate negotiated under the new contracts, while 95% receive a share of any rewards along with the other consumer classes. For margin-sharing mechanisms I conjecture that the utility manages to sell off 5% of both the excess gas and pipeline capacity, since pipeline capacity plans and off—system 24 Residential Small Commercial Industrial $ % $ % $ % Consumer Choice -$0.80 -8.99% -$0.49 -6.58% -$0.21 -4.60% Price Cap -$0.53 -6.00% -$0.49 -6.58% -$0.41 -9.21% GCIM -$0.29 -3.30% -$0.30 4.05% - — earnings-sharing -$0.09 -0.99% -$0.07 -1.01% —$0.06 -1.32% margin-sharing -$0.41 -4.60% -$0.35 -4.68% -$0.03 -0.77% Service-Quality Plan $0.47 +5.31% $0.40 +5.42% - - Table 1.3 Expectations of plausible impacts of the mechanisms on prices sales plans are often implemented jointly. The utility keeps 15% of the revenues and gives the rest to the residential and commercial customers. 5% of industrial customers are assumed to benefit from buying the excess resources at competitive rates (that is, gas at a price one standard deviation below the mean commodity price, and transmission and distribution resources at 10% below their mean costs). Service-quality plans may require infrastructure and service force investments raising the distribution and transmission costs by 10% and 5%, respectively. It is assumed that industrial customers don’t share any benefits or costs from these programs. Table 1.3 displays the plausible effects on prices of each of the studied mechanisms, in absolute and percentage terms. These estimates show the ideal outcomes under suc- cessfully implemented programs. Administration and transaction costs of each program, accounting treatment of any stranded assets, and constraints placed on the extent of the programs or on the reward allocation may result in smaller price reductions. These expectations suggest that consumer-choice programs and price caps are the strongest in reducing prices (by 46—90% and 60—92%, respectively), since their benefits come from savings in all of the utilities’ operations. Gas-cost incentive mechanisms have a weaker expected effect on prices (3.3—4.1%), because they affect only the commodity 25 portion of the price, and get shared with shareholders. Since ratepayers receive most of the revenues from margin-sharing mechanisms, and excess resources in all portions of the costs can be sold off, these programs may outperform gas-cost incentive mechanisms (08—46%). Under the sizing of potential effects of earnings-sharing mechanisms, these plans are expected to benefit ratepayers only marginally (LO—1.3%). I performed a sensitivity analysis of these expected results. I imposed alternative assumptions on the composition of the utilities’ total costs (i.e., the same for all consumer classes as for the residential class, or the industrial class); on the possible percentage savings due to efficiency improvements, increased competition and the acquisition of lower- cost resources (5% to 20%), and on the earnings from contracts with new industrial consumers under the earnings-sharing programs (0% to 20%); on the number of new contracts under the earnings-sharing program (0% to 20%); on the sharing of savings and earnings between the company and the consumers (10% to 75% going to the utility); on the price elasticity of demand of individual consumer classes (-0.1 to -0.3 for residents, -0.15 to -0.5 for small businesses, and -0.15 to -1.0 for industrial customers, in line with the prior empirical literature); and on the effective strength of the third degree discrimination across consumer classes (competitive to monopolistic). The results changed up to 20% with the variation in the composition of utilities’ costs, particularly for policies that emphasize only some of the costs. When the possible cost savings, including the cost of the commodity, fall to 5%, the price reduction under each policy can decrease as much as threefold. If they rise to 20%, the price reduction increases by 40%. If a utility under an earnings-sharing program acquires 20% of additional con- tracts (rather than 10%), the reduction in residential and commercial prices can jump twofold, and the reduction in industrial prices can jump threefold. As the portion of all savings and earnings that the utilities pass to consumers increases, the price reductions 26 can increase by 50% under the price caps and gas-cost incentive mechanisms, by over 100% under the earnings-sharing programs, and by only 6% under the margin-sharing programs. Under this program, the portion that the utility keeps is already low.6 If, on the other hand, utilities are allowed to keep a lower portion of the savings, the price reductions can fall up to approximately twofold under all policies for all consumer classes. As the relative price elasticity of demand across consumer classes increases, industrial consumers can receive up to two times greater price reductions, and residential consumers can receive up to five times lower price reductions, between the least and the most different relative elasticities. If utilities become more likely to price-discriminate between consumer classes (for instance, if the regulator becomes more lenient or if the cross-subsidization of prices is more difficult to identify), price reduction for the consumer class will fall by 14%, and the price reduction of industrial customers will increase by 20%. Overall, the numbers in Table 1.3 are indicative of the price changes we could expect under the alternative policies. The most important factors determining the price changes are the actual possibilities for cost savings, and the sharing of savings with consumers. Other unobserved factors not discussed here are transaction, monitoring and accounting costs under the deregulatory policies, which will reduce any beneficial effects of the policies on prices. 6This ignores the fact that the lower portion that the utility can keep, the lower its incentive to minimize costs, particularly under the price caps. 27 1.3 Estimation Results Table 1.4 shows the results of the panel regressions using fixed effects with three respective consumer prices as the dependent variables.7 The first four rows of the tables show the coefficients on the regulatory policies. The coefficients on the consumer-choice program are overall negative. The implemented choice programs are estimated to lower the residential, commercial and industrial prices by 5.5%, 4.8% and 2.2%.8 In the states considering adoption of the choice programs, utilities are preparing by charging 07—23% lower prices across the board (Row 2).9 Price caps have the expected negative sign for residential and industrial customers, lowering prices by 0.1% and 11.1%. Commercial customers may see a 7.9% jump in rates. As Table 1.2 above indicated, few utilities are regulated by price caps. Small commercial consumers tend to be also treated differently across states, so this coefficient may be the result of a small treatment group, unobserved heterogeneity and perhaps an omitted variable explaining the status of the commercial customers in a state.10 Sliding- scale plans are estimated to raise the three consumer prices by 0.6%, 1.9% and 1.4%, respectively. Service-quality plans are predicted to decrease residential and commercial prices in the intermediate term by 1.9% and 4.8%, while raising industrial price by 6.9%. Greater availability of underground gas-storage capacity in a state leads to lower prices 7Similar analysis was performed with ordinary least-squares regressions, using binary variables for US regions, and controlling for arbitrary heteroskedasticity and autocorrelation on the utility level. 8Coefficients in the following tables come from log-normal regressions, and can thus be interpreted as percent effects on the dependent variable. For small coefficients such as those above, this interpretation is accurate. For larger coefficients, computing % e f f eat, j = 8B2] — I, where Bij is a coefficient from a log-normal regression, would give us more precise marginal effects. 9In addition to the analysis using information on the state where each utility operates, I attempted to match each utility with its county, using the utilities’ addresses in the Form BIA-176, to use county- specific demographic and economic trends. Due to problems with the reported addresses, and uncertainty about utilities’ service territories, these estimation results were very noisy, and are omitted here. 10Depending on the state, either all or only small commercial customers are considered part of the core customers. Some states limit participation in the incentive program and sharing of the rewards to the residential class only. This inconsistency causes differential treatment of these consumers across states. It may even cause self-selection of small businesses in how they register with their utility. 28 Residential Commercial Industrial Choice— -0.055** -0.048* -0.022 implemented (0.025) (0.027) (0.038) Choice—considered -0.017 -0.007 -0.023 (0.014) (0.016) (0.023) Price cap -0.001 0.079 -0.111* (0.057) (0.051) (0.057) Sliding-scale plan 0.006 0.019 0.014 (0.032) (0.034) (0.045) Service-quality plan —0.019 -0.048 0.069 (0.059) (0.048) (0.064) Storage capacity -0.003* -0.002 -0.001 (0.002) (0.002) (0.003) Volume (excl. own -0.084*** -0.107*** -0.124** consumer class) (0.025) (0.032) (0059) Volume2 (excl, own 0.003*** 0.003*** 0.004** consumer class) (0001) (0-001) (0-002) Heating degree days -0.006 -0.015** -0.041*** (0.006) (0.007) (0.011) Cooling degree days 0.006** 0.009** 0.004 (0.003) (0.004) (0.005) Personal income 0.026 0.013 0.031 (0.017) (0.021) (0.033) Unemployment rate 0.002*** 0.001*** 0.002*** (0) (0) (0001) Utility wages 0.023 0.012 0.031 (0.021) (0.025) (0.034) Corporate income 0.005** 0 -0.001 tax (0.003) (0.002) (0.003) Constant 2.150*** 2.457*** 2.463*** (0.189) (0.261) (0.47) Observations 2,066 2, 105 1 ,404 R2 0.24 0.21 0.27 * statistically significant at 10%; ** 5%; *** 1%, two—tailed tests. Prices of gas and of alternative fuels are in logarithmic form. Fixed effects are at the state level. All variables in monetary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Table 1.4 Panel Regressions with Fixed Effects 29 at all utilities in a state for all customer classes. Utilities use these storages to protect themselves from pipeline congestion during peak demand seasons, and to build reserves of low cost gas. Since data on the operating capacity of utilities and their pipelines is miss- ing, the utilities’ volume of gas sold, excluding consumption by the own consumer class, is used to proxy for this capacity.11 Coefficients on the volume and volume squared jointly imply that at the average capacity of utilities, larger utilities tend to charge slightly lower rates. As the capacity of an average-sized utility increases by ten percent (from 10.3 to 11.33 million Mcf), its residential price is predicted to fall by 0.13 percent. All regressions here use heating and cooling degree-days normalized by their long-term averages in that state, to better control for the temporal variation in demand for heating and cooling. Regional variation in climate and demand for gas has been incorporated in the utilities’ infrastructure, and does not affect the intermediate or long-term prices. The coefficients on the degree days show that prices rise in response to high temperatures, when cooling is necessary, and fall with lower temperatures. Demand for heating gas is high but relatively stable in cold temperatures, and is accounted for in the pipeline capacity, planned gas purchases, and margins. Uncertainty over the need for gas in summer arises due to unex- pected jumps in demand for cooling, when gas-powered electric generators get dispatched without warning to aid coal-burning generators [Hollas, 1999]. Personal income proxies for the ability of consumers in all customer classes to afford heating gas. Personal income has the expected, positive coefficients in all columns of Table 1.4. The unemployment rate has a stable positive effect, which possibly results from the presence of public programs subsidizing the prices of the unemployed or paying their heating bills without giving them incentives to conserve gas. This coefficient could 1J‘Other proxies were tried in similar regressions, such as utilities’ total annual costs, sales in monetary terms, number of customers, number of states where it is operating, indicator for whether it is operating in its headquarter state. 30 also result from high collinearity of unemployment with other measures of consumers’ ability to pay. Wages in the utility industry have a positive effect on all prices. This agrees with the fact that these wages affect utilities’ costs directly and positively, and are also expected to positively affect the residential demand for gas. Corporate income taxes have a positive effect on residential prices, and no effect on commercial and industrial prices. Corporate taxes enter utilities’ costs, but are also expected to lower the commercial and industrial customers’ ability to pay for gas. Overall, the specifications reported in Table 1.4 explain approximately a quarter of variation in the three respective consumer prices. The policy variables are jointly not statistically significant, but all variables jointly are significant even at a one percent level. 1.3.1 Seemingly-Unrelated Price Regressions Residuals in the price equations arise from imperfect measurement of both the inde- pendent and the dependent variables, as well as from any omitted variables. Some of the imprecisions in measurement may be common across the equations, and some variables may be omitted from all three equations. Residuals in the three price equations may thus be correlated, and may in part be explained by a common process. As a result, standard errors on some independent variables and the sum of squared errors for the entire equa- tions may be larger than if we had information on this process, because it could explain a portion of the residuals. To measure more accurately the contribution of each regressor in explaining variation in prices, I use the fact that several exogenous variables appear only in a subset of the three equations to identify a seemingly-unrelated regression model, to control for the correlation among residuals in individual price equations. On the demand side, I use the fact that each consumer class has a different measure of 31 gross income, income tax rate, alternative fuel substitutable for gas, and time when gas is demanded. Residential customers adjust their consumption primarily in response to night temperatures, when they are at home. Commercial customers, on the other hand, mostly respond to fluctuations in temperatures during operating hours. Large industrial customers are assumed here to operate at all shifts, and adjust their consumption of gas during both days and nights. On the supply side, underground storage facilities may be used for ensuring uninterrupted service to residential and commercial customers only. In the absence of reliable information on the utilities’ capacity, I use the volume sold to other consumer classes as a proxy for capacity in a particular price equation, and these proxies vary across the three equations.12 Since volume demanded by members of a consumer class is endogenous in the price equation of that consumer class, I also instrument for the volume of gas sold to that con- sumer class. Instruments for the demand include the number of heating and cooling degree days, consumer incomes, unemployment rates and business bankruptcy rates, income tax rates, and the prices of alternative fuels. Degree days, and bankruptcy and consumer income tax rates are assumed to impact gas prices only through demand. Income levels and unemployment rates are allowed to also affect prices directly in the second stage re- gression (such as through the unobserved stringency of regulation which may depend on residents’ incomes). Table 1.5 summarizes the results of the model of seemingly-unrelated regressions of gas prices for individual consumer classes.13 Coefficients in the first row show that the consumer-choice programs have cut residential rates by 5.2%, and commercial and indus- 12Individual regulatory policies may affect prices of only some consumer classes, so I ran additional specifications where sliding-scale programs affected only residential and commercial customers (the core customers), or affected them differently than industrial customers. 13I also ran the three price equations independently, using panel methods, with instrumental variables for the endogenous demand. I considered various sets of instruments. 32 trial rates by 9.4—10.1%. This implies that controlling better for consumer demand re- sulted in reversing the ranking of coefficients on consumer choice across the three consumer classes, compared to that in the panel method regressions above. This is an interesting and important result. Coefficient in the residential price regression remained practically unchanged, while coefficients in the commercial, and particularly in the industrial price regressions, rose in absolute value. This suggests that coefficients in the OLS regressions (Table 1.4), and particularly in regressions of prices of larger consumers, suffer from at- tenuation bias due to the omission of the feedback of prices on the volume demanded. Controlling for the feedback affects particularly the second and the third columns, which agrees with the prior that larger customers, and particularly industrial customers, are more responsive to the prices of gas. Price caps are predicted to have no effect on residential prices and lower industrial rates by 20.0%, while raising commercial rates by 9.4%. Once again we see an unexpected effect of price caps on the commercial price, suggesting that the price of this consumer class may be determined by additional processes than those modeled here. sliding-scale programs are estimated to lower residential rates by 0.6%, commercial prices by 1.4% and industrial rates by 2.6%. The greatest benefit is thus predicted to go again to the industrial class, and the smallest to the residential class. These results can be compared to the benchmark panel regressions above. Most coefficients preserve their signs and magnitudes, except for the sliding-scale programs, which are now estimated to lower all consumer rates modestly. Compared to panel method regressions above, coefficient on price caps and sliding-scale programs changed the most in the industrial price regression, confirming the strongest responsiveness of this consumer class to prices. The differences in all coefficients compared to the panel method regressions above come from my modeling of the demand differently. Differences in standard errors also come 33 from modeling of the structure of residuals differently. Since the seemingly-unrelated regressions model used here requires that observations in all equation be identical—a balanced panel—the number of observations here is significantly lower than in the previ- ous specification, which obviously also affects the coefficients and standard errors. The seemingly-unrelated regressions model explains more than a quarter of variation in all prices, and the policy variables included in it are jointly statistically significant at even a 1% level (and also 1% level for all explanatory variables). This fit is thus better than under separate panel data regressions with fixed effects, reported above. The lower part of Table 1.5 shows the coefficients on the instrumented demand and the other variables jointly satisfying the exclusion restrictions in the seemingly-unrelated regressions. The first row shows the coefficients on the instrumented demand for gas, corrected for the feedback from prices.14 Since I am dealing with intermediate-term prices and demands, the negative and significant coefficients in regressions imply better utilization of capacity, and falling marginal costs of procurement (implying non-binding capacity constraints). The coefficients rise in economic and statistical significance from the residential to the industrial prices (from 0.6% to 3.9% throughout the table, and from insignificant to significant at 1% level), suggesting that the larger the individual customers, the lower the costs of serving them on the margin. Alternatively, the more resources a utility has, the more competitively it can compete for larger consumers. 1.3.2 Price Growth under Deregulation In addition to the models estimated above, I investigate gas prices and their growth at different utilities. Table 1.6 and Figure 1.2 report the changes in levels and growth rates of 14The first-stage regressions estimated consumer demands using a set of variables on climate and con- sumer ability to pay. These regressions achieved R-squared of 0.30, 0.26 and 0.28, (and F statistics suggesting joint significance of all coefficients at a 1% level), for the three consumer classes. 34 Residential Commercial Industrial Choice—implemented -0.052 -0.094* —0.101 (0.055) (0.050) (0.088) Choice—considered 0.003 -0.002 -0.044 (0.028) (0.026) (0.045) Price cap 0.000 0.094** —0.200*** (0.041) (0.038) (0.068) Sliding-scale plan -0.006 -0.014 -0.026 (0.029) (0.026) (0.047) Variables Satisfying the Exclusion Restrictions Own volume -0.006 -0.035*** -0.039*** (instrum.) (0.008) (0.007) (0.007) Volume (excl. own 0.040 -0.023 -0.137*** cons. class) (0.032) (0.030) (0.049) Volume2 (excl, own -0.001 0.001 0.005*** cons. class) (0001) (0-001) (0-002) Price of electricity -0.001 0.004 0.032 (own cons. class) (0.019) (0.017) (0.033) Observations 759 759 759 R2 0.33 0.21 0.27 * statistically significant at 10%; ** 5%; *** 1%, two-tailed tests. Prices of gas and of alternative fuels are in logarithmic form. Fixed effects in all regressions are on the state level. Standard errors are corrected for arbitrary cor- relation across regressions. All variables in monetary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Other variables in the second-stage regression are identical to those in the panel regressions. Table 1.5 Seemingly-Unrelated Regressions with Instruments for Endogenous Demand 35 % Effect on % Effect on % Effect on Residential Price Commercial Price Industrial Price Choice program -0.6%’ -0.5% 1.3% Price cap 0.3% -5.9% -18.2% Gas cost plan —4.4% 5.7% —7.6% Earnings-sharing -9.5% -20. 1% -3.9% Off system sales & 4.3% —6.8% 5.4% Capac. release plan Service-quality plan -3.5% -11.5% -0.9% % Growth in % Growth in % Growth in Residential Price Commercial Price Industrial Price Choice program -1.7%* -3.8% -0.9%* Price cap -2.4% 0.1% 1.4%* Gas cost plan 0.1% -1.6% 2.8% Earnings-sharing 6.7% 4.0% 8.3% Off system sales & -1.8% 2.6% -10.6% Capac. release plan Service-quality plan -3.9% -0.3% -7.4% ‘ statistically significant at 15%; * 10%, two—tailed tests. Standard errors are corrected for arbitrary heteroskedasticity and autocorre- lation at utility. Control variables are demeaned by their averages over time. All variables in monetary terms are in 1996 dollars. Dependent variables are corrected for inflation and normalized to start at the same level across firms 3 years before deregulation. Table 1.6 Differences between Before— and After-Implementation Coefficients gas prices after implementation of each policy estimated in a difference-in-differcncc model of a group of utilities operating in multiple states, to control for unobserved time—varying utility-specific characteristics.15 Consumer-choice programs, margin-sharing plans, and service-quality programs are estimated to lead to slower price growth rates compared to prior years and other utilities. This indicates that the plans may have long-term impacts on rates exceeding short-run benefits. 15This allows me to estimate the level and growth rate of prices before and after the implementation of mechanism at a utility (compared to the branches who never adopt one), under the assumption that all branches of a utility have the same unobserved time-varying characteristics. In addition to using a sample of utilities under deregulatory treatment in one state with subsidiaries in other states, I ran this model on the entire dataset, and a sample consisting of all large investor-owned utilities. In general, the more inclusive the sample, the noisier the results. 36 Price ($IMcf) Residential ........................ -1 0 1 2 3 -x - Consumer choice — - Price cap Gas cost plan , ------- Earnings sharing —8— Off system sales -x - Consumer chonce Figure 1.2. Price Trends after Deregulation 37 Overall, the difference—in-difference model explains less variation in all three consumer prices than other models (17%, 10% and 20%, respectively). The policy variables are jointly statistically significant at a 1% level after the policy implementation, for residential and industrial consumer prices, but insignificant for the commercial consumer price. The ’before—implernentation’ variables are jointly significant at a 10% level for the industrial price, but are not significant for the other two consumer classes. To study the price growth over time in more detail, I also use an ordinary least- squares model with indicators for the phase of implementation of the policies at individual utilities. I disintegrate the policy treatment by its phase at the utility: 1-2 years before the implementation; 1-2 years after the implementation; and more than two years after the implementation. The effects on prices right after the policy implementation are larger than in later years for most sliding-scale programs and for price caps, suggesting either the deterioration of the incentive power of the mechanisms, or increased competition among utilities and strengthened integration of the gas market with fewer arbitrage opportunities. consumer- choice programs are predicted to bring greater benefits to ratepayers over time, lowering all prices by 1.1—3.2% during the first two years, and by 2.7—7.5% in later years. As in the seemingly-unrelated regressions in Table 1.5, consumer-choice programs are predicted to benefit larger customers more, and this effect grows in significance in later years. This result is unexpected given that consumer-choice programs are put in place to induce com- petition particularly in the residential consumer market. It suggests that utilities may use any improvements in efficiency, economies of scale, or presence in more geographic markets to compete for industrial consumers more intensively. One explanation is in the possible third-degree price-discrimination based on the greater price elasticity of de- mand by larger customers. Another possible explanation is that utilities respond to the 38 strengthened competition in the residential market by focusing on retention of their larger customers. In either case, this result suggests that there is a latent impact that has been omitted from this regression. Figure 1.3 illustrates the effects of the deregulatory policies on prices over time. In this figure, prices under the rate-of-return regulation would be shown by a horizontal line at the levels three years before deregulation. Table 1.7 presents numerical results of these regressions. Overall, the difference-in-difference model explains about a quarter of all variation in all consumer prices. In general, the policy variables are jointly statistically significantly different from zero after the policy implementation, but are insignificant for variables denoting the state before the implementation. This could imply that our concern about self-selection of utilities into policy treatment may not be warranted, since their prices before deregulation do not indicate any difference from other utilities, even if the coefficients are almost everywhere negative, for sliding-scale and consumer-choice programs. 1.3.3 Instrumenting for the Endogenous Policy Implementation The policies examined in this study have been promoted by state officials, special interest groups, or individual utilities. We may ask about the information and the ex- pectations that these parties shared that induced them to adopt deregulation, that other parties did not share (for instance, Hollas 1989, Primeaux et a1. 1984, White et al. 1996). Understanding the determinants of policy implementation may allow me to test for the evidence that the control variables in my model take part in this process. Using this information, I may also need to pose weaker assumptions on the relationships among control variables than if I did not have this information. Implementation of a mechanism may be directly correlated with the utilities’ recent 39 $4 $3 I I r I i -3 -2 -1 0 1 2 3 Years from Implementation - - - Consumer choice — - Price cap — Sliding scale Figure 1.3. Prices by Phase of Implementation of Deregulation 40 Residential Commercial Industrial Price Price Price 1—2 Years before Choice -0.017 0.007 -0.007 (0.02) (0.02) (0.03) 1—2 Years after Choice -0.024 -0.011 -0.032 (0.02) (0.02) (0.03) More Years after Choice 0027 -0.049** -0.075** (0.02) (0.02) (0.04) 1—2 Years before Price cap 0.082 0.052 0.122** (0.06) (0.05) (0.06) 1—2 Years after Price cap 0.007 0.007 0.07 (0.04) (0.05) (0.09) More Years after Price cap 0.038 0.049 0.028 (0.05) (0.04) (0.1) 1—2 Years before Sliding scale -0.033 -0.041 -0.051 (0.06) (0.04) (0.08) 1—2 Years after Sliding scale -0.011 -0.026 -0.031 (0.04) (0.04) (0.05) More Years after Sliding scale -0.002 0.016 0.03 (0.03) (0.04) (0.05) Observations 2,066 2,105 1,404 112 0.25 0.22 0.29 * statistically significant at 10%; ** 5%; *** 1%, two-tailed tests. Prices of gas and of alternative fuels are in logarithmic form. Fixed effects are at the state level. Standard errors are corrected for arbitrary heteroskedasticity and autocorrelation at utility. All variables in monetary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Table 1.7 ‘Phase of Implementation’ Regressions price, with the utilities’ unobserved quality, or with the state’s unobserved characteristic or regulatory climate. Implementation of a policy may be a response to the utilities’ current prices. However, regulatory lags of two to three years prevent state commissions from effectively reacting to current price levels [Comnes et al., 1995]. Back and forth negotiation also alleviates the power that a commission or the utility could exercise in setting of the mechanism [Tardiff and Taylor, 2003]. I can thus look for evidence of the determination of policy implementation by regressing an indicator for whether the mechanism would be implemented on the utilities’ price lags (refer to Tables 1.9 and 41 1.10) [Mathios and Rogers, 1989].16 Some utilities and states may be predisposed to deregulate due to some unobserved quality they possess. Above I have controlled for such latent time-constant qualities by including any observable utility and state characteristics and unobserved fixed effects in the regressions. If the unobserved quality changes after a mechanism is implemented, my estimate of the effect of the mechanism on prices may be biased unless I find a good proxy or instrument for this quality. I control for observable economic variables varying over time at the utility or in the state economy, proxying for regulatory climate [Greenstein et al., 1995]. If the unobserved quality affected the utility’s prices even before the mechanism was implemented, I can test for this effect by regressing an indicator for whether the mechanism would later be implemented, or the time until deregulation, on prices and other utility and state characteristics (refer to Section 1.3.4). I also use the difference in difference model, to compare coefficients for utilities who never adopted deregulation, those who would adopt it in future years, and those currently under a deregulatory policy. In these regressions, utilities who never adopted any of the three deregulatory policies represent the benchmark group of utilities.17 Table 1.6 reports on the differences in coefficients between utilities before deregulation, and those currently deregulated. Any unexplained effect on prices that these utilities benefit from compared to never-treated utilities gets subtracted from the estimated effect of the policy on prices. These regressions assumed that there was no endogenous determination of deregula- tion; that it was time-constant and only differed by utility; or that I had good proxies 16Since I have found that consumer-choice programs may lead to small price reductions even in the two years before their introduction, I may, however, worry about endogeneity of even recent lagged prices. Since lagged prices from earlier years are expected to be very weakly related to future policy decisions, and since their inclusion limits the size of the available data, I restrict my analysis to prices lagged three years. 17In addition to a full sample of all utilities, I use a sample of utilities operating in multiple states, and a sample of large investor-owned utilities. Due to the adverse effects of the selection of these subsamples on variation within the data, I only report the results for the overall sample. 42 available for that process. If, however, current prices indeed directly influence current deregulation efforts, I need instruments that are good in explaining the presence of a deregulatory policy (either determining it or strongly correlated with it) and, conditional on this policy and other regressors, have no effect on gas prices. Status of deregulation in other industries in the state (telecommunications and energy), and deregulation of gas utilities in other US states are arguably such variables.18 In the first stage of this pro- cedure I obtain the fitted values of the status of each policy at a utility or in a state, assuming no feedback from current prices. Since the dependent variables are binary, I use probit regressions in this first stage, and I interpret the fitted values of the policies as the probabilities that a given mechanism is in place at a utility or state, given its characteristics.19 The explanatory variables. include the above mentioned instruments, as well as selected variables appearing in the second-stage regressions that are likely to explain the status of deregulation, namely the utility’s size and ownership type, and the state’s measures of income, unemployment and bankruptcy rates, income tax rates, and the portion of utilities in the state that are investor-owned. The first-stage regressions estimating consumer demands achieved R-squared of 0.30, 0.26 and 0.28 (with joint significance of all coefficients at 1% level), for the three consumer classes. The first-stage regressions estimating the presence of consumer-choice programs, price caps, sliding-scale programs and service-quality plans achieved R-squared of 0.32, 0.35, 0.52 and 0.50 (with joint significance of all coefficients even at a 1% level in a log- likelihood ratio Chi2 test), respectively, implying that my exogenous instruments explain between a third and a half of the variation in the status of deregulation across US states, statistically significantly. 18To test for the first requirement, I regress the status of deregulation in the gas industry on those in other industries and states. 19Since the deregulatory mechanisms can be revoked or reestablished in any year, treating the status of a policy as not determined by its status in the previous year is reasonable. 43 Table 1.8 reports the coefficients of interest in the regressions using instrumental vari- ables for the endogenous demand and for each of the deregulatory policies. Consumer- choice programs are estimated to lower residential and commercial prices by 9.0—12.6%, and industrial prices by 20.1%. Sliding-scale programs lower commercial prices by 13.7%, but their effect on the other consumer classes is close to zero and has a positive sign. Price caps lower residential prices by 1.3% and industrial prices by 14.5%, but have small and positive effect on commercial prices. These coefficients are very similar to those in the specifications in Sections 1.3—1.3.2, so using exogenous instruments for these policies did not change the estimated impact that the policies have on prices. Provided that my in- struments are indeed exogenous and explain the deregulation process well, I may not need to worry about the endogeneity of these policies. Coefficients on the service-quality plans, on the other hand, switch signs to positive, compared to Tables 1.4 and 1.6. This may imply that generators who lower prices through lowering service standards are assigned service-quality plans to correct for this problem, and these plans result in prices that are higher than without these programs, but still lower than at other utilities. Controlling for latent characteristics of the utilities and for the endogenous decision to implement service-quality plans at selected utilities helps me to identify the cost of these programs to consumers as 54—88% of their respective original prices. 1.3.4 Testing for the Endogeneity of Mechanism Implementation To evaluate the role of prices and other economic variables on the process of deregula- tion explicitly, I run a probability model of the implementation of individual mechanisms, and a pooled ordinary least-squares model with the timing of the implementation of each policy as a dependent variable. Under the hypothesis that the deregulation efforts are exogenous in the price regressions, prices and other regressors from the price equations 44 Residential Small Commer- Industrial cial Choice— -O.126* -0.090* -O.201* implemented (0.071) (0.046) (0.141) Sliding-scale plan 0.04 -0.137* 0.096 (0.072) (0.076) (0.115) Price cap -0.013 0.051 -0.145** (0.049) (0.049) (0.073) Service-qual. plan 0.057 0.054 0.088 (0.130) (0.107) (0.191) Volume demanded 0.740* 0.33 0.09 (0.391) (0.365) (0.153) Observations 1,181 1,354 602 R2 0.32 0.20 0.27 * statistically significant at 10%; ** 5%; *** 1%, two—tailed tests. Prices of gas and of alternative fuels are in logarithmic form. Fixed effects in all regressions are on the state level. Standard errors are corrected for arbitrary het- eroskedasticity and autocorrelation at utility. All variables in monetary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Other variables in the second-stage regression are identical to those in the panel regressions, and are omitted in the table to save space. Table 1.8 Regressions with Instruments for Endogenous Demand and Regulatory Poli- cies 45 will not help explain the probability and the timing of implementation of any policy. The subsample used in the ‘timing of implementation’ analysis includes utilities who had not received the mechanisms yet but who would receive them in subsequent years. The probit regressions include all observations for investor-owned utilities that currently do not hold incentive mechanisms—and thus even the utilities that would never adopt one. For regressors in any equation to be exogenous, I need zero feedback from the dependent variable on the regressors. In the probit and the ‘timing’ regressions, I am using only a subsample of observations—the control group and the pretreatment group—so I need not worry about the feedback from the mechanisms on regressors. Table 1.9 presents the results of the ordinary least-squares regressions on pooled cross- sectional data, where the year of implementation is the dependent variable. Table 1.10 presents the probability models of the implementation of each policy. Coefficients in the first set of regressions can be interpreted as the years to the mechanism implementation. Negative coefficients imply that the explanatory variable speeds up the deregulation, with the unit of impact being one year. The probit regressions estimate the probability of the future adoption of an incentive mechanism at the utility or in the state. The coefficients can be interpreted as the mean percent impacts (x100) on the probability of future deregulation. In both models, the probability and the time until mechanism implementation are made a function of residential prices, per capita income in the state, unemployment and business bankruptcy rates, income tax rates, type and size of the utility, and deregulation efforts in the telecommunications and the electricity industries in the state. I would expect the coefficients in the two sets of regressions to have opposite signs, because the factors that bring about deregulation faster will bring it with higher certainty. Tables 1.9 and 1.10 show the results of the two sets of regressions for consumer-choice 46 programs and sliding-scale plans. These specifications result in an R-squared of 0.84 and a pseudo R—squared of 0.37. The same regressions were run for price caps, but suffered from small sample sizes. The treatment and before-treatment groups were also small compared to the number of untreated observations. The first two rows in Table 1.9 show the coefficients on the residential prices demeaned by their seven year average (first row), and demeaned by the national average (second row). These variables denote the current price at the utility or in state, relative to prices in prior years (first row), and relative to other utilities and states (second row). Under the conjecture that high prices in the most recent year speed up deregulation, I would expect negative coefficients in the first row. These coefficients are indeed negative, but small and statistically insignificant, and imply that a 10% increase in own price over the preceding years brings the implementation of a sliding-scale plan closer by 0—4 months. Under a similar conjecture that prices higher than those in other states and utilities induce faster deregulation with higher certainty, I would expect negative coefficients in the second row of Table 1.9 and positive coeflicients in the first row of Table 1.10. Here most coefficients carry the wrong signs, but are insignificant. Coefficients in Table 1.10 imply that a 10% increase in gas prices compared to prices in other states has a marginal effect on the probability of deregulation of 0% to -0.1%. These coefficients jointly suggest that residential prices, as varying over time and across utilities, do not explain the probability and timing of the mechanism implementation. Whether the telecommunications and electricity industries in a state have become deregulated or plan on becoming deregulated would be expected to be positively corre- lated with, or have a positive impact on the speed and probability of deregulation in the gas industry. Deregulation in the telecommunications industry is predicted to induce implementation of sliding-scale programs earlier by 1—1.5 years, but has an unexpected 47 Cons. Choice Sliding Scale —in State —at Utility Resident. price within utility -0.001 -0.258 -0.357 / state (0.14) (0.30) (0.41) Resident. price across states (2011?)? (30:2? $0230? State telecom 0.294 -1.507 -1.015 deregulation—ever (0.71) (1.82) (0.89) *** Personal income within state $42727? -3513; 44,3223) Personal income across states -0268 .0011 -0527“ (0.20) (0.89) (0.24) Volume of gas sold to 0.078 nonresid. customers (0.08) Observations 12 22 52 * statistically significant at 10%; ** 5%; *** 1%, two-tailed tests. Dependent variable is in years. Standard errors are corrected for arbitrary het- eroskedasticity and autocorrelation on the utility level. All variables in mone- tary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Table 1.9 Pooled OLS Regressions of the Year of Implementation 48 Cons. Choice Sliding Scale —in State —at Utility Resident. price across states .0008 0007 .0056 (0.03) (0.05) (0.06) State telecom -12.448*** 1.847*** deregulation—ever (1.56) (0.64) State electricity 0.080 1.838“ deregulation—ever (0.76) (0.85) State telecom -0.221 1.316 4058*" deregulation—current (0.55) (1.06) (0.88) State electricity -1.098 0.600*** deregulation—current (0.79) (0.20) Personal income across states 0230 0'1“ 0743*“ (0.14) (0.49) (0.13) Volume of gas sold to 0.273** nonresid. customers (0.13) Observations 1 1 6 1 25 800 * statistically significant at 10%; ** 5%; *** 1%, two-tailed tests. Dependent variable is binary, with 1 representing deregulation. Standard errors are corrected for arbitrary heteroskedasticity and autocorrelation at utility. All variables in monetary terms are in 1996 dollars. Control variables are demeaned by their averages over time. Table 1.10 Regressions of the Probability of Implementation 49 positive effect on the time until the implementation of consumer-choice programs, by approximately four months.20 Deregulation in the telecommunications and the energy industries, in the current year or ever, has a mixed effect on the probability of adoption of the consumer-choice and sliding-scale programs in the gas industry (Rows 2—4 in Table 1.10). The coefficients are sporadic due to small sample sizes in these regressions I cannot rule out or confirm whether deregulation in other public utility industries incites or slows down deregulation in the gas market. Positive shocks to per capita income, as varying within a state over time, have mixed effects on the timing of deregulation in the gas industry, postponing adoption of consumer choice but expediting adoption of sliding-scale programs (Row 4 in Table 1.9). Shocks to current personal incomes relative to incomes in other states appear to speed up deregula- tion, but have a mixed effect on the probability of implementation of the two considered policies. A 10% increase in state incomes over other states has a marginal effect of 3.6% on the probability of adopting a consumer-choice program, but -1.1% on the probability of adopting a sliding—scale program. Size of an individual utility (proxied by the volume of gas sold to nonresidential customers) appears to bring implementation of sliding-scale programs slightly later (by one month), but with higher certainty (by 0.4%), for a 10% increase in the utility’s size.21 The same regressions were run for price caps, but suffered from small sample sizes. Even in the above ‘timing of implementation’ regressions, some treatment or before- treatment groups are small compared to the number of untreated observations. Unless deregulation came in very late years for a utility, this utility enters the ‘timing of im- plementation’ regressions with few observations. The probit regressions, in comparison, 201 do not include the energy industry deregulation here due to a problem with the number of observations in this regression. 21This proxy—volume of gas sold to nonresidential customers—could be endogenous in the regressions because utility’s state of restructuring may affect its sales. 50 include all utilities that had not received an incentive mechanism before the year of the observation. This increases the sample size, but it also introduces additional unexplained heterogeneity due to all-inclusiveness of this sample. Utility-level probit regressions suffer from the small portion of sample that undergoes treatment in future years—the dependent variable is zero for most observations. Explanatory variables used in these regressions are limited to sets that do not further decrease the size of those small treatment groups (due to missing values), or over-identify the regressions given small sample sizes. 51 1.3.5 Limitations of the Results Regression results presented in Sections 1.3—1.3.4 agree with my prior expectations on the direction and size of the price impacts of deregulation, but suffer from substantial unexplained variation. Any unmeasured variables that were omitted from the regressions render the results ineflicient. Controlling for time-constant and time-varying unobserved effects with the use of selected proxies may not have succeeded in controlling the omitted variation away. I have also avoided the discussion of the spillover effects of policies on other utilities in a state or in other states, such as a knowledge spillover or competitive pressure.22 Given the nature of my data, I was also unable to disentangle the impact of the mechanisms on current prices from that on prices in adjacent periods. Such rela- tionship may be due to accounting conventions regarding cost recovery, accounting for a write-off of technology investments, longer-term learning when a new policy is adopted, raised expectations under individual policies and particularly price caps, lagged sharing of rewards under sliding-scale plans, agreements signed after a policy came into effect, sig- naling and attempts at entry preclusion under consumer-choice programs, and any other lagged effects. Finally, this paper studied the cumulative effect of the implementation of incentive plans on gas prices, and abstracted from matching the incentive effect to reductions in individual cost components.23 221 did run regressions similar to those above with indicators for the presence of policies at other utilities in the state. Their coefficients were overall close to zero, and were thus excluded here to preserve degrees of freedom. 23I did run regression specifications with indicators for lags in policies, for other deregulation efforts at other utilities, and for the number of investor-owned utilities in a state. Their coefficients were mostly too small to report in the presence of greater price shocks. 52 1.4 Conclusions My estimation model led to many interesting findings regarding the impact of state deregulatory mechanisms on consumer prices. The coefficients on the regulatory policies carried, for the most part, the expected signs and magnitudes across specifications, and agreed with my prior expectations of the plausible impacts. Consumer-choice programs are predicted to cause significant drops in all prices, with a consistent effect for residential consumers across specifications (2.2—12.6%). Interestingly, even utilities expecting to begin operating under a choice program within the next two years lower their prices (by 07—23%), perhaps to strengthen customer loyalty or preclude entry. After the implementation of the choice, the effect on rates magnifies over time. Price caps are also shown to result in lower prices for the residential and industrial cus- tomers (OD—1.3% and 111—20.0%), but their effect on small-commercial prices is positive in the estimation. This unexpected result can be explained by the inconsistent treatment of this consumer class across states, and by the small number of price caps in the in- dustry. The effects of the sliding-scale programs on prices are mostly insignificant and vary around zero (with most coefficients between -2% and +2%), supporting Greenstein et a1. [1995] conclusion that the sliding-scale regulation does not depart significantly from the rate—of—return regulation. A conjecture that utilities are given sufficient motivation to minimize costs even without these plans cannot be rejected. With all sliding-scale plans merged under a single binary variable, and with only seven years of data, some of the longer-term incentive power of the mechanisms may have remained undetected. A competing explanation is that sliding-scale plans limited to selected operations of a utility may induce the utility to perversely substitute inputs to report savings in the selected operations, but losses over all operations. Indeed, the Minnesota PSC found that customers of a utility with a sliding-scale plan received higher overall gas costs, while 53 providing their utility with millions of dollars in incentives. The estimated coefficients on the policies are lower than my optimistic expectations in Section 1.2.4, presumably due to administrative, information-gathering and other costs under the policies. My coefficients on consumer-choice programs are approximately half the size of my prior expectations. If those expectations were reasonable, this gives me an idea about the overhead costs of incentive regulation. On price caps, my coefficients for the residential price are close to zero, much lower than my prior expectations; For industrial customers, however, the coefficients often exceed my expectations. For both policies, the ranking of coefficients across consumer classes is consistent with the conjec- ture that utilities may be setting relative prices strategically as under the third-degree price-discrimination. Overall, my results confirm the proposition by Beesley and Littlechild [1989] that competition can go further than price controls in the traditionally monopolistic and tech- nologically stagnant natural gas industry. Promotion of consumer-choice programs in selected states has succeeded in instilling sufficient level of competition resulting in lower prices than under the traditionally prescribed price caps or the piloted sliding-scale pro- grams. 54 THE IMPACT OF ENVIRONMENTAL REGULATION ON 502 CONCENTRATIONS AND DAMAGES Sulfur dioxide (502) emissions from energy generators cause great damages to human health. Their aggregate volume in the US is thus controlled by a fixed number of emis- sion allowances. This policy has been found to lead to significant health improvements compared to preexisting emission levels. Emission allowances are, however, not the only policy that can achieve lower 302 emission levels. Whether emission allowances achieve improvements over other policies of similar stringency depends on the spatial distribution of emissions under each policy, because the population affected by them differs by region. This paper compares empirically the 302 concentrations and the damages they cause under the market for emission allowances, a uniform emission tax, and a system of emission caps, testing the proposition of Stavins [1996] that if firms’ marginal abatement costs and marginal emission damages are correlated, emission caps and emission fees can lead to different damages. Emission caps, according to Stavins [1996], are likely to be preferred under most of the plausible relative distributions of marginal damages and marginal costs. Emission caps, disallowing spatial redistribution of emissions, have also been thought to prevent extreme concentration levels (‘hot spots’), and pollution in particularly sensitive areas [Shadbegian et al., 2004, Wolverton, 2002b]. This paper evaluates these hypotheses, and shows what concentrations and health impacts each environmental policy achieves across US states and nationwide. The state-by-state comparison determines which regions are winners and which are losers under each policy, even if the aggregate sum of the damages remains similar. 55 2.1 Motivation $02 emissions pose great risks to human health, creating damages valued at tens of billions of dollars annually. Compared to uniformly diffused pollutants such as 002, S 02 emissions are not distributed evenly across regions, but stay in the vicinity of their source, where they can cause hot spots of pollution and high health related damages. If each unit of emissions caused identical damages to human health, no matter where it was produced or what the total emission level at that source was, environmental policies achieving the same aggregate emission levels would produce the same aggregate health damages regardless of the distribution of emissions. However, the impact of 502 emissions on human health depends on the size of the population affected in each region. If a significant amount of S 02 incidentally lands in heavily populated areas, not only regional levels but also the aggregate level of health damages can be greater than if the 5'02 were concentrated in a less densely populated area. Policy that redistributed a given aggregate amount of S 02 from a less populated area to a more populated area could increase total damages (for instance Mendelsohn 1986, or Shadbegian et a1. 2004). Among the possible schemes for controlling 502 emissions, the EPA has opted to mandate a maximum aggregate level of emissions and allow energy generators to cooperate in achieving this level. Under the Title IV program of the 1990 Clean Air Act Amendment, the EPA assigns generators emission allowances based on their historic production levels, and allows them to trade these allowances freely without regard for the location of the respective sources. This essay contributes to the empirical literature by comparing the distribution of regional air quality and health damages, and their aggregate levels, that would result from three alternative well established environmental policies. In a partial equilibrium model of the energy industry, the currently used market for emission allowances is compared to 56 a uniform emission tax, and to a set of generator-level emission caps assigned based on generators’ historic production levels. These policy instruments have all been considered by the US Environmental Protection Agency (EPA) for the control of 802 emissions from the energy industry.1 In agreement with the EPA’s objective, the stringency of the three policies compared in this paper is adjusted so that they lead to the same aggregate emissions [Kete, 1992]. Theoretical regulatory literature suggests that the system of tradable allowances and the uniform emission tax should lead to identical outcomes (provided that the allowance market is competitive), because they give energy producers the same incentives for emis- sion abatement on the margin [Tietenberg, 1985]. Verification of this equality would indicate that the introduction of a competitive allowance market without transaction costs does not create other costs of regulation or distortions compared to a tax. In a model of energy industry, equivalence of these two policy scenarios also indicates that the model has been correctly specified. In comparison of tradable allowances or a tax to a set of emission caps, Weitzman [1974] and Stavins [1996] suggest that their ranking in terms of both damages and abatement costs depends on the relative slopes of the marginal damage and the marginal abatement cost functions. I follow the empirical literature in assuming constant marginal damages, so the marginal abatement cost function is always steeper than the marginal damage function. The ranking of price and quantity instruments also depends on the correlation between the marginal damages and the marginal abatement costs. Positive correlation tends to strongly favor emission caps, while negative correlation does not necessarily change the ranking in favor of taxes and allowances [Stavins, 1996]. If we knew what the 1502 emissions result from the burning of fossil fuels, particularly in electricity generation, industrial production, indoor heating and transportation [Whitney, 2005]. In the US, the electricity industry is responsible for roughly two thirds of all emissions of $02. 57 correlation was, we could predict the difference in damages between emission caps and the uniform tax [Mendelsohn, 1986, Stavins, 1996]. Unfortunately, the theory does not tell us whether correlation between marginal dam- ages and marginal abatement costs exists, or what is its sign. Since I am considering a uniform tax fixed exogenously, and a set of emission caps also fixed exogenously, their comparison at individual generators is an empirical question [Atkinson and Tietenberg, 1987, Tietenberg, 1995]. If the assignment of emission caps is incidentally positively re- lated to generators’ marginal damages, emission caps could perform poorly in limiting environmental damages. Previous empirical evidence is mixed on the existence of a relationship between the type of generators and the population affected by them, 011 the incidence of emission cap assignments, or on the pattern of trade of emission allowances under the Title IV program [Burtraw and Mansur, 1999, Ellerman et al., 2000, Shadbegian et al., 2004, Wolverton, 2002a,b]. Since emission caps restrict regional emission levels to a portion of the historic levels, while the other two policies impose no regional restrictions, one conjecture is that emission caps would achieve a more favorable distribution of emissions [Shadbegian et al., 2004]. I thus assess whether the emission caps indeed lead to lower aggregate damages by restricting regional emission, concentration and damage levels. The alternative possibility is that by limiting the movement of emissions, the system of emission caps may restrict even trades that would lower the aggregate damages, such as away from heavily populated states [Ellerman et al., 2000]. Since each environmental policy can lead to lower damages in a subset of states and higher damages in other states, state-by-state comparison tells me which states are the net winners and net losers under each policy, even when the aggregate sum of damages remains similar. Even though damages are only one criterion for the selection of a regulatory instru- 58 ment, this paper focuses only on them, because our understanding of their valuation and regional distribution is particularly sparse and deserves detailed analysis [Argonne National Lab, Burtraw et al., 1998b, EPA, i]. I report the industry costs of emission abate- ment in each policy scenario, but I do not discuss their regional distribution. Previous empirical literature has found the industry costs of emission abatement to be lower, and more observable and certain than the damages, and proponents of either environmental policy have used the differences in damages as an important factor for advocating one policy over another (for instance, Burtraw and Mansur 1999, Ellerman et al. 2000 on one side, and Haas 1999, Shadbegian et al. 2004 on the other).2 This paper also abstains from the discussion of consumers’ welfare when the price level changes, generators’ profits and government revenue, in line with the vast majority of empirical literature. Among dam- ages, this paper considers only health impacts, ignoring irnpacts on visibility, non-human health, and damages to material objects, because human health damages account for the vast majority of the total damages and their existence is well accepted among scientists and policy makers. To estimate the environmental impacts of alternative 502 policies imposed on the US energy industry, I find the distribution of generators’ emissions under each environ- mental policy, convert them to regional concentrations using the Advanced Statistical Trajectory Regional Air Pollution model [Argonne National Lab], and evaluate these lev- els using concentration-response functions developed by the EPA [i]. I develop a numerical partial-equilibrium model of the energy industry to derive the distribution of emissions as generators’ profit-maximizing responses to the market forces and the environmental regu- lation. The model includes all major participants in the US energy industry: generators, consumers, system operators, as well as state regulators. Generators are portrayed care 2In this paper, it also turns out that the industry costs of emission abatement and their differences across policies are small. Refer to Section 2.8. 59 fully as competing in prices in markets with downward sloping demands. Their behavior is subject to physical and regulatory constraints, and marginally rising costs of generation, transmission and abatement. In this industry model, I can easily impose the alterna- tive environmental policies, and I can adjust their stringency to yield identical aggregate emissions. To obtain realistic solutions in my energy model, I use historic data on many industry variables and parameters, including information on current power—generation and emission-cleaning technologies, energy demand and fuel supply. I find that the range of concentration levels under the allowance market is no wider than under emission caps. This implies that the system of allowances did not result in extreme concentration levels compared to the emission caps, supporting the findings in Ellerman ct al. [2000], GAO and EPA [d]. I also find that the 502 concentration levels across US states vary systematically across the environmental policies. The system of allowances currently used in the US and the uniform emission tax lead to very similar emission profiles, in agreement with their conceptual equivalence. These policies achieve lower 802 concentrations than emission caps in the northeastern US states, supporting the findings in Shadbegian et al. [2004]. Emission caps, on the other hand, favor the southwestern, south-central and southeastern states, including heavily populated Califor- nia, Texas and Florida. These redistributions in regional concentrations lead to differences in regional and importantly even aggregate damages. Among my three policies, emission caps lead to the lowest aggregate damages (or $47.7 billion), outperforming the EPA’s system of allowances by $452 million. The system of allowances and the uniform emission tax lead to very similar aggregate damages, of approximately $48.2 billion, and differ by only $2.4 million. Their identical performance was expected, due to the similar incentives on the margin that they give generators. Similarity of their resulting damages lends itself as a verification 60 that the greater difference between these two policies and the emission caps is a result of economic forces rather than computational imprecisions in the simulation. The $2.4 million difference in aggregate damages between the system of emission allowances and the emission tax, which can be attributed to model imprecisions, corresponds to only one half of one percent of the $452 million difference between these policies and the system of emission caps. The fact that even $452 million represents only one percent of the absolute level of aggregate damages stems from our restriction on aggregate emissions to be constant across all policies. Regional redistribution of emissions therefore has limited power in reducing the national sum of damages. In all southern and southeastern states, emission caps lead to particularly low damages compared to the system of allowances, outperforming the latter by $840 million. In all northeastern and New England states, emission caps lead to damages higher by $390 million.3 In sum, these results support the theoretical findings in Mendelsohn [1986] and Stavins [1996], and the empirical findings in Shadbegian et al. [2004], Wolverton [2002b] and Haas [1999], that under spatially distributed marginal damages, emission allowances could lead to great losses compared to the command and control policies. Furthermore, health damages realized in each US state vary significantly across the considered policies, and under each policy some states win and others lose. 2.2 Literature The 1971 Report of the President’s Council of Economic Advisers on Priorities and Ef- ficiency [Lerner, 1971] initiated the discussion of optimal environmental regulation under uncertainty, and ground-breaking theoretical studies by Montgomery [1972], Weitzman 3Both areas have the same population, of approximately 100 million. 61 [1974], F ishelson [1976] and Adar and Griffin [1976] followed. For a general externality, Weitzman [1974] derived the conditions under which price regulation dominated quota regulation in the presence of heterogeneity, different relative slopes, and stochasticity in the generators’ marginal abatement cost functions and the marginal damage functions. Mendelsohn [1986] showed the differences in aggregate damages under price and quantity instruments when marginal damages differ by region but all regions are treated equally under the exogenously given policies. Stavins [1996] showed that if heterogeneity in gener- ators’ abatement cost functions is inadvertently related to the heterogeneity in generators’ marginal emission damages, the sign of the relationship determines the optimal instru- ment. To deal with the spatial variation in marginal damages caused by pollution, under certainty, Montgomery [1972] suggested stringent non-violation conditions under which the trade of emission allowances would be greatly limited. Atkinson and Tietenberg [1982], Krupnick et al. [1983] and McGartland and Oates [1985] proposed milder conditions under which generators could trade their emissions at an arbitrary rate, only subject to constraints on the concentrations in their receptor zones. The possible constraints were given by the levels of concentrations before the trading program, or even levels before individual trades took place. One problem with these proposals is that, in them, individual emission trades affect the subsequent pollution offsets not only for the two trading partners, but for all generators that pollute in the affected regions. Individual pollution offsets thus depend on the order of trades, and on the actual rate of trade among previous traders. As a result, the exact location of the trading solution is uncertain [Atkinson and Tietenberg, 1987]. Klaassen et al. [1994] proposed exchange rates on emission trading under which gen- erators would trade their emissions freely, only subject to the exchange rates based on 62 the generators’ marginal abatement costs in the least social cost solution. Since firms’ decision to trade emissions depends only on their respective marginal costs of abatement, this policy induces firms to reach the least social cost solution on their own (refer also to Forsund and Navdal 1998 and Burtraw et al. 1998a). One problem is that the regulator must know where the least cost. solution lies, but in that case the regulator could use a simpler mechanism to enforce this solution. Another problem is that the aggregate as well as regional pollution levels under this policy can exceed their targeted levels and depend on the initial allocation of allowances, and possibly on the order of trades [Klaassen et al., 1994] Atkinson and Tietenberg [1987] and T ietenberg [2000, 1985, 1995] summarize the proposals for environmental policy when marginal damages from emissions vary across regions, with emphasis on zonal emission permits and rules on their trade. Tietenberg [1995] reports that while theoretical literature can help us identify the a priori optimal instrument, empirical comparison is necessary under the actual distribution of emissions and the affected population, the actual relationship between emissions, concentrations and damages, and the actual allocation of the regulatory instruments. Much of the current empirical literature assesses the environmental benefits under policies that have been suggested as alternatives to the tradable allowance market. Un- der the National Acid Precipitation Assessment Program and the Acid Rain Program, the EPA, the US Department of Energy (DOE) and Resources for the Future have de- veloped models of the energy industry focusing on the choice of the emission-abatement technology [Argonne National Lab, Paul and Burtraw, 2002], source-receptor models of emission diffusion [Chang et al., 1991, Latimer, 1996, Shannon and Sisterson, 1992], and concentration-response valuation models [Argonne National Lab]. These models have been used to compare the current EPA policy with the pre—Title IV status of regulation, 63 or 1980 conditions, to evaluate the benefit of the current policy (such as Burtraw and Mansur 1999, Burtraw et al. 1998b, Ellerman et al. 2000, EPA j,m, Rezek and Millea 2003). Particular features of the Title IV, such as its emission trade and banking provi- sions, have been assessed [Burtraw, 1996, Burtraw and Mansur, 1999, Shadbegian et al., 2004] Among different impacts of the policies, most empiricalliterature has focused on the emission damages or the emission-abatement costs born by the energy industry. Only a. few studies have discussed measures of consumer surplus (for instance, Coggins and Smith 1993), generators’ profits [Burtraw et al., 2001], or government revenue [Burtraw et al., 2001, Jorgenson and VVilcoxen, 1993]. Among the different damages due to 502, most literature has computed only the health and mortality damages, since these significantly overshadow such impacts as lowered visibility, losses in fishing and crops, deterioration of buildings and statues, wildlife losses and extinctions, deterioration of the ecosystem and other impacts [Burtraw et al., 1998b, EPA, j,m, Haas, 1999, Rezek and Millea, 2003, Shadbegian et al., 2004]. This essay adds to the empirical literature by evaluating the emissions, the resulting concentrations and health damages, and their regional distributions, under three com- peting environmental policies that lead to identical aggregate emission levels. For that purpose, I construct a realistic model of the energy industry with the alternative environ- mental policies imposed, to derive emission profiles that are generators’ best responses to all market forces, industry constraints, and the environmental policy. Sections 2.3 to 2.5.2 discuss the energy industry model, and the impact of individual environmental policies on model generators. 64 2.3 Energy Industry Model This section, and the following Section 2.4, develop a partial equilibrium model of the energy industry designed to compute the S 02 emission and concentration levels resulting under the three alternative environmental policies. In each policy scenario, energy gen- erators are allowed to adjust their behavior, including their output and emission of $02, to the given environmental policy in order to maximize their profits under a given set of cost and demand schedules. The equilibrium distribution of emissions is used to compute the air concentrations and the health damages under each policy scenario. The model contains three types of agents—generators, consumers and system opera- tors.4 Generators respond to each other’s actions and to federal and local regulation. All model agents are assumed to have perfect and symmetric knowledge of the consequences of their actions and actions of all other agents. All model parameters are assumed to be public knowledge. By finding a solution to the set of equilibrium equations for each mar- ket agent and for the market, the model derives the levels of generators’ profit-maximizing production, trade, and environmental compliance intensity, and consumers’ equilibrium consumption levels and prices. The model takes parameters of generators’ and operators’ cost schedules; parameters of consumers’ demands; physical and technological constraints; all input prices; and gov- ernment regulation as given. The model is static, and all model agents select their optimal responses simultaneously. Time frame considered here is short to medium term when gen- erators cannot adjust their capital investment, but can respond by changing the intensity of their production and emission abatement [Palmer et al., 2002]. In this time frame, operators cannot invest in expanding the transmission network, and consumers cannot 4Implicitly, there is also a federal environmental regulator and state regulators of competition in the energy market. 65 change their demand schedule in response to events outside of the national electricity market. Consumers in the model are homogeneous, coming from a single customer class, but differ in number across states. No distinction is made between time of day, or time of year in modeling costs and demands (following, for instance, Haas 1999, Palmer and Burtraw 1996). In each state a representative consumer is modeled. His demand schedule corresponds to the volume purchased by all real-world customers in a state at a given price. Being conceptually able to buy energy from any generator in the US, consumers choose the generators charging them the lowest prices. Sections 2.3 and 2.4 describe the objectives of these agents and their mutual relationships in detail. Appendix A.3 summarizes the formal problems that all model agents face. The model has a set of generators, who produce energy to satisfy the demand by all consumers, and comply with environmental regulation. The energy market is perfectly competitive, and generators compete for consumers in prices. The amounts of energy and emission abatement that individual generators can provide are constrained by their pro- duction, transmission and emission-abatement capacities. Due to regional differences in the available resources and due to diminishing productivity and limited substitutability in these resources, generators’ marginal costs vary regionally and across output levels. Generators compete with each other non-cooperatively, make their optimal choices simul- taneously under full and symmetric information, and take each others’ actions and the market prices of energy as given. The nationwide energy industry is modeled as competitive, only subject to trans- mission costs and physical constraints between the North American Electric Reliability Council (NERC) regions [Burtraw et al., 2003, Paul and Burtraw, 2002]. I assume compet- itive marginal cost pricing at all generators, regardless of the form of the state regulation. 66 I distinguish generators in restructured and regulated states only by their access to the transmission grid and ability to compete for customers in other states [Palmer and Bur- traw, 1996] (refer to Section 2.5.2). Since over half of US states have already implemented retail restructuring, and the majority of the remaining states expect to restructure over the next several years [DOE—EIA, b,e, DOE—EIA Annual Energy Outlook, Wolak, 2003], modeling the energy industry as pricing competitively does not deviate from the real status of the US restructuring. Paul and Burtraw [2002] use marginal cost pricing na- tionwide in their scenario of restructuring. Palmer and Burtraw [1996], Palmer et al. [2002], and the Stanford Energy Modeling Forum study a full nationwide restructuring scenario without regard for different phases of restructuring across states, claiming that most states will restructure by 2008. Burtraw et al. [2003] evaluate different scenarios on the status of restructuring across US states. Other simulation literature has assumed different levels of competition in the industry, from naturally monopolistic and regulated by local authorities [Cronshaw and Kruse, 1996, Haas, 1999], oligopolistic with various levels of competition [Day et al., 2002, Hobbs, 2001, Wei and Smeers, 1999] and various assumptions on agent interaction [Chen et al., 2004, He and Song, 2003, Hogan, 1997]. I assume profit maximization at each generator regardless of the current type of reg- ulation in the generator’s state. This assumption allows easier interpretation of each generator’s motive, and makes modeling convenient because only one kind of first order conditions have to be used, and generators’ fixed costs need not be estimated. This as- sumption is also often used in the simulation literature [Burtraw et al., 2000, Palmer and Burtraw, 1996, Palmer et al., 2002], and is reasonable empirically, since most states are predicted to undergo restructuring by 2008.5 5With an alternative. assumption on the profits of regulated generators to equal zero, the model solution would depend on my ability to estimate generators’ average capital costs. These costs differ across generators, and the data on some components of capital costs may be unavailable. For instance, the existence of any assets stranded due to industry restructuring differs across generators, and the possibility 67 While I abstract from modeling energy as a heterogeneous commodity with idiosyn- cratic flow and storage properties [Bai et al., 1997, Borenstein et al., 2000, Hogan, 1996], I ensure that my model satisfies physically justified network constraints, and transmission costs [Palmer et al., 2002, Paul and Burtraw, 2002]. The energy model distinguishes thir- teen NERC regions, in agreement with the institutional setting in the US (refer to NERC b, or Paul and Burtraw 2002). Each region is modeled as being overseen by a non-profit independent system operator, who enforces open access to the network, routes the may to comply with all physical constraints, and charges the traders a corresponding trans- mission fee [Ivanic, 2004, Varaiya and Wu, 1997]. Following Ivanic [2004], operators are modeled as non-optimizing agents overseeing the network and assigning network losses and costs to the responsible traders. Existence of system operators also allows me to easily differentiate between trades and transmission fees within regions and across regions [Paul and Burtraw, 2002]. The energy model in Paul and Burtraw [2002] does not include system operators explicitly, but assumes that average transmission costs on interregional lines are computed and charged directly to each generator. In the regulatory literature, operators in the US energy industry have been modeled in a number of ways, with a range of duties ranging from providing generators with information on the capacity utilization and assigning line losses and transmission costs to the responsible agents, to matching individual suppliers and buyers in order to maximize a measure of welfare [Oren, 1998, Varaiya and Wu, 1997]. Operators may own transmission facilities, or may administer trading on a network owned by an energy producer or a third party [Joskow and Tirole, 2000]. Assumptions on operators’ motives vary from assuming no optimization, through maximization of social welfare, to maximization of the network to pass them to consumers via prices differs case by case [Paul and Burtraw, 2002]. Another problem is that it may be impossible to achieve zero profits at each generator, or that this condition may call for very low or high output levels at individual generators, that the market may not support in one of the policy scenarios. 68 owners’ profits [Hobbs, 2001, Varaiya and Wu, 1997]. The roles of operators vary also empirically across US regions. Ivanic [2004] defends the modeling of operators as non- optimizing agents rather than maximizers of a measure of regional welfare, citing empirical evidence at the Electric Reliability Council of Texas and the Mid-America Interconnected Network. Varaiya and Wu [1997] contrast the non-interventionist system operators in the US, to operators matching individual sellers and buyers in the United Kingdom. Under the allowance trading scenario, I model the allowance trading market as sta- tic (with perfect foresight and symmetric information) since generators tend to make long-term plans with their allowances rather than dynamically respond to the trading patterns of other generators [Haas, 1999]. The allowance market is assumed competitive, and transaction costs and market power play insignificant role in it [Haas, 1999, Joskow et al., 1998, Paul and Burtraw, 2002]. Generators treat their allocation of allowances and allowance prices as exogenous [Haas, 1999, Schmalensee et al., 1998]. In order to hold the emission level constant, I do not allow generators to bank their allowances for future years under the scenario with tradable allowances, following, for instance, Cason and Gangadharan [2003] and Haas [1999]. This is reasonable because banking was most pronounced during the first years under the Title IV, while today most generators have depleted their banked allowances, and the allowable annual emission levels are expected to stay unchanged in the coming years. The following pages introduce the problem that each model agent faces, and Sections 2.3.5 and 2.3.6 describe the market solution. After showing the properties of the basic model, Sections 2.4 through 2.4.5 lay out the specific functional representation of the model. Numerical issues are resolved in Section 2.5. 69 2.3. 1 Energy Generators Energy generators are modeled as choosing their production level and emission-abatement intensity as optimal responses to other generators’ actions and consumers’ demands. These choices are also subject to the environmental policy, trading rules, and physical limitations on generation, transmission and emission-abatement intensity. Generators are assumed to accept other generators’ and consumers’ optimizing behavior as given and certain. Their problem is static. Generator i’s total revenue in the competitive energy market is the sum of its rev- enues from all buyers j, 2 j q, jpj’ where pj is price in buyer j’s market, and can vary across buyers. Generators do not have their own customer base; rather they compete for all customers in the state, and in other states—when trading rules permit [Paul and Burtraw, 2002].6 Generator’s output is the sum of its sales to all customers, q,- = E j qz’j- Generator’s sales are constrained by its production capacity, and transmission capacity with each trading partner, as in Paul and Burtraw [2002]. Generating costs cg, may be a nonlinear function of the output level ‘12" cg,- are assumed to rise at an increasing rate in q,, as the availability and substitutability of all factors diminishes, and marginal productivity falls. 092' = 692' (42') = 692' Zqz'j (21) Here q,- j are the volumes of energy sold to individual customers j. Energy transmission involves costs marginally increasing in the volume of each sale qz-j, and in the utilization of the network segment capacity by trade qz-j, as energy losses from the additional volume traded increase. Marginal transmission costs may vary across 6Generators will not find it profitable to buy and resell energy (due to transmission costs, and assumed price taking behavior). Rather, consumers can buy directly from multiple generators. 70 Variable Description Variable Description qz- Generator i’s output (1 j Demand by cust. j 9ij i’s sale to cust. j 0,-3- i’s share in cust. j’s con- sumption e,- i’s total emissions pj Customer j ’3 price a,- Emission abat. intensity Hi i’s profit cg,- i’s total generating cost p A Market allowance price Caz' i’s emission abat. cost te Emission tax Ctz' i’s transmission cost Ctz'j Total transmission cost on trade between 2’ & cust. 3' ch, ch,- j Operator’s transm. cost t hz' j Per-unit transm. fee on on segment h, on trade be- segment h on trade be- tweenz'&j tweenz'&j Table 2.1 Energy Industry Model Variables 71 generators and are endogenous to the volume of trading, as in Borenstein and Bushnell [1998], Borenstein et al. [2000] and Ivanic [2004], while they are assumed uniform and constant in Paul and Burtraw [2002]. Ctij is the total cost of transporting qz'j from generator 1' to consumer j: Ctz'j = Ctij (Qij) (2-2) Tfansmission capacities may be asymmetric across generator’s customers j [N ERC, a, Paul and Burtraw, 2002]. Generator’s trades within a region are assumed to not affect the capacity and transmission costs available to other generators, following Paul and Burtraw [2002]. This simplifying assumption is used because it leads to reasonable model results in an industry with many small spatially-dispersed generators serving multiple customers, and it follows from my limited knowledge of the transmission costs and network capacities within regions [Paul and Burtraw, 2002]. Since qz-j is a sale from an aggregated generator 2' to a representative consumer in a state 3' (refer to Section 2.7, discussing calibration of my model), as in Paul and Burtraw [2002] and Haas [1999], this trade encompasses trading activity by many agents in the real industry, and can be viewed as proxying for all trading on a particular part of the network (refer to Section 2.5.2). If generator 1' and consumer j are in different NERC regions, an additional per unit fee t hz' j is charged by a system operator for transmission of their trade on the interregional network segment h. This fee ensures that in the equilibrium the operator is reimbursed for all transmission costs on the network segment. Since these costs may depend on the volume of trading between all other generators m and buyers n, Zmn qmn, and may not be linear in i’s trading volume, the operator assigns a fixed fee to each generator— customer pair that the generators take as exogenously given. Under perfect and symmetric information, this fee corresponds exactly to the operator’s average cost in the equilibrium. The operator’s costs are discussed more in Section 2.3.3, and using specific functional 72 forms in Section 2.4.4. 502 emissions are a simple function increasing in the generator’s output q,- and falling in the generator’s emission-abatement intensity ai, ei(q,', a2). 0.,- represents the intensity of the generator’s emission abatement, as a portion of original emissions removed. a,- is constrained to be between 0 and 100 percent. a,- is a meaningful concept, commonly used to identify efficiency and determine costs of abatement technologies [EPA, e, Paul and Burtraw, 2002, Srivastava, 2000], and is convenient for modeling (as in Haas 1999). Emissions will be modeled as linear in both parameters (12‘ and (1,, since all evidence suggests that doubling the volume of a particular fuel doubles the volume of emissions, and doubling the abated portion of original emissions halves the resulting emissions. Emission-abatement costs Caz’ are increasing in both q,- and (1,, without a priori evidence on the precise relationship. cat = Caz‘ ((123%) (2-3) 2.3.2 Energy Consumers Consumer j is characterized by an exogenous demand function that is monotonically decreasing in price. The consumer is not modeled as a utility maximizer within the model; rather, demand function dj can be interpreted as a solution to the consumer’s problem, which determines his volume purchased as a function of energy price (for instance Carlson et al. 2000, Haas 1999, Paul and Burtraw 2002). dj = 613(le (24) Consumer j purchases his energy only from the generator charging the lowest price. 73 In case two generators 2' offer an identical price to the consumer, the consumer assigns market shares Uij to them randomly.7 Writing the price that generator 2' offers customer j as pij~ and prices by all other generators as pj, generator i’s market share is: 0 if pij > pj Uij (1933290) = [0,1] isz‘j =Pj I ipr < pj 2.3.3 Independent System Operators Independent system operator oversees the trade of energy between its N ERC region and other regions. Operator ensures open access to the transmission network, so the network can be used by all generators and customers (refer to Section 2.5.2). The op- erator also oversees traders’ compliance with the physical capacity of individual network segments, and collects fees from traders to exactly cover all transmission costs on each interregional network segment. The operator’s transmission cost on network segment h, 0),, depends on the size of each trade, as well as on the utilization of capacity of the network segment by all trades jointly, for instance due to marginally rising line losses. The cost that the Operator incurs due to a trade between generator 2' and consumer j, Chij’ thus also depends on the sum of trades on this segment by all other generators and consumers: Chij = Chij ((1133 Zan) (2.5) mm. 7Alternatively, I can interpret this decision rule spatially, so that a generator with the lowest price captures the entire state. If several generators are tied as having the lowest price, these generators can be thought of receiving a service area in the state. Since the representative generators in my model may actually include several real-world generators, these individual generators can be thought of as serving different parts of a state, even when a single representative generator receives 0i = 1 in that state. 74 where subscripts mn refer to all generator-consumer pairs trading on network segment h. The operator collects per-unit transmission fees thij on trades from generators z' to consumers j, which compensate the operator for the average transmission costs on h that * are due to this trade in the solution, 1,31. This transmission fee covers exactly the qij average of the trade-specific costs, plus a part of the common, network utilization costs, based on the portion of total trading activity on h. that this trade represents (refer to Equation 2.19). Operator thus exactly recoups all of its costs from the generators. a: Chij _ Chij ((123, 2172.72 qfim) _ * t ..= h” ‘15,") ‘12" where stars represent the values of variables in the solution. Such average pricing of transmission services does not result in passing of the actual incremental costs of transmission to the generator, and is therefore not expected to result in an efficient utilization of the transmission network on the margin. Arizu et al. 2001 point out inherent inefficiency as a cormnon critique of public nonprofit operators, as against for- profit network owners. Since system operators are most often nonprofit organizations (for instance, Midwest, New England, New York, California—Nevada, etc.), this assumption is justified empirically as consistent with a zero profit goal, even in the presence of fixed costs or rising marginal costs. When marginal transmission costs depend on the behavior of other traders, however, this assumption also makes calculation of the fee more tractable. Paul and Burtraw [2002] use average transmission pricing in their simulation model to avoid calculating fees that are structured based on different components. 75 2.3.4 Generators’ Profits The above expressions jointly define generator i’s profit function II,- as the difference between the generator’s revenues from all consumers j, and the total costs of production, emission abatement, transmission, and environmental compliance. Here, for clarity of ex— position, the cost of compliance under alternative policies is represented by W(Zj qz'j, ai). Hi (sz’az‘) = 2((11'3' 'Pij) ’Cgil')—Ctij(’)‘cai(')-§: (thijqz'j) +W (2-7) J .7 where -t(: - e,- (qzj, ai) Emission tax W = p A - £2, — e,- qi, a,) under Emission allowances ’\ez' - E,- — e,- (972" ai) Emission caps Without the last term, W, this expression would give the generator’s profit function in the case without environmental regulation. The second to last term represents the transmission fees charged by a system operator on all of 27’s interregional trades with customers j, across interregional segments h. With environmental policies in place, an additional term enter this basic formulation. In the scenario with a uniform emission tax, the cost of this tax for each ton of i’s emissions must be subtracted. In the scenario with a market for tradable allowances, each generator is allocated a fixed number of allowances E, and must possess an allowance to emit each unit of emissions. The allowance price p A affects both the value of allowances allocated to the generator and the cost of a unit of emissions 8 In a scenario with caps on i. generators’ emissions, there is no direct cost of emitting, but the amount of i’s emissions is constrained from above by the level of the generator’s cap E2" Emission cap imposes 76 a possibly binding constraint on the generator’s optimization, which is represented in the generator’s problem by a shadow cost. )‘ez' is a Lagrange multiplier standing for the marginal cost of the emission cap in US dollars of generator’s profit per one ton increase in the emission cap. 2.3.5 Energy Industry Model Behavior In the presence of perfect, Bertrand competition among generators, if a generator wants to sell any volume to a customer, he must offer a price no higher than the price of any other generator in the customer’s state. Generator whose marginal costs exceed such a price and whose price would exceed prices of other generators in the state is for simplicity assumed not to compete in that state. As a result, only offers that a customer may accept are observed. With many competing generators in each state, and with perfect information, generators take the prices in each state as given, and only generators that can charge the market price compete for the customer. In what follows, I will use the equilibrium Bertrand competition result to simplify notation, and write the price of generators selling to customer j simply as pj. Under perfect information, other generators who cannot charge pj do not offer any energy to j, and their price in j’s market is unidentified. All generators that sell any volume of energy to j receive price pj. Generator 2' has two decision variables with which to maximize its objective function II,- given in Equation 2.7: sales to all of its buyers j, qz-j (where Zj qij = q,), and emission—abatement intensity aza8 These two variables determine the generator’s emis- sions, and generating, transmission and abatement costs. The first order conditions for 8Generators do not import energy for resale to consumers, because of transmission costs. Instead con— sumers can procure energy directly from all generators (for instance, Palmer and Burtraw 1996, or Paul and Burtraw 2002). 77 the maximization of Equation 2.7 with respect to q,- j and a,- are: an, _0 an, _ — _ — — 0 aqij (9a,- For qz'jv the generator simply equates the marginal direct costs of selling energy with the prices collected from consumers. For (1,, the generator equates the marginal cost of reducing emissions with the marginal savings due to the compliance with the environ- mental policy. For expositional clarity, the derivative of the cost of compliance with each 3W(Zj qz'jflz') and 6W(Zj(1ijaai) 6g,- J 8a, environmental policy is denoted in the following equations. The first order condition with respect to a sale to agent j is thus: where —t - Be; Emission tax 8 3?? gng; = —p A . (1:) under Emission allowances Be- . . ‘Aei - Emiss10n caps Here, the third term represents a per-unit charge by an operator for a sale across two regions. Since the transmission cost incurred by an operator from a particular trade increases in the size of that trade and depends on trades by other generators as well, the operator charges generators a flat per-unit fee, which by construction exactly amounts to the operator’s average cost in the equilibrium. The generator views this fee as exogenous. Individual trades are assumed small compared to the capacity of h, Th, and there are many 78 trades on each segment, so generator 2' takes the trading activity of other generators as given (for instance, Boucher and Smeers 2001). Under different forms of environmental regulation, an additional term enters Equation 2.8. The generator must subtract the marginal cost of an emission tax, the marginal cost of an emission allowance, or the marginal shadow cost imposed by an emission cap. The generator thus sells energy until its marginal costs rise to the competitive price it can receive from a particular consumer. This can happen if the generator’s direct costs rise, or if the marginal shadow cost of the generator’s emission cap rises sufficiently. The first order condition for emission-abatement intensity (1,; once again depends on the environmental policy implemented in the market: 6_II,; = 6cm- 6W aai —_aai + fie—i = 0 (2.9) where Be- t Emission tax €565: % = p143? under Emission allowances z z 86 A ez’ “2' Emission caps With a uniform per-unit emission tax te, the generator abates its emissions only until the marginal abatement costs rise to the level of the marginal tax savings that the generator can achieve through this. Under the system of tradable allowances, the generator chooses emission abatement so that its marginal abatement cost equals the marginal opportunity cost of its emissions—the market allowance price [Coggins and Swinton, 1996]. With a cap on emissions, generator 2' abates its emissions until the marginal cost of abatement, and the marginal benefit—in terms of the shadow cost of the 79 emission constraint—become equated. Consumer j observes his realization of the demand function and procures energy at price pj until his demand at that price is satisfied. dj (Pj) = Zqzj (2.10) Prices differ across consumers 3' because of regional differences in transmission costs and capacities, regulatory restrictions on trade and pricing, and the availability of gener- ators and their cost schedules. System operator performs interregional trades between generators and consumers sub- ject to the restriction on its profit on each network segment h to be zero, and on the trans- mission costs to be charged to the responsible generators [Rau, 2000]. Refer to Equation 2.19. The operator charges each generator a transmission fee that exactly offsets the op- erator’s average cost of transmitting energy from that generator via a network segment. His average profit on each network segment h is thus zero. 0 . . _”_h. = W . _ Chi = (2.11) (12' j 3 2.3.6 Properties of the Market Solution The equilibrium is characterized by a set of values of endogenous variables that solve Equations 2.8, 2.9 and 2.10. This set comprises energy trades qz'j for each generator—~ buyer pair 2’ and j, abatement intensities a,- for each generator 1', and energy price pj for each consumer j. Under individual environmental policy scenarios, an additional variable ensures generators’ compliance (exogenous emission tax t, endogenous shadow costs of emission caps )‘ez‘v or an endogenous market price of emission allowances p A). Appendix 80 A.3 lists the system of equations solved in the model and the unknowns that ensure exact identification of the system. The solution exists because generators’ cost functions are continuous and increasing in ‘h’jv consumers’ demands are continuous and decreasing in prices, and constraints on generators are linear. The solution is unique because all cost functions are strictly increas- ing and strictly convex, and consumer demands are strictly decreasing. The energy sales of each generator and his choice of abatement intensity (qij and a2) uniquely maximize generators’ profits, given their costs and compliance with the environmental policy and all physical constraints. Generator 2' cannot increase its profit by selling energy or abating emissions at a different level. Energy prices pj clear the available supply and demand for energy in each consumer j’s market, and nationwide, and ensure that no generator can increase its profit unilaterally by moving some production from one consumer to another, given i’s transmission costs, or by changing price in any market, given i’s marginal costs. All pj exactly cover the marginal costs of generators serving consumer j, inclusive of operators’ transmission fees for consumers out of region. Generators offer an identical energy price pj to a particular consumer j, and are assigned market shares 0,- j that no generator wants to increase or decrease, given pj. With qz-j and pj, consumer j’s demand dj(pj) is exactly satisfied. Given qz-j, system operators exactly cover the costs of transporting energy on all segments h. 2.4 Functional Forms Used in the Energy Industry Model The next three sections introduce the specific functional forms used to define genera- tors’, consumers’ and operators’ objective functions in the model of the energy industry, along with their justification. The following Section 2.5 discusses the routine that com- 81 puter program follows when searching for a market solution in the system of necessary equations, and the issues encountered in building such a computation model with the assumed functional forms and relationships among model agents. 2.4.1 Generators Generator 2' faces production costs cg,- as a function of its total output qi. Variable generating costs are a function of the amount of fuel used, and the administrative, labor and other non-fuel operating and maintenance costs. qz- _ 092' = [sz’ / Hi(02')0id0i +G1i4i+GQiqi2 + [G3iQ,-] (2.12) s O 1 V Variahfe costs Capztal costs This functional form is flexible to allow multiple sources of generators’ costs, as in Crew and Kleindorfer [1986]. In my numerical model, parameters of this function are calibrated to allow the model to achieve the greatest fit along several criteria (refer to Section 2.7). The fuel costs can be written as sz' f6” Hi(0,-)oz- d0,- , where Pfi is the generator’s cost of fuel, and generator’s marginal heat rate H,- is a nonlinear function of output level qz- [California Energy Commission].9 G1,- is a parameter representing the per-unit linear non-fuel variable cost.10 The quadratic term (with the parameter 027;) represents all non-fuel costs that marginally increase with the output level, due to the diminishing productivity of all inputs and the increase in their marginal costs as the utilization of 91n the simulation, the following expression for marginal heat rate for coal-burning generators is adopted from Roberts and Goudarzi [1998]: Hz' = 9.603 — 0.093 - qi + 0.073 - agei - 0.070 - age30 +1: —0.046 - bitumi + 0.062 - ligm'tei + 0.029 - ai. Here 92' is the generator’s output in megawatt-hours, agei is age in years, age30+i is an indicator for whether the age exceeds 30 years, bitumz- and lignitei are indicators for two particular types of coal, and ai is the S 02 abatement intensity. 10In Haas [1999], fuel costs are divided by a nationwide constant 311— = 0.985 representing fuel costs 2 as a constant portion of the variable costs. 82 all inputs approaches their available levels (California Energy Commission, Wisconsin Dept. of Administration). Less productive and higher cost resources are brought into the production process [Crew and Kleindorfer, 1986]. G3,- represents the annualized capital recovery charge and depreciation cost per unit of the generator’s capacity. Since my numerical model will be solving a set of profit-maximizing first order conditions, this last term will get dropped, because it depends only on the generator’s production capacity, and not the actual output or the level of emission abatement. Transmission of energy among generators, system Operators and customers involves costs Ctz' marginally increasing in the size of each trade qz-j, and in the utilization rate of the network capacity [Backerman et al., 2000, Borenstein et al., 2000, Rau, 2000]. For trades within a region, I assume a single generator-buyer pair on each network segment, so all transmission costs are internalized, and sellers realize the full impact of their trade on the total transmission costs. My justification is that generators and consumers in the US are spatially distributed, and the delivery lines to individual customers may be private property of the generator.11 Assuming no congestion within regions is common in the empirical literature, due to missing data on capacities and their utilization on local lines, and a lesser need to consider the presence of multiple traders on a single network segment [Paul and Burtraw, 2002]. Paul and Burtraw [2002] and Palmer et al. [2002] assume transmission costs within each region to be zero and capacities to be non-binding, for simplicity, and due to the authors’ lack of data on these costs. For trades across two regions, these studies assume generators to pay average transmission and delivery costs, even under competitive marginal cost pricing. 11Even though the model aggregates individual market participants into representative generators and statewide representative consumers, individual generators can reasonably be thought of as serving differ- ent areas in a state, or using proprietary network lines. 83 Generator’s total transmission cost Cti is a sum of the transmission costs of the sale of energy to each buyer. These costs have linear and quadratic components, and also depend on the capacity of the line where each sale is transported, TU" 012', ng- and C3,- are parameters. 2 ‘12' ' 6a = Cu 2 (12' j + 022' Z qij + 031-2: -—, (2-13) j j ' W W Linear transm. cost Quadratic transm. cost Capacity util. costs Sales of energy to consumers in a different NERC region must pass through an interre- gional network segment h common to all trading partners between the two regions. This segment is overseen by a system operator, who incurs transmission costs for transporting all energy via this segment. As in Paul and Burtraw [2002], generators using this interre- gional segment are assumed to pay a fixed per-unit fee t hi j equal to the operator’s average transmission cost. Of the operator’s total cost ch, a portion Chi j can be attributed to the trade between generator i and consumer j. The revenue that a generator receives from such a trade must cover the cost of transmission within the generator’s and the consumer’s regions, Cti~ as well as Chij (given in Equation 2.19).12 Generators’ trade within a region does not affect the capacity and transmission costs borne by other generators. This is a reasonable approximation, because generators are spatially distributed and can cater to their local customers so that all their transmission costs, and concerns over network utilization are internalized. On the interregional network segments that generators share among themselves, individual traders view the amount of trading by other traders and the average transmission costs as given. There are many 12 Chi j may be rising nonlinearly in the size of the trade between i and j, and can also depend on the use of segment h by all other traders. In the absence of more complicated pricing schemes, the operator designated to operate with zero profits charges generators the expected average cost of transmission in the solution. Section 2.4.4 discusses the operator’s problem in more detail. 84 Par. Description Par Description Q,- Generating capacity (MW h) All- Variable emission abat. cost param. ($/Ton) H,(q,-) Generator’s marginal heat A2,- Param. on linear emission rate (kBtu/MWh) abat. cost ($/% Abated) sz’ Cost of generator’s fuel A3,- Param. on quadratic abat. ($/mthu) cost ($/%2 Abated) G 1,- Variable generating over- C1,; Param. on linear transm. head cost ($/MWh) cost ($/MWh Transported) G2,: Param. on quadratic vari- Cg, Param. on quadratic able gener. cost ($/ M Wh2) transm. cost ($/ M Wh2 Transported) G3,- Cost of capital ($/MWh C3, Param. on transm. line Generating Capacity) utilization cost ($/MWh Transported) Tij Transm. capacity on seg— e Constant price elasticity of ment between i & j (MWh) demand (Unitless) éfi Fuel emission factor (Short 6,- Linear demand shifter Ton / Btu) (Unitless) E, E,- Aggregate, and generator’s emission cap (Ton) Table 2.2 Energy Industry Model Parameters capacity. that the generator abates. agents using these networks, and each trade represents a small portion of the network Generator’s emissions e,- are a function of the amount of fuel used, fg’ Hi(0i)0i do, , the fuel emission factor éfi’ and the intensity of emission abatement ai. éfi determines the sulfur content as a portion of fuel weight, and a, determines the portion of emissions - q,- ei = efi(1— ai)/0 112-(0&0,- do,- 85 Cost of emission abatement Cai is a function of the abatement intensity, and the pre- abatement emissions, which depend on the generator’s output level, heat rate and fuel sulfur content [Paul and Burtraw, 2002]. Cai is assumed linearly increasing in emissions (both pre—abatement and post-abatement), holding the abatement intensity constant. This agrees with a common assumption that emission-abatement technologies are capable of removing a certain portion of generator’s emissions (for instance, Srivastava 2000), and have a constant variable cost [Argonne National Lab, Ellerman et al., 1997, Srivastava, 2000]. This means that if a generator abates emissions at a constant rate (in terms of the percentage of emissions removed), such as at its maximum rate, the generator faces a constant per-ton cost in lost energy, water, scrubber material, and other resources. The abatement cost function is also convex in the abatement intensity, represented by a percent of the pre-abatement emissions. With this representation, incremental abate- ment costs per percentage of emissions abated are low at low levels of abatement intensity, regardless of the generator’s size, and become large or infeasible as a,- approaches 100%. This corresponds with the fact that technologies that remove a greater portion of emis- sions have high relative installation and operating costs, regardless of the generator’s size [Argonne National Lab, Ellerman et al., 1997, Paul and Burtraw, 2002]. _ (12' cai = [Anefi "’2' /0 112102901 (102' ] + [A2iai+A3ia22] (2-15) \ Variable abatement cost Annualized fixed abat. cost Technologies that remove a small portion of emissions, such as coal blending, are often modeled as having no retrofitting or operating costs [Argonne National Lab, Paul and Burtraw, 2002]. Coal switching, which removes a higher proportion of emissions, is modeled to have small capital costs [Argonne National Lab]. Scrubbers, on the other hand, remove 90—98 percent of emissions, but require high installation and operating costs. For technologies requiring upfront investments, the installation, retrofitting and 86 capital costs enter the generators’ first. order conditions in this static model, to represent generators’ decision regarding the adoption of a particular abatement technology. I use the quadratic form for simplicity and as a reasonable impact of the planned emission- abatement intensity on a generator’s annualized installation and operating costs. Importantly, if a2: = 0, Cai = 0. If the pre-abatement emissions Aliéf, f6)” Hz-(oi) 0,- d0,- equal zero, such as when a generator uses sulfur-free fuel, this generator can choose a,- = 0 and incur no abatement costs. .422- and A3,- are parameters of the annualized capi- tal abatement cost, and operating cost, that may depend on the generator’s age, capacity and production technology. These parameters are estimated in the calibration-stage of my model, from within narrow ranges suggested in the literature [EPA, f, Srivastava, 2000] (refer to Section 2.7). 2.4.2 Generators’ Profits The functions above jointly define a generator’s competitive profit II,- as the revenue from sales less the costs of production, transmission, emission abatement, and environ- mental compliance: q,- - Hi = Z (qij “1027) " [Pficli [0 Hi(0i)0i (102' + 022' '42‘2 + 03202] J x v J ‘ v ’ Generating costs Revenue 2 Q‘,‘ - Clizqij+c2izqi2j+03iz (T272) ‘ZZ(’hijqij) g j j 2' h j , Transmission costs - 4i — [Aliefiai/O Hi(0i)0i d0,- + A2iai + A3,;a22] -+- W (2.16) 1 Emission abatement cost 87 where t 6(1 —a,-) afiq fgiH ,- (0i) 0,- doz- Emission tax W = pA [(1a,)efz fg’H i (02-) 0,- do,- — E1] under Emission allowances Aei - [(1 —a,-) e f2 fg’I-I ,- (0i) 0i do,- — E 2‘] Emission caps The first row shows the generator’s revenue from selling energy at exogenously given prices, less generating costs. The second row shows the marginally increasing cost of transmission. For energy sales to consumers j in other regions, the second row includes an additional transmission fee charged by a system operator for the usage of interregional segments h (refer to Equation 2.19). The third line shows the emission-abatement costs, and the costs of compliance with an environmental policy, W. Under the alternative environmental policies (as in Equation 2.7), this term becomes the generator’s cost of a uniform emission tax, the net expenditure on tradable allowances, or the shadow cost of an emission cap. 2.4.3 Consumers Consumption of each representative consumer j consists of imports of that consumer from all generators i, dj = 2i qij- The consumer pays price pj. Demand schedules decreasing in price with constant price elasticity e are assumed, as in Borenstein et al. [2000], Palmer and Burtraw [1996], Paul and Burtraw [2002] or Palmer et a1. [2002]. dj (Pj) = 53' '1)? (2.17) 53- is an exogenous parameter calibrated in my numerical model for each state, and e is a nationwide price elasticity of demand, taken from Borenstein and Bushnell [1998], 88 Paul and Burtraw [2002] and Wade [2003]. Borenstein and Bushnell [1998] advocate the constant elasticity representation of consumer demand, against a linear representation (used for instance in Haas 1999), as being realistic for high prices. Energ is a homogenous good that each consumer buys from a seller with the lowest price. If multiple providers offer the same price pj, the consumer decides randomly how much to buy from each generator, until his demand at that price is satisfied. Generators with a higher than the minimum price receive zero market share in consumer j ’3 state. 2.4.4 Independent System Operators My representation of the independent system operators corresponds to the lesser role assigned to them in Varaiya and Wu [1997] and Oren [1998]. Operators monitor energy trade across NERC regions on every network segment h, and realize costs and energy losses that accrue on every segment. These costs are marginally increasing in the size of each trade on the segment, as well as in the utilization of the network capacity by all trades together [Backerman et al., 2000, Borenstein and Bushnell, 1998]. 2 Zn qij Th (2.18) Ch = Z [C1hqz'j + C2hqi2j] + 03h 2] In order to recoup all transmission costs, and charge each pair of trading partners i and j for their contribution to the total interregional transmission costs ch, the operator levies a per-unit fee t hi j on generators that incorporates the costs that have accrued directly due to qz-j, (Cl h + C2hqij)» as well as a part of the common charge based on the two . . 2 traders’ portion in the total usage of the segment, ( (.1211, .CBh [EMJQMJ ). This 2] i] h 89 fee equals Chi] Zmn (177172] 2 (2.19) ‘ 1 t--=——=C +C q--+——C [ hZ] qij 1h 2h 2] Zmn an 3h Th Here, mn are those pairs of generators and consumers who trade on the interregional network segment h, and i j is one such pair. 2.4.5 Energy Industry Model Behavior The level of energy sales q,- j and emission-abatement intensity a, determine generator i ’5 total output level qi, emissions 8i» as well as all generator’s costs. Sales to individual consumers by all generators jointly determine energy prices in each state, and generators’ revenues and profits. Generators’ direct expenditures on the emission tax or on the allowances are also determined. These variables are determined from the following two first order conditions. Generator i’s first order condition with respect to trade with agent j, qijv is: 8111 671,-: = 0 = p) -[PfiGliHi(qi)+ 2022' 'qz'j]- thij Price M arg. variable cost Oper.’s transm. fee qi ' _ 8W _ Cu + 2022- . qij + 203iT—‘27 - [Aliaz-Hz-(qz-kfi] + aqij (2.20) i . , , r v J J M arg. abatement cost M arg. transm. cost where ’Hi(qi)éfi - te - (1 — ai) Emission tax g% = “‘Hi(qi)éfi - p A - (1 — 02') under Emission allowances ‘Aei - Hi(qij)éfi(1 - (2,) Emission caps 90 The first term on the first line shows the marginal revenue from selling to consumer j in the competitive market. The second term shows the marginal generating cost. The last term on the first line indicates that for trades across two regions, an additional trans- mission fee is charged by a system operator to exactly cover its costs in the equilibrium. Generator 2' views this fee as exogenous. Under each environmental policy, an additional term 5622—: enters the basic formulation of the generator’s first order condition with respect to (12' j“ This term represents the marginal cost of an emission tax, the opportunity cost of emissions under the system of emission allowances, or the marginal shadow cost of an emission cap. The second first order condition, with respect to emission-abatement intensity ai, depends once again on the environmental policy used: (911- _ qi BW 87‘: = 0 = _\[A1iefi/(’) Hi(0i)0i (10,; + A27; + 2A3i ' a,- J + a (2.21) M arg. abaiEment cost where teéfz' fgioH,(o,-)o,- do,- Emission tax gE—IV; = PAéfz' fg’ 112-(000,- do,- under Emission allowances Aeiéfi [61’ Hi(02’)0i doz- Emission caps Under a uniform emission tax, the generator compares the marginal cost of emission abatement with the tax savings due to lower S 02 emissions. Under the system of tradable emission allowances, tax te in this expression is simply replaced with the market allowance price p A, because generators view this price as exogenous. Under emission caps, the marginal decrease in the shadow cost of the generator’semission cap enters this first order condition in place of the explicit benefits from emission abatement under the other 91 policies. Consumer j procures energy from all generators at price pj until 2% = 53' 'P} (2.22) 2 System operator must satisfy two conditions. First, its profit on any network segment h is constrained to equal zero. Second, the operator must assign all transmission costs to generators whose trades caused them. By construction, the per-unit fee that the operator charges generator i for transmission to consumer j via network segment h equals the * C . . operator’s average cost of that trade in the solution, if hi 3' = %l (as in Equation 2.19). if Summed up across all units traded and all generator-consumer pairs on network segment h, these fees equal the operator’s total transmission cost on that segment, and so the system operator earns zero profit. 2.5 Numerical Approach to Modeling Energy Industry The customized industry model does not capture all characteristics of the US energy industry, but is a good approximation of the institutional settings and the relationships among market agents. It serves well my purpose of computing the short-term response of the industry to environmental regulation, including the resulting emission levels. The static, steady state modeling here is appropriate, because the model is mainly interested in the time frame when generators cannot change their production capacity and technology, but can adjust the volume generated and the intensity of emission abatement (as in [Haas, 1999]).13 Static modeling is also consistent with a commitment of the environmental 13The model ignores borrowing constraints and uncertainties over the future realizations of abatement costs. This allows me to consider plants’ past investment in abatement technologies, or even use the information on the plants’ actual installments (see Footnote 20). 92 regulator to a steady policy [Weitzman, 1978]. From this model, conclusions can be formed about the long-term effects of the policies, including the changes to the make-up of the industry. Palmer et al. [2002] solve their thirty-year industry model as a series of static models. The numerical model indirectly maximizes each agent’s objective function using a square system of first-order equations (Equations 2.20, 2.21 and 2.22) in the General Algebraic Modeling System (GAMS) Rutherford and Paltsev [2000]. For a solution to correspond to a market equilibrium, model variables must solve all equations Paul and Burtraw [2002]. The model starts with an arbitrary set of values for all model variables, computes the infeasibilities in all equations, and proceeds iteratively by changing the values of variables in a way that achieves the greatest decrease in those infeasibilities. The solution is achieved when the infeasibilities in all equations are below a small number (10-9). To ensure that the model is stable and that it comes to an empirically realistic solution, I choose starting values for all variables close to the counterfactual preregulation values (as in Shadbegian et al. 2004). I first run the model without any regulation imposed, report the resulting values of all variables, and use these as starting values in solving individual scenarios. As a result, any imprecisions in the solution that the algorithm cannot solve affect all scenarios similarly. In order to solve the first order conditions, GAMS modeling software requires all functions to have well defined continuous first derivatives. In the process of solving the model, GAMS makes small perturbations in model variables and evaluates their effects on the infeasibilities in model equations. Based on these effects, it chooses the direction of its further search of a solution. With discontinuous functions, the change to the infeasibilities can be so large and inaccurate that the search will proceed in the wrong direction [ARKI 93 Consulting]. The continuous representation of all model functions makes the numerical model trans- parent, because the values of all variables can be tracked as the model searches for the solution, and smoothly converges to it. In this way, the model can update all variables incrementally when a single variable undertakes a deviation. This is particularly useful and realistic with respect to finding market prices and market shares, because GAMS mimics the incremental decision-making and deviating of individual agents, rather than industry-wide random search for a market price until supply and demand are equated. GAMS checks whether each agent could profitably deviate, and the small deviations do not result in discontinuous changes in the rest of the market. To solve my model in GAMS, I convert all discontinuous functions in my theoretical model into continuous representations. Consumer’s purchase from each generator (assign- ment of market shares to individual generators), discontinuous in price, is one function that needs to be converted. The shadow cost of the emission constraints, under the emis- sion caps scenario, is another. In addition, to ensure that the numerical results under each scenario comply with the empirically observed physical constraints in the energy market, I create dummy cost terms that disallow the simulation algorithm to exceed such constraints. In particular, I constrain generator’s output to be between zero and the generator’s observed production capacity; volume transmitted over a single network segment—between zero and the line’s capacity, in each direction; and, emission-abatement intensity—between zero and one. The model is first calibrated to fit the historic values in several criteria of interest (refer to Section 2.7) and to conform with physical constraints without the help of these dummy terms. These terms are then added to the model, to ensure satisfaction of all constraints under the alternative policy scenarios.14 14Since two of the three environmental policy scenarios are counterfactual, and since we do not observe all combinations of model variables that result in the alternative scenarios, our inference to other policies 94 I use highly-nonlinear representations of these functions that approximate well the discontinuous relationships. Footnote 15 gives a particular example of the fit of my continuous representation to the consumer-choice function, and Figure A.5 shows the similarity between step functions and their chosen continuous approximations. The following two sections describe how discontinuous functions enter my numerical model, and still keep their economic meaning. Section 2.5.1 describes how I have found numerically the desired stringency for individual environmental policies. Section 2.5.2 discusses energy trading rules and their incorporation in the model. Approximation of the Consumer’s Decision In order to find an equilibrium in each consumer’s market, by matching each gen- erator’s supply with each consumer’s demand, I allow individual generators i to offer consumers j price-quantity offers p,- j and qij- These price offers exactly cover the gener- ators’ marginal costs of providing qij' With many providers available to the consumer, the consumer observes all offers, and assigns market shares to generators based on their prices, buying all energy from the generators with the lowest price, and deciding ran- domly between generators with the same price. In my numerical model, in order for the consumer to compare a generator’s price to the prices of other generators, I compute the average volume-weighted price the consumer pays as _ 22(qij'1’ij) p. _ (2.23) J 22' Qij This representation helps in assigning each generator the volume that consumer j buys from him in Equation 2.24, because the consumer must only compare a pair of prices at may find a conflict between the calibrated functional forms and parameters, and the observed physical constraints. 95 a time: pij and pj. pj gets updated as new price-quantity offers arrive. Since multiple markets clear simultaneously, prices and generators’ volumes in different consumer mar- kets affect each other. In the solution, pj is at the lowest price offered to j, because the lowest pricing generator receives a market share of essentially one. Equation 2.24 allows me to assign a market share of essentially one to a generator when even a small price difference exists. In order to represent consumer behavior under Bertrand competition in my numerical model, I make the market share that a consumer assigns to each generator a continuous and deterministic function of the generator’s price. These market shares must not only be consistent with the consumer’s choice under Bertrand competition, but must also be consistent with generators’ marginal cost pricing, and profit maximization across different consumers. If two generators offer a consumer identical prices, my model assigns them deterministic market shares based on what output each of them can provide to this con- sumer. Even under small or no price differences, these market shares can be very different. As the price difference increases, the market share of the generator with the lower price quickly approaches 100%, approximating well the discontinuous counterpart in the the- oretical model. Figure A.5.e in Appendix A.4 indicates that a generator charging a 1% (5% and 10%, respectively) lower price than other generators receives a market share of 70.3% (91.6% and 95.7%). At the uniform prices offered to a particular consumer, generators may offer different volumes, since their marginal generating and transmission costs rise in the volume of energy tendered, and differ across generators. Each consumer may thus purchase energy from multiple sources. In order to represent j ’s assignment of market shares to generators i as a continuous and deterministic function, I define the share of generator i in j ’8 total 96 consumption, Uij’ as 0.5 + %arctan (pj — Pij) (2 24) 0,] . 1 2k 05 + 7,- arctan (pj — pkj)] This function determines market shares even for generators with identical prices. Arc tangent function, with a continuously defined derivative, is a good numerical approxima— tion of the step function that the consumer’s decision in Bertrand competition represents [Chen and Mangasarian, 1993, Rau, 2000]. 15 The constants 0.5 and % normalize the numerator and the denominator to ensure that they are bounded between zero and one. The function is very flat. and near unity for p,- j < pj, and falls quickly at a critical value pj to a new level near zero where it becomes fiat again. Refer to Figure A.5 and discussion of the properties of tangent and are tangent functions in Appendix A.4. The denomina- tor is the same for all individual p,- j and all generators, and ensures that a,- j are always between zero and one, and sum up to one for any consumer. For a seller with a low price, the numerator will be large. This seller should satisfy all of the consumer’s demand, and will satisfy virtually all demand in this numerical representation. Generators with higher prices will provide the little residual demanded energy, in the decreasing order of their price. Footnote 15 shows that these residual volumes, and revenues and profits that they lead to, are very small. Merging Equations 2.17, 2.23 and 2.24, consumer j’s demand 15For illustration of the goodness of fit, consider two generators with marginally increasing total costs, C1 = qu +qu and Cg = 2q2j + 2‘12)” selling to a consumer with demand function Z,- qij = 10 -pj. With perfect information and Bertrand competition between the two generators, the generators’ offers to the consumer are qu = 2 and (123' = 3, at pi = $5. Generators earn profits 111 = 4 and H2 = 4.5. I could verify that Equation 2.24 would give the generators market shares of 01 = 0.4 and 02 = 0.6. If the first generator’s cost function was instead 01 = 6q1j + flit]? j’ the second generator would supply all energy, (12 j = 4 (and q1 j = 0), at price pi = $6. It would earn H2 = 8. In this case, Equation 2.24 in my simulation would still allocate a positive market share to each generator, 01 = 0.012 and 02 = 0.988. The prices p1 j’ 1223- and outputs q1, q2 that allow Equation 2.24 to hold and are consistent with generators’ costs and consumer’s demand are p1 j = 6.016, pgj = 5.976, q1 = 0.048 and Q2 = 3.976. In the simulation, generators earn profits H1 = 3.8 - 10"4 and 112 = 7.903. 97 from generator i is: 2],; (qkj'ij) 0.5 + %arctan . — Pz' ' 6 , ‘21: (In J z], (qkj -pk,-) 1 >31: (qkj'ij) k k] 2k 0.5 + f arctan . - pij \ V 1 k qk] Avg.price \ J M Share of consumer’ s demand Approximation of the Generators’ Physical Constraints Generators’ output, transmission via particular network segments, and emission of S 02 under the emission cap policy, are physically constrained by the available infrastruc- ture and the regulatory policy. The functional forms used throughout Section 2.4 may not ensure that important model variables achieve values within their feasible ranges, be- cause the functional forms and parameters are based on the empirically observed values and may not apply precisely under the counterfactual other policies. In other words, we observe values of all variables (e.g., costs) when all other variables (e.g., outputs) are within a certain range, but our inference to other ranges (of output) may be imprecise. After I calibrate the energy model, I add nonlinear dummy terms to generators’ direct costs in the first order conditions, to represent the shadow costs of the constraints to the generators. These ensure that model variables do not exceed their allowed ranges. Using continuous terms, rather than traditionally used binary variables, I avoid numerical problems with discontinuity at corner solutions, and I can determine the shadow value of these constraints to generators’ profits. Compared to imposing fixed constraints on model variables, using these shadow values allows the numerical model to achieve equality in the first order conditions. With equality, these equations are considered to be solved. Tangent representations of the implicit costs of physical constraints are used because of their well defined derivatives for all values of the considered arguments [Rau, 2000] 98 and their good approximation of the relationship between the choice variables and the A - f (constraint) functions in lagrangian inequality optimization problems (refer to Figure A.5 in Appendix A.4). Generators’ profit-maximizing first order condition with respect to output (2.20), ex- cluding the terms due to environmental regulation, becomes 611- 42" 3,—2, = 0 = Pj — PfiGIiHi(q’i) + 2G2, - qz-j - Cli + 2022' - qz-j + 2037;75- ‘IZJ Ti]. _ WX 1r.qz-o 2 ‘AliHi(Qilefz' — thij - ’TZG’ (1 + tan (—Qz]) ) \ Gener. constraint shadow cost 71' (szek qij - sz'gtk qik) + Skj k] j k] \ WXT Transm. constrdint shadow cost The last term on the second line is a continuous representation of the shadow cost of the generating constraint that is close to zero for values of output between zero and the generator’s capacity Q,- but rapidly increases without bound when capacity is reached. The last tangent term represents the transmission constraint burden for each of i’s trading partners j, and depends on the trading activity on the given network segment by all other agents. This term is close to zero for trade volumes smaller than the pipeline constraint. Here It represents generator i’s state. The volume of trade on the network segment between states It and j is calculated as the difference between sales by all generators in state It to customer j, and the sales by generators in state j to the customer in state It. Shifting parameter Skj allows transmission constraints to be asymmetric among two trading partners (as in Paul and Burtraw 2002). Shifter S k j determines how much extra volume of energy can be transmitted one way, and how much less the other way (refer to Figure A.5 in Appendix A.4). 99 X A’XGv Parameters on shadow cost terms for the abatement- X E, XT intensity, output, emissions, and transmission constraints (Unitless) Si j Asymmetric transmission constraint shifter (MWh) 100 Generators’ first order condition with respect to emission-abatement intensity similarly uses an approximation for the shadow cost of the abatement constraint (here implicitly 0 and 100% of emissions). an, _ qi _ qr —8a- = O = teefi/() Hi (Oi)0i d0,- — Aliefiai/O’ Hi(0i)0i d0,- + 2122' + 21132-61, Z — 1rXA (1+ tan (sol-)2) —_,_—/ Abat. constraint shadow cost (2.26) In the emission cap scenario, the shadow cost of the generator’s emission constraint is also modeled as continuous. It enters the generator’s first order condition with respect ”XE we 2 _ 1 t —_—’ 2.2 Ei ( + an(Ei) ) ( 7) where E,- is the generator’s emission cap. to output as 2.5.1 Modeling of Environmental Policies This section describes how I incorporate the alternative environmental policies in my simulation model. I first identify the targeted stringency of each of the environmental policies, that will lead to aggregate emissions of E. In the scenario with a nationwide emission tax, the level of the tax is selected by trial and error so that in decentralized equilibrium, generators choose emission levels summing up to E. The tax enters generators’ profit-maximizing first order conditions. With this tax, I find the market solution to the system of Equations 2.20, 2.21 and 2.22. When I achieve 2,- e,- = E, I have found the correct tax and the solution to the emission tax 101 scenario. In the scenario with emission caps, the caps on generators are set based on their pre- regulation production levels. I estimate these levels as those that would result in my energy model, with no environmental regulation imposed (the counterfactual emissions, in Shadbegian et al. 2004). This is more sensible than using generators’ historic produc- tion, because any differences between my model, and the historic state of the industry16, could result in insensible emission caps with no relation to generators’ production capaci- ties. This is especially true since the energy industry in the US has undergone significant reorganization between 1988 and 1996, while my model is static, and uses simplifying assumptions such as on the properties of the transmission network (following Paul and Burtraw 2002). The model was also calibrated using representative generators and con- sumers, and focuses on the fit of statewide and aggregate variables. The model may not achieve correct values at individual generators, particularly at small generators or 17, and so comparing the model derived values with actual those burning alternative fuels emission caps may cause problems. The energy industry model is first run without any constraints on emissions. If the aggregate emissions in the equilibrium exceed E, all generators receive an emission cap based on the ratio of their equilibrium output in this scenario to the output of all gen- erators, that would bring the sum of resulting emissions down to E [Shadbegian et al., 2004]. This is consistent with the way the EPA distributed allowances under the Title IV of the Clean Air Act [Ellerman et al., 2000]. After I derive the pre—regulation production shares, I solve the industry model, where emission caps E,- equal the pre-regulation output levels at all generators multiplied by 16Under the Title IV, production levels in year 1988 are considered. 17For instance, my measure of marginal and average heat rate uses a functional form that provides ood g fit for higher output levels, but not necessarily for very low levels [Bushnell and Wolfram, 2005, Roberts and Goudarzi, 1998]. 102 different scalars until the equilibrium aggregate emissions equal E. With 2:,- e,- = E, I have found the appropriate emission caps and the solution to the emission cap scenario.18 Under the nationwide market for $02 allowances, generators are first allocated E al— lowances. As in the emission cap scenario, generators are allocated a portion of allowances summing up to E based on their portion of the nationwide pre—regulation production. I run the energy model without any environmental regulation, and observe generators’ out- put levels. I simply divide generators’ output in this solution by the aggregate output, and multiply my desired E by the resulting fraction. In the allowance trading scenario genera- tors may buy and sell allowances, so any excess allowances are traded off in a competitive allowance market and are used for emitting. The problem with non-binding emission constraints is not present in this scenario. Once I know the allocation of allowances, I can run the energy model once to find the solution to the allowance market scenario. 2.5.2 Energy Trading Rules The energy model imposes several rules on interregional trade in energy that approx- imate well the trends in the US energy industry, and ensure that: 0 Trading across N ERC regions is subject to network capacity constraints which may not be constant or even symmetric across regions. Constraints only affect energy trades among regions, not within them, since information on transmission capacities between individual generators and their local customers is often missing, and these constraints are arguably less important (following Paul and Burtraw 2002). 0 Generators sell directly to consumers within their N ERC region, but must go through a system operator to sell to other regions. This requirement simply forces gener- 18This differs from simply dividing E by pre—regulation aggregate emissions, and using that as the correct ratio, since emission caps in the latter method may not be binding for all generators, and these generators may produce less emissions than required to achieve exactly E. 103 ators to pass their trades through the agent that maintains interregional network segments and assigns transmission charges to all responsible traders. Trades within a state are conducted directly between the generator and the consumer, and are only subject to transmission costs. This corresponds with the differential treatment of energy trading within regions and across regions in Paul and Burtraw [2002]. All literature dealing with energy trade on a common network assume the involvement of a system operator, transmission authority, line owner or another institution (for instance, Oren 1998). 0 States within each N ERC region are divided among those that have permitted re- structuring, and those that have not. Generators regulated in the latter states are allowed to import energy to satisfy their requirement to serve local customers, but do not export energy to consumers out of state, so as not to increase prices and risks for their core customers. As an alternative justification, these generators may lack motives to trade [White 2005]. 0 Energy transmission involves costs including possible energy losses, that are mar- ginally increasing in the volume of the trade (for instance, Backerman et al. 2000, Borenstein and Bushnell 1998). Trades across regions are administered by system operators in both regions, who face transmission charges increasing in the volume of the trade and the utilization of capacity of the interregional network segment by all traders. By construction, system operators earn zero profit, and must therefore charge a markup equal to their average costs of transporting energy from a generator in one region to a consumer in another region [Paul and Burtraw, 2002]. 104 For simplicity, and without affect on my results, I assume that the two operators between the dispatching and the receiving region realize a common cost of using the specific interregional network segment, and charge the buyer a single, joint transmission fee. It covers average costs of sending the trade via the particular network segment. In my model, rather than associating transmission costs with each system operator, I thus associate transmission costs and fees with the network segment connecting the generator’s and the consumer’s regions (for instance, [Paul and Burtraw, 2002]). 2.6 Energy Industry Data The supply of energy in the US is a complex network of energy producers, transmission companies and distributors, of different ownership, technology and input mix, and access to the nationwide grid. For simplicity, I focus on energy generators, and assign them all tasks from procurement of fuel, to distribution of energy to the consumer [Haas, 1999, Paul and Burtraw, 2002]. In most plants generator is a basic unit producing and selling energy, with exactly one boiler attached [Carlson et al., 2000]. Many statistics at the US Department of Energy and the EPA are available on generator level. The EPA also assigns emission standards, including emission allowances, on generator level [Carlson et al., 2000]. Where data was not available for individual generators, data for entire plants, parent companies, or states was collected from the US Department of Energy or the EPA. The model thus uses first order equations for individual generators, representative customers, and operators in each NERC region. In order to solve generators’ problem and find the market-clearing equilibrium in a system of thousands of equations, I aggregate all smaller generators by their similar features into representative generators. This allows me to include fringe generators that use non—traditional fuels or operate only seasonally, 105 without increasing the data size. Generators burning fuels other than coal have also small 502 emissions and are not allocated emission allowances, and so they do not affect the emissions market directly and can be modeled less precisely. Firm aggregation is standard in the modeling literature. Haas [1999] puts all generators together and focuses on the plant level. Paul and Burtraw [2002] and Palmer et a1. [2002] use model plants that aggregate individual plants by fuel type, technology, vintage year, and existing abatement technology, following the aggregation method used in EPA [k,l]. Large plants (plants ' covering more than 5% of the national market in Paul and Burtraw [2002]) are given a special role in most studies including this one. Under data aggregation, I start with 681 generators. In each state I group together generators that are either small with annual historic generation below 10 GWh or do not burn coal, while large coal-burning generators are retained individually, as they represent the vast majority of the power generating capacity as well as the actual generation in the US. I separate out small coal generators into two groups by size (below and above 5 GWh) and three groups by efficiency (average heat rate below 8,000; 8,000 to 12,000; and above). I further aggregate generators based on their existence status, fuel type and ownership. Observations whose data is missing. Using this aggregation, I reduce the number of generator observations to 206. This selective aggregation preserves heterogeneity and authenticity in the modeled market, while reducing the effective number of interacting agents and equations. Table A.4 in Appendix A.5 presents the categories into which generators are split. The generator-level data come mainly from two sources, the US Department of En- ergy’s Energy Information Administration (EIA) and the Environmental Protection Agency. The data are on 681 largest generators in 267 plants throughout the 48 continental US states. Since my sample comprises only 36.43% of all generators, responsible for 45.53% 106 of the actual generation of energy and 55.00% of generating capacity in the US, the state and US—wide quantities in the simulation are divided by 45.53% to match the empirical observations for US states and the industry as a whole. I use the assumption that the unobserved generators are similar to generators in my dataset, and that the omission of the fringe generators does not substantially alter the level of competition, heterogeneity, and availability of resources to the modeled generators. I also incorporate the information on the status of restructuring in the energy industry in each state, and infrastructure in each of the 13 NERC regions. I use the observed margin requirements for energy generation in each NERC region, regional transmission capability and transmission charges, and status of restructuring in each state, to model the generation and transmission constraints accurately (refer to Appendix A.5). 2.6.1 Demand for Energy Data Historic statewide energy demands and prices come from the EIA, which reports gener- ators’ monthly energy revenues and sales by consumer class, and also statistics on utilities’ purchases, disposition and energy losses [DOE~EIA, k,m]. In-state demands for energy are calibrated using historic volumes demanded and prices, and price elasticities of demand 5 assumed identical across regions [Bohi and Zimmerman, 1984, Borenstein et al., 2000, Paul and Burtraw, 2002, Wade, 2003]. Only one generic consumer class is modeled, with a time-constant demand function [Haas, 1999]. The price elasticity of demand is assumed to be -0.20 [Bohi and Zimmerman, 1984].19 19Wade [2003] estimates the price elasticity of demand between -0.10 and -0.246, Reiss and White [2004] between 0.00 and -0.39, and Electric Power Research Institute [a] between -0.15 and -0.35. Borenstein et al. [2000] use the elasticity of -0.10, while Paul and Burtraw [2002] use -0.30. 107 2.6.2 Generators’ Emission-Abatement Data The EPA reports statistics on generators’ operation and compliance with the Title IV, including the allowance allocation and trade, pollutant controls installed at the generators, emission factors and total emissions, as well as the generators’ technical specifications, such as fuel usage and coal characteristics [EPA, a,c,e]. EPA [l], Srivastava [2000] and Electric Power Research Institute [b] also project costs of various emission-abatement technologies. Generators’ S 02 abatement cost function, Cai’ is calibrated from the parameters that they report to the EPA, and modeled as continuous [Klaassen et al., 1994]. I derive the generators’ level of emission abatement without regard for the scrubbing units that have actually been installed.20 This is because I assume perfect and symmetric informa- tion among generators, and model generators’ decisions about abatement technologies as endogenous, to make the emission profiles clearly comparable across the environmental policy scenarios.21 2.6.3 502 Concentrations and Health Damages Data After deriving the equilibrium emission profile for the energy industry under each scenario, I aggregate the emissions to the state level, add background emissions of 502 from non-energy sources in the state, and map the total emissions into air concentrations of S 02 in each state (for instance, Tietenberg 1985). In the following expression, J: j denotes 20Some plants have installed scrubbers fearing high future costs of other abatement technologies, but would not have installed them with the ex post information [Rose et al., 1993]. Some studies impose the existence of these scrubbers on all evaluated policy scenarios [Burtraw and Mansur, 1999, Palmer et al., 2002]. 21H I imposed an arbitrary abatement technology at different generators, based on their often imperfect beliefs, the impacts of individual policies would not be as clear as under a full-information model, and would be difficult to predict. Under a different policy, different generators could have made a wrong decision. This paper can be interpreted as estimating how each policy would have been expected to perform under the Title IV, as well as in the upcoming years. 108 the 502 concentration level in state j, Tsj is the constant transportation coefficient mapping each unit of emissions in state 3 to concentrations in state j, and as are the background emissions in state s. ’13,“: 81') = 2 TS]. - 2(62') + és (2.28) iEs 3 iEs Unlike other pollutants (such as 002), 502 does not accumulate in the air, so its concentrations depend only on its emissions in the same time period. I use 7’3 j estimated for each pair of US states in the Advanced Statistical Trajectory Regional Air Pollution model (deve10ped under the National Acid Precipitation Assessment Program), as re- ported in the RFF’s Tracking and Analysis Framework [Argonne National Lab].22 The data on the population’s health responses to the concentrations of sulphur compounds are taken mainly from the EPA [i]. This survey estimates the impacts of air concentrations per microgram of 302 on human health in various health-impact pathways. The EPA [i] also reports the monetary value of each health impact, and the part of population affected in a particular pathway. Tables 3.1 and 3.2 report these estimates. Information on emission diffusion and on damages they cause is available only for emissions aggregated to the state level. Regardless of which generator in a state emits a ton of 302, same marginal damages are observed. D = :2]; [xj 4),]- wk 47%] (2.29) J 22The EPA has built a competing Climatological Regional Dispersion Model [Abt Associates, a, Latimer, 1996]. The EPA has also developed a nonlinear Regional Acid Deposition Model that maps plants’ emissions into air concentrations and depositions using pollutants’ chemical attributes [Chang et al., 1991, Clark, 1989, Shannon, 1985, Venkatram et al., 1989]. This model requires detailed climatological information for shorter units of time, and is infeasible for analysis in my paper. Shannon and Sisterson [1992] compare the two diffusion models, and justify the use of the ASTRAP. 109 where i kj is the size of population affected in a health-impact pathway k in state 3'23; ”k is the monetary value per incident in health-impact pathway k; and m], is the estimated number of incidents per one unit increase in 802 concentrations. 772,, is the central estimate from the medical literature, which, under symmetry of the estimate distributions, is the arithmetic average of the lower and upper values of estimates in the literature, reported in the fourth column in Tables 3.1 and 3.2. ”k is reported in column six. The aggregate damages are simply a sum of damages caused by each generator (D = 2, Di)- Under the assumption that generators’ emission levels do not affect damages caused by other generators, the damages caused by generator i’s emissions are D1031) = Z: [mifleil WM '11], 4711,] (2.30) 3' k where 1:,- j denotes the contribution of i’s emissions to the air concentration in state j. With a linear relationship between emissions and concentration levels, as the one used in this paper, the damages caused by all generators are simply a sum of damages cause by each generator. The marginal effect of emissions also simply equals the average effect, or the effect of the first unit of emissions. Generator i’s marginal damage is then 6D- 30 . - ——Z‘il<>1 (2.3.) Thus, marginal damages caused by generator i are the damages that any ton of S 02 from this generator causes, and are independent of the level of total emissions at this generator as well as at other generators. Figure 2.1 shows the distribution of marginal damages across generators in different 231 control for the state demographics (refer to column three in Tables 3.1 and 3.2), so if different age groups have different responses to 502 concentrations, damages to the two groups are estimated separately and added. 110 states. The figure shows that generators in low populated parts of the US and near US borders and coasts cause the lowest marginal damages. The US average of these damages, weighted by the amount of regional emissions under the system of tradable allowances scenario, is $5,240 per ton of emissions. The range of estimated marginal damages in Figure 2.1 is very similar to the range of $1,743—9,649 in Burtraw et al. [1998b], who use the same source-receptor relationships and data from the EPA [i]. In comparison, Shadbegian et al. [2004] estimates marginal damages to be between $10,000—20,000 for 80% of generators, with a median of $15,000. Rezek and Millea [2003], on the other hand, estimate the average marginal damage to be only $2,500, with a range of $650—4,500. Their study, focusing on the Eastern US, finds that the marginal damages are the highest in the North-Central and the Northeastern US states, while they are the lowest in the Atlantic and the Southeastern US states. Figure 2.1 agrees with these findings. Next section discusses the process of calibrating unknown parameters using data avail- able from the above sources. Section 2.8 presents the results of my energy model under the three environmental policies, and computes the impacts of the estimated $02 emissions in dollar terms using the above distribution of marginal damages. 2.7 Energy Industry Model Calibration I construct a model of the energy industry that incorporates realistically the relation- ships among all major participants in the US energy industry. I use empirical data on individual agents and their mutual relationships in the market. Nevertheless, a number of parameters in my model must be calibrated due to imprecise evidence on their values. I use data on the industry and the generator level described in Appendix A.5 to fix all known model parameters to exact values or narrow ranges. The parametric forms used for all model functions are based on the available empirical evidence, but may be the reduced 111 9,500 i— D Constant Marginal Damages l r 7.500 l 8,500 f ' _ Hl'n F l P 5,500 —;-]‘—[ I I y-[fl—H—r— 1— ~FH~ l l I l] 4,500 I].—]l—>—(~.—»—.)——_.]_...[_Jt_.._,._,)_[._._,,_,_.,_,,_,,_,,_,,__,_,_, [n 3.5w-1 r—«t—tr-qn-r—dv—i—ti-tr-«r—fih—1~——r—1r—)—~—1~)—<—AH—_~_.—(_g 2,500, —~—~~—___~_~_____ ________wt__s_. 1,m riI I-rflIflInfi TflIflIflI I I I I I I I I I I I I n I I I I I II I I I I I I I I I I I I I 2 Figure 2.1. Marginal Damages from $02 for Generators in Different States (%)—States Ordered by Concentrations under System of Allowances _ 112 representations of the true relationships among variables. Parameters known imprecisely for individual generators are allowed to adjust (within an allowed range) in my model to a level that achieves the greatest fit of my variables of interest with their historic values.24 Paul and Burtraw [2002] report that they calibrate their model to account for omitted costs, effects of special programs present at selected generators (such as long-term fuel supply contracts) and unknown demand shifters. In the process of calibration of my numerical model, I select a multi-objective function that represents well the measure of fit of my model to the actual US energy industry. The variables that help me measure the fit of the model are those that are determined endogenously in the model, report on the performance of my model in an important way, jointly ensure that the superior fit of one variable is not detrimental to the fit of another variable (such as prices, and quantities), and are observed in my historic data. The fit of my model is measured in five dimensions: generators’ energy output, 302 emissions and emission-abatement intensity, and customers’ consumption and prices. There are different ways to calibrate models with multiple objectives, including linear weighting (assigning relative importance to deviations in each variable); lexicographic cal- ibration (calibration of one variable at a time in the order of their importance); hierarchi- cal optimization (allowing only limited deviations in certain variables); goal programming (defining an aspiration level for the fit of each variable); or multi-attribute utility analysis (specifying an explicit relationship how the deviations in different variables are traded off) [Evans et al., 1991, Kalvelagen, 2002, Steuer and Na, 2003]. Paul and Burtraw [2002] report that they calibrate generators’ prices first, and then consumer demands. With- out guidance on the relative importance of individual variables to the performance of 24H, for instance, marginal costs of service depend on the number of customers or demand by each customer (as noted in Crew and Kleindorfer 1979, pp. 161—166), parameters C 1,- and 02,- are calibrated to provide the best fit, given such unobserved nonconstant costs. 113 my model, or on the goals of the fit in each variable, I use the linear weighting method [Kalvelagen, 2002, Malczewski, 1999, Steuer and Na, 2003]. I fit all five variables to their historic values simultaneously, while I vary all unknown and uncertain parameters in the model. The following expression is minimized. " 2 _ 2‘2 ._~.2 d-—d- ._ . 1 [(12 (1,] 1 [J J] 1 [J J -:—=- +—:: —=—— +—: 12. q; J . dj J j J 4 2 JZiEjlz 8i éi) Eiai “92"2 —— .2 +J:[e +[ 5i j (23) In the expression, hats above variables represent values derived in the model, and tildes represent variable means. Deviations between model variables and their historic values are included, for: generators’ output; state-level consumption levels, prices and emissions; and national emission-abatement levels. These deviations are normalized by the variable means, to avoid issues with variable units and to define deviations in percentage terms. In Equation 2.32, individual parts of the objective carry a weight. There are many weighting schemes that would allow me to choose among the Pareto-efficient calibration outcomes, in the sense of a trade-off between the fit of individual variables that cannot improve the fit of all variables simultaneously [Kalvelagen, 2002, Suntornsaratoon et al., 1999]. In Equation 2.32, the weights on individual variables are the inverses of the number of deviations that are summed for the particular variable. I and J stand for the number of generators and states in the model. The relative deviation of generators’ mean output, emission-level or abatement intensity is thus given the same weight as that of the mean state consumption or price. These weights were selected so that a percentage deviation in any model variable is equally undesirable. These weights do not affect model behavior under any policy scenario, and do not drive my results. Section A.2 justifies the use of my 114 weights, and reports on other evaluated weights, and the sensitivity of the fit of individual parameters and variables to the changes in weights. With no information on the levels of model parameters, I would allow them to vary without bound, and my model could fit the historic variable values perfectly. Paul and Burtraw [2002], for instance, achieve perfectly fitting prices by not restricting the adder that their calibration assigns to the costs of each generator. Using these prices, they estimate customer demands, varying the demand shifters without restriction to obtain perfectly fitting values. Imposing the bounds I have for most model parameters, I am not able to achieve perfect fit of all model variables, but I force the model to adjust variable levels so that one variable is not estimated precisely at the expense of a model parameter, or another variable. Table A.1 in Appendix A.2 reports on the ranges for each parameter used in my calibration. The advantage of restricting the ranges of my calibrated parameters is that they become more robust to any imprecisions in my historic data (due to data entry issues, or historic shocks to a variable that are not explained by the correct functional forms). Such calibrated parameters can be used to find more consistent fitted value of the variables across policy scenarios. While parameters calibrated without any restriction can lead to a perfect fit of all variables to their historic values, they may lead to poor predictions of variables in all alternative scenarios. As a measure of fit, I have computed the sums of squared explained (SSE), unexplained (SSR) and total (SST) variation in q}, 22-6 j 6”,, dj, 133' and 5.,- across generators i and states j, weighted as in the objective function. I then derived the resulting R2 as the ratio of SSE to SST. For my model, using the objective function in Equation 2.32, R2 equals 0.702, implying that 70.2 percent of variation in the five model variables of interest is explained using the assumed functional forms and the allowed parameter ranges. Figure A.1 in Appendix A.2.1 shows histograms of mean deviations of the simulated 115 values of model variables from their observed levels. Model variables plotted in the figure are constrained by the known values or ranges of values of model parameters, and by zero, which affect their distribution around the historic values. Due to the effective upper bounds on generator’s volumes produced and transmitted, due to quadratically rising marginal costs and information on factor prices and other cost parameters, left skew in the distributions of output and consumption levels is possible. Since emission levels depend on the generators’ optimal intensity of abatement, which is estimated within the model and presumably differs from empirically observed levels (see Footnote 20 in Section 2.6.3), deviations in emissions have a particularly wide distribution. Prices are effectively constrained by all of the above bounds and by non-negativity. Since prices are used in this model to make all markets clear, and bring together generators of different type, size and emission factors, I observe a small proportion of prices that are far below their expected values. Comparative statics in the simulation have verified that the calibrated model predicts correct qualitative responses of main model variables to stringency of environmental poli- cies, and to shocks in the cost, demand and capacity parameters. As expected, more stringent environmental policy results in lower emissions (by definition), greater abate- ment costs and abatement intensity, higher energy prices and lower energy output levels. Positive shocks to generating costs lead to higher energy prices, reduced consumption and output levels, lower emissions, and lower abatement intensity and abatement costs. An increase in the generating or transmission capacity has the opposite effects, because they effectively lower generators’ costs of generation and transmission. An increase in de- mand shifters (53- results in greater generating and emission-abatement intensities, greater generating and abatement costs, and higher energy prices. The energy industry model described in Sections 2.3 and 2.4 was calibrated using his- 116 toric data on the state and the generator level. After the calibration run, since generators’ historic physical capacities for energy production and transmission are observed, I verify that the estimated levels did not violate these capacities.25 With model parameters and variable starting values fixed at their calibrated levels, I impose the alternative environ- mental policies on the industry, and observe the behavior of all agents and the entire market. The emission tax policy is used as a benchmark scenario, since it is expected to lead to the same market solution as the allowance trading system. The tax is set to achieve the same aggregate emission level as the system of allowances currently used in the US. Emission tax scenario is also more convenient numerically. Compared to the allowance trading scenario, the emission tax does not require simultaneous clearing in the allowance market, since the tax is assigned exogenously. Due to a smaller number of model equations to solve, each with a small imprecision, the emission tax scenario is expected to lead to more precise results, which is particularly desirable in the calibration run of the model. 2.8 Energy Industry Model Results Sections 2.8.1 to 2.8.3 present the model results under each environmental policy. Generators’ output and emission levels, emission-abatement intensity, the resulting 502 concentration levels, and consumers’ prices and consumption levels are reported. Section 2.8.1 discusses the results of the emission tax scenario. Since this scenario is used as a benchmark case under which the industry model is calibrated, in addition to reporting the values of the model variables, this section evaluates the fit of these values to the historic values observed in the US in 1996. Sections 2.8.2 and 2.8.3 present the results of the 25m the simulation of the alternative policy scenarios, I impose the capacity constraints on generators’ output and transmission to other NERC regions explicitly. Nevertheless, these constraints are binding for less than ten percent of all generators. 117 allowance trading, and the emission caps scenarios. The values in all tables that follow can be compared to the 1996 levels under the system of tradable emission allowances, obtained directly from the data and presented in Table A.5 in Appendix A.5. Sections 2.8.4 and 2.8.5 compare the impacts under the alternative environmental policies on 8'02 concentrations and health damages. 2.8.1 Emission Tax Scenario Results Table 2.3 reports on the average US energy price, aggregate energy output and con- sumption, and 502 emissions and abatement intensity, under an emission tax of $90 per ton of 502. This value is the mean 1996 price of allowances (EPA b, EPA o). For variables whose historic values I can observe, I report the R2 as a measure of fit, as the ratio of the total historic variation on state level in a variable that is explained in the simulation. The rest of variables were compared against industry-wide statistics reported annually in DOE—EIA [(1]. Table 2.3 shows that the model explains 56.9—75.3% of the historic state-by-state vari- ation in output, consumption and emission levels, and 23.4% of all price variation. Since I lack information on generators’ emission-abatement intensity, I cannot evaluate the fit of this variable on smaller than a national level. Similarly, information on energy industry revenues and emission-abatement costs is available only at the national level. At this level, emission-abatement intensity in the model of 21.91% compares to approximately 30% observed historically26, industry revenues of $335.6 billion compare to $260.4 bil- lion, and abatement costs of $2.6 billion compare to approximately $2.5 billion. Figure A.1 in Appendix A.2.1 presents histograms of the fit of prices, consumption and output levels, and emissions with the historic data for all US states. 26This figure, however, includes the effects of a common practice in the 1990s to store emission allowances for future use. 118 Unlike volume variables, prices are not constrained above by any physical capacity. With inelastic demand for energy and with physical constraints on the volumes of pro- duction and emissions, prices effectively ensure that all volume variables in the model fit. Imprecision in prices can help achieve a better fit in output, consumption, emissions and emission abatement, so the weaker fit of prices in this model is expected. Good fit of the volume variables also indicates realistic generating and transmission constraints in the model. Variable Industry Value R2 Avg. Consumer Price ($/MWh) 91.35 0.234 Energy Output (TWh) 4,080.74 0.643 Consumption (TWh) 3,673.38 0.753 8'02 Emissions (1,000 Short Tons) 9,226.83 0.698 Avg. Abatement Intensity (%) 21.91 — Revenue ($ million) 335,579.96 - Abatement Cost ($ million) 2,555.96 - Emission Tax Expenditure ($ million) 830.41 — Table 2.3 Aggregate Statistics: Emission Tax Scenario (Tax of $90/ Ton) Table 2.3 shows that with the emission tax of $90, energy industry spends $830.4 million on the tax itself and $2.6 billion on emission abatement. This result is consistent with the previous estimates of the industry-wide abatement costs, between $2.5 billion [EPA, f] and $3.2 billion [Congressional Budget Office]. Table 2.4 gives the range of generators’ emissions and concentration levels across the US states resulting under the emission tax scenario. The table accounts for background emissions of 302 from non-utility sources and from abroad [Argonne National Lab, Bas- com et al., 1996]. The average concentration level is obtained by weighting the state concentration levels by state population. The averages of both variables are closer to the lower bounds of their ranges. Histograms A.4 in Appendix A.2.1 show that the distrib- 119 ution of $02 concentrations across the US states is skewed to the right with a long tail, implying that hot spots of pollution may be a problem in parts of the US. Interestingly, the average level exceeds the median for the state emission levels, but the ranking is reversed for the state concentrations. One reason is that adding 302 emissions from other than energy producing sources changes the distribution of total state-by-state emissions. Another reason is that the effect of generators’ emissions on 302 concentrations depends on the generators’ location. Redistribution of emissions across generators thus changes the resulting concentrations across US states. Emissions Concentrations State Minimum 0.17 3.06 State Average 5,897.65 23.15 State Median 5,519.11 28.16 State Maximum 31,423.11 84.97 Table 2.4 5'02 Emissions (Pounds per Sq. Mile) and Concentrations (pg / m3) by State: Emission Tax Scenario (Tax of $90/ Ton) 2.8.2 Allowance Market Scenario Results The following two tables show the energy market solution under the tradable allowance market scenario. The equilibrium allowance price is $89.35 per ton of 302, and 888,021 allowances get traded in the market, which is comparable to the $100 allowance prices and the volume of trade at 540,000 allowances reported in Ellerman et al. [1997]. Comparing the results to Tables 2.3 and 2.4, we see that the emission tax and the allowance trading scenarios achieve very similar values for output levels, prices, emission-abatement efforts, and the resulting S 02 concentration levels. Small differences are attributable to residuals in the alternative versions of the sim- 120 ulation. Since the program must clear an extra market under the tradable allowances scenario, infeasibilities in model equations (on the order of 10—9), allowed by the model- ing software, distort the outcome under this scenario.27 Equations particularly sensitive to these infeasibilities are those determining prices, market shares, and the abatement intensity in percentage terms (Equations 2.23, 2.24 and 2.21). The simulation confirms that in the emission allowance market, with E allowances freely tradable subject to no restrictions, the market solution is the same as under the emission-tax scenario with the tax set to achieve the aggregate emissions of E. Variable Industry Value Avg. Consumer Price ($/MWh) 87.10 Industry Output (TWh) 4,108.66 Consumption (TWh) 3,702.22 502 Emissions (1,000 Short Tons) 9,200.00 Avg. Abatement Intensity (%) 21.11 Industry Revenue ($ million) 325,635.75 Industry Abatement Cost ($ million) 2,495.33 Table 2.5 Aggregate Statistics: Tradable Allowance Scenario (9.2 Million Allowances with Equilibrium Price $89.35) Emissions Concentrations State Minimum 0.20 3.10 State Average 5,897.65 23.20 State Median 5,491.03 28.18 State Maximum 30,854.16 84.69 Table 2.6 302 Emissions (Pounds per Sq. Mile) and Concentrations (pg/m3) by State: 'Ifadable Allowance Scenario (9.2 Million Allowances with Equilibrium Price $89.35) 27When either simulation is run starting near the solution to the emission tax scenario, both policies quickly find the same solution, in that starting point. 121 2.8.3 Emission Cap Scenario Results The following tables report on my model results under the emission cap scenario, with the cap on generators’ emissions based on their historic production levels. A cap achiev- ing the same aggregate equilibrium emissions as under the other scenarios, 9.2 million tons, was at 72% of the pre—regulation aggregate emission level. Caps to emit 14.34 mil- lion tons of 502 were assigned. Only 32.2% of all generators were constrained by their emission caps, while the rest of generators had equilibrium emissions strictly below their caps. Table 2.7 shows that the average price of energy is higher and output is lower than under the previous two scenarios. Due to higher energy prices, consumption falls, and as a result output falls and the level of abatement falls as a percent of the equilibrium emissions. Aggregate emissions are very close to the level under the emission tax, with a small difference attributable to the small allowed infeasibilities in model equations (dis- cussed already in Section 2.8.2) and to the limited number of iterations the model used to converge.28 Industry revenue rises due to higher energy prices and low price elasticity of demand 5. Since any non-binding emission caps cannot be transferred among generators, generators cannot directly offset each others’ abatement intensity. Generators with high marginal abatement costs cannot buy a greater emission cap from lower cost generators. To trade the requirement to abate emissions indirectly, generators can trade their energy output, subject to capacity constraints and transmission charges. Because of the limited options for environmental compliance, the industry-wide abatement costs rise by $223 million compared to the allowance trading scenario even though the industry output and the 28The model iteratively resets the emission cap to achieve the target level of emissions, and with every iteration gets closer to its aggregate emission goal. Due to time considerations, the model was run only ten times in the GAMS program. During the last run, with emission caps already determined, an additional limit of 30,000 iterations was used in the model for finding the equilibrium values of all of the model variables. 122 average abatement intensity fall (the last fact is consistent with Tietenberg 1995). Variable Industry Value Avg. Consumer Price ($/MWh) 97.22 Industry Output (TWh) 3,954.04 Consumption (TWh) 3,539.56 502 Emissions (1,000 Short Tons) 9,201.90 Avg. Abatement Intensity (%) 18.01 Industry Revenue ($ million) 357,484.91 Industry Abatement Cost ($ million) 2,717.88 Table 2.7 Aggregate Statistics: Emission Cap Scenario (Caps of 72% of Historic Emis- sion Levels) . Table 2.8 shows the range of emissions and air concentrations observed across US states under the emission cap scenario. Compared to Tables 2.4 and 2.6, the distribution of state emission levels changed, resulting in a higher minimum and median levels, but a lower maximum. The changes from the other scenarios thus occur in states with low and high emission levels. These emission levels translate into a distribution of air concentrations of $02 that has a higher minimum, median and, interestingly, even maximum levels, but a lower mean than the other policy scenarios. Under the emission caps, more states experience an above-average concentration level, but the average of these concentrations is lower (i.e., smaller area under the distribution of concentrations). Emissions Concentrations State Minimum 0.48 3.27 State Average 5,898.85 23.02 State Median 6,289.23 28.37 State Maximum 30,773.81 85.28 Table 2.8 5'02 Emissions (Pounds per Sq. Mile) and Concentrations (pg/7113) by State: Emission Cap Scenario (Caps of 72% of Historic Emission Levels) 123 2.8.4 Comparison of $02 Concentrations The three policy scenarios resulted in almost identical aggregate emission levels, 9.2 million short tons, as I desired, with minor deviations due to residual infeasibilities in the equations of the numerical model. These deviations represent less than 0.03% of the level of emissions. Comparing the ranges of statewide concentration levels in Tables 2.4, 2.6 and 2.8, it is interesting to note that higher nationwide emission levels do not necessarily translate into higher concentration levels.29 Emission caps based on generators’ historic output levels are estimated to have the highest minimum and maximum levels of concentrations, but also the lowest average levels. The allowance trading scenario results in a lower minimum, median and maximum levels of concentrations, indicating that it does not yield significant hot spots of pollution, in agreement with Ellerman et al. [2000], Swift [2000]. Figure 2.2 shows the distributions of 5'02 concentrations across states under the sys- tem of tradable allowances. States are ordered by their concentration levels. Individual state levels are connected by a line. The fact that this line is curved in confirms that more US states have lower rather than higher concentrations, and that the distribution of concentrations is skewed to the right (refer to histograms A.4 in Appendix A.2.1). Thirteen states have 302 concentrations below ten, and twenty-eight states below thirty micrograms per cubic meter. Only ten states have concentrations above sixty micrograms per cubic meter. The western and northwestern states have the lowest concentrations (below 10 45:73), followed by west-central states (15—20 41%), and southern and south- m m central US states (mostly 25—40 51%). Northeastern and north-central states have overall high concentrations under this policy (their arithmetic average is 52 14%). The highest m 29Table 2.9 shows that the estimated differences in aggregate damages are also not explained by the differences in aggregate emission levels. 124 75 ”Mu—.1 UEmissionAllownces _' f so ”Hts—HM,“ _,(t' 45 fi’~-[L—~—-—_n.—___..,. 30 1.7 Haws—[Heu—Hj—H-qu—uL—H. _ 'f 15 H—r-Hi—H—HHJHFr—i-‘Hr-l-r-1-4~-‘r-~—~-+~~H~i-r-][ r "’1 onTnTn'H'l-l" lillllIIIVIIIIIIlIIIIVIIIIIIIIII s esgassasssssseesssazss:2sssizsgsssezasssaasgnsz Figure 2.2. .302 Concentrations under the System of Tradable Allowances (%)—States Ordered by Concentrations m concentrations are in the coal producing east-central region (over 72 #3" These results agree with a large number of empirical studies that have found that 502 pollution is a much smaller problem in the western half of the US, than in the eastern half, and that the greatest pollution levels are in the northeast and the east-central region (for instance Shadbegian et al. 2004). Figure 2.3 shows the differences in concentration levels under the emission tax and the emission caps scenarios, against those under the system of tradable allowances. Dif- ferences in concentrations, rather than the actual values of the concentrations are shown for clarity of the comparison. The states in Figure 2.3 are again ordered according to their concentrations under the system of tradable allowances. As expected, the emission tax leads to a very similar distribution of concentrations as the system of allowances (the 125 4.5 J :1 Emission Allowances x Emission Tax 0 Emission Caps 3.0 i o o O O o o 1.5 ‘ o o o o o 0 0 oo o O 0 o o Xe xx X x 0_0figfifiaaaggmgaogsgoufiuéfigjogmmébéfimfia653800550 DOD on x0 0 O 4.5 « ° ° 0 o '3.0 I I T I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I - -.i 52958 252§° 5252255 211‘?!)”5°S28=28§B2§2¢E§22285§§53 Figure 2.3. Differences in 502 Concentrations against Those under the Sys- tem of Tradable Allowances (%)—States Ordered by Concentrations under m System of Allowances line is close to zero for all states). Any differences are attributable to the small residual infeasibilities in the solution to the simulation. Interestingly, emission caps lead to lower concentrations especially in states in the second quartile of the range of concentrations (refer to histograms A.4 in Appendix A.2.1), while they increase pollution in states in the third and fourth quartile of the range of concentrations. Any improvement in aggregate damages under the emission caps must therefore come from the low concentrations that they achieve in states that have low concentrations under all policies, and especially in California and Texas. Figure 2.3 shows that the emission tax and the system of tradable allowances lead to lower concentrations than the emission caps in northern states, the northeastern states and several states in New England—for instance, Minnesota, Wisconsin, New Jersey and 126 Rhode Island. This agrees with the findings in Burtraw and Mansur [1999] that the trade of allowances resulted in particularly low concentrations in the northeast. The emission caps, in comparison, lead to particularly low levels of concentrations in several states in the southeast and the southwest, such as California, Oklahoma, Texas, Arkansas, Louisiana and Mississippi. These states incidently have large populations. 2.8.5 Comparison of 502 Emission Damages Equation 2.29 in Section 2.6.3 shows that damages from 5'02 are a function of $02 concentration levels in each state as well as the size of population affected by those concentrations. Given that population size and demographics vary across US states, concentration profiles under each regulatory policy can lead to different estimated health impacts in each state and nationwide. Table 2.9 shows the aggregate health damages resulting under each policy scenario. Emission caps lead to the lowest morbidity as well as mortality damages, and total dam- ages lower by $452 million than those under the allowance trading market currently in place in the U330 Emission tax and the system of emission allowances lead to very similar estimated damages, that differ by only $2 million on the national level. This is good news since these policies were expected to perform identically. Morbid. Damage Mortal. Damage Total Damage ($ million) ($ million) ($ million) Emission Allowances 7,127.67 41,030.24 48,157.91 Emission Tax 7,127.88 41,027.60 48,155.48 Emission Caps 7,065.60 40,639.81 47,705.41 Table 2.9 5'02 Health Impacts under Alternative Policies 30Table A.13 in Appendix A.7 reports on the impacts of the concentration levels under each policy scenario by individual health-impact pathway. 127 Emission caps helped to reduce 502 concentration levels in states with overall low concentrations under all policies, particularly several southwestern, midwestern and south- eastern states. These states incidentally have high populations. Thanks to this, emission caps achieved the lowest aggregate health damages among the three policies, even though they led to significantly higher concentration levels in several northeastern and New Eng- land states. The system of allowances and the uniform emission tax lead to almost identical ag- gregate damages, as expected. This similarity of damages helps to verify that the greater difference between these two policies and the emission caps is a result of economic forces rather than computational imprecisions in the model. The difference in aggregate damages between the system of emission allowances and the emission tax, which can be attributed to model imprecisions, is $2.4 million. This corresponds to only one half of one percent of the $452 million difference between these two policies and the system of emission caps. The fact that even $452 million represents only one percent of the absolute level of aggre- gate damages under all policies stems from keeping aggregate emissions constant across all policies. Regional redistribution of these emissions has limited power in reducing the national sum of damages. My estimates of the aggregate damages are in line with the previous literature eval- uating similar policies. American Lung Association [b] and Centers for Disease Control estimate the annual health damages of $40—$60 billion. The estimates of annual damages vary greatly across studies and years, and reach as high as $167 billion in 2010 [Schneider, 2004a,b]. Shadbegian et al. [2004], using high marginal damages of about $15,000 per ton of emissions and a different sour-receptor diffusion model, estimate the savings in aggregate damages of $1.3 billion under the emission caps, as compared to the system of tradable allowances. Since the policy scenarios compared in my analysis assume identical, 128 and low aggregate emission levels (compared to the pre-19908), figures in Table 2.9 and their differences are lower than in studies evaluating pre-regulation levels or comparing vastly different modes of regulation. Burtraw and Mansur [1999], for instance, find that the system of tradable allowance achieves $125 million lower health damages than the emission caps of the same stringency, as in my study, but they assume imperfect foresight and suboptimal abatement technologies at a number of generators. Rezek and Millea [2003] estimate annual benefits under the Title IV of $14 billion, as compared to the 1980 emission level. Burtraw et al. [1998b], EPA [i], Hubbell [2001] estimate the benefits in 1996 due to reduced mortality of around $5 billion compared to 1990, and benefits of $13 billion in 2010. Figure 2.4 presents the health damages realized in each US state under the allowance trading scenario. This figure significantly differs from Figure 2.2, because here the 5'02 concentrations in each state are converted to health impacts, and multiplied by the mon- etary value of the impact and the size of each affected segment of the population.31 Figure 2.4 shows that the northwestern states, with low 802 concentrations, inciden- tally have low population levels, and thus enjoy the lowest annual statewide damages from the energy industry emissions, around $78 million (the average of the left-most 12 states). Large states, such as California, Florida, Michigan and Texas incur high damages ($1,698, $1,815, $1,792 and $1,570 million, respectively) even when their 302 concentra- tions are low. States incurring the highest damages are New Jersey, New York, Ohio and Pennsylvania, with annual damages of $2,616, $4,542, $4,404 and $4,246 million. Figure 2.5 shows the spatial distribution of the differences in damages between the emission tax and the emission caps scenarios, and the system of tradable allowances. Differences, rather than actual values of the damages, are shown for clarity. This figure 31Since marginal damages are per ton of emissions, for the emitting state, whereas concentrations are in micrograms per meter, in the receptor state, I cannot simply multiply values in Figures 2.1 and 2.2. 129 4,500 i F 4,000 _ C1 Emission Allowances 3,500 _ 3,000 J _ 2,500 a ‘_ ___ 2,000 r-l —— H H w l l F 1,500 .— >— H —l L— —‘ i—l )1 1,000 _ _,___-__AH_M 5m m H H H i-l fl? .— r— ‘fl—l H H H o n III‘Ia AI n I‘L‘LII-l Ila In InI InIflIflI ”InInI I I HIHI I II1I1.1I I I I III” IHI IflI I I I I 529533 2S§§285222% ’aoszazzsgs we 32322<225= Figure 2.4. Health Damages under the System of 'Ifadable Allowances ($ million)—States Ordered by Concentrations under System of Allowances confirms that the system of tradable allowances and the emission tax lead to very similar levels of damages in each state, while emission caps redistribute damages across several important states. California, Ohio and Texas receive significantly lower damages (by $478, $66 and $224 million, respectively), while Massachusetts, Michigan, New Jersey, Virginia and Wisconsin see higher damages ($52, $35, $198, $39 and $45 million). In percentage terms, the greatest fall in damages from the system of allowances to emission caps occurs in California (-28%), Texas (-14%), Oklahoma (41%) and Nevada (-9%), while the greatest increase occurs in New Jersey (+896), Wisconsin (+7%) and New Hampshire (+670). In sum, results in this section indicate that the choice of policy instrument affects the level of aggregate damages even when the aggregate emissions are held constant. Emission caps based on generators’ historic production levels are estimated to lead to $452 million lower aggregate damages than the emission tax or the currently used system of tradable 130 200 Cl 100 -1 00 -200 O -300 400 . . 0 Emission Allowances x Emission Tax .500 ° 0 Emission Caps ¢> h och 2w 2 ‘4 «2 omfi ozgaw zo§§285§2x505$ fig§zéi<8zozz- Eh§zo28§§§53 Figure 2.5. Differences in Health Damages against Those under the System of 'Ifadable Allowances ($ million)—States Ordered by Concentrations under System of Allowances 131 allowances. Furthermore, damages do not change uniformly for all regions across any two policies, but favor one group of states at the expense of other states. Among the compared policies, emission caps lead to lower concentrations and thus also damages in the southeastern, south-central and southwestern states, including the heavily populated states of Florida, Texas and California. Emission tax and the system of emission allowances, on the other hand, favored the northern, northeastern and New England states, including New Jersey, New York, Virginia and the Great Lakes states.32 2.9 Conclusions A large body of literature has found that the environmental benefits under the Title IV program of the 1990 Clean Air Act Amendment greatly exceed the costs of abatement borne by generators under most parametric assumptions. However, most studies have compared the Title IV program to the pre-Title IV state of the industry, and policies leading to significantly higher 302 emission levels than the Title IV. The large estimated benefits of the Title IV stem from the reductions in emissions. Since the EPA has different options as to how to achieve these levels, it is more appropriate to compare the Title IV to feasible policies with the same stringency. In this paper I have tested the predictions made in Weitzman [1974], Mendelsohn [1986] and Stavins [1996], and previous results in Haas [1999], Ellerman et al. [2000] and Shadbegian et al. [2004], regarding the relative performance of the price and the quantity regulation in limiting health damages from 302. The model in this paper has been 32In particular, the five states where emission caps achieve the lowest concentrations compared to the system of allowances have 62 million residents (and 82 million in the top ten states), while the five states with the highest relative concentrations under this policy have only 22 million residents (38 million in the bottom ten states). The differences in concentrations across the two policies are large in the heavily populated states where emission caps are winning in terms of concentrations, but are low in the heavily populated states where emission caps are losing. 132 careful to use only policies that have been considered by the EPA, are established in the literature and are directly comparable—those that lead to the same aggregate emissions. Even though the aggregate emissions were held unchanged across policies, significant redistribution in energy generation, emissions and the associated damages resulted across US regions. In agreement with Ellerman et al. [2000], I have not found evidence of hot spots of pollution under the system of tradable allowances. This policy actually led to more homogeneous concentration levels across the US than the emission caps. Even though none of the policies led to extreme concentration levels in any part of the US, the aggregate differences amounted to hundreds of millions of dollars when converted to the resulting health damages. Emission caps were estimated to achieve the lowest aggregate damages annually ($47.705 billion), outperforming the Environmental Protection Agency’s system of allowances by $452 million. This result agrees qualitatively with the findings in Haas [1999] and Shadbe- gian et al. [2004], even though they estimate the difference to be over one billion dollars. The system of tradable allowances and the uniform emission tax lead to very similar distributions of 502 emissions and concentrations, as expected. Hence, they also lead to very similar health damages, of $48.16 billion nationwide. The similarity in performance between the emission tax and the system of tradable allowances stems from their identical conceptual impacts on generators’ behavior at the margin. Any difference between them came from the limitations in my computational model. Compared to the emission tax and the tradable allowances, emission caps lead to the lowest S 02 concentrations in the southern US states, but the highest concentrations in the northern and northeastern states, in agreement with Shadbegian et al. [2004]. However, since emission caps lead to significant decreases in concentrations and damages in several highly populated states in the south, they outperform the emission tax and the system of 133 tradable allowances in aggregate damages. These results provide evidence that generators in different parts of the US and, impor- tantly, in regions with different sensitivity to pollution, react differently to the alternative modes of regulation. In our controlled model, this arises from the difference in gener- ators’ cost functions and the allocation of emission caps, and to a smaller degree from the differences in regional demands and delineations of regional boundaries. Whether there are underlying reasons for a relationship between generators’ costs and environ- mental damages (for instance, Morgan and Shadbegian 2003, Wolverton 2002a,b), or it exists by chance [EPA, h], our results are in line with the theoretical prediction in Stavins [1996], that emission caps tend to be preferred to price instruments in the presence of a correlation between generators’ costs and damages. I have estimated significant differences in the aggregate and regional damages across individual policies, that are due to the differences in the equilibrium 5'02 concentra- tions. However, since the relationship between concentrations and actual damages has not been established with certainty in the medical or economic literature, it deserves fur- ther scrutiny. The third chapter of this dissertation compares the health damages among the three environmental policies under different assumptions on the impacts caused by marginal units of 302 concentrations. 134 THE IMPACT OF RISING MARGINAL RESPONSES TO 802 ON HEALTH DAMAGES The relationship between emission levels and their damages is a primary determinant in the selection of a regulatory environmental policy. If the marginal damage function rises faster in emissions than firms’ marginal abatement cost function, caps on emissions are expected to be preferred to price instruments, in terms of the expected environmental damages and abatement costs, while if it rises slower, price instruments are expected to dominate [Upton, 1971, Weitzman, 1974]. If the marginal abatement costs and the marginal damages are correlated for individual firms, however, this ranking may be over- turned. Positive correlation favors caps, while negative correlation would have to be strong to overturn the preference for caps to favor price instruments [Stavins, 1996]. If firms with lower emission-abatement costs are located in more sensitive areas, for instance, emission tax or a system of tradable allowances may lead to an improvement in environmental damages compared to emission caps, because more emission-abatement activity occurs where it is more needed. The empirical economic literature has not verified these theoretical findings thoroughly. No economic studies comparing alternative environmental policies have scrutinized the marginal damage function, and all have assumed it to be constant for all units of pollution. All the while, medical literature acknowledges that the exact form of this function is not certain, and that constant marginal damages are used simply because they cannot be statistically ruled out, even though other forms with increasing marginal damages have been suggested. This paper fills an important gap in the empirical literature by evaluating the validity of the theoretical results in Stavins [1996]. It evaluates damages caused by three competing regulatory policies under different slopes of the marginal damage function, and tests 135 whether price and quantity regulatory instruments change ranking in the damages as the marginal damage function becomes steeper. As Chapter 2 of this dissertation has shown, emission caps lead to lower damages across the US than a uniform emission tax and a system of emission allowances under constant marginal damages Given this result, I test whether this ranking is sensitive to the slope of the marginal damage function, particularly for slopes that medical evidence currently supports. Health damages account for the vast majority of impacts of pollution [Argonne Na- tional Lab, Burtraw et al., 1998b, EPA, i], and have often been evaluated alone, without consideration for other, non-health damages. Our knowledge of health damage valuation is particularly sparse in our discussion of the benefits and costs of emission abatement [Burtraw et al., 1998b], so my focus is on the in-depth study of variations in the health damages across policies, across the slopes of the marginal damage function, and across US regions. In this paper I abstain from the discussion of other measures of aggregate welfare under each regulatory policy, including generators’ profits, consumer surplus or government revenue. This allows me to focus on residents’ health responses, without specifying the regulator’s objective function. I also omit the discussion of generators’ emission-abatement decisions. The analysis of damages is itself a rich area giving rise to useful conclusions about the health impacts of each policy, and the discussion of firms’ costs would compromise the detailed discussion of regional impacts. The energy industry is also not modeled explicitly here, so firms’ emission-abatement decisions are not part of this paper. Instead, equilibrium emission profiles are taken from the energy model in Chapter 2 of this dissertation. I compare three environmental policies that are well established in the economic lit- erature and that have been considered for control of sulfur dioxide (502) emissions in the US: a system of tradable allowances currently used by the US Environmental Pro- 136 tection Agency (EPA); a uniform emission tax; and a system of emission caps based on generators’ pre—regulation output levels. Each policy is modeled to lead to the same ag- gregate level of emissions, so that any differences stem from the regional redistribution of emissions under the alternative policies. These policies, and their impacts on the en- ergy industry, were introduced in the previous chapter. After I derive the state—by-state concentrations of S 02 under each policy, I compute their impact on human health using different assumptions on the parameters of the marginal damage function. I find that for all considered forms of the marginal damage function, the system of emis- sion caps leads to the lowest aggregate damages, outperforming the tradable allowances and the emission tax by up to $452.5 million. As the slope of the marginal damage func- tion increases, however, this advantage of emission caps over the two competing policies falls to $26.1 million. The advantage of emission caps in terms of environmental damages is never overturned completely for the considered functional forms, implying a negative but small correlation between firms’ abatement costs and damages, and confirming our preference for emission caps [Stavins, 1996]. I find that the marginal damage function would have to be steeper than what the current evidence suggests for price instruments to outperform emission caps in aggregate damages. Unfortunately, the $26.1 million difference appears to be in the range of a possible modeling error, since the difference in aggregate damages between the emission tax and the system of emission allowances scenarios—two theoretically equivalent scenarios—is itself $65.6 million. Nevertheless, given that the latter policies systematically result in higher aggregate damages than emission caps under all considered forms of the marginal damage function, it is most plausible that emission caps truly lead to a less harmful distribution of emissions even under this form of marginal damages. Since the system of emission allowances and the emission tax lead to very similar outcomes, whereas emission 137 caps perform differently under most scenarios, I confirm that the results are driven by economic forces under each policy, rather than by randomness in the model. $26.1 million, or even $452.5 million, is a small difference compared to the absolute level of aggregate damages under any policy. This, however, results from holding of the aggregate emissions constant under all three alternative policy scenarios. Regional redistribution of emissions therefore has limited power in reducing the aggregate damages, when the high levels of these damages are dictated by the amount of allowed pollution. System of tradable allowances leads to lower damages in the northern and northeastern states, by $390 million under constant marginal damages, and by up to $600 million under linearly rising marginal damages, compared to emission caps. Emission caps, on the other hand, lead to lower damages than the system of allowances in the southern US, including California, Texas and Florida. Under constant marginal damages, emission caps outperform allowances in this region by $840 million, while with linearly rising marginal damages, this difference grows to $670 million.1 These results stem from the differences in the distribution of 502 concentrations under all policies. Emission caps lead to particularly low concentrations in several heavily populated states in the southern US, but tradable allowances bring about more equally distributed concentration levels. As the slope of the marginal damage function increases, the advantage of emission caps falls. The true marginal damage function would have to rise at even a greater rate than what the current medical evidence suggests for the system of allowances to outperform emission caps in the aggregate damages. These results agree with Shadbegian et al. [2004] and Haas [1999] that the US Environ- mental Protection Agency’s (EPA) current policy leads to the deterioration in aggregate health conditions compared to a system of emission caps. This, moreover, holds for a 1Southern states, on one hand, and northern and northeastern states, on the other hand, have similar population levels (of approximately 100 million), so this comparison makes sense. 138 wide range of slopes of the marginal damage function. The system of tradable allowances redistributes $02 concentrations in an adverse way, and with these concentrations, the allowed slopes of the marginal damage function are insufficient to overturn the ranking of this policy against the system of emission caps. 3.1 Damages from 302 Concentrations Under an increasing marginal damage function, correlation of firms’ marginal abate- ment costs and their marginal damages may result from systematic differences in the emis- sion levels, and may be both positive and negative. Firms with high marginal abatement costs compared to other firms may decide to remove a lower portion of their emissions, or may shift some production and emission activity to other firms. In the first case, their emissions would be greater than at other firms, and so would be the damages that their emissions cause on the margin. In the latter case, their emissions would fall, and so would their damages on the margin. Empirically, the comparison of damages under the different policies depends also on the exogenous parameters determining firms’ costs, demands for firms’ energy, firms’ locations, and the allocation of the regulatory instruments [Tietenberg, 1995]. The exogenously given size of the affected population determines the damage that each unit of a firm’s emissions causes. When marginal damages rise in the regional pollution level, each firm’s marginal damages depend on emissions from other sources in the region. The impact of each regulatory policy on damages caused by each firm thus depends also on the policy’s impact on emissions from other sources. Regulatory policy may not only affect the aggregate damages, but may have vastly different impacts on individual regions, through its impact on regional pollution levels. Under each policy, some regions may receive less pollution and damages at the expense 139 of other regions, even when the aggregate damages stay unchanged. When the marginal damage function assumes a different slope, the estimated damages in each region will change relative to those in other regions even under the same environmental policy. Un- derstanding of the form of the marginal damage function is thus crucial to evaluating both the aggregate and regional impacts. Using empirically observed emission levels and reported health impacts, medical lit- erature has tried to estimate the form of the damage function. Due to great unexplained variation in the available medical data, the exact shape of the function remains unknown (for instance, Abt Associates a,b, Dewees 1991). Some studies report that linearity of the damage function (that is, constant marginal damage function) cannot be rejected statis- tically, and is thus retained by default, even though other functional forms fit the data as well [Krumm and Graves, 1982, Lave and Seskin, 1977, Lipfert, 1984]. Consequently, empirical economic literature assessing damages from 502 emissions has exclusively as- sumed constant marginal damages (for instance, Burtraw and Mansur 1999, Burtraw et al. 1998b, EPA i,m, Gray and Shadbegian 2002, Haas 1999). Since this assumption represents an extreme among its alternatives in medical literature—which all suggest nondecreasing marginal damages—it may bias results in favor of one policy over others. 3.2 Literature Since the 1995 implementation of the market of tradable allowance, the Title IV pro- gram of the Clean Air Act, several economic studies have evaluated the distribution of $02 concentrations and the associated environmental damages resulting under this pol- icy. Ellerman et al. [2000] found that redistribution of emissions due to allowance trading had a beneficial effect, since it incidentally induced the dirtiest generators, in the most polluted regions, to clean emissions most intensively. Burtraw and Mansur [1999], EPA [h] 140 and other studies including Chapter 2 of this dissertation have confirmed that allowance trading has resulted in a more equal distribution of concentrations across states than poli- cies with no emission trading that have led to similar aggregate emission levels. However, Shadbegian et al. [2004], Haas [1999], and Chapter 2 of this dissertation also show that, compared to policies that disallow the trade of emissions, Title IV has led to particularly harmful distribution of concentrations in terms of monetary damages. Chapter 2 of this dissertation has shown that Title IV gives several heavily populated US states very high pollution levels. Even though there has been a substantial volume of research on the health impacts of 5'02, there is still uncertainty about the exact way that emissions affect human health. There are many sources of this uncertainty [Krupnick and Morgenstem, 2002]. Modeling of the emission diffusion and decay may be imprecise. Background emissions from other sources, or the underlying population affected by the pollutant may be known imprecisely. Biological and behavioral adjustments of the population to pollution may affect the im- pacts. The impacts of a unit of air concentration on health, and its monetary value, may be unknown. Major uncertainty is due to our limited knowledge of the marginal health responses to different concentration levels of the pollutant [Curtiss and Rabl, 1996b, Freeman, 1996, Krumm and Graves, 1982, Lipfert, 1984]. Marginal damages may be constant, heteroge- neous across individuals or climate zones, or dependent on concentrations of other sub- stances and on other climatological conditions [Ruff, 1978]. Surveys of medical literature such as the American Lung Association [a] and the EPA [i] report ranges of estimates for the marginal effects, pointing out that these estimates may not apply to all units of concentrations. Although all estimates of marginal damages in the empirical studies are uncertain and 141 carry wide probability distributions around them, economic literature has taken them to imply linear damage functions, for simplicity or as a local approximation in comparisons of similar policies. Since economic literature compares policy scenarios with vastly different aggregate emission levels and different spatial distributions of emissions, this assumption may affect the results. As theoretical literature suggests, using only a constant marginal damage function when all of its alternatives are nondecreasing may systematically favor one regulatory policy over another [Dewees, 1992]. In 1995 the EPA [i] surveyed major medical literature of the health effects from air concentrations of sulfates, and reported all known pathways in which sulfates affect hu- man health. This study identified which impacts were most significant economically, and recommended further inquiry into whether marginal effects were constant or greater for higher concentrations of 502 for individual health-impact pathways. While most medical studies report constant marginal damage estimates for all health- impact pathways (for instance, [Chestnut, 1995, Dewees, 1992, EPA, i, T01 and Downing, 2000, Violette and Chestnut, 1983]), some medical studies (for instance, Curtiss and Rabl 1996b, Watson and Ridker 1984) and economic studies [Morgan, 1983, Tietenberg, 1992] have recognized that marginal damages may grow in concentration levels, but did not pinpoint a particular functional form.2 Dewees [1992] points out that most of theoretical economic literature allows for rising marginal damages (such as Baumol and Oates 1993, Mendelsohn 1986, Mills and Graves 1986, Ostro 1987, Pearce and Turner 1990, Seneca and Taussig 1974, Tietenberg 1992). Several studies have used a quadratic representation of the damage function, and thus a linearly rising marginal damage function, to illustrate the impacts of non-constant marginal damages [Hoel and Karp, 2001, Mendelsohn, 1986, 2h is possible to construct examples in which marginal damages fall in concentration levels—for instance, for extremely high concentration levels when the majority of population is already affected—but these scenarios are unlikely with our empirical evidence. Medical literature ignores the possibility of decreasing marginal damages. 142 Newell and Pizer, 2003, Quirion, 2004, 2005, Stavins, 1996, Weitzman, 1974, Yates and Cronshaw, 2001]. But even in the medical literature, Krumm and Graves [1982] estimate the effect of 502 concentrations on hospital admissions to be quadratic. For several health-impact pathways, the medical literature has also proposed the log-linear repre- sentation of the health damage function, under which a unit increase in concentrations results in a constant percentage impact on human health [Daniels et al., 2004, Ostro, 1987, Schwartz, 2000]. Abt Associates [a,b] acknowledge that both the linear and the log-linear forms have a justification. In addition to the debate about functional form, there is disagreement in the medical literature about the existence of a threshold of safe concentrations and its level [Abt Asso- ciates, b, Argonne National Lab, Burtraw and Mansur, 1999, Daniels et al., 2004, EPA, i, Lave and Seskin, 1977, Lipfert, 1984, Ruff, 1978]. Theoretical studies often compare such a threshold to concentrations resulting under different regulatory policies, to determine the optimal form and stringency of regulation [Dewees, 1992, McGartland and Oates, 1985, Morgan, 1983]. In the following section I introduce the compared environmental policies, and their expected impacts on the aggregate and regional health conditions. Section 3.4 describes my health damage model and justifies my selection of functional form for the marginal damage function. Section 3.6 reports the results. 3.3 Compared Environmental Policies In this paper I compare three established environmental policies leading to the same aggregate level of $02 emissions. This class is relevant since the EPA has adhered to mandating maximum allowable US-wide emissions. It is also interesting, because it is a priori unclear which policy would lead to the lowest damages, when regulatory instruments 143 are assigned exogenously to individual firms [Atkinson and Tietenberg, 1987, Tietenberg, 1995]. The following policies are compared: a system of tradable allowances as it currently exists under the Title IV of the Clean Air Act, with 9,200 allowances; a uniform emission tax of $90 per ton of 502 emissions; and a system of generator-specific emission caps at 72% of the generators’ historic emission levels. In a scenario with a uniform emission tax, the level of tax is selected so that in a decentralized equilibrium, generators choose emission levels summing up to E. In the scenario with emission caps, the energy industry model is first run without any emission constraints (as a pre—regulation scenario, as in Shadbegian et al. 2004). If the aggregate emissions in the equilibrium exceed E, all generators receive an emission cap proportional to the ratio of their equilibrium output in the pre-regulation scenario to the output of all generators, that would bring the sum of resulting emissions down to E. I solve this repeatedly with differently scaled emission caps, until the equilibrium aggregate emissions equal E. The sum of emission caps may not equal E, since some generators’ caps may be slack. Under a nationwide market for 502 allowances, generators are first allocated al- lowances summing up to E, again based on their portion in the nationwide pre-regulation production. In this scenario generators may buy and sell allowances, so any excess al- lowances are traded off in a competitive allowance market, and used for emitting. Hence the sum of all allowances equals E. Under an allowance trading scenario, I model the allowance market as static and competitive. Transaction costs and market power play no role in it, and generators treat their allocation of allowances and the allowance price as exogenous [Joskow et al., 1998, Schmalensee et al., 1998]. 144 3.3.1 Expectations from the Policies The uniform emission tax and the system of tradable allowances give generators the same incentives to produce and trade energy and abate emissions on the margin, and so they are expected to lead to the same distribution of 502 emissions and health damages. The existing empirical literature finds that these policies can lead to deterioration of regional health conditions compared to emission caps, because they redistribute emissions without regard for the existing pollution levels and for damages to human health [Haas, 1999, Shadbegian et al., 2004, Wolverton, 2002b]. Since emission caps keep regional emission levels in check and proportional to historic production levels, they are expected to result in a more equal distribution of emission and pollution levels, as long as the historic production levels that they are based on are distributed evenly. As long as the allocation of emission caps is not correlated with marginal damages caused by individual sources (i.e., with their 8'02 diffusion pattern or with the size of the affected population) in a detrimental way, emission caps should result in lower aggregate damages than the uniform emission tax and the system of tradable allowances. When marginal damages rise with concentration levels, the ranking of policies is par- ticularly sensitive to the correlation of marginal damages and the equilibrium emissions from individual generators. Marginal damages may be correlated with nearby generators’ cost schedules or emission levels, for instance, through differences in the regional grades of coal [Ellerman et al., 2000]. Differences in marginal damages may also result from endogenous location and pollution decisions by generators, and endogenous population mobility [Shadbegian et al., 2004, Wolverton, 2002a,b]. Ellerman et al. [2000] claim that, under the Title IV, emissions got redistributed to regions with actually lower marginal damages, but they do not compute the resulting health damages. Shadbegian et al. [2004] find that damages rose by $1.3 billion (using high marginal damage estimates) under Ti- 145 tle IV, as compared to a no-trade solution equivalent to the emission cap scenario in my study. Shadbegian et al. [2004] also find that there is significant variation in damages across US regions, and some regions gain under the allowance system, while other regions lose. The following section introduces the emission damages model. This model uses equilib- rium emissions from the three policy scenarios, as derived in Chapter 2 of this dissertation, and computes the associated health damages under different parametric assumptions on the marginal damage function. Section 3.4 discusses the choice of the functional form, and Section 3.5.1 shows how the damages are calculated using the existing data and the parameters of the chosen function. 3.4 Emission Damages Model After deriving the equilibrium emissions in the energy industry for each policy sce- nario, I aggregate the generators’ emissions to the state level, and map them into air concentrations of 5'02 in all receptor states. I include 502 emissions from non-utility sources (moving, agricultural and unregulated industrial sources) and from abroad, with the assumption that they are exogenous and uncorrelated with the emissions from the US energy industry [Argonne National Lab]. Emissions from individual states and industries become mixed in the receptor states, and their impact on human health is through the resulting concentration levels. Figures 2.2 and 2.3 in Section 2.8 (and Tables 2.4, 2.6 and 2.8) present the ranges of statewide concentration levels under the three alternative scenarios. These concentration profiles are evaluated in the health damages model under the different considered forms of the marginal damage function. Since health related effects dominate the damages from pollution, I focus on these 146 damages and their level as a function of air concentrations [Burtraw et al., 1998b, EPA, j,m, Haas, 1999, Rezek and Millea, 2003, Shadbegian et al., 2004]. I use the ranges of marginal damage estimates in various health-impact pathways (such as cardiopulmonary health effects, treatment costs, discomfort, and mortality risks) given in peer-reviewed medical literature. Because of low a priori importance and poor empirical evidence on their values, I ignore other identified damages from 502 emissions, such as due to low- ered visibility, losses in fishing and crops, deterioration of buildings and statues, wildlife losses and extinctions, deterioration of the ecosystem and others [Argonne National Lab, Burtraw et al., 1998b]. For most health-impact pathways, I find multiple competing estimates across different medical studies. These different values give me the low and the high estimates for the marginal health impacts in each pathway, between which lie the true marginal impacts for all units of S 02 concentrations [Argonne National Lab]. I assume away the existence of a safe level of $02 concentrations under which damages are zero, in agreement with the current knowledge [Abt Associates, b, Argonne National Lab, Daniels et al., 2004, Lave and Seskin, 1977, McGartland and Oates, 1985]. The value of marginal damages at each level of concentrations comes from within the range of estimates in the medical literature, but to pinpoint it precisely, I define the relationship between 502 concentrations and the marginal damages they cause. To choose the form for this function, given limited guidance from the empirical literature, I impose several requirements on behavior of this function. a Marginal damage function must be continuous and nondecreasing for the plausi- ble range of concentrations, a requirement that is consistent with the functions assumed in prior theoretical and empirical economic literature, and medical litera- ture. Dewees [1991, 1992], EPA [i], Morgan [1983], for instance, defend continuous 147 representation as the most plausible form. Adar and Griffin [1976], Curtiss and Rabl [1996a,b], Mendelsohn [1986], Stavins [1996], Watson and Ridker [1984], Weitzman [1974] on the theoretical front and Abt Associates [b], Daniels et al. [2004], Ostro [1987], Schwartz [2000] on the medical front, all assume varying but always nonde- creasing forms. a The slope of the marginal damage function, or its first derivative with respect to concentrations, must be monotonic. This ensures that the function has no inflec- tion points at any concentrations, since these are not supported by any empirical evidence. a For concentrations observed under all policy scenarios, marginal damage function must also be bounded by the range of estimates in the medical literature.3 Using this range, there is ground for comparison with prior empirical studies that use these estimates (including Burtraw et al. 1998b, EPA In, Rezek and Millea 2003), whereas estimates from outside of the range would be difficult to compare.4 In addition to these requirements, I also look for functional forms that are able to approximate forms used in prior theoretical and empirical literature—most importantly the constant, linearly rising, exponential, and step functions.5 Since one goal is to compare health damages under each policy across the plausible functional forms, all evaluated parametric forms of the function must satisfy the above requirements. Equation 3.1 satisfies these requirements. It is continuous, nondecreasing, with the lowest estimate from the medical literature (M Dl) as the marginal damage at the lowest 3The results obtained with such constrained estimates of marginal impacts may warrant extensions to other values. 4All inframarginal units of concentrations must also be assigned marginal damages from this range, so that the aggregate damages can be compared with prior studies in levels. 5These marginal damage functions give rise to linearly increasing. quadratic, log-normal and piece-wise linearly rising damage functions. 148 realized 802 concentration (C1), and the highest estimate in the literature (M D3) as the damage at the highest realized concentration level (C3). Marginal damages for the intermediate concentrations (Cg), M D2, are determined by parameter b giving the rise of the function. C3 — C2 A/ID2(C2) = A103 - (A1133 — IWDI) - C—T (3.1) '3'- ’l where MD1= MD1+;(MD3 — MDl) and MD3 = MD3 — 3(MD3 — MDl) (3.2) For b > 0, the modeled bounds on the marginal damages, M D1 and M D3, lie strictly within the range allowed by the medical literature, M D1 to M D3. Substituting Equation 3.2 into Equation 3.1, we get: 713ng) = 1WD3 — g (fl/103 — MD1)- (1- b) ggeg-E- (MD3 — N101) (3.3) Equation 3.3 was chosen because it is convenient to work with, and is insensitive to any specific values for concentrations or marginal damage estimates. In this expression, the marginal damage function depends linearly on the allowed range of marginal damages, M D1 to M D3, and the observed concentration levels, C1 to C3. This functional form was selected with particular data issues in mind. For one, health damage estimates are for marginal rather than average damages. For some estimates, the relevant level of 302 concentrations is not reported, and estimates for inframarginal or different concentration levels are generally missing. This functional form simply ob- 149 serves the range of estimated marginal damages (regardless under which concentrations they were estimated) and a range of concentrations, and allows any non-decreasing linear curve that satisfies those ranges, while preserving the mean marginal damage estimate at the mean observed concentration level. As the concentration level moves from the minimum observed level to the maximum observed level, the marginal damage linearly rises from the minimum allowed level to the maximum allowed level in each health-impact pathway. The actual slope of the function, in terms of (per capita) dollars per 15% of $02 concentrations can be generated once damages are computed in each health-impact pathway. Since the information on the true range of marginal damages is missing, I chose a functional form that allows me to manipulate a single parameter (b) and still satisfy all of my requirements on the value and shape of the function. This is particularly helpful since I have identified at least nine pathways in which the pollutant affects human health, each of which has a different range of estimated marginal damages and thus a different possible slope. Thanks to using the levels of concentrations and marginal damages as relative to the minimum and maximum observed values, Equation 3.3 applies to any number of known health-impact pathways, and does not require multiple parameters.6 If a single estimate of the marginal damages is available, the marginal damages that I use collapse to that value, .MDI = 1UD3 = W1 = W3 = W2. b determines how steep the function is, specifically, how much of the range of estimates in the literature is the function allowed to take. b = 1 corresponds to marginal damages constant at the means of the estimates in literature. This is reasonable because the estimate ranges in medical literature are for the most part symmetric [Argonne National Lab, EPA, i]. This case is equivalent to the approach used in previous literature. When 6Equation 3.3 can also be modified to accept different threshold concentration levels in each health-impact pathway. 150 b = 0, marginal damages rise at the maximum allowed rate that depends on our current understanding of the size of marginal damages. For 0 < b < 1, the function is allowed to rise at a slower rate. Depending on what one believes about the true range of marginal damages, or how one trusts the current range of estimates, one can systematically omit the outermost estimates. For any b, if the concentrations or our evidence regarding marginal damages change, my model will still use marginal damages within the correct range for all observed concentration levels.7 3.5 Numerical Calculation Using Available Data The energy industry is assumed competitive, and generators can sell energy to con- sumers nation-wide only subject to transmission costs. Consumers buy energy only from the generators that charge them the lowest price. Under perfect competition among gen- erators, all generators that compete in a consumer’s state take the market price as given, and divide the consumer’s demand at that price among themselves. Knowing the equilib- rium prices, generators decide on the volume sold to each consumer, and on the intensity of their emission abatement. Section 2.8 in Chapter 2 of this dissertation presents the results of the energy model under each environmental policy scenario. To model the strategic response of the energy industry to environmental regulation, I have used data on the industry infrastructure from Paul and Burtraw [2002] and the North American Electric Reliability Council [NERC, a,b], and generator-level statistics from the US Department of Energy’s Energr Information Administration (EIA) and the EPA. Information on energy demands and prices come 7For inframarginal units of concentrations (C < Cl), I use marginal damages W1, rather than projecting Equation 3.3 to the units of pollution that all states have in common under all policies. This assumption allows me to compare the computed total damages to those in previous literature, since my marginal damages come from within [M D1, M D3] for all units of concentrations. Since in this paper I am interested in differences in damages between individual policies, damages at C S C1 have no effect on the comparison. 151 from the DOE—EIA [k,m], and information on price elasticity of demand from Bohi and Zimmerman [1984] and Wade [2003]. Data on generators’ compliance with the Title IV is from the EPA [a,c,e]. The EPA [l] and Srivastava [2000] project the costs of various emission—abatement technologies. I use a reduced-form diffusion model to convert state-by—state emissions to the cor- responding air concentrations. This model sums the equilibrium 502 emissions derived in the energy industry, and any emissions from non—energy generating sources in each state, as well as from abroad, and uses constant transportation coefficients to convert the emissions into concentrations of $02 in each receptor state [Forsund and Navdal, 1998, T ietenberg, 1985]. In the following expression, the S 02 concentration level in state j (Cj) depends on the emissions from energy producers in state 3 (es), background emissions from non-energy producers in state 3 (es), and a transportation coefficient mapping each unit of emissions in state 3 to concentrations in state j (rsj). c, = Z [rsj - (e, + as] (3.4) S I use Tsj estimated for each pair of US states in the Advanced Statistical Trajectory Regional Air Pollution model (developed under the National Acid Precipitation Assess- ment Program), as reported by the Argonne National Lab. 3.5.1 Calculation of Damages Calculation of marginal health damages (MD) from S 02 concentrations (Cj) can be disintegrated into three parts, for each of which I have collected data. (Refer to Equations 3.5.) One, the number of individuals in state j affected in health-impact pathway k, ikj' 152 Two, the size of an individual’s marginal response in pathway k, m k, with the number of incidents or the acuteness of the condition as the units (for instance, probability of death, or number of days in the hospital). Three, the value in dollars per unit of incident in pathway k, vk. Using the ranges of estimates of marginal health responses in each pathway k (min mk to max mk), the minimum and maximum marginal damages caused by 502 concentra- tions in state j (used in Equation 3.2) are computed as: Mlej = ikj -min mk - "k and MD3kj = ikj -max mk - ”k (3.5) The state population and demographic distribution data come from the US Bureau of Census. Tables 3.1 and 3.2 report on the portion of the state population affected by each pathway (this and the size of the population jointly define ii”); the size of the marginal health response per individual per year, mk; and their estimated per-unit value in US dollars, vk, along with the original publications responsible for the estimates. Compilation of health response estimates comes mainly from the comprehensive study by the EPA [i] and Chestnut [1995] on the benefits of the Title IV program.8 These esti- mates are in the number of health incidents per microgram increase in the concentration 9 of sulfur compounds per cubic meter. I follow the widely used practice in empirical literature of assuming constant marginal monetary value of each response, independent of the size of the response or the concen- 10 tration level. While this relationship may not be constant in reality , and there exists a 8The US Department of Natural Resources-Division of Air Quality, American Lung Association [a] and National Acid Precipitation Assessment Program exerted other initiatives to obtain health response estimates. 9502, sulfates 302-, and all small particulate matter PM. According to Srivastava [2000], sulfates account for more than 47% of small particulate matter, and are often modeled as having the same properties as sulfates [EPA, i]. 10For instance, discomfort due to another day of respiratory problems may not be the same for each 153 range of estimates for the monetary value of each kind of incident, I use central values of the available estimates as the constant per—incident cost [Argonne National Lab, Burtraw et al., 1998b, EPA, i]. Tables 3.1 and 3.2 show the central estimates of the values of each health incident. 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E3 .3 8 338:8 .38: 389:8 3:2 38-8 8 A 88. 8 288 .38: 858.6 833 6395 \ a 850m .339 8.385%: 033/ mm: :0 maomQE_ don Buovm< ooSom 33m— 6395 8:33:33: 156 In order to calculate the aggregate damages D resulting under any policy, I sum up damages ij(Cj) accruing in all states j and all health-impact pathways k. ij is a definite integral of the marginal damage function for health-impact pathway k, evaluated between 0 and Cj. C. J— D = anjwj) = kZ/O MD2kJ-(C)dC U j As I reported in Section 3.4, in order to always use marginal damages from within the ranges in Tables 3.1 and 3.2, I use A! Dl kj as the marginal damage in health-impact pathway 1: and state j for all units of concentrations below C1. _ C'— D = Z [AIlej 'Cl +,/C1] 1‘41)ij d0 ’0 Since Cl equals the lowest observed concentration level, cumulative damages accruing under all units of concentrations up to 01 are identical under all policies, and thus get subtracted out if we care only about the differences in damages across policies. Rewriting the above expression using Equation 3.3, I get: b D = Z [Mlej + -2- (MD3kj — MleJ-)] -Cl kj C. J b / kj 1 C3 — C ”6‘37: ' (1 ’ b) ' (WW — Mlejll dc Upon performing the integration and plugging in the individual components from 157 Equations 3.5, I get: q D = Zikj wok - C1 [minmk + g (maxmk — minmk) kj ‘ . ' . b 1——b 0' kj _ . . l . b 1—b Cl ‘ ‘iEzkj ~vk - C1 maxmk — (maxmk — mmmk) - (5 + W (C3 — 7)) J . . This expression is a function of 502 concentration in a state C -, the chosen lepe pa- rameter b, data-observed parameters ikj and vk, bounds on marginal health responses min m k and max m k‘ and bounds on the observed concentration levels Cl and C3. 3.6 Results of the Emission Damages Model In this section, I present the aggregate health damages and their distribution across US states estimated under the three different policy scenarios: a system of emission allowances, a uniform emission tax and a system of emission caps. The following tables and figures use the distribution of 302 concentrations under each policy and alternative values for the slope parameter b to evaluate Equation 3.6. In computing these figures, I added background concentrations of 502 from other sources to the concentrations from my model-generated emissions, computed the health impacts, and subtracted health impacts that would result under the background concen- trations alone. These numbers correspond to the nationwide annual damages caused by S 02 emissions from the energy industry. Appendix A.7 breaks down the figures in these tables by health-impact pathway. Section 3.6.1 presents the results under constant marginal damages. The following 158 section, 3.6.2, presents the results under rising marginal damages, with the greatest slope justified by medical evidence. In addition, I have evaluated slopes between these extreme values. Aggregate damages computed under these slopes, and the differences in damages across the three policies were between those reported in Sections 3.6.1 and 3.6.2, and are thus omitted here. They are presented in Appendix A.8.1, along with the results under additional functional forms. Appendix A.8.1 also solves for the slope of the marginal damage function at which emission caps achieve the same aggregate damages as the system of emission allowances. 3.6.1 Results with Constant Marginal Damages Table 3.3 reports on the aggregate annual health damages under the alternative envi- ronmental policies, when marginal damages from 502 concentrations are constant (b = 1). Morbid. Dam- Mortal. Damages Total Damages ($ ages ($ million) ($ million) million) Emission Allowances 7,127.668 41,030.238 48,157.906 Emission Tax 7,127.884 41,027.598 48,155.482 Emission Caps 7,065.603 40,639.810 47,705.413 Table 3.3 302 Health Impacts under Alternative Policies: Constant Marginal Damages (b=1) The estimates of the aggregate damages and their differences in Table 3.3 are in line with the previous literature evaluating similar policies [American Lung Association, b, Centers for Disease Control, Shadbegian et al., 2004], but lower than in studies evaluating pre—regulation levels or comparing vastly different modes of regulation [Burtraw et al., 1998b, EPA, i, Hubbell, 2001, Rezek and Millea, 2003]. The results show that with constant marginal damages from 302 concentrations, 159 emission caps lead to the lowest estimated aggregate damages. These damages are lower than under the system of tradable allowances by $452 million, or by $390 million in mortality damages and by $62 million in morbidity damages. Shadbegian et al. [2004] found a total difference of $1.3 billion, but they used high estimates of marginal damages, of $15,000, compared to less than $5,000 in my study and in other literature [Burtraw et al., 1998b, Rezek and Millea, 2003]. Table 3.3 shows that the uniform emission tax and the system of allowances lead to very similar damages, which are both greater than under emission caps. This confirms that the results are driven by firms’ motives and economic forces under each policy, rather than by an imprecision in the solution to the model. The differences across policies are small compared to the absolute levels of the aggregate damages, but this results from the requirement to keep aggregate emissions constant under all three alternative policy scenarios. Regional redistribution of emissions under each policy has limited power in reducing the aggregate sum of damages, when the high levels of these damages are dictated by the amount of allowed nationwide pollution. The similarity of the tax and the system of allowances scenarios, and their diversion from emission caps indicate that these results are plausibly meaningful and non-random. Differences in damages across policies come from two sources of heterogeneity in mar- ginal damages caused by generators’ emissions: different diffusion patterns from individual generators, and different population densities and demographics in the receptor regions. Emissions from different generators have different impacts on S 02 concentrations in each state. Also, while each unit of emissions arriving in a particular region causes the same incremental health damage as other units in that region, emissions arriving in differently populated regions have different estimated health impacts. Figures 2.2 and 2.3 in Section 2.8.4 show the distribution of 302 concentrations under the three policies. These figures 160 Show that the western US states have the lowest 502 concentrations under all policies, while the north-central and northeastern states have the highest concentrations. The fig- ures show that the emission tax and the system of tradable allowances cause very similar distributions of 502 concentrations. They differ because of imperfections in the model of the energy industry, but by less than 0.5 fig in each state (refer to Figure 2.3). The fact that regional distribution of damages is similar under the system of emission allowances and the emission tax, whereas it differs under the system of emission caps, provides fur- ther evidence that the results are driven by economic forces under each policy, rather than by randomness in the model. Emission caps are shown to favor the southern and southwestern states in the con- centrations achieved, while the emission tax and the system of tradable allowances favor the northern and northeastern states, in agreement with the findings in Burtraw and Mansur [1999]. Figure 2.1 in Section 2.6.3 presents the spatial distribution of marginal damages that generators in each US state cause, when constant marginal damage function is assumed. This figure shows that the impact that a generator has on health damages depends on the population in the receptor states of its emissions. Generators in coastal and border states cause low marginal damages, since a portion of their emissions flows out of the US mainland [Shadbegian et al., 2004]. Generators in the northwestern and western US states cause low marginal damages, because their emissions concentrate in lightly populated areas. Figures 2.4 and 2.5 in Section 2.8.5 show the total damages realized in each state under the three policies, with a constant marginal damage function assumed. These figures indicate that states with low 502 concentrations and low population levels face low total damages. Comparing the alternative environmental policies, one sees that the relative damages are proportional to the relative 302 concentration levels under each 161 policy, as is expected under a constant marginal damage function. Among the three policies, emission caps assign the lowest relative damages to California, Texas and Ohio (by $478 million, $224 million and $66 million, or -28%, -14% and -l°/c, respectively), while giving the highest damages to New Jersey, Massachusetts and Wisconsin (by $198 million, $52 million and $45 million, or 8%, 4% and 7%). Figure A.6 in Appendix A.7 shows the differences in statewide damages across the three policies in percentage terms, rather than in dollar terms. 3.6.2 Results with Marginal Damages Rising at a Constant Rate Table 3.4 shows health damages resulting under the three alternative policy scenarios, when marginal damages rise at a constant, maximum allowable rate. That is, b = 0. Again, emission caps lead to lower damages than the system of tradable allowances and the emission tax scenarios, by $26.09 million and $91.65 million. Morbid. Dam- Mortal. Damages Total Damages ($ ages ($ million) ($ million) million) Emission Allowances 3,849.703 32,189.777 36,039.479 Emission Tax 3,867.726 32,237.317 36,105.043 Emission Caps 3.897.643 32,115.749 36,013.391 Table 3.4 502 Health Impacts under Alternative Policies: Marginal Damages Rising Linearly at Maximum Slope (b = 0) In both Tables 3.3 and 3.4, emission caps yield the best outcomes, compared to the system of allowances and the emission tax scenarios. The apparent reason is that they achieve low 5'02 concentrations in heavily populated states. Emission caps outperform the system of emission allowances in the total damages by $26.1 million, while the emission tax lags behind, by another $65.6 million. 162 The $26.1 million difference appears to be in the range of a possible modeling error, since the difference in aggregate damages between the emission tax and the system of emission allowances scenarios is more than twice greater. Nevertheless, both the uni- form emission tax and the system of allowances result in systematically higher aggregate damages than emission caps under all considered forms of the marginal damage function. Even with an imprecision in their equilibrium distributions of emissions, it is plausible that this imprecision does not reach $26.1 million below the damages where the system of emission allowances ended. Plausibly, emission caps still truly lead to a less harmful distribution of emissions even under this form of marginal damages, and this is thanks to their economic properties, and not due to residual infeasibilities in the energy model equilibrium. The slope parameter b is not an actual slope of the marginal damage function, because the steepness of the function still depends on the ranges of observed concentrations Cl—C3 and medical estimates M Dl—M D3. Rather than one marginal damage function, we also have fifteen such relationships, for each health-impact pathway. To find the actual slope of the marginal damage function across all pathways, we need to use the individual slopes in Appendix A.7 Table A.16 and convert them to monetary units per capita. Since these slopes refer only to the populations affected in the individual health-impact pathways, we need to multiply the slopes by the portion of the population that is affected. The results imply that when the marginal damages in each pathway rise at the maximum allowed rate, incremental annual health damages from a 1% increase in concentrations rise by $42.39 per US resident.11 If I let the slope of the marginal damage function to rise beyond what the range of estimates in medical literature allows, the system of emission allowances would eventually 11Figures 3.1 and 2.1 show total marginal damages per one ton increase in emissions from a particular state. 163 come to dominate over emission caps in the aggregate damages. For that to happen, the true parameter b would have to be -0.06. Alternatively, I would need to expand the range of permissible marginal damage estimates (M Dl, M D3) from their existing values in medical literature by 12 percent. Figure 2.3 in Section 2.8 shows that, on one hand, the system of emission caps inci- dently lowers 5'02 levels in states with low pollution even under the other policies, and raises them in states with high pollution even under the other policies. On the other hand, emission caps lead to a wider distribution of $02 concentrations than the system of allowances or the emission tax. These differences in concentration levels become more important in computing regional and aggregate damages when marginal damages rise in the concentration levels. The advantage of emission caps to the other two policies thus falls, because damages added in more polluted states exceed the damages avoided in less polluted states. Tables 3.3 and 3.4 confirm this. Marginal Damages Figures 3.1 and 3.2 report on the damages caused nationwide by marginal units of emissions coming from each state, when the marginal damage function rises in 8'02 con- centrations at a constant, maximum allowed rate (b = 0). For instance, the figures Show that if a generator in California emits one more ton of S 02, the marginal damages in all surrounding states would amount to $7,000, given the existing levels of emissions at other generators. The range of marginal damages estimated in Figure 3.1 is wider than in Figure 2.1 (Sec- tion 2.6.3) showing the marginal damages across states under a constant marginal damage function. With a rising marginal damage function, states with lower $02 emissions and thus even concentrations (shown on the left hand side of Figure 3.1, which is ordered 164 by state concentration levels under the emission allowances scenario) face lower marginal damages, while states with higher concentrations face higher marginal damages. Gener- ators in heavily populated regions, far from coasts and borders, and in states with high 502 concentrations caused by all generators, are estimated to cause the highest damages per ton of 502.12 Figures 2.1 and 3.1 show ranges of marginal damages ($1,743——9,649) almost identical to the range used in Burtraw et al. [1998b]. In comparison, Shadbegian et al. [2004] use much higher estimates of marginal damages ($10,000—20,000), while Rezek and Millea [2003] use lower values ($650-4,500). Rezek and Millea [2003] find that, in the eastern half of the US, marginal damages are the highest in the north-central and the northeastern states, while they are the lowest in the Atlantic and the southeastern states. With the exception of four states in New England (Massachusetts, Maine, New Hampshire and Delaware), Figure 2.1 shows the same results. The average marginal damage in the northeastern states (including all states in New England), weighted by the size of each state, is $5,900, while the weighted average in all southeastern states is $5,700. Figure 3.2 shows the differences in marginal damages across US states, measured against the marginal damages under the tradable allowance scenario. These differences are due to differences in state concentration levels across the policies. As expected, mar- ginal damages in each state are similar under the emission tax and the system of tradable allowances, since the concentration levels are almost identical. Under the emission cap scenario, marginal damages are significantly lower in several US states with 502 con- centrations in the second quartile of their range, particularly southern states such as California, Texas, Arkansas and Louisiana (by $401, $145, $114 and $91, respectively). Marginal damages are higher under emission caps in states in the third and the fourth quartiles of the 802 concentrations such as in New England and the northeast. New Jer- 12Marginal damages in Figure 2.1 depend on the first two factors—population level and the presence of sensitive receptor zones around the emitting state—but not on the concentration levels. 165 El Emission Allowances 8,400 7,400 6,400 5,400 4,400 3,400 ' 2,400 -nfllflnflfl I], .. [7' I YIIII III IIIII177 gaeggaaszgsasssaasses;sasgsssizagsazsaagaazaééfifiz Figure 3.1. Marginal Damages under the System of 'Ifadable Allowances with Rising Marginal Damages ($)—-—States Ordered by Concentrations under Sys- tem of Allowances sey, Rhode Island, Virginia and Wisconsin receive the highest marginal damages under emission caps relative to the other policies, by $361, $164, $120 and $119. This agrees with the finding that this scenario leads to a more heterogeneous distribution of concen- trations, favoring states with low concentrations under the other policies, and causing high concentrations in states that have higher concentrations under all policies. Total Statewide Damages Figures 3.3 and 3.4 show the distribution of total statewide damages under the three environmental policies, when the marginal damage function rises at a constant, maximum allowed rate (b = 0). These figures can be compared to Figures 2.4 and 2.5 in Section 2.8.5, showing results for the case of the constant marginal damage function. With increasing 166 315 ,_ 0 Emission Allowances x Emission Tax 0 Emission Caps 210 105 '105 O -210 -315 420 VITIIIU IIYIIUYITIIIIYY ll'TFT‘TTrI O aaeséa assgzasséarss “difi sgszgssagsazeaagga asagcsz Figure 3.2. Differences in Marginal Damages against Those under the System of Tradable Allowances with Rising Marginal Damages ($)——-States Ordered by Concentrations under System of Allowances 167 315 ~ :1 Emission Allowances x Emission Tax 0 Emission Caps 1 210 105 ~105 -210 -315 420 I'IYIIYITM O 8§9528ES§E285§§353 Xs O I IIIIYrT‘III “:25 525255 L < 0( m: g... 0 o>4-z zz-¢»§§ YIUIIFI gsg<§§52 Figure 3.2. Differences in Marginal Damages against Those under the System of 'Il‘adable Allowances with Rising Marginal Damages ($)——States Ordered by Concentrations under System of Allowances 167 marginal damages, damages estimated in all states are lower because of lower values of the function at inframarginal units of concentrations. The differences between Figures 2.4 and 3.3 must be interpreted with caution, because the change in the marginal damage function results in important differences of the aver- age damages per ton of emissions, and of the value of total damages in each state and nationally. While it makes sense to compare regulatory policies under a particular form of the marginal damage function, and it makes sense to compare total damages under a single policy across functional forms, we cannot directly compare one policy under con- stant marginal damages with another policy under rising marginal damages. Damages under particular policies across functional forms of the marginal damage function can be compared, because this comparison quantifies our uncertainty about the slope of the marginal damage function. Depending on what the actual functional form is, the total damages under all policies could assume a wide range of values. Comparison of Figures 2.4 and 3.3 reveals that depending on the damages I attribute to all inframarginal units of concentrations, my estimated total damages can change sig- nificantly. Under the system of tradable allowances, and using marginal damages rising at a constant rate, I estimated total damages in each state to be 11—41 percent lower (and 25 percent lower nationwide) than using a constant marginal damage function. States with the greatest total damages are mostly northeastern states, including New York, Ohio and Pennsylvania, each with approximately $3.4 billion in annual damages (compared to $4.4 billion under constant marginal damages). States with the lowest damages are all north- western US states, with total statewide damages around $36 million (compared to $78 million under constant marginal damages). Figure 3.4 shows the statewide damages under the emission tax and the emission caps scenarios, as compared to those under the system of tradable allowances. As under 168 4,500 4,000 El Emission Allowances 3,500 3,000 _ 2am . ._ 2mm s __ ,7 15m) ~~~ —— +- 1,000 _ h—1I—1 i—niI——(h-——1I——r—4-—4~ 5°° ' lllll "—7 o n. n“. 'anl lnl'l III1--1l.l1ll‘l.ll-ln l.l‘IIl-l'l‘ll-l mnl'l ll fl ill I I . ll asesgs HSE§8 “sic éswd§fiwfi°525528 £3 “#3 §§gz 8&EEEZ Figure 3.3. Health Damages under the System of 'Ifadable Allowances with Rising Marginal Damages ($ million)—States Ordered by Concentrations un- der System of Allowances the constant marginal damage function (Figure 2.5 in Section 2.8.5), emission tax and the system of allowances achieve similar damages in all states, while emission caps are shown to assign significantly different damage levels in several states. California, Texas, Louisiana and Oklahoma, for instance, face $429, $149, $28 and $25 million lower damages (corresponding to 34, 16, 6 and 12 percent), respectively, while New Jersey, New York, Virginia and Wisconsin, for instance, face damages higher by $246, $76, $60 and $35 million (or 11, 2, 3 and 8%). Figure A.7 in Appendix A.7 shows these differences in statewide damages across the three policies in percentage terms rather than in dollars. 169 %0 6 1w 0 50 o O O O O )( O Q X fisaaaaaaaaaauaegnqaaéaagggfifigfigflaagugagééfiéfiuaflu$ x O o O -50 X -150 {3 -250 -350 . . c1 Emissm Allowances x Emsion' TI)! 0 . . 450 I IIIIIII I T I Y Y I YYYYYYYYYYYY W—rOIEYmissl|°ln 10;”? YYYYY Q>O (00*- |.1JC)<(EZ(J))g0280E§O_ Figure 3.4. Differences in Damages against Those under the System of Trad- able Allowances with Rising Marginal Damages ($ million)—States Ordered by Concentrations under System of Allowances 170 3.6.3 Analysis Comparing Tables 3.3 and 3.4, I see that the morbidity and mortality damages fell by approximately 46% and 22% (and total damages by approx. 25%), as the marginal damage function changed from being flat (b = 1) to adopting the highest data-supported slope (b = 0).13 The area under the marginal damage function evaluated between Cl and C3 is identical for both sets of parameters, because both functions are linear, so this may seem strange. However, because state concentrations of 302 are distributed non-uniformly between Cl and C3, parameter b affects aggregate damages between these tables. With a uniform distribution of concentrations on (01,03), all policies would yield the same estimated damages under both sets of parameters. All estimates within each table, and across the two tables, would be identical. It makes sense to compare the numbers in these two tables, because with only a range of estimates available for the marginal damages, both functional forms are plausible and lead to valid estimates of the total damages. With both the constant and the increasing marginal damages, stateby-state differ- ences in populations ikj and 502 concentration levels Cj are the main determinants of state damages and the variation in them. Differences in concentration levels across policies determine the ranking of the policies in each state in terms of the damages. Since emission caps yield significantly lower concentrations than the other two policies in several heavily populated states, they lead to the lowest damages there and nationwide, even though they lead to higher concentrations in other states. This is true under both assumptions on the slope of the marginal damage function. For instance, five states where emission caps achieve the lowest concentrations compared to the system of allowances 13Table A.16 in Appendix A.7 shows the number of health incidents per capita in each health-impact pathway for a one-unit change in the 502 concentration. 171 have 62 million residents, while five states with the highest relative concentrations under this policy have only 22 million residents. The differences in concentrations are large in the heavily populated states where emission caps dominate, but are low in the heavily populated states where emission caps lead to higher concentrations than the alternative policies. With marginal damages rising in concentration levels, states with high concentration levels receive disproportionately higher marginal and total damages than states with low concentrations. Concentration levels across states, Cj, grow in importance relative to the state populations 2' k j in their impact on the total health responses to marginal units of concentrations, m kj(Cj) - 2' k 3" Since allowances shifted some concentrations from more polluted states to less polluted states (from the northeastern states, which are in the third and the fourth quartiles of the range of concentrations, to the southern states, which are in the second quartile), the aggregate damages under this policy fell relative to emission caps. Emission caps, for instance, lead to 1 52% or greater reduction in concentration levels in only five states, compared to the system of allowances, and lead to concentration levels higher by 1 15% or more in twelve states. Emission caps lead to up to 5.72 11% increases m m in concentrations, compared to the system of allowances, while the greatest reduction in concentrations they achieve relative to allowances is 3.01 fig. Between Tables 3.3 and 3.4, as the marginal damage function changed from constant to increasing, aggregate damages under the system of tradable allowances fell by $12.12 billion, while they fell only by $11.69 billion under the emission caps. In the southeastern and southern states, where emission caps led to $840 million lower damages than the system of allowances with constant marginal damages, their advantage falls to $670 million with rising marginal damages. On the other hand, the $390 million advantage of the system of allowances in the northeastern states, with constant marginal 172 damages, actually rises to $600 million with rising marginal damages. These two areas— the southeastern and southern states versus the northeastern states—have approximately the same population of 100 million. 3.7 Conclusions For over three decades, theoretical regulatory literature has stressed the importance of the slope of the marginal damage function and its correlation with generators’ marginal abatement costs in the choice of a regulatory instrument. Medical studies have admitted uncertainty about the exact relationship between S 02 concentrations and health impacts, suggesting constant to increasing marginal damages. The empirical economic literature has, however, continued to assume constant marginal damages, even though this form represents the lower limit on the slope of the function, suggested in the medical literature. As a result, existing estimates of the 502 emission damages may be biased, and some regulatory alternatives may be unduly favored at the expense of other policies. In this paper I have shown that the slope of the marginal damage function affects the relative performance of the price and the quantity regulatory instruments in the aggregate damages. I have also shown that with the current evidence on the slope of the marginal damage function, emission caps systematically lead to lower damages than the system of emission allowances. Were I to allow even greater slopes for the marginal damage function, unsupported by current medical literature, I would find the slope at which exacerbated damages in some regions (in the Northeast) would outweigh damage savings in other regions (in the South) under the emission caps scenario, as compared to the system of allowances. In that case the system of tradable allowances would come to dominate emission caps in aggregate damages. Under all policies, most pollution occurs in the heavily populated Eastern and N orth- 173 eastern US, while little pollution occurs in the West and the Northwest. This suggests that generators’ emissions may be positively correlated, and the emission-abatement costs may thus be negatively correlated with the marginal damages these emissions cause, con— ditions under which Stavins [1996] finds that price instruments start catching up with emission caps in the sum of aggregate damages and emission-abatement costs. Indeed, emission caps lead to particularly low damages compared to the system of allowances under constant marginal damages, but the difference against the tax and the system of allowances falls as the slope of the marginal damage function increases. This is because, compared to the allowances, emission caps lead to a more unequal distribution of 502 concentrations across the US. Among the compared environmental policies, the system of emission caps is shown to favor the southern US states, and lead to particularly high damages in the northeastern US states. Under an increasing marginal damage function, this result is exacerbated, and several heavily polluted states in the Northeast receive much higher total damages than under the system of tradable allowances. Damages in less polluted states are lower under emission caps compared to the system of allowances, but by less. This raises the issue of justice in the distribution of damages across states, and the rate of tradeoff between damages in the least polluted, and the most polluted states. This issue warrants further analysis. 174 APPENDIX A.1 Structural Change Test Although I cannot control for the possibility of third degree discrimination across con- sumer classes without the appropriate instruments, I examine whether the implementation of deregulatory policies constituted a regime change for the setting of relative prices. I test whether the correlation of residuals in the residential and commercial price regressions has changed at the time of the mechanism implementation. To apply this procedure, I regress the residuals from the commercial panel regression with fixed effects (Column 2 in Table 1.4), uc, on the residuals in the residential regression (Column 1), w, and a set of interaction terms of ur with binary variables for the status of each policy. uc = 1'30 - ur +131 - (ur ~policy) + 5 (A.1) [31 is a vector of the coefficients of interest. I test the null hypothesis of 51 = 0 for indi- vidual fil and as a vector. Rejection of this hypothesis would imply that these coefficients are individually or jointly significantly different from zero, and the implementation of the policies did change the joint-relative—price setting mechanism between the residential and commercial prices at the time of the implementation. The failure to reject would sug- gest that although there may exist simultaneous determination between the two prices, its underlying principles remained unchanged with the introduction of the mechanisms. Estimating the above equation for all investor owned providers gives me the following 175 results: Tic = 0.737 ur + 0.064 ur price cap + 0.056 ur sliding scale + 0,035 ur choice (A.2) (0.010) (0.199) (0.100) (0.039) where the parentheses report standard errors. None of the coefficients on the interaction terms are significantly different from zero even at a 15% level, while the coefficient on ur is significant even at a 1% level. The F statistic of the joint. significance of the three interaction terms is 0.40, with p-value of 0.75. I thus fail to reject H0 : ,81 = 0 at any reasonable level of significance. Although I still need to worry about the joint determination of prices, and treat the three price equations as seemingly unrelated regressions, I can assume that the same principles were used to set the relative prices both before and after the introduction of the policies. Stigler and Friedland [1962] similarly found no effect of the establishment of public service commissions on relative prices of individual consumer classes. The high significance of the coefficient on ur is consistent with the fact that several regressors appear in all three respective price equations, and I use imprecise proxies to control for them. A.2 Selection of Weights in the Calibration Objective The objective in Equation 2.32 maximizes the fit of the main control variables in the benchmark scenario of the model to their historic observations. In selecting variables and their units of analysis for the objective function, I am limited by the available historic data. Individual components of generators’ costs are, for instance, unreported, and data on abatement intensity is available only on nationwide level. 176 Parameter Range Parameter Range éj (Unitless) 20,000-750,000 C3,- ($/MW2) 0—0.25 Gli ($/MW) 5—20 A17; (if/Ton) 30—75 02,- ($/MW2) 0.014105 A2,- ($/% Abat. Intensity) 200010000 01, ($/MW) 1—3 A3, (90:? Abatement (H.500 02,- ($/MW2) 0—1 Intensity) Table A.1 Free Parameters and Their Ranges Used in Calibration Guidance on the appropriate weights giving individual parts in Equation 2.32 relative importance is missing. variables, and on different level of aggregation. I assign the same weight to percentage deviations in all variables, thus treating the fit in all variables, relative to their levels, equally. Since individual variables are observed a different number of times in the model (e.g., prices on state level, while output on generator level), I also need to decide how to weight the number of deviations in each dimension. To select the appropriate weights, and to evaluate the sensitivity of the model results to changes in the weights, I ran calibration It is unclear how one should compare deviations in different using three different sets of weights (as in Suntornsaratoon et a1. 1999): o Weights 1: The weights reported in Equation 2.32, using inverses of the number of agent-specific deviations for each variable (i.e., with a focus on the fit of nationwide statistics). 0 Weights 2: Unit-weights on each deviation, giving the same importance to output of one generator, for example, as to a state price, or state emission level (i.e., with a focus on the statistics for each agent in the model). In Equation 2.32, I and J would be set to one. This set of weights acknowledges the data available to me, and gives each piece of data, and the corresponding variable value in my model equal weight. 177 o Weights 3—State—level weights: deviations in state output, consumption, price, emis- sions and emission-abatement are given the same weight. So, generators’ output is first summed up for each state, before comparing it to state-level data; average abatement intensity for each state is compared to the nationwide statistic. These weights were chosen because of their a priori relevance. Even though I lack information on how to weight deviations across different variables, I can assign the same importance to deviations on the same geographic level (As in Weights 1 and 3), or on each unit of observation (Weights 2). The first set of weights assigns the same importance to deviations on the same geographic—industry-wide—level. The second set of weights gives the same importance to each observed deviation in the objective function, regardless whether it is on the generator or consumer level. The third set of weights considers deviations on the state level, considering generator-level deviations only through their impact on statewide deviations. Table A2 compares Weights 2 and Weights 3 as compared to Weights 1 in their effect on the calibrated parameters and model variables. Mean deviations of the variables from the benchmark, normalized by the variable means, are reported. Weights 1 serve as a benchmark from which all deviations are measured. Table A2 indicates that the choice of the set of weights has a small effect on individual parameters. Parameters respond to the different weights by only 51—10% of their value. Generators’ cost parameters change by 8—12%, depending which set of weights is used. Output and consumption variables vary by 8—9% across the selected weights. Energy price and the abatement intensity are especially insensitive to the choice of weights, since they vary by 4—6% across the weights. The small sensitivity of prices is likely a result of my assumption on the high level of competition in the energy market. Between the nationwide and state-level weights (Weights 1 and Weights 3) there is especially little 178 Normalized Mean Deviations Parameter or Variable Weights 2 Weights 3 Generating cost params. (G1,, 02,-, G3,) 11.23% 12.15% Ti‘ansmission cost params. (C1,, C2,, C32) 7.67% 8.02% Emission abat. cost params. (Ali, 142,-, A3,) 9.56% 10.63% Consumer demand shifter (6]) 8.89% 12.59% Generators’ output (q,) 8.14% 8.44% State consumption (dj) 8.51% 9.60% State energy price (pj) 4.33% 5.88% State emissions (22-6 j e2) 9.35% 12.30% Industry abatement intensity (Z,- a,) 5.37% 0.15% Table A2 Parameter Variation under Weights 2 & Weights 3 Compared to Parameters under Weights 1 (% Mean Deviations) change in the abatement intensity, implying that my model results in very similar levels of average abatement intensity in each state. I choose the first set of weights, because the fit of the entire model on the national level is my ultimate objective, and on that level, I want to ensure that the fit of any variable is not achieved at the expense of another variable. Since the model uses representative consumers and generators aggregated by their type, matching my calibrated results for individual agents to their historic data may be asking the model too much, particularly when I do not have all data on all generators, and I let the aggregated generators proxy for non—reporting or fringe firms missing from my data. The assumption that any unobserved firms are identical to those in my sample is more likely to hold on the national rather than local level. Appendix A.5 reports historic statistics for the US energy industry, taken directly from the data. I used these data to calibrate the model. 179 A.2.1 Model Calibration Results Histograms in Figure A.1 show the goodness of fit of the simulated variables with the historic values. For each variable, the histograms report the portion of observations whose deviations from the historic levels in logarithmic terms fall within a range of values on the x-axis: Number -1 on the x-axis means that the calibrated value is ten times lower than the historic value, while +1 means that the calibrated value exceeds the historic value ten times. All variables are shown to be correctly centered and have narrow distributions around the historic levels (for most observations, the difference of the calibrated and historic values, in logarithmic terms, is zero). Some variables have wider distributions around the correct values than others, and some variables have skewed distributions, implying that the model systematically under-predicts or over-predicts these variables for a portion of observations. The values that are estimated with the systematic and greatest error are for the generators with the smallest generating capacities, and generators using alternative fuels with very high or very low average heat rates and emission factors. These histograms give all generators the same weight, so the variation that they show is worse than in the actual model, because the particularly high imprecisions at fringe generators receive the same attention as the well-fitting observations at the largest generators. Generators’ prices derived in the calibration have a symmetric distribution around their historic values (refer to Figure A.2.1). Prices evaluated on the state, rather than on the generator level, have a small rightward tail. The model overestimates prices in states that have very low energy prices in my historic data—northwestern and southern states. Consumption of energy by state is very well estimated in the model, with only four of the smallest states (in the northeast) estimated to have a twice larger or smaller consumption than the historic level. Generators’ emission levels in the model have also a very narrow distribution around the historic values, with a small left tail. Approximately 180 10% of generators (the smallest generators) are estimated to have emissions twice lower or less than the historic levels. These errors disappear on the state level. Generators’ output levels in the model, on the contrary, are slightly skewed to the right, due to 2% of generators (again the smallest generators) whose output is estimated at a 2.2—2.6 multiple of the historic level. Table A.3 lists the parameters that were allowed to adjust freely in order to minimize the objective function, along with their mean calibrated values. Parameter Calibr. Mean Parameter Calibr. Mean 6,- (Unitless) 429,578.44 C3,- ($/MW2) 0.20 Gli ($/MW) 5.29 Ali ($/Ton) 42.54 02,- (cents/MW2) 2.99 A2,- (8/% Abat. Intensity) 3,985.82 Cl,- ($/MW) 2.36 A3,. (3;/%2 Abat, 1,154.62 C21- ($/ M W2) 0.53 Intensity) Table A.3 Free Parameters & Their Calibrated Means Histograms in Figure A.4 show the distribution of statewide S 02 concentrations under the alternative environmental policies, as the portion of states fitting in individual ranges of concentrations. 181 .1,5 -1 0.5 1 -0.5 0 Diflarenoe of log: (a) State Consumption (GWh) if , 7,,, i”, 7, .7 -2 .1 0 1 Diflueneedlogs (b) State Generation (GWh) -04 0 0.4 0.8 Difference of logs (c) Generators‘ Production (GWh) Figure A.1. Relative Deviations of Model Variables from Historic Values ( 1) 182 0.5 Mama of logs (a) State Avg. Pricm ($/MWh) ’-18 .1 O 1 18 Difletaneodlogs (b) Generators' Avg. Prices ($/MWli) 40 -3.2 -2 0.8 2 -1.2 0 Difference of logs (c) State 502 Emissions (1,000 Short Tons) Figure A.2. Relative Deviations of Model Variables from Historic Values (2) 183 50 40 20 1o - 0 — — -5.5 -4 -2.5 '1 0 0-5 DMetenee of logs (a) Generators‘ $02 Emissions (1,000 Short Tons) 40 ,_ , i 1 30 3 l g .. 10 0 —0.2 —0.1 0 0.1 0.2 Diflerenoeoflogs b Stt SO C ce tr tions ( ) a e 2 on n a. (51%) so . , 3Peroent3 o __ __ —5 4 -3 -2 -1 0 Difference of logs (c) All Variables Jointly Figure A.3. Relative Deviations of Model Variables from Historic Values (3) 184 25 as ’ t 20 20 is ‘5 10 1o 5 5 0 086243240485664728088 0.08162432404856647'2mm AIS/ml Ala/m3 (a) Emission Tax of $90/Ton (b) "Ii-adablc Emission Allowances (9.2 Million Tons) ’ as 0 08824&4048566472m88 .08624324048566472maflm ug/m3 Ala/m3 (c) Emission Caps of 72% of Historic Emissions (d) Observed 1996 Concentrations Figure A.4. Distribution of $02 Concentrations under Alternative Policies (149/m3) A.3 Energy Industry Model Set of Equations and Unknowns Generator 2' earns profit II,- as a difference between its revenue (output sold to each consumer j, qZ-j, multiplied by the competitive price in the consumer’s market pj), and the costs of its production (Cgilv regional transmission (ctij), emissions abatement (Cat) and environmental policy compliance (W), and interregional transmission fees (2 j thijqz'j)' The generator takes market prices pj Vj as given. Subscripts i, h and j represent the generator 2', each consumer j and each interregional network segment h across which 2' transports energy to consumers. 0., represents the portion of one’s pre-abatement emis- sions that 2' removes, to achieve e,- emissions. The cost of environmental compliance depends on the policy in place, and is a function of 2’s output, q, = E j qz-j, and emission- abatement intensity, a, Section 2.3.4 shows the generator’s profit function in Equation 2.7. Generator maximizes II,- by choosing the volumes of energy sold to each consumer, and the emission-abatement intensity. If we represent the number of consumers in the market as J, generator 2' has J + 1 decision variables with which it maximizes its profit, the sales to each of the J consumers, qz'j’ and the emission-abatement intensity, a,. The following first-order equations are solved with the profit-maximizing values of q, j and ai. The first order conditions with respect to the sales to agents j are: W - thij + E— = 0 (A.3) where There are J of these equations, one for each consumer j. The first order condition for emission-abatement intensity is: 186 —te - Eq—L Emission tax 1.7 £31 = ‘pA' as). under Emission allowances z] 1.7 Be- . . “Aei - q- . Emissmn caps 2] 8H, 8cm- 6W _ __ = 0 A.4 (9az 8a,; 8a, ( ) where te - 3% Emission tax 2 82V -_- pA' 8:: under Emission allowances z 2 )‘e2' - 3&1 Emission caps 8. Here p A is the market price of emission allowances, which individual generators assume given, and t is an exogenous emission tax. In the emission caps scenario, Aez‘ is an endogenous shadow cost of the generator’s emission cap that ensures that, in the model, generator’s emissions will not exceed the cap, and that the two first order conditions will hold with equality, when the emission constraint binds. In the scenario with emission allowances, p A ensures that the excess demand for allowances is exactly zero. If we write the generator’s purchase of allowances in the market, (1 A21 as a function of the generator’s allocation of allowances E2" output ‘12" emission-abatement intensity a,, and we write the output and the emission-abatement intensity as functions of the allowance price p A1 then the equilibrium allowance price must solve ZdAi(qiv ai’pA’ Er) = Z [61 (qz'(PAz')»az'(PAz')) - 1737;] = 0 (A5) 2 ’l 187 Consumer prices pj are determined from consumers’ demand functions. Consumer j meets his demand schedule exactly, with the appropriate Qij Vi and pj. Prices pj thus clear supply and demand of energy in all consumer markets. mm=2%@1 mm 1 Generators take prices pj as given. System operator charges generators i a per-unit transmission fee t hi j for their inter- regional trade with consumers j, so that in the equilibrium it exactly covers its costs Chi j on all network segments h. thij 'qu = Chiflqu) (A-7) A.3.1 Emotional Form Representations The following expressions show the functional forms adopted for the above system of equations in the energy model. The generator has J + 1 first-order profit-maximizing conditions, determining the values of q,- j and a,. The first order conditions with respect to qij are: an, 547'} = 0 = pj — [PfiGIiHi(qi) + 2022' "Ml — thij €12" _ 8W - Cu +20% ‘(Iij +203i§~% - lAliaiHi 10 GWh (10) used individually; 5 GWh < q,- < 10 GWh merged as medium-sized (49); 5 GWh > q, merged as small-sized (132); Unknown size (15) Fuel type Coal (107); Natural gas (40); Petroleum (39); Other— Nuclear, Hydro, Heat, Biomass, Wind (20) Ownership Investor-owned, Private & Cooperative (103); Municipal (24); State & Federal (11) ; Undetermined (68) State 48 continental US states Combustion effec- H,- g 8, 000 (5); 8, 000 < H,- 3 12,000 (130); F,- > 12,000 tiveness (Hi) (71) Table A.4 Criteria for Selection of Model Generators 502 emissions and concentrations are reported in Table A.6 and Figure A.4.d. This figure can be compared to $02 concentrations estimated under the three alternative policies (Histograms a, b and c in Figure A.4). The left half of Table A.15 in Appendix A.7 shows the derived health impacts and monetary damages resulting from the 1996 emission levels. These values can be directly compared against the model generated damages for each policy scenario, in Table A.13 in Appendix A.7. Finally, Figures A.1— A.3 show the fit of major variables in the emission allowances scenario of my model to the historic, 1996 observed values. Avg. Consumer Price ($/l\IWh) 74.20 Energy Output (TWh) 3,840.02 Consumption (TWh) 3,447.16 502 Emissions (1,000 Short Tons) 10,925.76 Table A.5 Aggregate Statistics: Historic 1996 Observations 194 Emissions Concentrations State Minimum 2.63 2.40 State Average 5,897.65 22.49 State Median 5,508.45 30.62 State Maximum 35,232.90 88.42 Table A.6 Historic 1996 802 Emissions (Pounds per Sq. Mile) and Concentrations ' (pg/777,3) by State A.6 Energy Industry Data Sources Data is available on each generator’s capacity, combustion technology, type of fuel used and fuel characteristics, and other technological specifications. Beside information on the basic technological characteristics of production I also collected data on the generators’ location and ownership status. In some cases I was able to fill in missing information based on the data reported by other generators. Such were the cases of emission allowances that I estimated from the reported allowances, and the missing cost of fuel that I approximated with the state-wide average. Observations with insufficient data were deleted. There were several reasons for deletion of an observation from the data set, including missing data on efficiency of generation (average heat rate), in which case I was unable to construct a production function for that generator; missing state location; missing price, in which case I could not calibrate the generator’s cost parameters. The US Energy Information Administration’s Form 867 reports historic sales of energy by consumer class on state level, and an inventory of all generators. The DOE—EIA [1] provides generators’ status and hours of operation, fuel use, production level and capacity, as well as the combustion technology. The DOE—EIA [j] reports generator-level statistics on fuel use, generation level and status, as well as the relationships between individual boilers and generators, for approximately 900 power plants. The Federal Energy Regu- 195 latory Commission’s Form 1 shows financial and operating statistics for approximately 180 major investor-owned utilities. EIA’s Form 412 reports similar data on 500 major publicly owned utilities, including all federal electric utilities. These sources were com- bined to avoid deleting observations when a piece of information is missing in one of the databases. Historic demands and energy prices come from the DOE—EIA [k], which reports gener- ators’ monthly energy revenues and sales by consumer class. The DOE—EIA [m] contains data on energr purchases, production and disposition, and energy losses for approximately 3,300 units. The Environmental Protection Agency reports statistics on generators’ Operation and compliance with the Title IV, including the allowance allocation and trade [EPA, c,e]. The EPA’s database AP-42 reports on the pollutant controls installed at generators, their fuel emission factors, as well as the generators’ technological specifications. This information supplements the DOE—EIA [j,l,n], which report generators’ quality of burned fuels and environmental equipment installations. The EPA’s Emissions & Generation Resource Integrated Database (EPA a) holds information on generators’ emissions, choice of ernission-abaten'ient technology, as well as their technical specifications such as the control efficiency, fuel usage and coal characteristics. The EPA [n] reports historic fuel consumption, and 502 and other emissions for large generators. The International Energy Agency’s Coal Power3 database reports the available types of $02 scrubbers [International Energy Agency]. The EPA [1] has projected costs of various emission-abatement technologies. Srivastava [2000] estimates the cost of scrub- bing using just four most important characteristics of coal-powered generators—capacity, average heat rate, coal sulfur content and coal heating value. The other processes and characteristics of generators are proxied by default values estimated in the Electric Power 196 Variable Generator-Level Simulation Data Sources Source Generating capacity Number of boilers Fuel type Fuel cost Capital cost Combustion technology Emission allow. allocat. Fuel emission factor Dist. from fuel source Average heat rate Fuel heating rate Ownership Types of plants Generator’s age EPA [a]—Generators, DOE—EIA [l], DOE— EIA [1], DOE-BIA [j] EPA [a]-Generators EPA [a]—Generators, DOE—EIA [l] Argonne National Lab, EIA DOE-BIA [0] EPA [a]—Generators, DOE—EIA [1] EPA, Argonne National Lab EPA [aj—Plants DOE—EIA [l], Argonne National Lab EPA [a]—Plants, EPA, EIA EPA [a]—Generators DOE—EIA [l], DOE—EIA [In] EPA [1], EPA [a]—Generators EPA [a]—Generators, DOE—EIA [l] State-Level Simulation Data Sources Retail restructuring Energy transmission losses Transmission cost Fuel usage Fuel cost Fuel Sulfur Content Price elasticity of demand Fuel transmission markup DOE—EIA [e] DOE-EIA [m], Paul and Burtraw [2002] EIA EPA [8] Argonne National Lab, DOE—EIA [a] Argonne National Lab, DOE—EIA [n], US Ge- ological Survey New York State Energy Office EIA Simulation Data Sources for N ERC Regions Transmission capability Reserve margin ments require- N ERC [a], Paul and Burtraw [2002] DOE—EIA [d], N ERC [b], Edison Electric In- stitute, Paul and Burtraw [2002] Table A.7 Various Simulation Data Sources ment Research Laboratory’s Coal Utility Environmental Cost Workbook [Keith et al., For calibration of model parameters, I used data on their plausible ranges and on his- Research Institute’s Technical Assessment Guide and the EPA’s National Risk Manage- 1999]. Data sources for particular variables and parameters in the model, and for calibra- tion of unknown parameters are summarized in Tables A.7 and A8. toric values of variables in the objective function again mainly from the US Department of 197 Generator-Level Calibration Data Sources Variable Source Generation DOE—EIA [k], EPA [a]—Generators Capacity utilization rate EPA [a]—Generators Scrubbing technology DOE—EIA [1], EPA, Argonne National Lab Emission allowance alloca— EPA Tables A.1-A4 & 1.2, Argonne Na- tion tional Lab Output emission factor EPA [a]—Plants Generator’s sales DOE-EIA [m] Number of customers DOE-EIA [k] Generator’s revenues DOE-EIA [k], DOE—EIA [m] energy price DOE—EIA [k] Fuel consumption DOE—BIA Annual Energy Outlook $02 emissions EPA [o], DOE—EIA [p], NYSEO, EPA [n] State-Level Calibration Data Sources Variable Source Consumption by state EIA Emission allowance trade EPA energy trade by state DOE—EIA [b,d] Emissions by state DOE—EIA [j], DOE—EIA [i], BIA-867, BIA-8608, BIA-906, FERC-423 Generation by state DOE—EIA [a,e,m] Plants’ revenues by state DOE—EIA [b,d] Energy price DOE—EIA [b,d] Fuel prices DOE—EIA [a] Calibration Data Sources for N ERC Regions Variable Source Energy transmission capa- Paul and Burtraw [2002] bility Energy transmission costs & DOE—EIA [m], Paul and Burtraw [2002] energy losses Table A8 Data Sources for Model Calibration Energy-O—Energy Information Administration and the Environmental Protection Agency. These data sources are listed in Table A8. All parameters were calibrated jointly using all available historic data. Table A9 reports the definitions of the NERC regions as used in this study, and the geographic distribution of my sample across these regions. Table A.10 reports the transmission capacities for trades across N ERC regions [Paul and Burtraw, 2002]. 198 N ERC Region Name States Gens. Gens. Repres. Region in Data Used in Gens. Code Model CNV California— CA 1,806 81 2 Nevada ECAR East Central IN, MI, OH, WV 1,667 474 43 Area Reliability ERCOT El. Reliab. TX 1,048 191 6 Council of Texas FRCC Florida Reliab. F L 718 235 7 Coordinating Council MAAC Mid-Atlantic DC, DE, MD, 1,057 54 10 Area Council NJ, PA MAIN Mid-America IL, WI 1,325 339 9 Interconnected Network MAPP Mid-America IA, MN, ND, 1,458 646 17 Power Pool NE, SD NE New England CT, MA, ME, 1,195 82 10 NH, RI, VT N WP Northwest Power ID, MT, NV, 978 133 22 Pool OR, UT, WA, WY NY New York NY 1,022 28 3 RA Rocky AZ, CO, NM 539 137 14 Mountain— Arizona SPP Southwest Power AR, KS, LA, 1,712 833 30 Pool MO, MS, OK STV Southeastern & AL, GA, KY, 2,166 410 33 Term. Valley NC, SC, TN, VA Council Total - - 16,691 3,643 206 Table A9 Spatial Distribution of Observations by NERC Region 199 muomwem Ommz mecca 835%an 2062:5259. Each. 2.< 554.2. c E3 2% c o o c o c o c o o >20 .23: o ”as.” as. o o o e was o o o o <2 25.2 owed a o o o o 3 m2 3 o o c 252 o as o o £3 non o o 83 sea a as o .25 o o o 83” o $3 o o o as.“ 83 o 83 >22 a o o c mas; o o o o o o o o 0022 o o a o o o o 8...; o o o o o 22 o o o o o o mow; o o o So.“ o 22 >2 o m: :2 85 o o o o o as; o o o 2%.: o o o as.“ 23.. o o o ”we.“ 0 o o 5.3 222 o o o o was.” o a 33 o o o o 33 922 o o o :w o o o o o o o o o .5022 o o o c 33 o o c o $3. as.“ o o 2.362 >20 <2 252 mam >3 0022 22 >2 mafia 2:22 0.3.52 .5022 5.02 ea / 882 200 Regulated States Restructured States AL, CA, CO, FL, GA, IA, ID, IN, AR, AZ, CT, DC, DE, IL, MA, MD, KS, KY, LA, MN, MO, MS, NC, ME, MI, MT, NH, NJ, NV, NY, ND, NE, NM, OK, SC, SD, TN, OH, OR, PA, RI, TX, VA UT, VT, WA, WI, WV, WY Table All Status of Restructuring of US States CN V 14 MAAC 13 NE 8 RA 14 ECAR 13 MAIN 13 NWP 15 SPP 13 ERCOT 13 MAPP 13 NY 15 STV 13 FRCC 9 Table A.12 N ERC Regions—Margin Reserve Requirements (%) Table A.11 reports how US states have been split in my model into regulated states, and restructured states. While the exact status and its provisions differ by state, this split approximates well the regulatory conditions faced across states, and has been adopted from Palmer et al. [2002]. Table A.12 shows the reserve margin requirements on output that generators in each region must comply with to ensure uninterrupted service to their customers DOE—EIA [o], Palmer et al. [2002]. A.7 Detailed Results of the Health Damage Estimation Figure 2.5 in Section 2.8.5, and Figure 3.4 in Section 3.6.2 have presented the dif- ferences in statewide damages under the emission tax and the emission caps scenarios, against those under the allowance trading system. In both figures, the system of emission caps has been shown to favor the southern states, while the emission tax and the tradable allowance scenarios have favored the states in the north and the northeast. 201 10% o 40% o 45% ° -20% -25% -30% 0 :1 Emission Allowances _ x Emission Tax -35% lllTliIl TUTTIITTTTII OIEIrnlisISi?nlcl.plslIlll H§9§§8255§ 88§§$§35 ‘é’u-ES‘" 50 2532' 8§BQE$EZ§§8285§§53 Figure A.6. Differences in Damages against Those under the System of Trad- able Allowances with Constant Marginal Damages (%)—States Ordered by Concentrations under System of Allowances In this appendix, I show additional and more detailed results on damages computed under each policy scenario. Figures A.6 and A.7 show damages derived in each state across the considered policies, for a constant and a linearly rising marginal damage function, as percentage differences from those under the allowance trading scenario. (Figures 2.5 and 3.4 showed the differences in dollar values.) Interestingly, in terms of the percent of damages avoided compared the system of allowances, emission caps are shown to favor California, Texas, Oklahoma, Nevada, Louisiana and Arkansas, who each avoid over five percent of damages. These states gain the most when the marginal damage function rises in concentrations. On the other hand, emission caps lead to five percent higher, or more, damages in New Jersey, Wisconsin, Minnesota, and most New England states, particularly with a rising marginal damage function. 202 10% 45% -20% 45% ~30% 65% <> O o o uEmwflmAmmumn__q xEmmmmTu IITTI'TTIIIII?IIIIII IVISIITIITIleilYolElrr'fsfiolnTcTaplslFlll m) E OF m zwxxg m4; (PO> mz own H295; MD§§285§2¥ho 5“; §2525§éosozzg Eh§5028§i§6z Figure A.7. Differences in Damages against Those under the System of Trad- able Allowances with Rising Marginal Damages (%)—States Ordered by Con- centrations under System of Allowances 203 Table A.13 presents the damages resulting under the three alternative environmental policies under the assumed constant marginal damages, for each health-impact pathway. This table provides more detail on the results given in Table 3.3 in Section 3.6. Table A.14 shows similar results for marginal damages linearly growing in concentration levels, under the historic range of S 02 concentrations, using the maximum slopes of the marginal damage functions that satisfy the marginal health responses in medical literature. 204 moweEeD E5952 3.3280 ”momozom «55.22252 2225 3395 £325 NOm. Ed. 289 2.3.93.9. «8.3 838.2. 22.3 338.3 2.82.: 2.2352 38. 8983. 1 32.83. 1 88.2.3.4. 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Pathway Constant MD. MD. rising linearly Impact Value ($103) Impact Value ($103) Adult chest discomf. 6,504,748 54,850 3,730,766 31,459 days Adult chronic 3,271,919 5,824,822 5,685,574 3,133,506 bronch. Asthma attacks 5,710,371 174,366 3,666,146 111,946 Cardiac hospital 5,183 64,011 4,341 53,605 adm. Child chronic bronch. 90,638 12,610 51,033 7,100 Child chronic cough 10668,186 61,022 4,688,653 26,819 Emerg. room visits 69,818 13,099 56,927 10,680 Lower respir. symp— 111,633,081 1,011,752 96,884,570 868,676 toms Respir. hospital 21,797 144,873 11,029 73,308 adm. Respir. symptom 132,352,227 368,644 89,185,853 232,152 days Restricted activ. 15,766,459 847,510 15,766,459 847,510 days Total Morbidity - 8,577,559 - 5,396,762 Mortality 16,956 49,000,895 14,057 40,621,534 Table A.15 Historic 1996 302 Health Impacts: Constant vs. Linearly Rising Marginal Damages Table A.16 presents the slopes of the marginal damage function by each health-impact pathway. The impacts on restricted activity days continue to be modeled as constant marginal damages, since I have only one reliable estimate from the health literature. The S 02 and S 04 concentration ranges used to obtain these slopes are from the scenario with a nationwide market with emission allowances, as the historic realization. 207 Pathway Mean Impact Slope Adult chest discomf. day 10.20 - 10_3 1.68 - 10-3 Adult chronic bronch. 115.00. 10-6 74.36 - 10—6 Asthma attacks 867.00 - 10‘6 433.04 - 10—6 Cardiac hospital adm. 13.50 - 10-6 3.06- 10-6 Child chr. bronch. 942.09 - 10-6 569.20-10—6 Child chr. cough-PM 46.12 - 10“3 33.13 - 10—3 Child chr. cough—802 49.97- 10*3 10.767 - 10—3 Emerg. room visits 181.85 - 10‘6 46.85 - 10—6 Lower respir. symptoms 148.00 - 10'"3 71.74 - 10"3 Respir. hospital adm.—PM 5677-10“6 39.13 - 10-6 Respir. hospital adm.—5'04 13.91 » 10-6 1.63- 10—6 Respir. symptom days 0.46 209.96 - 10’3 Restricted activ. days—PM 57.50 - 10"3 0 Restricted activ. days—$04 91.10 - 10'"3 0 Mortality 0.55 137.30 - 10—3 Table A.16 Maximum Slopes of the Marginal Concentration Response Functions (Per Capita Incidents in Affected Population per 149%) m A.8 Other Forms of the Marginal Damage Function With an increasing marginal damage function, damages in all states have been shown to fall compared to the constant marginal damages case, because of a lower assumed impact by inframarginal units of concentrations, and the corresponding lower average damages. These are interesting findings in themselves, because even with similar values for marginal damages, the aggregate damages can be estimated even 29% apart, depending on the modeled impacts of all inframarginal units of concentrations. Since there is a concern that hot spots of 502 concentrations may be particularly harmful [Ellerman et al., 2000, Swift, 2000], my marginal damage function could be mod— ified to allow a greater rate of increase in marginal damages at higher concentration levels. Equation 3.1 can be rewritten as: 208 _ a W2(CQ) = m3 _ (1753 — m1) . (gfi—g—Z) (A.12) 3 - 1 where W1 and W3 are as defined in Equations 3.2. Marginal damages for the in- termediate concentrations (C2), W2, are determined by two parameters: b once again determines the average rise of the damage function, and a determines its local curvature—— the rate of acceleration in the rise of marginal damages as the air concentration in a state approaches the maximum empirically observed level. Parameter a allows me to choose the relative severity of marginal damages caused by hot spots of pollution, and approximates a range of plausible forms of the functions, from constantly rising marginal damages, through exponential functions, to step functions. a is the constant elasticity of the distance between local marginal damages and the maximum observed marginal damages (W3 —-W2), with respect to the distance between the local and the maximum observed concentration level (C3 — C2). Marginal damages change in proportion to the proximity of the concentration level to the maximum level. For a E (0, 1) the slope of the marginal damage function is close to zero at concentrations near C1, and grows monotonically at an accelerating rate as concentrations approach C3.1 Marginal damage function becomes more curved as (1 falls. With a = 1, marginal damages rise at a constant rate, and with a —) 0 they approximate a step function with a threshold at C3, 2 where marginal damages jump up from close to M D1 to M D3. The condition that marginal damages grow at a non-decelerating rate is not taken 1For b = 1, the marginal cost function is constant, and completely flat for all a. 2For the empirical identification of Equation A.12, we would need to estimate parameters a and b. When the regulator learns the level of concentrations at which health damages rise quickly without bound, it could fit the marginal damage function using information on the distribution of concentrations across states, the number of health incidents and treatment costs incurred in individual states under particular concentrations, or the aggregate damages incurred with a given distribution of concentrations. Since a affects the rise of marginal damages particularly at high concentration levels, whereas 5 affects it everywhere the same way, these parameters are presumably distinguishable in the data, and the regulator could estimate one of them by narrowing down the allowable range for the other parameter sufficiently. 209 MD :* ————————————————————— L 3, 'I I -| .— I I l l ' ---'w "JI l-----a-—-----—----- -»;—« I I MD2 I I | I | | ' l . l , . - . r 1 ' . . l C MDI C1 a=o.8, b=0.2 c3 ------------ - a=o.2, b=0.8 " ' a=0.5,b=0.2 Figure A.8. Illustration of the Modeled Realizations of the Damage Function from literature, but is suggested by the concern in the literature over thresholds of safe concentrations and hot spots. It guarantees that marginal damages will not converge at a certain value at high concentrations, but instead will grow quickly without bound. No literature to my knowledge discusses more than the sign of the first derivative of the marginal damage function, but this is always assumed nonnegative [Abt Associates, b, Curtiss and Rabl, 1996a,b, Daniels et al., 2004, Ostro, 1987, Schwartz, 2000, Stavins, 1996, Watson and Ridker, 1984]. Marginal damages over the domain (C1, C3) are always bounded between M D1 and M D3, as desired. Figure A.8 demonstrates the effects of parameters a and b on the modeled marginal damage function, when the estimated statewide concentration levels are between C1 and C3 micrograms per cubic meter. As in Equation 3.6, upon performing the integration of Equation A.12 and plugging in the individual components from Equations 3.5, I get total aggregate damages of: 210 D = Zikj-vk-C1[minmk + g (maxmk — minmk) kj ‘ . _ 1—b(C3—Cj)a+1 b - +kzjlkj 'vk [maxkaj + (maxmk —m1nmk) (0+1 (C3 —C1)a _ EC. . , 1— b b l ‘Zij'vk [maxka1+(maxmk — mlnmk) (m(C3 — C1) — 5C1) kj . (A.13) This is a function of chosen parameters a and b, ranges of estimates from the medical literature min mk and max m k, observed parameters ikj and vk, observed concentration levels Cj and their nationwide range C1—C3. A.8.1 Aggregate Damages Estimated under Additional Parameters Table A.17 summarizes the differences in aggregate damages between the emission tax and the system of emission caps, against those under the system of tradable allowances, for different values of parameters a and b. The relative damages under the system of tradable allowances are thus $0. Values are in million US dollars, in aggregate annual damages. Positive numbers imply that the policy is estimated to lead to higher aggre- gate damages than the system of tradable allowances, and negative numbers imply that aggregate damages are lower under the given policy. This table shows that emission caps lead to the lowest aggregate damages across all considered values for a and b. Since with constant marginal damages (b = 1) the value of a does not matter, the right-most column carries the same numbers across different a. The difference between the damages under the emission caps and those under the other two environmental policies exceeds $300 million for half of the evaluated values of a and b. 211 a \ b 0.00 0.25 0.50 0.75 1.00 Emission 0.00 -0.812 -1.215 -1.618 -2.021 -2.424 Tax 0.25 19.210 14.072 8.934 3.795 -2.424 0.50 36.758 27.131 17.503 7.876 —2.424 0.75 52.124 38.566 25.007 11.448 -2.424 1.00 65.564 48.567 31.570 14.573 -2.424 a \ b 0.00 0.25 0.50 0.75 1.00 Emission 0.0 -313.811 -346.834 -379.858 -412.882 -452.493 Caps 0.25 -226.146 -281.583 -337.021 -392.459 -452.493 0.50 -150.024 -224.927 -299.831 374.735 -452.493 0.75 -83.778 -175.624 -267.470 -359.316 -452.493 1.00 -26.088 -132.689 -239.290 -345.892 -452.493 Table A.17 Differences in Damages against Those under the Emission Allowance Scenario, across Different a and b (3 million) Figure A.9 shows the differences in damages under the emission tax and the emission caps, as compared to the system of allowances, when marginal damages increase in con- centration levels at a constant rate, a = 1, but with different slopes, b E [0, 1]. Values on the horizontal axis—zero to one—indicate the values assumed for the slope parameter b. Units on the vertical axis are $million. Figure A.9 shows that the emission tax and the system of tradable allowances perform similarly, with any differences due to numerical imprecisions in the energy model (refer to Section 2.8.2). Emission caps outperform both of these policies in aggregate damages for all considered slopes of the damage function, b, and particularly at low slopes. As the slope of the marginal damage function rises, the advantage of emission caps in terms of the aggregate damages monotonically falls to mere $26.1 million nationwide. This confirms that the improvement under the emission caps comes mainly from their control of $02 concentrations in heavily populated states at the expense of less populated states, and not from bringing about a more equal distribution of concentrations, or uniformly lower 212 concentrations. Unfortunately, the $26.1 million difference appears to be in the range of a possible modeling error, since the difference in aggregate damages between the emission tax and the system of emission allowances scenarios is itself $65.6 million. Given that the latter policies systematically result in higher aggregate damages than emission caps under all considered forms of the marginal damage function, it is plausible that emission caps truly lead to a less harmful distribution of emissions even under this form of marginal damages, and that this is thanks to their economic properties, and not due to residual infeasibilities in the energy model equilibrium. A similar issue is that $26.1 million, or even $452.5 million, is a small difference compared to the absolute level of aggregate damages under any policy. However, this stems from the decision in this paper to hold aggregate emissions constant under all three alternative policy scenarios. Regional redistribution of emissions therefore has limited power in reducing the aggregate sum of damages, when the high levels of these damages are dictated by the amount of allowed pollution. The fact that the system of emission allowances and the emission tax lead to very similar outcomes, whereas emission caps perform differently under most scenarios, is a confirmation that the results are driven by economic forces under each policy, rather than by randomness in the simulation. Figure A.10 shows nearly a mirror image of Figure A.9. This figure shows again the differences in aggregate damages under the emission tax and the emission caps, against the system of allowances. Here marginal damages rise at the greatest average rate, b = 0, and the function’s curvature is allowed to vary, a E [0, 1]. Large a indicates a close to linearly increasing function, and small a indicates a very curved function that is nearly constant for C2 6 (Cl, C3) near W1, and close to C3 quickly rises to W3. This figure confirms that emission caps lead to the lowest aggregate damages under all considered parametric 213 - - - Emission Allowances ‘ ' \ -350 ‘ —Emission Tax °\.\ ----E ' ' s -. 400 _ mussmn Cap ‘-. \.- -450 I . . \H - 0.25 0.50 0.75 1.00 Figure A.9. Differences in Damages against Those under the Emission Al- lowance Scenario across Different Slopes b (a = 1) ($ million) 214 -350 - - - - Emission Allowances — Emission Tax '400 ‘ -- - - - Emission Caps -450 —1— l l l - 0.25 0.50 0.75 1.00 Figure A.10. Differences in Damages against Those under the Emission Al- lowance Scenario across Different Curvatures a (b = 0) (3 million) values, and particularly for marginal damage functions that are nearly constant for most concentration levels (low a). With marginal damages steadily rising in concentrations (high a), emission caps lose their advantage. 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