Measuring Unilateral Market Power in Wholesale Electricity Markets: The California Market,1998–2000
By F RANK A.W OLAK*
This paper measures the unilateral incentive each of thefive largest electricity suppliers in California had to exercise market power in the state’s wholesale market during the four-month period from1June to30September of1998, 1999,and2000.Using the actual bids submitted to the California Independent System Opera-tor’s(CAISO)real-time energy market,I com-pute the hourly price elasticity of the ex post residual demand curve faced by each supplier evaluated at the market-clearing price for that hour.The inverse of this hourly ex post residual demand elasticity quantifies the extent to which that supplier is able to raise the hourly real-time energy price above its marginal cost of supply-ing the last megawatt-hour(MWh)it sells in the CAISO’s real-time energy market.I use the average hourly value of the inverse of thefirm-level residual demand elasticity over the period 1June to30September of each year as a sum-mary measure of the extent of unilateral market power possessed by each supplier.
For eachfirm,this measure of unilateral mar-ket power is significantly higher in2000relative to the corr
espondingfirm-level values in1998 and1999.For each of thefivefirms,this mea-sure is slightly higher in1998than1999.Sev-erin Borenstein et al.(2002)(hereafter BBW) report quantitatively similar results across these three years for their market-level measures of the amount market power exercised in the Cal-ifornia market.The average value of their market-level measure was significantly higher during 2000than in either1998or1999,and the aver-age value in1998was slightly higher than the average value in1999.
Thefirm-level results presented below are consistent with the view that the enormous in-crease in the amount of market power exercised in the California market beginning in June of 2000documented in BBW was due to a sub-stantial increase in the amount of unilateral mar-ket power possessed by each of thefive large suppliers in California.The many investigations of the causes of the California Electricity Crisis currently underway have not uncovered evi-dence that suggests suppliers coordinated their actions to raise prices in California.Thefirm-level measures of market power presented be-low indicate that coordinated actions by suppliers were unnecessary to bring about the substantial price increases that occurred during the period from1June2000to30September 2000.My results are consistent with these price increases in the CAISO’s real-time market be-ing the result of the expected profit-maximizing response of each of thefive suppliers to the bidding behavior of all other market partici-pants in the California market.
I.Measuring Firm-Level Market Power Understanding how suppliers formulate their expected profit-maximizing bidding strategy is a necessaryfirst step toward measuringfirm-level market power in a bid-based electricity market.Wolak(2000)presents a model of expected profit-maximizing bidding behavior in a wholesale electricity market.That paper dem-onstrates that computing afirm’s expected profit-maximizing bidding strategy,under certain conditions,reduces tofinding the set of ex post profit-maximizing price and quantity pairs for all possible residual demand realizations that thefirm might face.Figure1presents an exam-ple of this procedure for the case of two possible residual demand realizations facingfirm A,a
*Department of Economics,Stanford University,Stanford,
CA94305-6072,and NBER(e-mail:wolak@zia.stanford.edu). Azeem Shaikh and Seung-Hyun Hong provided outstanding research assistance.I am grateful to Severin Borenstein,Jim Bushnell,Peter Reiss,and Catherine Wolfram for helpful comments on a previous draft.
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participant in a bid-based wholesale electricity market.
Let MC(q )equal the marginal cost of output level q .Let DR i (p )equal the residual demand realization,for state of the world i ,for i ϭ1or 2.The residual demand facing firm A is equal to the market demand for that hour for state of the world i ,Q i d ,less the aggregate supply bid curve of all other market participants for that hour,SO i (p ),for state of the world i .The function SO i (p )gives the total amount of energy all other market participants besides firm A are willing to supply to the market during that hour at price,p ,under state of the world i .Mathe-matically,DR i (p )ϭQ i d ϪSO i (p ).Because the market is a simultaneous auction,at the time firm A submits its willingness-to-supply bid it does not know which of these two residual-demand-curve realizations will occur.
A firm with the marginal-cost curve given in Figure 1would formulate its expected pro fit-maximizing bid curve,S (p ),as follows.It would compute the pro fit-maximizing price and quantity pair associated with each realization of the residual demand curve.If residual demand realization DR 1(p )occurs,the firm would like to produce at the output level q 1where the marginal-revenue curve associated with DR 1(p )crosses MC(q ),firm A ’s marginal-cost curve.The market price at this level of output by firm
A is equal to p 1.The pro fit-maximizing price and quantity pair associated with residual de-mand realization DR 2(p )is equal to (p 2,q 2).If firm A faced these two possible residual-demand realizations,its expected pro fit-maximizing bid-ding strategy would be any function passing through t
he two pro fit-maximizing price and quantity pairs (p 1,q 1)and (p 2,q 2).The curve drawn in Figure 1is one possible expected pro fit-maximizing bidding strategy.Extending this procedure to the case of more than two possible states of the world is straightforward,so long as distribution of the residual demand curves satis fies certain regularity conditions given in Wolak (2000).In this case,firm A ’s expected pro fit-maximizing bid curve,S (p ),is the function passing through all of the ex post pro fit-maximizing price and quantity pairs as-sociated with all of the possible residual-demand-curve realizations.
This logic has the following implication.Re-gardless of the residual-demand realization,the following equation holds for each hour of the day,h ,and each supplier,j :(1)
͑P h ϪMC jh ͒/P h ϭϪ1/␧hj
where P h is the market price in hour h ,MC jh is the marginal cost of the highest cost MWh produced by firm j in hour h ,and ␧hj is elas-ticity of the residual demand curve facing firm j during hour h evaluated at P h .Mathematically,␧hj ϭDR Јjh (P h )(P h /DR jh (P h )).De fine L hj ϭϪ1/␧hj as the Lerner Index for firm j in hour h .By the logic of Figure 1,it is expected-pro fit-maximizing for supplier j to submit a bid curve in hour h ,S jh (p ),such that all points of inter-section between it and any possi
ble residual demand curve firm j might face in that hour occur at prices where equation (1)holds for that residual-demand-curve realization and resulting market-clearing price,P h .If supplier j is able to find such a bid curve,then it cannot increase its expected pro fits by changing S jh (p ),given the bids submitted by all of it competitors and all possible market-demand realizations Q h d during hour h .
By this logic,the value of L hj ϭϪ1/␧hj is a measure of the unilateral market power that firm j possesses in hour h .I use bids submitted by all participants in the CAISO ’s real-time market to compute L hj for each supplier j and all hours
in
F IGURE 1.C OMPUTIN
G THE E XPECTED P ROFIT -M AXIMIZING
B ID
C URVE S (p )
426AEA PAPERS AND PROCEEDINGS MAY 2003
my sample.The average hourly value of L hj for each supplier for the period from1June to30 September is an annual measure of the amount unilateral market power possessed by thatfirm. Although the conditions required for equa-tion(1)to hold exactly for all possible residual-demand realizations are not strictly valid for CAISO real-time market,deviations from equa-tion(1)are unlikely to be economically signif-icant.As discussed in Wolak(2000),the market rules may prohibit thefirm from submitting a bid curve that is sufficientlyflexible to intersect all possible residual-demand-curve realizations at their ex post profit-maximizing price and quantity pairs.Figure4.1of Wolak(2003)gives an example of how market rules might constrain the bid curves a supplier is able to submit for the ca
se of the Australian electricity market.In this market,suppliers are able to submit up to ten quantity bid increments per generating unit each half-hour of the day,subject to the constraints that all quantity increments are positive and they sum to less than or equal to the capacity of the generating unit.1Associated with each of these quantity increments are prices that must be set once per day.
As shown infigure4.1of Wolak(2003),this restriction can constrain how much afirm’s bid-supply curves can vary across half-hours of the day.To assess the importance of this restric-tion on the ability of suppliers to set prices that satisfy equation(1)for all possible residual-demand realizations for each half-hour of the day,Wolak(2000)compares the actual variable profits earned by a supplier in the Australia electricity market to the variable profits the sup-plier would earn if it were able to set the price that satisfies equation(1)for the realized resid-ual demand curve for that half-hour.Using for-ward contract quantity information and the most plausible estimate of the marginal cost of sup-plying electricity from thisfirm’s units,I found that,averaged over my four-month sample pe-riod,the ratio of the variable profits earned from prices determined by solving equation(1)to variable profits determined from actual produc-tion by thefirm and the actual market-clearing price was1.12.This implies that the actual bids submitted by thisfirm yielded market prices that produced variable profits that were approxi-mately90percent of the variable profits that the firm could have obtained had it set
prices that satisfied equation(1)for all hours for the bids submitted by all other market participants and the actual realization of demand for that half hour.
As noted in Wolak(2001),there are two possible explanations for this difference in vari-able profits.Thefirst is that bidding rules con-strain the ability offirms to set prices that satisfy equation(1)for all possible residual-demand realizations.The second is that the ac-tual bids submitted by market participants were not expected-profit-maximizing.Wolak(2001) explores this hypothesis and computes esti-mates of the daily expected-profit-maximizing bidding strategy for thisfirm for each day dur-ing the sample period and compares them to the realized profits assumingfirms played this strat-egy instead of the bids they actually submitted. Ifind that roughly half of this difference be-tween the variable profits at prices that satisfy equation(1)and actual variable profits,can be explained by the fact that thefirm did not sub-mit the expected-profit-maximizing bidding strategy.Taken together these results suggest that an expected-profit-maximizingfirm operat-ing in the Australian electricity market would not be overly constrained by the market rules from setting a price during each half-hour of the day that satisfies equation(1).
The CAISO’s real-time market rules are even less likely to constrain the ability of suppliers to set prices that satisfy equation(1).Market par-ticipants are allowed to set10quantity incre-ments during e
ach hour of the day for each generation unit,but different from the Austra-lian market they can change the price bids as-sociated with each quantity bid on an hourly basis.This provides tremendousflexibility in how the bid curves of a market participant can vary across hours of the day.Further evidence for the view that suppliers to the CAISO real-time market are not overly constrained by the market rules is that they rarely,if ever,use all 10bid-price/quantity increments during any hour of the day.For these reasons,equation(1) is likely to hold with a small enough error for L jh to be a useful measure offirm-level market
1Electricity-generating plants are typically composed of a number of generating units.For example,a1,500-megawatt(MW)facility may be composed of three500 MW units.427
VOL.93NO.2COMPETITION POLICY IN NETWORK INDUSTRIES
power.Because hourly deviations from equality in equation(1)are likely,I focus on the differ-ences in average values L jh across the years to assess changes in the amount of unilateral mar-ket power possessed by each supplier.
A factor that may cause hourly CAISO real-time prices to fail to satisfy equation(1)is the forwardfinancial obligations of suppliers to provide electricity to the real-time market.As is demonstrat
ed in Wolak(2000),afirm’s forward financial contract position exerts an enormous influence on its expected-profit-maximizing bidding behavior.This paper demonstrates that, given a supplier’s marginal-cost curve,virtually any bid-supply curve can be rationalized as expected-profit-maximizing by appropriate se-lection of a portfolio of forward contract posi-tions.This fact was used by Wolak(2003)to show how the assumption of expected-profit-maximizing behavior and an estimate of the firm’s marginal-cost curve could be used to recover credible estimates of the hourly forward financial contract position of a supplier.
BBW notes that approximately85percent of the electricity delivered in the CAISO control area during thefirst three years of the market was purchased in the California Power Ex-change’s(PX)day-ahead market with approxi-mately5percent purchased in the CAISO’s real-time market.The remaining quantity elec-tricity was supplied through long-term contracts scheduled for delivery in advance of the real-time market.Because the CAISO’s real-time energy market is an imbalance market where suppliers and retailers buy and sell incremental and decremental amounts of energy relative to their day-ahead supply and demand commit-ments,thefirms bidding into the CAISO’s real-time market do not have forward contract obligations to supply additional energy into this market.Consequently,forward contract obliga-tions are not a factor causing equation(1)to fail for the CAISO real-time market.
II.Empirical Implementation Computing the hourly value of the inverse of the residual demand elasticity facing each of the five large suppliers evaluated at a prespecified price is relatively straightforward.The process involvesfirst computing the aggregate demand for electricity in the CAISO’s real-time energy market and subtracting from that the total amount supplied at this price by all market participants besides thefirm j.This yields the value of the residual demand facing supplier j during hour h at that price.Computing the slope of the residual demand curve at the market-clearing price involves some approximation be-cause,strictly speaking,all residual demand curves are step functions.Nevertheless,there are large numbers of steps in these residual demand curves,particularly in the neighbor-hood of the market-clearing price.To compute the slope of the residual demand curve at the hourly market-clearing price,Ifind the closest price above P h such that the residual demand is less than the value at P h.Call this P h(low),and DR jh(P h(low))the associated value of the re-sidual demand.Next Ifind the closest price below P h such that residual demand is greater than the value at P h.Call this P h(high),and DR jh(P h(high))the associated value of the re-sidual demand.The elasticity of the residual demand curve facingfirm j during hour h at price P h is equal to the arc elasticity,computed as
(2)␧jhϭ
DR jh͑P h͑high͒͒ϪDR jh͑P h͑low͒͒
P h͑high͒ϪP h͑low͒
ϫ
P h͑high͒ϩP h͑low͒
DR jh͑P h͑high͒͒ϩDR jh͑P h͑low͒͒.
I experimented with computing the slope of the residual demand curve using afirst-difference approach setting P h(low)and P h(high) equal to a prespecified value below and above P h,such as$1.However,this procedure does not guarantee that the difference between DR jh(P h(high))and DR jh(P h(low))is positive and therefore can produce zero values of␧jh. Nevertheless,results using$0.50,$1,and$5 to determine P h(low)and P h(high)did not pro-duce noticeably different distributions of non-zero values of L hj.
Afinal issue associated with computing the residual demand elasticity is the fact that the CAISO’s state-wide real-time market some-times separates into a number of zonal markets when there is insufficient transmission capacity across regions of California to transfer all of the low-priced energy f
rom one geographic area to
428AEA PAPERS AND PROCEEDINGS MAY2003
other geographic areas.As noted in BBW (2002),initially the CAISO control area was divided into two congestion zones.Effective1 February2000,an additional congestion zone was added.When there is transmission conges-tion across zones,only suppliers with units lo-cated in the congestion zone can meet an incremental increase in the demand for energy in that congestion zone.This means that there are fewer suppliers able to meet an increase in demand in that congestion zone.For this reason, I would expect that the elasticity of afirm’s residual demand curve when there is transmis-sion congestion will be smaller in absolute value.Determining which units are able to sup-ply additional demand within a congestion zone
when there is transmission congestion is not straightforward.For this reason,the present analysis is restricted to hours with no transmis-sion congestion.During the vast majority of hours of the sample period,there is no conges-tion,although the fraction of hours with con-gestion in the transmission network in2000was significantly higher than in1998or1999.For this reason,excluding hours with congestion should bias my results againstfinding higher average values forfirm-level Lerner indexes i
n 2000because,as noted above,thefirm-level Lerner index should be higher during hours with congestion,because fewer suppliers are avail-able to serve demand in any given congestion zone.
III.Empirical Results
To measure the ability of suppliers to exer-cise market power by raising prices accurately, I must exclude hours when this should not oc-cur.As noted in BBW,the cheapest natural-gas-fired generating unit should not have a marginal cost less than$20/MWh,even at the natural-gas prices than existed during1998and1999.By the late summer of2000natural-gas prices were almost three times higher than during the sum-mer of1998and1999.Consequently,hours when the CAISO real-time price is below$20/ MWh is a very conservative estimate of the times when market power is unlikely to be exercised.This cutoff price also biases against finding an increased level of unilateral market power in2000,because higher natural gas prices during the summer of2000significantly raised the price below which market power was
unlikely to be exercised.Higher values of the
ziacutoff price yielded qualitatively similar results.
Table1lists the mean and standard error of Ϫ1times the hourly inverse residual demand elasticity for each of the large suppliers to the
California market.The results are quantitatively
similar for allfirms across the three years,and
none of thefirm-level means is statistically sig-
nificantly different from any other for the same
year.For these two reasons,I report results by
anonymousfirm number,rather than byfirm
name.Uniformly across thefive large suppliers
to the California market,Ifind that the mean
hourly value of L hjϭϪ1/␧hj for all hours without congestion and prices above$20/MWh are significantly higher in2000relative to1998 and1999.In addition,I alsofind that the mean value of L hj fo
r1998is slightly higher than the corresponding value for1999for the portfolio of generating units owned by each of thefive suppliers(AES/Williams,Duke,Dynegy, Mirant,and Reliant).Thefirm-level means for 2000are significantly greater than those for 1998and1999at standard levels of statistical significance.For some of thefirms,the means for1998are statistically significantly greater than the means for1999.
These results are consistent with the BBW
market-level results indicating that substantially
larger amounts of market power were exercised
during2000relative to1998or1999.BBW also
found larger amounts of market power exercised
during June–September of1998relative to
those same months in1999.Taken together the
results in Table1and those in BBW answer the T ABLE1—A VERAGE H OURLY V ALUE OF L
hj
from1June to30September for Hours with Prices Above$20/MWh
Firm
Mean(SE)
199819992000 10.0450.0350.164
(0.007)(0.008)(0.029) 20.0390.0280.164
(0.007)(0.007)(0.029) 30.0540.0320.095
(0.009)(0.008)(0.028) 40.0650.0320.189
(0.013)(0.007)(0.032) 50.0550.0350.161
(0.009)(0.008)(0.029)
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VOL.93NO.2COMPETITION POLICY IN NETWORK INDUSTRIES
often asked question:“Why did suppliers with-hold energy when spot prices were so high.”The answer provided by Table1is:“Because it was in their unilateral profit-maximizing inter-est to do so,given the bids submitted by all other suppliers to the California market.”
IV.Conclusions and Directions
for Future Research
The results in Table1show that collusive behavior on the part of suppliers to the Califor-nia market is unnecessary to explain the enor-mous increase in market power exercised starting in June2000,documented in BBW.The bidding behavior of all other suppliers to the California market during this time left AES/ Williams,Duke,Dynegy,Mirant,and Reliant with residual demand curves that made it uni-laterally expected-profit-maximizing for each firm to bid to raise prices significantly in excess of the marginal cost of their highest-cost unit operating.Although my results cannot rule out explanations involving collusive behavior by suppliers,these are unnecessary to rationalize differences in the extent of market power exer-cised in the California market across itsfirst three years of operation.
There are a number of directions for future research.Thefirst is incorporating hours when there is transmission congestion in the CAISO real-time market.Preliminary work along these lines confirms the intuition that the residual demand curves faced by thefive large suppliers tend to be significantly less elastic during hours with congestion.A second direction for future research is to perform a similar analysis for the California PX day-ahead market.Because sup-pliers have the opportunity to sell their capacity in the CAISO ancillary services markets and the real-time energy market,measuring the extent of market power exercised in the California PX using this methodology is significantly more complicated.
REFERENCES
Borenstein,Severin;Bushnell,James and Wolak, Frank A.“Measuring Market Inefficiencies in California’s Restructured Wholesale Elec-tricity Market.”American Economic Review, December2002,92(5),pp.1376–1405. Wolak,Frank A.“An Empirical Analysis of the Impact of Hedge Contracts on Bidding Be-havior in a Competitive Electricity Market.”International Economic Journal,Summer 2000,14(2),pp.1–40.
.“A Model of Optimal Bidding Behav-ior in a Competitive Electricity Market.”Un-published manuscript,Stanford University, January2001.
.“Identification and Estimation of Cost Functions Using Observed Bid Data:An Ap-plication to Electricity Markets,”in M.Dew-atripont,L.P.Hansen,and S.J.Turnovsky, eds.,Advances in economics and economet-rics:Theory and applications,Eighth World Congress,Vol.II.New York:Cambridge University Press,2003,pp.133–69.
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