Market Power in Power Markets: An Analysis of Residual Demand Curves in California’s Day-ahead Energy Market (1998-2000)

Abstract 2000, with a focus on its day-ahead energy market and its five non-utility thermal generating companies. Our goal is to assess whether the hourly bids of market participants, together with information on thermal unit characteristics and power output, suggest that the five suppliers were behaving in line with Nash supply function competition, bidding close to their marginal costs or restraining quantities relative to the Nash level. The analysis of residual demand inverse elasticities suggests that the five thermal generators had an incentive to exercise unilateral market power that was not always fully exploited. A comparison of market-clearing prices, estimated marginal costs and marginal revenues finds that firm conduct was broadly consistent with Nash supply function competition or more competitive than Nash behavior in most of our sample.


INTRODUCTION
Producer market power can be defined as the ability of a supplier "to profitably raise prices above competitive levels and maintain those prices for a significant time period" (U.S.Department of Energy, 2000).A distinction is often made between vertical and horizontal market power.The former is exercised when a firm involved in two different activities in the supply chain (e.g., power generation and transmission) uses its dominance in one area to raise prices and increase overall profits.In liberalized electricity markets, separating ownership of generation, transmission and distribution or requiring transmission owners to give nondiscriminatory access to their transmission systems addresses issues of vertical market power.However, unbundling does not exclude the possibility of horizontal market power, which occurs when a firm is able to affect prices because of concentration in a single step of the supply chain (e.g., power generation).
In the case of horizontal market power in generation, a supplier could maintain high prices by reducing output below competitive levels (Werden, 1996), or by exploiting the unique characteristics of electric networks, for instance increasing output to create bottlenecks in the transmission system (Cardell, Cullen Hitt and Hogan, 1997).Such exercise of market power could arise as a For nearly a century, electricity in California was provided by three investor-owned utilities (IOUs) that operated generation, transmission and distribution facilities: Pacific Gas & Electric (PG&E) in northern California, Southern California Edison (SCE) and San Diego Gas & Electric (SDG&E) in the southern part of the state.The state was highly dependent on power imports, which represented roughly 20% of its supply, and had high retail electricity prices.In an attempt to create a more competitive and lower cost electricity system, in 1992 the California Public Utilities Commission initiated a market review process, which led to Assembly Bill 1890 in 1996 and the opening of a restructured electricity market in April 1998.
The IOUs were required to provide open access to their transmission and distribution system, and to divest most of their fossil-fueled generation capacity (mainly powered by natural gas) to five private firms (Duke, Dynegy, Reliant, Mirant and AES Williams). 2By the end of the divestiture process, the five firms had approximately the same size and owned nearly 17,000 MW, representing about 30% of the total electricity generation capacity in California.
Moreover, two new institutions, the California Power Exchange (PX, or CalPX) and the California Independent System Operator (ISO, or CaISO), were created to manage the operations of the grid and the trading of energy and ancillary services.The PX operated the day-ahead and hour-ahead energy markets, designed as two-sided uniform price auctions, 3 and acted as a Scheduling Coordinator (SC-an intermediary for transactions between generators and load serving entities responsible for submitting balanced energy schedules to the system operator). 4The ISO managed transmission congestion and monitored the hourly acquisition of four ancillary service products (regulation, spinning reserves, non-spinning reserves and replacement reserves), both day-ahead and hour-ahead.In addition, the ISO operated a real-time energy market, in which deviations between predicted and actual supply and demand were balanced in real time.The real-time energy market was also designed as a uniform-price auction: a generator supplying more than its dayahead energy schedule (or a load consuming less than its day-ahead schedule) would be paid the real-time price for the deviation between its schedule and actual supply, while a generator supplying less than its day-ahead energy schedule (or a load consuming more than its day-ahead schedule) would pay the real-time price for the deviation.Bohn, Klevorick and Stalon (1999) provide a detailed description of how the PX and the ISO markets worked.In particular, day-ahead operations can be summarized as follows.On the day prior to the actual dispatch, generators typically submitted energy supply portfolio bids, 5 while load serving entities placed demand portfolio bids for any or all of the 24 hours in the following day. 6Bidders could place up to 16 price and quantity energy bids in any hour.Sales bids were ranked in merit order (from lowest to highest offer price), creating an aggregate supply curve for the day-ahead energy market; similarly, purchase bids were ranked in merit order (from highest to lowest offer price), resulting in an aggregate demand curve for the day-ahead energy market.The PX aggregate curves were obtained by linear interpolation, and the hourly market-clearing price was determined by the intersection of aggregate demand and supply curves.Because the market was designed as a uniform price auction, all accepted sellers (buyers) received (paid) the same market-clearing price, regardless of their bid price.The day-ahead market initially cleared without regards to grid limitations, and the resulting market-clearing price was known as the unconstrained PX price.
Successful bidders were then required to provide the PX with their initial preferred schedules (i.e., to break down their portfolio bids by generation unit and load) and to submit bids for ancillary services and adjustment bids. 7The PX (as well as other SCs) transmitted the day-ahead schedules to the ISO, that would conduct the ancillary services auctions and check whether the energy schedules created congestion among the zones in which California was divided (SP15 in the south and NP15 in the north; a third congestion zone, ZP26, was added between the original two zones in February 2000).If there was no congestion, the unconstrained PX price would become the price generators participating in the PX received for their power supply in that hour; each zonal price would in this case be equal to the unconstrained price.If, on the other hand, the day-ahead schedules resulted in inter-zonal congestion, SCs would submit revised day-ahead schedules, and 8. Utilities recovered their stranded costs through a Competition Transition Charge (CTC) payment, equal to the difference between the fixed retail price and the cost of purchasing electricity on the PX (Ritschel and Smestad, 2003).
9. Hour 18 is chosen for the reasons explained in Section 4. The day-ahead market-clearing quantity and forecast load are obtained from the University of California Energy Institute (2004).
10.In 2000, when PX prices started to rise, it became unclear whether utilities would be able to collect their stranded costs through the CTC payment prior to the March 2002 deadline; this created an additional incentive for the major buyers to shift power purchases from the PX to the ISO, in an attempt to lower prices on the day-ahead market.Our comparison indicates that accepted day-ahead demand bids were below day-ahead forecast load by about 8,000 MW (18% of power peak load) in 2000, on average, while during the two previous years the gap had been approximately equal to 5,000 MW (10% of power peak load); the difference between the means of the two populations is statistically significant in the three years.The implementation of this strategy likely contributed to the sustained price differentials between the PX and the ISO energy prices documented by Borenstein, Bushnell, Knittel and Wolfram (2008).
the ISO performed additional rounds of iteration of congestion management until the day-ahead schedules were finalized.The PX zonal market-clearing prices were the ones paid to the generators in case of congestion.
California's electricity wholesale market began operations in April 1998.The volumes settled on the PX market represented about 85% of the total energy demand in California; about 5% of the electricity delivered in the CAISO control area was sold in the ISO's real-time energy market, while the remaining quantity was supplied through long-term bilateral contracts (Kim and Knittel, 2006;Puller, 2007;Wolak, 2003).Some features of California's electricity market design were considered problematic because they could create perverse incentives for market participants; three of them are particularly relevant.First, utilities were required to sell through the PX or the ISO the power supplied by their generating units, and purchase through the PX or the ISO the power needed to satisfy their load obligations.Therefore, a large fraction of total demand was not covered by long-term forward contracts, but was purchased on the more volatile day-ahead, hourahead and real-time energy markets.At the same time, consumers could switch to a competing Energy Service Provider (ESP) or continue being served by their default provider (one of the three IOUs) at a frozen retail price equal to 90 percent of its 1996 level (Wolak, 2005).The expectation was that wholesale prices would be lower than retail prices, allowing the utilities to recover their stranded costs by March 2002, 8 and that a significant fraction of retail customers would migrate to competing ESPs, so that the utilities' net short position would not be large.In practice, however, only a small fraction of customers (about 12% according to Joskow, 2001) actually shifted to competing ESPs; as a result, utilities were consistently short the difference between service demand and supply from their generating assets, and had to buy at volatile wholesale prices while selling at fixed regulated prices, thus being unable to hedge spot price risk.The lack of forward financial contracting also raised supplier incentives to withhold generating capacity from the market in order to increase wholesale prices.
A second problematic feature of California's market design was the requirement to submit balanced schedules to the PX.This implied that utilities had to purchase most of their power requirements on the PX and rely on the real-time energy market only to cover last-minute imbalances.However, an optimal bidding strategy would have shifted purchases from the day-ahead to the real-time energy market, if ISO prices were expected to be lower than PX prices.One way to implement this strategy, while continuing to formally comply with the balanced schedule requirement, consisted of under-scheduling load in the PX, relative to the day-ahead forecast (Sweeney, 2002).We have compared the total volume of transactions cleared on the day-ahead energy market and the day-ahead forecast load in a representative hour of operation (hour 18), 9 and concluded that the former were indeed lower than the latter, on average. 1011.This opportunity cost was equal to the higher of three amounts: a) the expected market-clearing price in the realtime energy market, if the generator's marginal unit was called upon to provide energy in the real-time market but had not offered its capacity in the ancillary services markets; b) the expected capacity payment in the ancillary services markets, if the unit made its capacity available in these markets but was not called upon to provide real-time energy; c) the expected capacity payment, plus the expected market-clearing price in the real-time energy market, if the unit offered its capacity in the ancillary services markets and was also called upon to provide real-time energy.
Third, California's electricity market consisted of eleven markets for energy and ancillary services that cleared sequentially.As pointed out by Harvey andHogan (2000, 2001) and Sweeney (2002), this structure created bidding incentives similar to those introduced by a pay-as-bid auction.In the day-ahead energy market, generators maximized their profits by bidding at a price reflecting the greater of their marginal production cost and their opportunity cost associated with the existence of the sequential markets. 11Therefore, in principle both the existence of opportunity costs and the exercise of supplier market power could lead to observed bid prices exceeding marginal generation costs.
Since May 2000, California's deregulated market confronted "a run of very bad luck" (Joskow, 2001).Power demand increased and imports from neighboring states were reduced, due to hot weather and strong economic growth.Rising natural gas prices resulted from increased demand for power generation, coupled with limitations in pipeline capacity and shortages determined by technical problems at storage facilities.Since power plants were operated more intensively than in previous years, break-downs determined capacity outages and emission permit prices NO x rose in southern California due to allowance shortages, particularly in the last quarter of the year 2000.These elements contributed to extremely high and volatile wholesale market prices, and to curtailed electricity consumption in response to supply shortages.
By the end of January 2001 the PX ceased operations because the IOUs could not pay for their power purchases, and two months later PG&E declared bankruptcy.After regulatory interventions both at the federal and state level, wholesale prices eventually began to fall in June 2001, and by August they had returned to levels observed in May 2000.Joskow (2001) and Sweeney (2002) describe in greater detail electricity deregulation in California and the reasons behind the collapse of its wholesale market.

LITERATURE ON THE MEASUREMENT OF SUPPLIER MARKET POWER IN CALIFORNIA'S WHOLESALE ELECTRICITY MARKET
In the aftermath of California's electricity crisis, several analyses focused on whether the five thermal suppliers had contributed to the high level of prices observed between the second half of 1999 and the end of 2000 through physical and/or economic withholding of their generation capacity.It is possible to identify three main approaches in the literature; our analysis is most closely related to the third of these.
Some studies rely on the competitive benchmark approach to measure the level of market power exercised by the thermal generators.The idea is to estimate the prices that would result if no supplier had the ability to exercise market power, and compare them to observed market prices (for example, by constructing a Lerner index).Borenstein, Bushnell and Wolak (2002) estimate competitive benchmark prices in the PX market, and compare them to actual prices from June 1998 to October 2000.The authors find significant departures from competitive pricing, particularly during summer months, and estimate that the exercise of market power may have contributed to raising energy prices by about 16%.Joskow and Kahn (2002) also simulate PX competitive bench-12.Harvey and Hogan suggest that a more relevant criterion for the identification of market power would be evidence that generators were physically withholding capacity (for energy production or reserve provision) when the energy price was above the opportunity cost (and not just the production cost).A similar analysis was performed by the Federal Energy Regulatory Commission on a limited number of hours, finding no clear evidence of significant physical withholding (Federal Energy Regulatory Commission, 2003b).
13. Relying on simulated data, Corts (1999) shows that if firms' underlying behavior is not the result of one of the three benchmark models of competition (competitive, Cournot or joint monopoly pricing) but of a different game (in Corts' simulations, a game of dynamic or tacit collusion), the true first order conditions will differ from the ones predicted by the static conduct parameter models.As a result, the first order conditions are mispecified and market power estimates are biased.
mark prices in the summer of 2000, taking better account of some market fundamentals (in particular, the price of permits), relative to Borenstein, Bushnell and Wolak (2002).The authors NO x find that actual prices in June, July and August 2000 were higher than estimated competitive benchmarks by 90%, 56% and 36%, respectively.The competitive benchmark approach has been criticized, based on the argument that inaccurate simulation models could produce erroneous estimates of competitive prices by ignoring commitment costs and ramping, must-run, transmission and reliability constraints (Harvey and Hogan, 2002).This in turn leads to incorrect conclusions regarding the exercise of market power (Harvey andHogan, 2000, 2001). 12In a study of the New England wholesale electricity market, Bushnell and Saravia (2002) find that, by not accounting for operating constraints, competitive benchmark prices tend to understate actual market-clearing prices by about 12%.
A second strand of the literature measures supplier market power relying on the estimation of a conduct parameter.Bresnahan (1989) defines the conduct parameter in terms of the following h i relation, obtained from firm i's first order condition: where is the inverse industry demand function, is firm i's marginal cost, is the firm's P M C q i i output and .Equation ( 1) is derived from a conjectural variation model, that describes a Q = q ∑ i i firm's belief about how the optimal behavior of rival firms will change as its output changes.For this reason, the concept of conduct parameter is closely related to the notion of conjectural variation and , where represents the aggregate variation of all other firms' output that firm i h = 1 + r r i i i assumes will result from increasing its own output.The conduct parameter can be thought of as an index of the competitiveness of the firm's conduct: a value of close to 0 corresponds to the h i competitive model, a value of close to 1 signals Cournot behavior, while close to N (N being the number of firms in the industry) indicates that firms are jointly maximizing profits.Puller (2007) combines the competitive benchmark approach described above with the estimation of conduct parameters to analyze PX energy prices from April 1998 to late 2000.His analysis suggests that, throughout the sample, the level of prices was consistent with that of a Cournot pricing game: in particular, in 2000 prices were above unilateral market power levels, but fell short of collusion prices.Empirical models estimating conduct parameters have also been criticized, as they may return biased estimates of market power. 13In the setting of the PX day-ahead energy market, Kim and Knittel (2006) use direct measures of marginal costs to calculate elasticity-adjusted Lerner indices, that are compared to estimated conduct parameters: the authors find that the former (which are arguably more accurate) usually fall outside of the 95% confidence intervals of the latter, which tend to overstate market power.
A third approach to estimate supplier market power in California is based on the analysis of the unit-specific supply bids placed on the ISO's real-time energy market.Sheffrin (2001) constructs hourly bid-cost mark-up indices for each of the five thermal generators between May and November 2000, and estimates that they were bidding full capacity at a price higher than marginal cost about 60% of the times.Bid data have also been used to calculate direct measures of market power.Wolak (2003) calculates the unilateral incentive of thermal generators to exercise market power in the California ISO's real-time energy market in the summer of 1998-2000, assuming expected profit-maximizing bidding behavior.Regardless of the actual residual demand realization in a given hour, a generator maximizing profits unilaterally would face the following first order condition: where is the market-clearing price in hour h, is the marginal cost of generation of firm j in hour h, and is the absolute value of the elasticity of the residual demand curve facing firm j ⑀ jh in hour h, evaluated at .Wolak estimates an empirical "Lerner index" based on the right side of P h equation ( 2): this measures the amount by which each firm is able to raise prices above its marginal cost of generation in a given hour, or each firm's unilateral incentive to exercise market power.If the generator faces a relatively steep part of its residual demand curve, a given percentage reduction in its supply creates a greater percentage increase in the market price: this results in a high inverse elasticity.On the other hand, if the generator faces a relatively flat part of its residual demand curve, a given percentage reduction in its supply creates a smaller percentage increase in the market price: this results in a low inverse elasticity.Wolak reports averages of hourly values from June to September of 1998, 1999 and 2000, finding higher levels for all firms in 2000; this supports his hypothesis that generators were able to exercise market power in the real-time energy market with no need of coordinating efforts.

METHODOLOGY AND DATA
The next four subsections describe the methodological approach and data used in this paper.In the first part of the analysis, the objective is to determine whether California's five thermal generators had a unilateral incentive to exercise market power in the PX day-ahead energy market.Similarly to Wolak (2003), we construct a direct measure of unilateral market power for each supplier, given by the hourly inverse elasticity of the residual demand faced in the PX, evaluated at market-clearing price (right side of equation ( 2)).
In the second part of the analysis, the goal is to understand whether generators truly behaved in line with Nash supply function competition (i.e., if they were exercising unilateral market power, given the bids of other market participants).Alternatively, they could have been bidding close to their marginal costs (i.e., they were price takers), or restraining quantities relative to the Nash level (which might be consistent with collusion or with a Cournot game, since Cournot equilibrium prices represent an upper bound to prices from supply function equilibrium models (Metzler, Hobbs and Pang, 2003)).Through a comparison of actual prices, estimated marginal costs and marginal revenues, we check whether the first order conditions of unilateral profit maximization were satisfied in the hours of our sample.
14.In his analysis of California's real-time energy market, Wolak (2003) also calculates residual demand arc elasticities; this is necessary because aggregate supply curves (and, consequently, residual demand curves) in the ISO's market were step functions.Contrary to the ISO, PX offer curves were piecewise linear functions obtained by interpolation.Thus, elasticities could also be computed at the exact residual demand faced by the generator at market-clearing price (point elasticities).Besides the arc elasticities presented in this paper, we calculated point elasticities and found them to be noisier and smaller (in absolute value) than arc elasticities.The reason is that point elasticities are based upon price-quantity combinations (along each firm's residual demand curve) below and above the market-clearing price that are very close, and thus typically define a narrow neighborhood around that price: as a result, point elasticities are usually calculated over a steep segment of the firm's residual demand function.On the other hand, the price-quantity combinations below and above the market-clearing price by a given range usually define a wider neighborhood around that price, so that arc elasticities are calculated over a flatter segment of the residual demand function.The choice of arc elasticities, rather than point elasticities, does not significantly affect the main conclusions of our analysis.
The number of observations varies by firm, depending on the date in which the thermal generator received the assets divested by the IOUs.On each day of the sample, similarly to Puller (2007) we consider a single hour of operation, hour 18: at this hour, ramping constraints on natural gas plants are unlikely to be binding, as generators have had enough time to ramp up their units to face late afternoon peak demand, but have not yet started ramping down.

Calculation of the Residual Demand Elasticities
Given the bids of all market participants (Federal Energy Regulatory Commission, 2003a), we derive the hourly aggregate supply function and the residual demand function faced by each thermal generator in the day-ahead energy market, using the same approach adopted by the PX.Then, we calculate arc elasticities of the residual demand, to account for the fact that thermal generators would be uncertain about the precise supply curves bid by their rivals and thus unable to anticipate the exact residual demand elasticity. 14Our methodology is graphically illustrated in Figure 1 and can be described as follows: (a) For each generator in the PX, we compute an interpolated supply function.Its prices are all the unique prices bid by that supplier; its quantities are obtained by interpolating the supplier's individual bids, and summing across bids.For example, assume that firm X submits two portfolio bids in a given hour.Figure 1 (a) shows how to obtain the interpolated supply function for the firm.(b) The aggregate supply function faced by firm X is also obtained by linear interpolation.
Its prices are all the unique prices bid by suppliers other than X; its quantities are obtained by interpolating the aggregate supply function of all suppliers but firm X, and summing across all aggregate supply functions.In the illustrative example, suppose two other generators (Y and Z) participate in the PX; each firm's interpolated supply function is obtained as described in Figure 1  (d) Similarly to the PX, we assume a linear functional form for the aggregate supply function in the neighborhood of the observed MCP and MCQ, and find the aggregate supply of all players but firm X at MCP.In the example, the aggregate supply faced by X at MCP is equal to 65.17 MW (Figure 1 (d)).(e) For the aggregate supply in the example, Figure 1 (e) shows the corresponding residual demand function.The residual demand faced by X at MCP is equal to 34.83 MW (point C).(f) Suppose that generator X can reasonably estimate its residual demand within a range equal to 10 MW.Given the residual demand faced by firm X at MCP, we find the two quantities which are, respectively, below and above that value by 10 MW.By linear interpolation, we also find the corresponding prices on the residual demand function.
In Figure 1 (e), these price-quantity combinations are identified as points D and E. (g) Given the residual demand faced by the generator at MCP (point C in Figure 1 (e)) and the two points along the residual demand function having a quantity below and above C by 10 MW (D and E), the negative slope of the residual demand function is 1/ , where: m faced by firm j in hour h at .In the illustrative example, the absolute elasticity of the P h residual demand faced by firm X at MCP, calculated with a range of 10 MW, is equal to 1.28.
Our residual demand elasticities are obtained with a range of 100 MW around the marketclearing price. 15As noted in Section 2, in case of congestion a generator's residual demand would be different than the one obtained from the portfolio bids initially placed on the day-ahead energy market; in general, the residual demand should be less elastic, due to the reduced number of suppliers able to serve demand in each congestion zone, and each generator would have a greater unilateral incentive to exercise market power.Given information on unit-specific initial preferred schedules and adjustment bids from the PX and other Scheduling Coordinators, the ISO could determine the effective residual demand faced by each supplier during congested hours.Since we only have the portfolio bids initially submitted by PX market participants, it is impossible for us to do so; for this reason, our analysis excludes congested hours.Over the three years of PX operation, hour 18 was congested 28% of the time in 1998, 44% of the time in 1999 and 43% of the time in 2000.Besides congested hours, we exclude hours in which a supplier offered a quantity close or equal to zero at MCP.This occurred when the residual demand faced by the firm was slightly negative (meaning that its competitors were supplying the quantity demanded at market-clearing price), or when the PX market-clearing price was lower than the firm's marginal cost.Thus, our residual demand elasticities are calculated based on a sample of 516 hours for Duke, 574 hours for Dynegy, 538 hours for Reliant, 362 hours for Mirant and 513 hours for AES Williams.
It is important to emphasize two aspects of the inverse elasticity as a measure of unilateral market power.The first is that the right side of equation ( 2) provides an indication of market power under the assumption that a firm is unilaterally maximizing its profits, given the realized bids of its competitors.This type of behavior is in line with what would be predicted by a supply function equilibrium model assuming a Nash conjecture, in which the firm optimizes the parameters of its bid function, treating the bids of other market participants as fixed (Day, Hobbs and Pang, 2002).However, if firm behavior is not consistent with unilateral profit maximization, the interpretation of the inverse elasticity as a Lerner index is incorrect, as equation ( 2) (derived from the first order conditions for unilateral profit maximization) does not hold.
The second point is that equation (2) may not be satisfied if market rules constrain the ability of the firm to submit flexible bids (i.e., bids intersecting all residual demand realizations at the ex post profit-maximizing price and quantity pairs), or if the supplier has significant forward contract positions.Both constraints were unlikely to be binding in California's electricity market after deregulation: in the day-ahead energy market, participants were able to submit up to sixteen price and quantity hourly bids, while in the real-time energy market they could submit up to ten price and quantity hourly bids.Moreover, as noted in Section 2, long-term forward contract positions were limited.Thus, in the context of California's day-ahead energy market in 1998-2000 equation (2) should hold, on average, if a supplier is unilaterally maximizing profits and produces on the elastic part of its residual demand function (i.e., where the absolute value of the elasticity is greater than 1).If, on the other hand, the absolute elasticity is less than 1 (and the inverse elasticity is larger than 1), restricting output would increase revenue and decrease cost, and so would necessarily be profit maximizing.Thus, if inverse elasticities are consistently greater than 1, it might be concluded that the firm was producing more than if it were truly maximizing profits unilaterally: in other words, that it was exercising less market power than predicted by a supply function equilibrium model assuming a Nash conjecture.

Calculation of the Marginal Costs of Generation
In the second part of the analysis, we derive an estimate for the hourly variable cost of electricity generation for each unit owned by the five thermal suppliers.In turn, this allows us to estimate each supplier's hourly marginal cost of generation, based on which units are on the margin.
The production cost of each generating unit is the sum of fuel costs, variable O&M costs and emission permit costs (if the unit participates in the RECLAIM 16 ), and is assumed to be NO x constant up to the unit's capacity.We do not account explicitly for the opportunity costs introduced by the presence of the later ancillary services and real-time markets.We also disregard unit commitment costs, which may lead to underestimating the units' production costs, as noted by Harvey and Hogan (2000).Nevertheless, the incidence of unit commitment costs should not be particularly relevant in a peak hour of operation like the one considered here (hour 18).
The proprietary database in Borenstein, Bushnell and Wolak (2002) provides unit-specific information on fuel type, nameplate capacity, average heat rates, estimated O&M costs, emis-NO x sion rates, emission permit costs and participation in the RECLAIM.Fuel costs (in $/MBtu) NO x are obtained from two sources.For natural gas units, the fuel cost is given by the daily spot price of natural gas delivered into Southern California from ElPaso NatGas Co. near the California-Arizona border.This time series was downloaded from Bloomberg Finance L.P., and adjusted by the distribution rates of the gas utility serving each generator. 17For the few units relying on jet fuel or fuel oil as their primary fuel, we use, respectively, the monthly California jet fuel retail sale price and the daily Los Angeles spot price for diesel reported by the U.S. Energy Information Administration (2012aAdministration ( , 2012b)).Fuel costs are then multiplied by the unit-specific heat rates, in MBtu/ MWh.The available emission permit cost is a quantity weighted monthly average paid for trades registered with SCAQMD, in $/lb.We multiply this value by each unit's emission rate (in lb/ NO x MWh), and add this term to the other variable costs of units subject to the RECLAIM.
The hourly power output for most generating units owned by the five thermal generators can be obtained from the EPA's Continuous Emissions Monitoring System (CEMS) (U.S. Environmental Protection Agency, 2012).While the CEMS data is fairly complete for AES Williams and Reliant, it is missing for units corresponding to about 5% of Duke's capacity, 30% of Dynegy's capacity and 15% of Mirant's capacity (Puller, 2007).This could lead to incorrect estimates for the marginal production costs of these firms.
The CEMS reports the gross output of each unit, which includes power sales to the grid and consumption for station operations.Since nameplate plant capacity and heat rates are intended as net, gross generation is converted to net generation with unit-specific factors provided by Steven Puller (personal communication).We disregard monthly variations in actual capacity that are due to temperature fluctuations, as these are likely to be relatively small.
The marginal cost of electricity generation for a firm is defined as a range, with a lower bound and an upper bound.A comparison between the output of each unit whose production is reported in the CEMS in a given hour and its nameplate capacity allows us to determine whether the unit has excess capacity.The firm's marginal cost is typically the cost of its most expensive operating unit which has excess capacity; in this case, the lower and upper bound of the marginal cost range coincide.When all operating units of a supplier are at capacity, the lower bound of the marginal cost range is the cost of the last operating unit, while the upper bound is the cost of the cheapest non-operating unit.

Calculation of the Marginal Revenues
Given the residual demand elasticity, the marginal revenue of generator j at hour h ( ) is obtained as: where is the PX market-clearing price in hour h and is the absolute value of the elasticity of P ⑀ h j h the residual demand curve facing firm j in hour h, evaluated at .P h

Definition of Hypotheses on Firm Behavior
A comparison of market-clearing prices, estimated marginal revenues and marginal costs allows us to check whether the first order conditions of unilateral profit maximization were satisfied in practice.First, we focus on the issue of whether or not there is evidence of oligopolistic behavior.For each of the suppliers, we classify the hours in our sample into three categories: H B ): Hours in which the PX market-clearing price is below our estimated lower bound for the supplier's marginal cost.This may occur if there are errors in the marginal cost estimates.Another possibility is that the marginal units were operated in the real-time energy market (without being scheduled in the day-ahead energy market) or were providing ancillary services.Section 5.2.1 discusses these possibilities further.H E ): Hours in which the PX market-clearing price is included in our estimated marginal cost range (i.e., above our estimated lower bound and below our upper bound).H A ): Hours in which the PX market-clearing price is higher than our estimated upper bound for the supplier's marginal cost.
If errors in our marginal cost estimates are unbiased and firms act competitively, we would expect to observe symmetry in this distribution, with the frequency of observations in the first and third categories being approximately equal.On the other hand, a significantly larger fraction of hours with prices above marginal cost would be consistent with a hypothesis of market power exercise.
We then classify the hours in which the PX price is above our estimated upper bound for each supplier's marginal cost into three additional categories: H A-Nash ): A unilaterally profit-maximizing firm would produce where the firm's marginal revenue equals its marginal cost.Evidence that a firm might be unilaterally profitmaximizing (i.e., behaving in line with a Nash supply function equilibrium model) would be suggested by an hourly marginal revenue between our estimated upper and lower cost bounds.H A-MoreC ): If the lower bound marginal cost is higher than marginal revenue, the firm would be producing more than the unilaterally profit-maximizing level of output.This setting is less competitive than perfect competition (because price is greater than marginal cost) but more competitive than unilateral profit maximization (because more is produced than under unilateral profit maximization).H A-LessC ): If the marginal revenue is higher than the upper bound marginal cost, the firm would be producing less than the unilaterally profit-maximizing level of output.This setting is less competitive than unilateral profit maximization; tacit collusion among firms or a Cournot game among the generators may yield this outcome.

What Measure of Market Power is Provided by the PX Residual Demand Inverse
Elasticities?
Using the methodology described in Section 4.1, we assess whether California's five thermal generators had an incentive to exercise unilateral market power in the PX day-ahead market.This is done by constructing a direct measure of market power, based on the hourly PX bids of market participants, for hour 18 between April 1998 and December 2000.The direct measure is the absolute value of the inverse elasticity of the residual demand function faced by each thermal generator, evaluated at the market-clearing price, consistently with Wolak's analysis of the smaller real-time energy market in California (Wolak, 2003).
Figures 2 (a)-(e) present 30-day moving averages of each firm's inverse arc elasticities.The vertical bars mark the beginning of the California electricity crisis in May 2000.
The inverse elasticities suggest that the five non-utility generators often had an exploitable incentive to exercise unilateral market power, as values lower than 1 indicate that they were typically operating on the elastic portion of their residual demand curve; however, their incentive was not appreciably higher during the electricity crisis.Moreover, in parts of the sample inverse arc elasticities are frequently above 1.This is particularly evident in the summer of 2000 for Duke, in December 2000 for Reliant and in November 1999 for AES Williams.As discussed in Section 4.1, inverse elasticities frequently above 1 suggest that thermal generators did not fully exploit their incentive to exercise unilateral market power, acting more competitively than what would be implied by a Nash supply function equilibrium model.We consider this question more carefully in the second part of the analysis (Section 5.2).
We compare the PX inverse arc elasticities with the ones estimated by Wolak (2003) for the ISO's real-time energy market.Table 1 reports each thermal supplier's average values in Wolak (2003) for the summer of 1998, 1999 and 2000, while Table 2 lists mean and standard error of the PX inverse elasticities over the same months.Since results for the ISO are quantitatively similar for all firms across 1998, 1999 and 2000, Wolak chooses to report them by anonymous firm number, rather than by firm name.Although for this reason a direct comparison of firm behavior in the PX and the ISO energy markets is not possible, the values presented in the two tables offer some general insights.
First, standard tests of statistical difference show that the PX inverse arc elasticities are significantly greater than those in the ISO market, suggesting that the incentive to exercise market power was higher in the PX than in the ISO.Second, in Wolak (2003) firm-level means are not statistically different from each other in the same year and are always lower than 1; we find that the opposite is true for the PX.Finally, Wolak finds that, for each thermal generator, the average hourly values of the ISO inverse elasticities are significantly higher in 2000 than in the two previous

Did Generator Behavior Satisfy the Necessary Conditions for the Exercise of Unilateral Market Power?
As discussed in Section 4.1, residual demand inverse elasticities provide an indication of market power under the assumption that a firm is unilaterally maximizing profits, given the realized bids of other market participants.However, this assumption may not necessarily be verified, if firm behavior is better explained by a different model of interaction with its competitors.The second objective of this analysis is to assess whether the necessary (or first order) conditions for the unilateral exercise of market power in the California PX day-ahead energy market were satisfied in practice.

Classification of hours by firm behavior, without accounting for uncertainty
A comparison of market-clearing prices, estimated marginal revenues and marginal costs represents a possible way of checking if generator behavior was in line with unilateral profit maximization.Results are presented in Tables 3(a)-(e).Our first classification (focusing on whether there is evidence of oligopolistic behavior) divides the hours in the sample into three categories, based on whether the PX price is below, within or above the estimated range for each supplier's hourly marginal cost of operation.As noted, a significantly larger fraction of hours with prices above marginal cost would be consistent with a hypothesis of market power exercise, assuming that the distribution of hours is not significantly skewed to the left.18.The difference between prices and lower bounds is below 5$/MWh 46% of the time for Duke, 44% for Dynegy, 33% for Reliant, 26% for Mirant and 46% for AES Williams.
PX market-clearing prices are below our estimated cost lower bound about 35% of the time, on average across all firms and years. 18One possible explanation is that the ISO's energy prices were higher than those in the PX and firms' marginal supply was offered in the real-time market, without being scheduled in the day-ahead market, or that units were providing ancillary services.CEMS data reports total production for each operating unit owned by a firm, and not just its day-ahead schedule.Suppose a competitive generator bid in the day-ahead energy market at a price approximately equal to the cost of its expected marginal unit X.If the generator also supplied energy in the real-time market, it may have needed to dispatch more expensive generating units than X, that had not been previously bid in the day-ahead market.This would result in a situation in which the marginal cost of production is greater than the unconstrained day-ahead energy price.On the other hand, if a generator dispatched in the energy market was also required to participate in the ancillary services market, it might have sold energy at less than marginal cost in order to obtain a higher margin in the ancillary services market.An alternative explanation for observing market-clearing prices below marginal costs is that there are errors in our marginal cost estimates.We note that if at least one firm has prices below marginal cost, one or more other suppliers fall in the same category 60% of the time in 1998, 75% of the time in 1999 and 85% of the time in 2000.Thus, it is possible that we are underestimating marginal costs for structural reasons (e.g., fuel or emission costs used in our marginal cost calculations are lower than the actual ones).
Based on the classification of hours into H B , H E and H A presented in Tables 3(a)-(e), generators were more likely to bid above their marginal cost than below it.Table 4(a) presents statistical tests of whether market-clearing prices were above each supplier's marginal costs more frequently than below them.We construct the normal approximation to the binomial test z = for the null hypothesis that , where p is the probability that the PX price is above x -Np p ≤ 0.5 Np(1p) Ί our estimated upper bound for marginal cost.In the test, x is the number of hours in which the PX price is above the upper bound, N is the number of hours in which the PX price is above the upper bound or below the lower bound, and p is 0.5.A rejection of the null hypothesis indicates that the supplier was bidding above marginal cost significantly more than 50% of the hours.We report test results for the entire sample period, for each of the three years and for the subperiod May-December 2000, which corresponds to the first phase of the California electricity crisis.
At 5% significance level, we reject the null hypothesis for each supplier over the period 1998-2000.The values of the test are generally well above the 5% critical value (1.65), with the exception of Dynegy.In each of the three years, suppliers were also generally bidding above marginal costs; evidence is particularly strong in the period May-December 2000.Note that a distribution of hours significantly skewed to the left could have a large fraction of observations in which the market-clearing price exceeds the marginal cost upper bound, and yet the average price is below the average upper bound.For each case in which we reject the null hypothesis of the z test, the average price is above the average upper bound, suggesting that the distribution of hours is not significantly skewed to the left.
The goal of our second classification in Tables 3(a)-(e) is to gain insights as to whether suppliers behaved consistently with Nash supply function competition, less competitively than Nash or more competitively than Nash. Table 4(b) presents statistical tests of whether marginal revenues For each firm and period, the first entry in the table is x (the number of hours in which ); the second entry is N MRϾ UB (the number of hours in which , plus the number of hours in which ).In parenthesis we report the value MRϾ UB MRϽ LB of the z test.No value is reported for Mirant in 1998 because the firm inherited PG&E's assets in April 1999.We also do not report the test value whenever the null hypothesis of the test in 4(a) cannot be rejected at any conventional level of significance.
19.Note that the average marginal revenue is also above the average cost lower bound, when the highly negative values for marginal revenue are set to zero.If we use a range of 200 MW, rather than 100 MW, around the market-clearing price to calculate the residual demand elasticities and the corresponding marginal revenues, Mirant's average marginal revenue in 1999-2000 remains below the average cost upper bound (and lower bound).were more frequently above each supplier's marginal costs than below them.We report results of the normal approximation to the binomial test z for the null hypothesis that , where p is the p ≤ 0.5 probability that the marginal revenue is above our estimated cost upper bound.Here, x is the number of hours in which the marginal revenue is above the upper bound, N is the number of hours in which the marginal revenue is above the upper bound or below the lower bound, and p is 0.5.A rejection of the null hypothesis indicates that the supplier's marginal revenue exceeded marginal cost significantly more than 50% of the hours.
At 5% level, we do not find a statistically significant proportion of each supplier's marginal revenues above marginal costs in the entire sample period (with the exception of Mirant) and in each of the three years (apart from Duke in 1998).While Duke's distribution of hours in 1998 is not significantly skewed to the left, Mirant's distribution in 1998-2000 exhibits some highly negative hourly values for marginal revenue, so that its average marginal revenue is above the average cost upper bound if the negative values are set to zero (but not so if they are included). 19Therefore, we generally find no statistical support for the alternative hypothesis that firm prevalent behavior 20.Dynegy's distribution of hours is not significantly skewed to the left; in Mirant's case, similarly to what noted above, the average marginal revenue is below the average cost upper bound if the highly negative values for marginal revenue are included, but not so if they are set to zero.
21. Dynegy's and AES Williams' distributions of hours are not significantly skewed to the left; in Mirant's case, the average marginal revenue is above the average broader upper bound for marginal cost if the highly negative values for marginal revenue are set to zero.
was less competitive than Nash; our results suggest that the five thermal generators acted a `la Nash or more competitively than Nash most of the time.On the other hand, in May-December 2000 Dynegy's and Mirant's marginal revenues were above marginal costs in a significantly larger fraction of hours. 20This result is in line with the one presented by Puller (2007): for these two firms, he estimates conduct parameters that are consistent with less competitive than Cournot behavior in the second half of 2000.

Classification of hours by firm behavior, accounting for uncertainty
Since the possibility of errors in our marginal cost estimates could significantly affect the results of the analysis, Tables 5( a)-(e) present an alternative classification of hours based on a broader set of bounds, to explicitly acknowledge uncertainty in these estimates.The broader bounds are obtained as follows: given the estimated range for the hourly marginal cost for each supplier, the new upper bound is defined as 1.1 times the original upper bound, while the new lower bound is equal to 0.9 times the original lower bound.We assume that the error in our cost estimates is consistent with the spread between actual prices and prices simulated using a competitive benchmark approach, as estimated by Bushnell and Saravia (2002).When accounting for uncertainty in the marginal cost estimates, we find stronger evidence that generators were more likely to bid above their marginal cost than below it: as shown in Table 6(a), we reject the null hypothesis of the z test for each firm and in each period, at 5% significance level.In all cases, the average PX price is above the average broader upper bound.The results of the test for less competitive than Nash behavior in Table 6(b) also suggest that suppliers were acting a `la Nash or more competitively than Nash in 1998-2000, with the exception of Mirant.The focus on the first months of the California electricity crisis confirms our previous findings regarding the prevalent less competitive than Nash behavior for Dynegy and Mirant in this part of the sample; we also find some evidence that AES Williams may have restricted its output relative to the Nash level, although this result is barely significant at a 5% level. 21

CONCLUSIONS
The California electricity crisis of 2000-2001 resulted from a combination of factors, including flawed market design and shortage conditions; however, the extent to which the five largest thermal generators (Duke, Dynegy, Reliant, Mirant and AES Williams) contributed to raising electricity prices before and during the crisis, through physical and/or economic withholding, remains controversial.A detailed examination of the behavior of individual plants owned by each supplier, as suggested by Harvey andHogan (2000, 2001), could provide convincing evidence of physical withholding; however, such a study is practically unfeasible, given that key data (such as unit declared outages, Reliability Must Run contracts and grid operator's instructions to reduce output to avoid congestion) are not publicly available.In the absence of such data, some researchers attempted to measure the degree of market power exercised by the five thermal generators by comparing actual market prices with simulated benchmarks, in most cases intended to reflect competitive conditions in California's electricity market (Borenstein, Bushnell and Wolak, 2002;Joskow and Kahn, 2002).The limitation of this approach is that, if the simulation model does not account for the operating constraints considered by the system operator, there will be a tendency to underestimate the level of competitive prices, leading to incorrect inference on the exercise of market power.Other analyses of California's electricity market relied on the estimation of conduct parameters to analyze the interaction among the five non-utility suppliers (Puller, 2007).This methodology may also return biased estimates of market power, as pointed out by Corts (1999).On the other hand, the availability of generator bids makes possible the application of more direct methods for measuring market power, such as the analysis of the residual demand curves faced by market participants.
In this paper, we take the latter approach to re-examine the exercise of supplier market power in California's power market in 1998-2000, with a focus on its day-ahead energy market (the PX), in which about 85% of the state's electricity was sold.The research goal is to assess whether the five non-utility thermal generating companies bid close to their marginal costs (i.e., if they were acting competitively), bid in line with Nash supply function competition (i.e., if they were exercising unilateral market power), or restrained quantities relative to the Nash level (possibly suggesting tacit collusion or a Cournot game among the generators).The analysis is based on hourly energy bids of all PX market participants, which were unavailable to previous studies, with the exception of Orea and Steinbuks (2012).Our analysis combines this database with information on technical characteristics, output and estimated marginal costs of thermal units owned by the five non-utility generators.
In the first part of our analysis, we follow Wolak (2003)'s approach and calculate a measure of the unilateral incentive of each generator to exercise market power in the PX day-ahead energy market.This measure is given by the inverse elasticity of the residual demand faced by each firm, in absolute value and evaluated at the market-clearing price.Our estimates of PX residual demand inverse elasticities suggest that thermal generators often had an incentive to exercise unilateral market power in the day-ahead energy market, although this incentive was not appreciably higher during the electricity crisis.Moreover, the incentive was not always fully exploited, as suggested by inverse elasticities higher than one in parts of our samples, indicating firm behavior that is more competitive than what would be implied by a Nash supply function equilibrium model.
The question then arises as to what benchmark model of competition could explain the interaction among the five thermal suppliers.In the second part of the analysis, we assess whether the necessary (or first order) conditions for the unilateral exercise of market power were satisfied in practice.First, we focus on whether there is evidence of oligopolistic behavior.For each of the suppliers, we classify the hours in our sample into three categories: hours in which prices are below our estimated lower bound for their marginal cost; hours in which prices are between our estimated lower and upper bound for marginal cost; hours in which prices are above our estimated cost upper bound.If firms act competitively, we would expect to observe symmetry in this distribution, with the frequency of observations in the first and third categories being approximately equal; on the other hand, a significantly larger fraction of hours with prices above marginal costs would be consistent with a hypothesis of market power exercise, assuming the distribution is not significantly skewed to the left.Second, we propose a classification for the hours in which PX prices are above each supplier's estimated marginal cost upper bound, distinguishing among Nash behavior (marginal revenue between the estimated marginal cost upper and lower bounds), more competitive than Nash behavior (marginal revenue below the estimated cost lower bound) and less competitive than Nash behavior (marginal revenue above the estimated cost upper bound).
The results of the first classification of hours are broadly consistent with the conclusions of most previous studies of California's electricity market in 1998-2000: on average, the five generators were more likely to bid available capacity into the PX market at prices above their marginal costs than below them.The evidence is particularly strong for the period May-December 2000, corresponding to the first phase of the California electricity crisis, regardless of whether or not uncertainty in the cost estimates is accounted for (in the form of broader or narrower bounds for the estimated marginal cost ranges).
Our second classification of hours generally finds no statistical support for the hypothesis that firm prevalent behavior was less competitive than Nash in 1998-2000, with the exception of Mirant.Results suggest instead that firms were acting either a `la Nash or more competitively than Nash most of the time, in line with the analysis of our residual demand inverse elasticities.We find that in May-December 2000 marginal revenues were above marginal costs in a significantly larger fraction of hours for Dynegy and Mirant.This result is consistent with Puller (2007), and could be motivated by the lack of production data for some of the peaking generators owned by the two firms, potentially leading to an underestimation of their marginal costs of operation.The decision to disregard hours in which congestion occurred could also affect our results; in particular, the tendency to restrict supply, relative to the Nash level, may be overestimated by the fact that we are considering uncongested hours only.If generators could not perfectly predict when congestion would occur and bid based on an expected residual demand curve, recognizing the probability of congestion, this curve would have been less elastic than an uncongested curve.As a result, unilaterally profit maximizing quantities would have been lower than what we found.
We note three limitations of our study.First, we consider only one peak hour of operation, hour 18: ideally, conclusions would be drawn based on a larger sample of observations.Second, the latter half of our analysis crucially relies on the estimated hourly marginal costs of generation for each supplier.These estimates may not correspond to the "true" marginal costs for several reasons.One is that we use average heat rates, O&M costs, emission rates and emission costs NO x that might deviate appreciably from the ones considered by the thermal generators when optimizing their decisions.Moreover, estimates for the marginal cost ranges are based on the hourly output of generating units reported in the CEMS; as previously noted, the fact that the CEMS is missing for several peaking units could lead to incorrect estimates for the marginal costs of electricity.A final possible reason why our marginal cost estimates might deviate from the true marginal costs is that we do not account explicitly for unit commitment costs, although we note that their incidence should not be too relevant in a peak hour of operation like the one considered in our analysis.
The third limitation comes from the fact that the paper focuses only on the day-ahead energy market.Although the PX accounted for about 85% of energy transactions, the structure of California's electricity market was in fact characterized by a total of eleven markets for energy and ancillary services that cleared sequentially.The presence of the later ancillary services and realtime energy markets may have created incentives for generators to submit bids that did not reflect their incremental production costs, but rather their marginal opportunity costs.Developing a multisettlement supply function model of California's electricity market is a formidable task (Anderson, 2004).Whether the existence of the later markets would have significantly distorted supplier behavior in the PX market remains an open question, although it should be noted that they were much smaller than the PX, both in terms of volume and value of transactions.
(a), and the aggregate supply function faced by X is derived as shown in Figure 1 (b).(c) Given the PX market-clearing price (MCP), along the aggregate supply function faced by firm X we find the closest price-quantity combination below the MCP and the closest price-quantity combination above the MCP.In the example, assume the PX market-clearing quantity (MCQ) is equal to 100 MW, and the MCP is 15 $/MW.The first combination is defined by point A in Figure 1 (c), while the second is given by point B. 15. Results are not sensitive to the choice of a particular range around the market-clearing price: elasticities obtained with a range of 200 MW provide similar indications.

Figure 1 :
Figure 1: Calculation of the Residual Demand Arc Elasticities, Graphical Illustration

Figure 1 :
Figure 1: Calculation of the Residual Demand Arc Elasticities, Graphical Illustration (continued)

Figure 1 :
Figure 1: Calculation of the Residual Demand Arc Elasticities, Graphical Illustration (continued)

Figure 2 :
Figure 2: Monthly Moving Averages of the Inverse Arc Elasticities

Table 1 : Average of Hourly Inverse Elasticities for the ISO Real-time Energy Market, 1998-2000
Wolak (2003)ove reports average inverse elasticities from June 1 to September 30 of each year.Source:Wolak (2003); the author reports results by anonymous firm number, not by firm name.

Table 2 : Average of Hourly Inverse Elasticities for the PX Day-ahead Energy Market, 1998-2000
Note: The table above reports average inverse elasticities from June 1 to September 30 of each year.No value is reported for Mirant in 1998 because the firm inherited PG&E's assets in April 1999.

Table 3 : Classification of Hours by Firm Behavior, without Accounting for Uncertainty in the Marginal Cost Estimates
Note: P is the PX unconstrained market-clearing price at hour 18; MR is the marginal revenue; LB (UB) stands for Lower Bound (Upper Bound) of the marginal cost range.P, LB, UB and MR are in $/MWh.No value is reported for Mirant in 1998 because the firm inherited PG&E's assets in April 1999.

Table 4 : Test for Oligopolistic Behavior (PϾMC vs. PϽMC) and for Less Competitive than Nash Behavior (MRϾMC vs. MRϽMC), without Accounting for Uncertainty in the Marginal Cost Estimates
No value is reported for Mirant in 1998 because the firm inherited PG&E's assets in April 1999.