RAND Journal of Economics
Vol. 39, No. 1, Spring 2008
pp. 86–114
Understanding strategic bidding in
multi-unit auctions: a case study of the Texas
electricity spot market
Ali Hortac¸su∗
and
Steven L. Puller∗∗
We examine the bidding behavior of firms in the Texas electricity spot market, where bidders
submit hourly supply schedules to sell power. We characterize an equilibrium model of bidding
and use detailed firm-level data on bids and marginal costs to compare actual bidding behavior to
theoretical benchmarks. Firms with large stakes in the market performed close to the theoretical
benchmark of static profit maximization. However, smaller firms utilized excessively steep bid
schedules significantly deviating from this benchmark. Further analysis suggests that payoff
scale has an important effect on firms’ willingness and ability to participate in complex, strategic
market environments.
1. Introduction
Many recent empirical analyses of oligopoly competition, including the analysis of bidding
in auction markets, rely crucially on assumptions regarding the model of firm behavior. In a
typical paper, a researcher has data on firms’ prices or bids and seeks to estimate the underlying
costs of production or valuation of the auctioned object. By assuming that firms behave according
to a particular strategic equilibrium model of profit maximization, the researcher can map firms’
∗
University of Chicago and NBER; hortacsu@uchicago.edu.
∗∗
Texas A&M University; puller@econmail.tamu.edu.
We thank seminar participants at various universities and conferences. We are grateful for assistance with data and
institutional knowledge from Parviz Adib, Tony Grasso, and Danielle Jaussaud at the Public Utility Commission of
Texas. The editor Igal Hendel, two anonymous referees, Severin Borenstein, Jim Bushnell, Stephen Holland, Marc
Ivaldi, Julie Holland Mortimer, Shmuel Oren, Peter Reiss, Steve Wiggins, Joaquim Winter, and Frank Wolak provided
very helpful comments. Hailing Zang, Anirban Sengupta, Jeremy Shapiro, and Joseph Wood provided capable research
assistance. Hortac¸su was a visitor at Harvard University and the Northwestern University Center for the Study of Industrial
Organization during the course of this research, and gratefully acknowledges both institutions’ hospitality and financial
support. Puller was a visitor at the University of California Energy Institute’s Center for the Study of Energy Markets,
for whose hospitality he is grateful. Hortac¸su acknowledges financial support from the National Science Foundation
(SES-0449625) and the Alfred P. Sloan Foundation, and Puller acknowledges support from the Texas Advanced Research
Program (010366-0202).
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HORTAC¸ SU AND PULLER / 87
observed pricing or bidding decisions into their unobserved costs or valuations.1
The inferences
drawn from such approaches rely on the assumed strategic behavior. In most instances, testing the
validity of a particular equilibrium model is left to the laboratory, where the researcher assigns
costs/valuations to subjects and compares the subject behavior to the behavior predicted by the
equilibrium model of competition. Outside of the laboratory, it is difficult to assess equilibrium
models because data usually are not available on bidder costs/valuations.
In this article, we analyze the recently restructured electricity market in Texas, where we
have the advantage of having very detailed bidding and marginal cost data on a rich cross-section
of generation firms. Our study builds on the work of Wolfram (1999) and Sweeting (2007) on the
electricity market of England and Wales, Wolak (2003a) on Australia, and Borenstein, Bushnell,
and Wolak (2002) and Puller (2007) on California, who also use marginal cost data to investigate
theories of oligopolistic firm behavior.2
These data allow us to construct benchmarks for each
firm’s optimal bid functions and compare those to the actual bids. Thus, we “measure” the extent
to which the different firms in our sample maximize expected profits and explore reasons for
observed deviations from (static) profit maximization.
To construct profit maximization benchmarks, we need to account for institutional complexities
of the Texas electricity market in our theoretical model. In this market, most of the electricity
is traded through bilateral forward contracts between generators and users of electricity. To
meet last-minute changes in aggregate electricity demand that fall beyond or below contracted
quantities, generation firms submit bids to adjust their production into an hourly “balancing
market” administered by ERCOT (Electric Reliability Council of Texas). Firms participating
in this market include large formerly regulated utilities, merchant generating firms, and small
municipal utilities and power cooperatives. The hourly market clearing mechanism is a multi-unit,
uniform-price auction—firms bid supply functions and winning sellers earn the price at which
aggregate supply bids equal demand.
We model competition in the hourly balancing market using Wilson’s (1979) “share auction”
formulation.3
In our model, firms choose bid functions to maximize expected profits under
uncertainty coming from two sources. First, total demand for balancing power is determined by
events such as weather shocks, so it is stochastic from the perspective of the bidder. Second, firms
cannot predict the equilibrium bids of their rivals with certainty because each firm possesses
private information on their own forward contracts to supply power. These contract obligations
determine the firms’ net buy or net sell positions in the balancing market, and therefore affect
bidding incentives.4
Because they are private information, these obligations generate uncertainty
from the perspective of other bidders. We characterize the Bayesian-Nash equilibrium of bidding
into the balancing market. We show that when supply schedules are restricted to be additively
separable in price and private information on contract quantities, equilibrium bid schedules are
“ex post optimal” and therefore are straightforward to compute, given information on firms’
contract positions and their marginal costs of generation.
A simiar benchmark, “best-response bidding,” is utilized in Wolak (2003a) and Sweeting
(2007) to analyze bidding behavior in the Australian, and England and Wales electricity markets.
1
See Bresnahan (1989) on empirical models of oligopolistic markets and Hendricks and Porter (forthcoming) and
Athey and Haile (forthcoming) for reviews of the recent empirical literature on auctions. Klemperer (2003) and Einav
(2004) clarify the connections between oligopoly models and auction models.
2
Several other papers use “outside” estimates of marginal cost to measure price-cost margins and test strategic
oligopoly models. For example, Genesove and Mullin (1998) analyze the sugar industry in the early 20th century.
Hendricks, Porter, and Boudreau (1987) investigate the ex post returns of bidders in Outer Continental Shelf oil and gas
lease auctions using drilling and production data from auctioned tracts. Bajari and Hortac¸su (2005) use experimental data
with assigned bidder valuations to gauge the performance of structural econometric models of auctions.
3
Ausubel and Cramton (2002), Wang and Zender (2002), Hortac¸su (2002b), and Viswanathan, Wang, and Witelski
(2002) develop this theoretical framework further. See Cramton (2004) for a particularly accessible account of these
models.
4
Wolak (2000) and Bushnell, Mansur, and Saravia (forthcoming) also point out that forward contract positions are
important determinants of bidding behavior.
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Wolak (2003a) builds on the Klemperer and Meyer (1989) supply-function equilibrium (SFE)
model to motivate this benchmark.5
In the SFE model, which is nested by the Wilson (1979) model,
the source of uncertainty is aggregate demand shifts, and firms do not possess private information
regarding each others’ marginal costs or contract positions. While the assumption that generation
costs are common knowledge across bidders is realistic in electricity markets, where a lot of
information is publicly available about each firm’s generation technology and the spot price of fuel,
it is less likely that firms have accurate information regarding each others’ contract positions on
a high-frequency basis. Our modelling framework allows for the presence of private information
regarding contract positions, and provides conditions under which “best-response bidding” can
be supported as an ex post optimal (Bayesian-Nash) equilibrium outcome. The ex post optimality
feature of this benchmark allows us to avoid pooling data across auctions, and hence avoids
potential measurement biases due to the presence of unobserved (to the econometrician) factors
that vary from auction to auction. In Section 4, we also provide a test of the conditions needed for
ex post optimality. Along with the ex post optimal bidding benchmark, we also test the ex ante
optimality of bidding. We assess whether one can outperform the bidders by constructing the ex
post optimal benchmark, conditioning on past realizations of the residual demand curve, which
is available to the bidders.
An important requirement for constructing all of these bidding benchmarks is having hourto-hour
information on contract positions. However, this information is typically not available to
economic researchers. Wolak (2003a) avoids this problem by utilizing proprietary information on
contracts obtained from a generation company in the Australian, market.6
Because our empirical
focus is to analyze the heterogeneity of bidding performance across a wide variety of firms
operating in ERCOT, and obtaining information on contract quantities for this wide array of firms
was not feasible, we develop a method to infer contract quantities using marginal cost data and the
observed bid function. Our method, described in Section 3, relies on a behavioral assumption that
is much weaker than profit maximization. In essence, we merely require bidders to understand
that they can end up being either net buyers, in which case, they should try to mark down the
market price, or net sellers, in which case they should mark up. This practice was acknowledged
by all of the firms that we interviewed during our research.7
The main empirical finding of the article is that larger firms perform closer to our
benchmark for (static) profit maximization. The smaller firms tend to submit bid functions that
are “excessively steep” so that these firms are not called to supply much power to the balancing
market even when it is ex post profit–maximizing to do so. In Section 5, we argue that this finding
is best explained by the presence of scale economies in setting up and maintaining a successful
bidding operation — an intuition confirmed by our interviews with traders in the market. Thus,
the observed patterns of bidding in this market can be “rationalized” given the fixed costs of
establishing a sophisticated trading operation. We discuss this cost of “ sophistication” in Section
5. Finally, we find some evidence of learning by the small firms over our sample period. The
learning rate is a 10% performance improvement per year.
The observed deviations from theoretical benchmarks are quantitatively important; we find
that this behavior leads to significant efficiency losses. In Section 6, we describe the two sources
of efficiency losses. The first is the efficiency loss due to the (optimal) exercise of market power
by profit-maximizing firms. The second is the efficiency loss due to the “excessive steepness” of
small firms’ bid schedules that we cannot reconcile with expected profit-maximizing behavior.
When we decompose the total efficiency losses into these two components, we find, somewhat
5
The SFE model has been influential in the modelling and analysis of electricity markets, as in Green and
Newbery (1992), Green (1996), Rudkevich (1999), Baldick, Grant, and Kahn (2004), and Crawford, Crespo, and Tauchen
(forthcoming).
6
Sweeting (2007), in contrast, makes the assumption that the generators have 80% contract cover, and tests
robustness to alternative assumptions.
7
Wolak (2003a) demonstrates how one can obtain contract quantities under the assumption of profit maximization.
Because our goal is to test profit maximization, the method proposed by Wolak is not feasible in our context.
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surprisingly, that the latter source of inefficiency is larger. The inefficiency generated by the
smaller firms suggests that market performance could be improved by the consolidation of smallfirm
bidding operations or the use of a market mechanism with less strategic complexity.
Our contributions to the growing literature on characterizing strategic behavior on restructured
electricity markets are both methodological and policy oriented. By applying the Wilson
(1979) model on share auctions, we extend the analysis of Wolak (2003a) and Sweeting (2007) to
the case where firms possess private information regarding their contract positions. We also devise
a method to estimate firms’ (private information) contract positions based on a weak behavioral
restriction. This allows us to conduct tests of ex post and ex ante profit maximization for a rich
cross-section of firms on this market for which information on contracts is not available.
We also believe that our empirical results have generalizable implications for settings outside
of the electricity industry. Aside from controlled experimental settings, there is limited empirical
evidence on the importance of payoff scale and learning in real-world strategic environments. We
present clear evidence that both mechanisms are in effect on ERCOT. We also document, however,
that deviations from profit-maximizing behavior are economically significant. We believe that
this latter finding has important implications for market design.
The outline of the rest of the article is as follows: in Section 2, we describe the institutional
setting of the Texas electricity balancing market. In Section 3, we model strategic bidding in this
market as a uniform-price share auction. We discuss the empirical implications of our model.
In Section 4, we compare our theoretical benchmarks with the actual bids in the data. Section 5
discusses these results and explores the role of payoff scale in explaining deviations from ex post
optimal bidding. Section 6 calculates the efficiency losses and Section 7 concludes.
2. How bidding occurs in ERCOT’s balancing energy market
We analyze electricity transactions that occur through spot-market auctions. In the Texas
wholesale electricity market, most trades occur via bilateral agreements. In addition to this
bilateral market, ERCOT, the system operator, conducts an auction to balance supply and demand
in real time. Approximately 2–5% of energy is traded in this “spot market,” called the Balancing
Energy Services auction, and we analyze the bidding into this auction.
The mechanics of electricity transactions on this market can be summarized as follows.8
One day before production and consumption occur, ERCOT accepts schedules of quantities of
electricity to inject and withdraw at specific locations on the transmission grid. Firms’ day-ahead
schedules are fixed quantities that do not vary in price. The day-ahead schedules may differ from
the firms’ forward contract position. Those supply (“generation”) and demand (“load”) schedules
also may differ from the actual production and consumption in real time for a variety of reasons
such as an unpredictably hot day or an outage at a power plant. The balancing market operates
in real time to balance actual load and generation. Depending upon whether more or less power
is needed than the day-ahead schedule, the balancing demand can be positive or negative. As
the time of production and consumption nears, ERCOT estimates how much balancing energy
is required. Because there are virtually no sources of demand that can respond to prices in real
time, balancing demand is perfectly inelastic.
Bidders offer to increase (INC) and decrease (DEC) the amount of power supplied relative
to their day-ahead schedule. Firms submit hourly INC and DEC bid schedules that must be
increasing monotonic step functions with up to 40 “ elbow” points (20 INC and 20 DEC bids).
These bids may be changed up until one hour prior to the operating hour. The bid schedules apply
to each of the four 15-minute intervals of the hour. In addition, the bidder observes real time
8
See Wilson (2002) and Joskow (2000) for more detailed discussions of transactions in restructured electricity
markets. Further details on the ERCOT market are in Baldick and Niu (2005).
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information on its units’ generation, the load it is obligated to serve, and its net short or long
position in the balancing market.9
Procurement occurs using a uniform-price, multi-unit auction. ERCOT clears the balancing
market four times every hour by intersecting the hourly aggregate bid function with the 15-minute
perfectly inelastic demand function. A generator called to INC is paid the market clearing price
for all INC sales (i.e., production beyond the day-ahead schedule). Likewise, a generator called
to DEC pays the market clearing price for the quantity of output reduced. A generator that DECs
reduces output and purchases power from ERCOT at the market clearing price to satisfy existing
contract obligations.
Bidders appear to have a great deal of information on the competitive environment when
they choose their bid functions. Our conversations with several market participants suggest that
traders have good information on their rivals’ marginal costs. The power plants in Texas have very
similar production technologies, and there are publicly available data on the fuel efficiency of
each generating unit. Traders appear to know the major generating units that are on- and offline at
any point in time. In addition, some market participants purchase real time data on the generation
of large rival plants from an energy information company named Genscape that developed a
technology measuring real time output with remote sensors installed near the transmission lines
out of a plant. This can be useful strategic information not only when initial bids are submitted
but also if the trader wants to change the bids an hour before the market clears.
However, even if firms have a good idea of each others’ marginal cost schedules, they seldom
have information about competitors’ contract obligations. These contracts are signed bilaterally
in an over-the-counter market where it is difficult to monitor transactions, and they are seldom
publicized. As pointed out by Wolak (2000, 2003a) and will become clear in the next Section,
these contract obligations significantly affect bidders’ incentives to exercise market power, hence
this constitutes a very important source of private information.
The information available to the bidders may allow them to accurately estimate the
distribution of their residual demand curve in an upcoming auction. The residual demand is
the perfectly inelastic total balancing demand minus bids by all other firms. Total demand is
stochastic, but shocks to total demand (e.g., weather) only shift residual demand left and right in
a parallel fashion. The distribution of rival bids can be inferred in two ways. A trader equipped
with knowledge of rivals’ marginal costs and the distribution of their contract positions can
compute (as we do in Section 3) the equilibrium mapping of costs and forward positions to
bids. Alternatively, and perhaps more plausibly, every trader has access to the aggregate supply
schedule with a two-day lag. By knowing the recent aggregate supply curve as well as her own
recent bids, the trader can infer the recent aggregate bids by all rivals. To the extent that rival
bids several days before are similar to current rival bids, the trader can infer the shape of residual
demand before placing her bids.
Congestion of the transmission grid poses a slight complication for our analysis. ERCOT is
geographically divided into several zones. If transmission lines between zones are not congested,
the balancing market is a single unified market across all Texas. However, when lines become
congested, ERCOT divides the state into separate markets with different market clearing prices.
During congested hours, bids by some firms are technically feasible while bids by others are not.
Therefore, our analysis uses only uncongested hours, which represent 74% of the time intervals
during our sample period.
We analyze weekdays from the beginning of the market in September 2001 to January 2003.
Although we can analyze any period of the day, we focus on 6:00–6:15 pm because the most
flexible type of generators that can respond to balancing calls without large adjustment costs are
9
Examples of both the bidding and operations interfaces can be found in a supplementary materials Section
at econweb.tamu.edu/puller/HPsupplementary.htm. We thank the real time trading desk at Bryan Texas Utilities and
Reliant/TexasGenco for allowing us to visit and observe their trading desk and allowing us to interview their traders. A
variety of other market participants provided very helpful insights into trading in the balancing market.
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likely to be online during this peak hour of the day. The average number of megawatts (MW)
traded (both positive and negative) during this time interval is 915 MW.10
Demand for balancing
power is both negative and positive in many 6:00-6:15 pm intervals—the interquartile range is
from −709 MW to +615 MW.
The Texas market consists of a variety of investor-owned utilities, independent power
producers, municipal utilities, and power cooperatives. The two largest players are the two large
former incumbent utilities: TXU and Reliant, owning 24% and 18% of capacity, respectively. The
other major investor-owned utilities, (and capacity shares) are Central Power and Light (7%) and
West Texas Utilities (2%). Municipal utilities, (e.g., City of San Antonio Public Service (8%) and
City of Austin (6%)) and power cooperatives (e.g., Lower Colorado River Authority (4%)) also
sell to the balancing market. Finally, there are a large number of merchant generation firms of
various sizes (e.g., Calpine (5%)). The generation technology is primarily fueled by natural gas
and coal with small amounts of nuclear, hydroelectric, and wind generation.
Each firm has some level of contract obligation to directly supply retail customers or provide
power to utilities that serve retail load. If the day-ahead generation schedule differs from the
contract obligation, the firm is either long or short entering into the balancing market. This
residual contract position affects bidding incentives in the auction (Wolak, 2003a). We propose a
method to estimate the long or short position in Section 3.
3. An equilibrium model of bidding on the ERCOT balancing market
We now provide a model of strategic behavior in this market that incorporates the uncertainty
faced by each firm when making their bidding decisions. To do this, we follow the uniform price
share auction setup of Wilson (1979). For ease of exposition, assume that firms sign forward
contracts and then bid all electricity through the auction, that is, assume that there is no dayahead
scheduling. This allows us to simplify notation. After deriving the model, we explain how
we map this model into a market with a day-ahead schedule followed by a balancing auction.
We index the costs of generation (at time t) of the N firms in this market by {Cit (q), i =
1, . . . , N}. We take total demand ˜Dt (p) = Dt (p) + εt to be the sum of a deterministic priceelastic
component and a stochastic constant term.11
Prior to the auction, each firm has signed
contracts to deliver certain quantities of power each hour, given by QCit , at a fixed price PCit .
We assume that these contracts have been written a long enough time ago that they are taken as
“sunk” decisions from the perspective of a bidder making real-time decisions on the balancing
market.12
In each time period t, each firm simultaneously submits a supply schedule, Sit (p, QCit ),
which we restrict to be continuously differentiable, with bounded derivatives. Given the supply
schedules of each firm, the auctioneer computes the market clearing price, pc
t , which satisfies the
market clearing condition
N
i=1
Sit pc
t , QCit = ˜Dt pc
t , (1)
Each firm gets paid Sit (pc
t , QCit )pc
t due to the uniform pricing rule. Hence, firm i’s ex post profit,
upon the realization of market clearing price pc
t , is
10
To compare this with other intervals, the average MW transacted across all intervals varies only slightly over the
day with an average volume of 890. Note that because firms can submit only one bid function for each hour, optimal bids
must cover a wide range of possible demand quantities. Demand varies by an average of 617 MW during each 6:00–7:00
pm bidding hour.
11
In our application, we assume that demand is perfectly inelastic. However, our model generalizes to the case
where D (p) ≤ 0.
12
Although the analysis of the two-stage game with endogenous contract quantity choices adds a further and
interesting strategic dimension, we found that traders who negotiate forward contracts and traders who bid in the
balancing (real-time) market are distinct, and often belong to different trading desks. Thus, our model can be thought of
as applying to the real-time trader.
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πit = Sit pc
t , QCit pc
t − Cit Sit(pc
t ) − pc
t − PCit QCit.
The firm’s payoff from its contract position is −(pc
t − PCit )QCit , because it has to refund its
customers any differential between the contract and market prices for the contracted sales. Wolak
(2003a) has shown this is identical to a contract for differences.
The most important source of uncertainty in the profit equation above is pc
t , the market
clearing price at time t. In a strategic equilibrium, the uncertainty in pc
t , from the perspective of
firm i, is due to two factors: the uncertainty in market demand, ˜Dt , and the unobserved components
of i’s competitors’ profit maximization problems, that is, the contract positions and prices of rival
firms, {(QC jt , PC jt ), j ∈ −i}.
Following the discussion in Section 2, each firm bidding into the market is assumed to know
its rivals’ total cost functions. This knowledge would be sufficient to calculate equilibrium bids
by rival firms, except the firm does not know its rivals’ contract positions. Thus, following Wilson
(1979), we look for a Bayesian-Nash equilibrium characterization of the game, in which firms’
strategies are of the form Sit (p, QCit ).
To characterize a Bayesian-Nash equilibrium, we define a probability measure over the
realizations of the market clearing price, from the perspective of firm i, conditional on firm i’s
private information contract quantity, QCit , and the fact that firm i submits the supply schedule,
ˆSit(p), while his competitors are playing their equilibrium bidding strategies, {S jt (p, QC jt ), j ∈
− i},
Hit(p, ˆSit(p); QCit) ≡ Pr pc
t ≤ p | QCit, ˆSit(p) ,
Utilizing the definition of the market clearing price in equation (1), we can rewrite this probability
distribution as,
Hit(p, ˆSit(p); QCit) = Pr
j −i
Sjt(p, QCjt) + ˆSit(p) ≥ ˜Dt (p) | QCit, ˆSit(p)
=
QC−it ×εt
1
j∈−i
Sjt(p, QCjt) + ˆSit(p) ≥ Dt (p) + εt dF(QC−it , εt | QCit),
where the first line follows from the fact that the event “pc
t ≤ p” is equivalent to there being
excess supply at price p. In the second line, 1{.} is the indicator function for the enclosed event,
and F(QC−it , εt | QCit ) denotes the joint distribution of the vector of contract quantities, {QC jt ,
j ∈ − i}, and the demand noise, εt , conditional on the contract position of bidder i, QCit .13
We now rewrite the bidder’s expected utility maximization problem, where U(π) is the utility
enjoyed by the bidder from making π dollars of profit. This general utility formulation allows for
both risk-averse and risk-neutral firms.
max
ˆSit(p)
¯p
p
¯
U(p ˆSit(p) − Cit(ˆSit(p)) − (p − PCit)QCit) dHit(p, ˆSit(p); QCit),
where the expectation is taken over all possible realizations of the market clearing price, weighted
by the probability density, d Hit(p, ˆSit(p); QCit). The Euler-Lagrange necessary condition for the
(pointwise) optimality of the supply schedule S∗
it (p) is given by14
p − Cit S∗
it(p) = S∗
it(p) − QCit
HS p, S∗
it(p); QCit
Hp p, S∗
it(p); QCit
, (2)
13
Observe that we have not imposed independence on this joint distribution; contract quantities and demand noise
can be correlated. However, as will be evident from the bidder’s objective function below, this is not a common value
environment, as other bidders’ contract quantities do not enter into the bidder’s ex post utility.
14
The proof can be found in Hortac¸su and Puller (2005).
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where
Hp p, S∗
it(p); QCit =
∂
∂ p
Pr pc
t ≤ p | QCit, S∗
it(p)
HS p, S∗
it(p); QCit =
∂
∂S
Pr pc
t ≤ p | QCit, S∗
it(p) ,
H p(p, S∗
it (p);QCit ) is the “density” of market clearing price when firm i bids S∗
it (p). H S(p, S∗
it
(p);QCit ) can be interpreted as the “shift” in the probability distribution of the market clearing
price, due to a change in S∗
it (p); that is, this is the term that captures the “market power” of firm
i. Notice that this derivative is always nonnegative, because an increase in supply weakly lowers
the market clearing price, which weakly increases the probability that the market clearing price
is lower than a given price p.
The above derivation relied on the assumption that supply schedules are continuously
differentiable. In reality, however, firms are allowed to bid 40 price-quantity points, restricting
supply schedules to (nondifferentiable) step functions. A characterization of bidding behavior
in uniform price auctions when the strategy space is restricted to a discrete number of steps is
pursued in McAdams (2006) and Kastl (2006a, 2006b). Kastl (2006b) obtains the result that as the
number of steps available to bidders grows without bound, necessary conditions characterizing
bidding behavior in the discrete strategy game converge to the necessary conditions for the game
with differentiable supply schedules.15
First-order condition (2) can be seen as a “markup” expression, where the markup in price
above the marginal cost depends on how much market power firm i can exercise by shifting the
distribution of the market clearing price through its own supply function S∗
it (p). As an intuitive
consequence, observe that if H S → 0, that is, there is no market power, price equals marginal
cost. Also, note that where S∗
it (p) < QCit , the firm is a net buyer and bids below marginal cost.
Finally, observe that where S∗
it (p) − QCit = 0, p = Cit (S∗
it (p)). This allows us to infer the
unobserved contract positions of the bidders.
Proposition 1. If Cit (S∗
it (p)) is observed, one can calculate the contract position QCit , by finding
the quantity where the supply function of the firm intersects its marginal cost function.
The empirical implementation of (2) requires the estimation of Hit (p, S∗
it (p);QCit ) (and its
partial derivatives), for each bidder i, in every period t. Hit (p, S∗
it (p);QCit ) is the equilibrium
belief of bidder i regarding the distribution of the market clearing price in auction t, conditional
on his bidding strategy, S∗
it (p). Obtaining econometric estimates of this probability distribution
might require strong parametric assumptions regarding the specification of bidder-specific beliefs,
and especially the role played by economic unobservables entering into bidders’ beliefs across
different time periods.16
The latter concern is potentially the most troublesome: if bidders
condition their beliefs on factors unobservable to the economist, estimating Hit (p, S∗
it (p);QCit )
by pooling data from a series of auctions without taking these unobservable factors into account
may lead to incorrect estimates.
Observe also that the set of first-order conditions (2) for each firm, when written as a
system of equations, characterizes equilibrium strategies, Sit (p, QCit ), for given primitives of the
game.17
The computation of equilibrium strategies is not a trivial task, however, because Hit (p,
S∗
it (p);QCit ) is determined endogenously through the market clearing condition (1) and depends
on the joint distribution of contract positions and the distribution of demand noise.
15
Although this is a comforting result from the perspective of assuming differentiable bid schedules, Kastl (2006a)
finds that if bidding extra points is a costly activity, the constrained optimal bidding behavior may depart significantly
from equation (2). We discuss some evidence regarding this possibility in Section 5.
16
Some of these assumptions and possible estimation strategies based on such assumptions are discussed in the
discriminatory (pay-as-bid) share auction context by Hortac¸su (2002a).
17
The primitives of this game are the set of firms that are participating, N, their cost curves Cit (q), i = 1, . . . , N,
the joint distribution of contract quantities, and the distribution of the uncertain demand component.
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However, we now show that the characterization of equilibrium strategies (2) is greatly
simplified when the functional form of the supply function strategies, Si (p, QCi ), is restricted to
a class of strategies that are additively separable in the private information possessed by bidders.
In the subsequent discussion, we drop the time subscript.
Proposition 2. If supply function strategies Si (p, QCi ) are restricted to the class of strategies
Si (p, QCi ) = αi (p) + βi (QCi ), the markup relation (2) is given by the familiar “inverse-elasticity”
markup rule p − Ci (Si (p, QCi )) = Si (p,QCi )−QCi
−RDi (p)
, where RDi (p) is the price derivative of the ex
post realization of the residual demand curve faced by bidder i.
Proof. See Appendix A.
The intuition underlying this result is straightforward. The additive separability restriction
implies that, in equilibrium, the residual demand function faced by bidders is also additively
separable in its random component—that is, all uncertainty (from the perspective of bidder i)
shifts the residual demand curve but does not rotate it. Given this, it is easily seen that (subject
to the concavity of the profit function), the bid function Si (p) provides a pointwise best-response
to every possible realization of the residual demand curve. This also means that the class of
additively separable equilibrium strategies, when they exist, are ex post optimal, in the sense that
seeing other bidders’ supply functions would not change bidder i’s choice of supply function.18
As an important caveat, however, note that the additive separability restriction is an a
priori restriction on bidding strategies. It is not necessarily true that every specification of
marginal cost functions, Ci (q), and joint distribution of contract quantities, QCi , will lead to
equilibrium strategies of this form.19
Hortac¸su and Puller (2005) work through an example in
which firms possess linear marginal cost curves (these can be asymmetric across firms), under
which equilibrium strategies are analytically characterizable, and satisfy the additive separability
restriction. Based on our inspection of actual marginal cost curves, linearity appears to be a
reasonable approximation. Finally, we note that the additive separability restriction is testable and
we provide several tests in Section 4.
This result has an immediate practical application.
Proposition 3. Suppose supply function strategies Si (p, QCi ) are restricted to the additively
separable class of strategies, Si (p, QCi ) = αi (p) + βi (QCi ). Then, given data on the marginal
cost function, one can compute the ex post optimal supply curve Sxpo
i (p), which is the ex post
best-response to the observed realization of the residual demand curve.
Observe that under the above restriction, a single realization of the residual demand curve,
RDi (p, ε, QC−i ), is enough to compute d
dp
RDi (p, ε, QC−i ) = RDi (p) for all realizations. Then,
for a range of prices, p ∈ [p
¯
, ¯p], one can solve the equation for S, in terms of p and QCi ,
p − Ci (S) =
S − QCi
−RDi (p)
(3)
to trace out Sxpo
(p, QCi ), which constitutes an ex post best response to all possible realizations
of residual demand.20
Thus, although additive separability is a restrictive assumption, its imposition aids us greatly
in solving for optimal supply schedules. Perhaps more importantly, ex post optimality aids us
in dealing with economic unobservables. Observe once again that the ex post optimal supply
18
The additive separability restriction appears to be crucial. Note that without this separability restriction, we
cannot, in general, collapse the stochastic terms (from the perspective of bidder i) into a single scalar random variable.
See Appendix A for further discussion of the case where private information leads to rotations in residual demand, as
opposed to shifts.
19
In particular, for certain specifications of marginal costs, a bidder’s best-response to additively separable bidding
strategies by her opponents may not be additively separable.
20
This could be extended to show that given QCi , one can compute the entire marginal cost curve rationalizing a
supply curve Si (p) observed in the data using a single realization of the residual demand curve.
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HORTAC¸ SU AND PULLER / 95
schedule corresponding to a given marginal cost schedule is derived using a single, ex post
observation of residual demand. The proposed empirical procedure does not pool data across
auctions and thus avoids the problem of making strong assumptions as to how to model the role
of unobservables.
4. Analysis of observed bid schedules.
In our empirical application, we implement Proposition 3. We use data on bidders’ marginal
cost functions to calculate the ex post optimal supply curve, which is also an equilibrium bid
function under the restrictions imposed in Proposition 2. Then we compare ex post optimal bid
schedules to actual bids.
Now we explain how we map the model of Section 3 into the actual market. As described in
Section 2, firms in ERCOT do not bid all electricity through the auction. Rather, the firms submit
a fixed-quantity day-ahead schedule, and then compete in the balancing auction to increase or
decrease supply from that day-ahead quantity. In order to implement Proposition 3 to model
bidding in the balancing auction, we modify our marginal cost function and contract quantity.
First, we account for the fact that the day-ahead schedule implies that some of the firm’s generating
capacity is already committed to produce the day-ahead quantity. Thus, we shift the total marginal
cost function to the left by the day-ahead quantity. This balancing marginal cost function represents
the marginal cost of increasing output and the marginal savings of reducing output relative to
the day-ahead schedule. Second, the day-ahead quantity is used to satisfy some of the firm’s
forward contract positions. Any remaining contract position, the balancing contract quantity, is
the QCit that affects bidding into the balancing market.21
Therefore, in the context of our notation
in Section 3, Sit (.) represents supply bids into the balancing market, Cit (q) represents the costs
savings of increasing/reducing output relative to the day-ahead schedule, and QCit represents the
quantity that the firm is long or short on its contracted sales after the day-ahead schedule and
upon entering the balancing market.
Our empirical strategy is illustrated in Figure 1. In order to measure the contract position,
QCit , we use Proposition 1. QCit is measured as the quantity at which the actual (balancing)
bid schedule, S0
i (p, QCi), intersects the (balancing) marginal cost function (point A in Figure
1).22
Note that Proposition 1 allows us to identify the contract position under certain forms of
suboptimal or nonequilibrium bidding. This identification approach is valid as long as the firm is
sufficiently sophisticated to bid above (below) marginal cost when it is a net seller (buyer), even if
it errs in the size of the markup. More formally, we can identify QCit in equation (2) even if firms
have incorrectly calculated HS(p,S∗
it(p);QCit)
Hp(p,S∗
it(p);QCit)
. Our conversations with various market participants lead
us to believe that traders clearly recognize the rationale for marking up bids for quantities greater
than the contract position (and vice versa), but traders have different heuristics for choosing the
size of the markup.
Each firm’s residual demand RDi (p) is the realized total demand minus the bids by all
rival firms. Suppose RD1 in Figure 1 is the actual realization of residual demand for firm i. We
calculate RD1(p) and find the ex post optimal (price, quantity) bid to be point B, where the
marginal revenue curve corresponding to RD1(p), MR1, intersects the marginal cost curve MC.
Also, we can calculate the ex post optimal bid under other possible realizations of uncertainty
(that is, other realizations of total balancing demand, ε, and rivals’ private information, QC−i ).
Because each form of uncertainty acts to shift residual demand in a parallel fashion, we can
consider another possible realization of residual demand as RD2—the realized residual demand
shifted parallel to the left. Under this realization of uncertainty, the optimal bidpoint is given by
21
Notice that the lumping of the day-ahead quantity and the balancing bids does not affect the strategic nature of
the game because the bidders are not provided any information about each others’ actions until the market clears.
22
One could be concerned that there is a small set of distinct contract quantities; however, the empirical distribution
we recover using Proposition 1 suggests that our assumption of a continuous differentiable distribution of contract
quantities is very reasonable.
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96 / THE RAND JOURNAL OF ECONOMICS
FIGURE 1
EMPIRICAL STRATEGY
Price
Quantity
Si
o (p,QCi)
MCi(q)
QCi
A
C
D
RD1
RD2
MR1
MR2
Si
xpo (p,QCi)
B
point C, where MR2 = MCi (q). We repeat this operation by adding parallel shifts to the actual
realization of the residual demand curve to find the set of ex post optimal points for various
realizations of uncertainty. The ex post optimal bid function is traced out by the set of ex post
optimal bid points to generate Sxpo
i (p, QCi ). Note that our assumption that the slope of residual
demand is independent of uncertainty is necessary for the set of ex post optimal points to be on
a monotonic bid function.
We should note that the residual demand function is a step function whose derivatives are
either zero or infinity, which renders the literal evaluation of equation 3 impossible. We follow two
methods to address this: first, we follow Wolak (2003a, 2003b) to obtain a “smoothed” version
of the residual demand function to calculate the marginal revenue curve.23
Second, we perform a
grid search on the “unsmoothed” residual demand function and find the ex post profit-maximizing
point for each parallel shift in residual demand. In practice, we found that the ex post profitability
benchmark that is generated by the grid search departs negligibly from the ex post profitability
benchmark generated by the “smoothed” residual demand.24
Data. We use hourly data on balancing demand and firm-level bids and marginal costs.
To construct each firm’s marginal cost function, we utilize data on the generating units that
are operating on a given hour and the hourly declared capacity of each unit. The marginal
cost of operating units represents the variable costs—fuel, operating and maintenance, and SO2
permit costs—of coal and natural gas-fired units. A growing body of literature has developed
on measuring the marginal cost of electricity production (for example, see Wolfram, 1999;
Borenstein, Bushnell and Wolak, 2002; Mansur, 2007; Puller, 2007; Joskow and Kahn, 2002;
Bushnell and Saravia, 2002; Bushnell, Mansur, and Saravia, forthcoming; Fabra and Toro, 2005)
and we use the same approach. Details of the data and additional institutional considerations are
discussed in Appendix B.
Our “marginal cost of balancing power” function is the costs of increasing production
(INCing) or the cost savings of reducing production (DECing) from the day-ahead scheduled
quantity. We construct this function by first calculating the total marginal cost function in a
23
Let {(p1, q1), . . . , (pK, q K )} represent the price and incremental quantities that form the residual demand curve
seen in the data. The smoothed version of this function is RD(p) =
K
k=1 qk κ( p−pk
h
), where κ(.) is a kernel function. With
this representation, the derivative of residual demand is RD (p) =
K
k=1 qk
1
h
κ ( p−pk
h
). We used a normal kernel and the
smoothing parameter, h = 10 MW throughout our analysis.
24
As an illustration, Reliant’s ex post profitability is 79% under “smoothed” residual demand and 70% under the
grid search.
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HORTAC¸ SU AND PULLER / 97
given hour, and then subtracting the quantity that has already been scheduled the day ahead.
Total marginal cost is the marginal production cost of units that are reported by ERCOT to be
operating and available in period t. It is reasonable to assume that firms produce in a least-cost
manner, so we stack up the marginal cost of each generating unit from cheapest to most expensive
and construct the total marginal cost function. We have data on how much generation has been
scheduled day-ahead by the firm. Thus, the marginal cost of supplying balancing power is the total
marginal cost function with the origin recentered at the day-ahead scheduled quantity. Certain
types of generating units that cannot supply power on short notice are then excluded from this
marginal cost stack. Natural gas-fired units, and to a lesser extent coal units, can be adjusted on
relatively short notice to other production levels. Other types of units such as nuclear, wind, and
hydroelectric, typically cannot respond to balancing market calls. Therefore, we exclude nuclear,
wind, and hydroelectric, generating units from the marginal cost portfolio for providing balancing
energy.25
We use bid schedules for each firm for the 6:00–7:00 pm hour of each noncongested weekday.
To determine the sales into the balancing market, we intersect the actual step bid function with
the realization of residual demand. This simulation of the market clearing process predicts actual
prices with only a 5% error.
Comparison of actual bids to ex post optimal bids. We compare each firm’s actual bids
to ex post optimal bids for each auction. Examples of this comparison for specific auctions are
shown in Figure 2 which displays representative actual and ex post optimal bid functions for three
large suppliers, Reliant, TXU, and Calpine—and for one small seller, Guadalupe. Competitive
bidding is offering the “MC curve” and optimal bidding is offering the “ex post optimal bid.” The
intersection of the actual bids and marginal cost schedules is the contract position. For quantities
above (below) the contract position, the ex post optimal bid function is above (below) marginal
cost. Visually, Reliant’s bids appear much closer to the optimal bids than to the marginal cost
function.
TXU is close to the ex post optimal bid function on the INC side (balancing MW > 0), but
bids below ex post optimal prices on the DEC side. We see this tendency for TXU to offer DECs
at only very low prices throughout our sample.
Calpine offers some DEC bids but does not offer to INC supply. Although Calpine does
offer INC bids in some periods, much of Calpine’s bids are to DEC supply. Those DEC offers are
often at prices substantially below ex post optimal bids.
Guadalupe submits bids that are much steeper than ex post optimal. Because it is a small
seller, Guadalupe’s residual demand function is relatively flat as compared to the residual demand
of the larger players. Nevertheless, it has some potential to bid strategically and exercise market
power. However, the actual bid functions are significantly above the optimal bids in INC periods
and below optimal bids in DEC periods. This suggests that bids significantly different from
marginal cost are not intended as a means to exercise market power, but rather to avoid being
called upon to change production from day-ahead schedules. Many small sellers show similar
bidding patterns. We discuss reasons underlying these patterns in Section 5.
The visual inspection of the figures is suggestive of the closeness of actual bidding behavior
to ex post optimal behavior, but a more meaningful metric to evaluate bidders’ performance is
to measure how much profit they have foregone ex post by deviating from the ex post optimal
bidding schedule.
To calculate the profit deviation, we calculate the difference of the producer surplus obtained
at the actual submitted price/quantity point (point D in Figure 1), and the surplus obtained at
the ex post optimal point (point B in Figure 1). We calculate this difference in each firm-auction
for 20 simulations of residual demand which we construct by adding uniformly distributed noise
25
Some hydroelectric units may be able to respond to balancing calls; however, these units represent less than 1%
of total capacity and are primarily owned by the Lower Colorado River Authority.
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FIGURE 2
EXAMPLES OF ACTUAL AND OPTIMAL BID FUNCTIONS
Reliant
-2000 -1500 -1000 -500 0 500 1000 1500 2000
0
5
10
15
20
25
30
35
40
45
50
Balancing Market Quantity (MW)
Price($/MWh)
Reliant on February 26, 2002 6:00-6:15pm
Residual Demand
Ex-post optimal bid
MC curve
Actual Bidcurve
TXU
-2000 -1500 -1000 -500 0 500 1000 1500 2000
0
5
10
15
20
25
30
35
40
45
50
Balancing Market Quantity (MW)
Price($/MWh)
TXU on March 6, 2002 6:00-6:15pm
Residual Demand
Ex-post optimal bid
MC curve
Actual Bidcurve
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FIGURE 2
CONTINUED.
Calpine
-2000 -1500 -1000 -500 0 500 1000 1500 2000
0
5
10
15
20
25
30
35
40
45
50
Balancing Market Quantity (MW)
Price($/MWh)
Calpine on March 19, 2002 6:00-6:15pm
Residual Demand
Ex-post optimal bid
MC curve
Actual Bidcurve
Guadalupe Power Partners
-2000 -1500 -1000 -500 0 500 1000 1500 2000
0
5
10
15
20
25
30
35
40
45
50
Balancing Market Quantity (MW)
Price($/MWh)
Guadalupe on May 3, 2002 6:00-6:15pm
Residual Demand
Ex-post optimal bid
MC curve
Actual Bidcurve
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(with support −200 MW to +200 MW) to the actual demand. These simulations allow us to
evaluate the optimality of several points on the bid function that could determine output under
other possible realizations of residual demand. The results are generally robust to the scale of the
noise added.
We also calculate the producer surplus achieved relative to a benchmark of “suboptimal”
behavior to compare how much distance is closed between the benchmark of suboptimal pricing
and optimal pricing.26
One possible benchmark is behaving nonstrategically and bidding marginal
cost. However, it appears that the “default” behavior is to bid to avoid being called to supply
balancing power. As shown in the sample figures, smaller firms choose to bid only small quantities
relative to both competitive and optimal bidding. Therefore, we measure performance as the
fraction of (dollar) distance between “no bidding” and ex post optimal bidding that is realized by
the actual bids. Producer surplus in the balancing market is
πit = Sit pc
t pc
t − Cit(Sit pc
t − pc
t − PCit QCit.
We calculate πit for three scenarios: (i) ex post optimal bidding (Sit = SXPO
it ), (ii) actual bidding
(Sit = SO
it ), and (iii) bidding to avoid the balancing market ((Sit = 0), that is, not bidding at all
and buying/selling at the market clearing price any net short or long position on contracts). Our
primary measure of performance is
Percent Achieved =
πActual
− πAvoid
πXPO − πAvoid
,
which we calculate for each firm in the market.
One should keep in mind that Percent Achieved is only a metric of the generator’s performance
in the balancing market. It does not account for the profitability of the vast majority of output
that is sold through bilateral transactions, and therefore may understate the overall profitability
of electricity sales. In order to measure the profits of bilateral sales, we would require data on
contract prices, but such data are not available. However, we can construct an upper bound for
overall profitability by assuming that each generator is maximizing profits in the bilateral market
but may be sacrificing profits in the smaller balancing market.
Upper Bound Total Percent Profitability = Percent Achieved ∗ %Sales in Balancing
+ 100% ∗ %Sales in Bilaterals
We compute each firm’s ex post profitability in each of the auctions in our sample. Table 1
compares output and producer surplus in the balancing market under actual and ex post optimal
bidding. Column 6 shows the average quantity sales if firms submit ex post optimal bids and
column 5 shows the average potential producer surplus from bidding ex post optimally rather than
not bidding. There are substantial differences in the profit potential for the firms in our sample:
for the largest firms with average sales of at least 250 MW under ex post optimal bidding, the
potential producer surplus averages about $2300/hour. Firms that would sell less than 250 MW
under ex post optimal bidding have potential producer surpluses averaging about $750/hour.
The first column displays the percent of potential profits achieved under the actual bid
schedules. Reliant achieves 79% of ex post optimal profits, or $3,422/hour of the $4,333/hour
of potential profits. The next two firms closest to ex post optimal profits are two relatively small
municipal utilities—Brownsville (50%) and Bryan (45%). TXU, the second-largest incumbent
utility, achieves 39% of potential profits, while the largest independent power producers, Tenaska
Gateway and Calpine, achieve 41% and 37%, respectively. The two other major incumbent
utilities—West Texas Utilities and Central Power and Light—capture only 8% of potential ex post
profits. The other large municipal utilities earn a moderate fraction of potential profits: Austin
26
We cannot use a measure such as the fraction of possible profits achieved because some firms tend to be short
on their contract positions entering the balancing market, and we would have to make an assumption about the contract
price. The measure we construct differences out the contract price and avoids this complication.
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TABLE 1 Outcomes under Actual, Ex post Optimal, and Naive Best-Response Bidding
Percent Achieved Producer Surplus Quantity Sales Upper
Relative to ($/hour) (MW) Bound
Total
XP Optimal Naive BR Actual Naive BR XP Optimal XP Optimal Actual Prof
Firm (1) (2) (3) (4) (5) (6) (7) (8)
Reliant 79% 80% 3,422 4,268 4,333 507 431 98%
Brownsville PUB 50% 50% 173 343 343 42 17 88%
City of Bryan 45% 45% 221 488 488 56 30 85%
Tenaska Gateway Partners 41% 41% 456 1,111 1,115 182 72 88%
TXU 39% 41% 1,243 3,056 3,159 441 133 97%
Calpine Corp 37% 38% 820 2,168 2,214 408 102 91%
Denton Municipal Electric 35% 35% 11 31 31 3 1 98%
Ingleside Cogeneration 31% 31% 171 541 541 81 25 79%
City of Austin 30% 31% 581 1,889 1,907 271 48 84%
Rio Nogales LP 28% 28% 109 393 393 60 10 93%
Lower Colorado River Auth 25% 25% 367 1,471 1,488 274 28 88%
City of San Antonio 23% 24% 290 1,221 1,241 266 49 90%
Gregory Power Partners 20% 20% 143 720 722 96 14 82%
Midlothian Energy 17% 17% 171 1,016 1,024 175 15 86%
Cogen Lyondell Inc 16% 16% 408 2,523 2,523 269 34 67%
Tractebel Power Inc 16% 16% 127 795 795 97 15 79%
Brazos Electric Power Coop 15% 15% 101 676 677 82 6 79%
Lamar Power Partners 15% 15% 266 1,800 1,808 272 30 79%
Mirant Wichita Falls 14% 14% 16 114 114 18 2 83%
BP Energy 14% 14% 134 993 994 135 17 80%
City of Garland 13% 13% 128 1,018 1,019 115 5 80%
Hays Energy 8% 8% 64 775 777 111 8 82%
West Texas Utilities 8% 8% 132 1,635 1,635 224 11 82%
Central Power and Light 8% 8% 185 2,375 2,407 352 35 80%
Guadalupe Power Partners 6% 6% 140 2,356 2,380 396 12 77%
Tenaska Frontier Partners 5% 5% 52 1,044 1,051 144 7 80%
South Texas Electric Coop 3% 3% 8 298 298 44 1 81%
Sweeney Cogeneration 2% 2% 10 409 409 46 2 85%
Brazos Valley Energy LP 0% 0% 1 134 134 12 0 68%
AES Deepwater 0% 0% 1 969 969 92 0 60%
Frontera General LP 0% 0% 0 984 1004 197 0 62%
TGC 0% 0% 0 405 405 70 0 81%
South Houston Green Power 0% 0% 0 60 60 7 0 70%
Air Liquide America −8% −8% −181 2,174 2,176 103 9 55%
Extex Laporte LP −81% −81% −1,230 1,497 1,497 92 116 41%
Producer surplus measures are all relative to profitability under not bidding into the balancing market and are measured
in average dollars for each 6–7 pm auction in our sample. Percent Achieved is the ratio of producer surplus under actual
bidding to producer surplus under the benchmark for optimal bidding (either ex post optimal or naive best-response).
Actual is the actual bids submitted by the firms. XP Optimal is ex post optimal bidding constructed as we describe in
Section 3. Naive BR is the naive best-response bid to rivals’ lagged bids as we describe in Section 4. Quantity of sales are
total volumes and, therefore, may sum to more than the average net demand for balancing energy. In column 8, the Upper
Bound for Total Profitability = (Percent Achieved XP Optimal∗%Sales in Balancing) + (100%∗%Sales in Bilateral) as
defined in Section 4.
(30%) and San Antonio (23%). The largest electricity cooperatives earn lower profits: Lower
Colorado River Authority (LCRA) (25%), Brazos (15%), and South Texas (3%).27
Several characteristics of bid schedules appear to drive the foregone ex post profits. We
examined many sets of actual and ex post optimal bid functions similar to Figure 2. The key
27
Note that two firms, Extex Laporte and Air Liquide, earn lower profits under actual bidding than bidding to “avoid
the market.” Both firms, which are infrequent participants in the balancing market, have positive contract positions and
relatively high-cost units available. Both bid so they are called to INC despite the fact that it would be more profitable to
not participate and buy its contract position from the market at a price lower than marginal cost.
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characteristic of underperforming bidders is that the actual bid functions tend to be “too steep”
relative to optimal bids. By bidding too high during INC hours and too low during DEC hours,
firms sell less than under ex post optimal bidding and forego individually profitable sales. As
shown in columns 6 and 7 of Table 1, firms sell less than the ex post optimal quantity on average.
Interestingly, the cause of foregone profits is not that firms are bidding more competitively than
individually optimal, but rather that bid prices are too high.
It is important to keep in mind that these profitability measures do not necessarily represent
generators’ overall performance in trading electricity. Many generators may focus their strategic
efforts in the bilateral market where the vast majority of transactions occur. If firms focus strategic
efforts on the bilateral markets, the overall performance is substantially higher. The upper bound
on total profitability, shown in column 8 of Table 1, ranges from 41% to 98% with a mean of
80%. These metrics are more likely to reflect the firms’ overall performance.
Additional tests of profit maximization. It is important to note that our calculations of
foregone profits rely on restrictions that we place on the economic environment. In particular, we
assume that bidders’ equilibrium perceptions of the uncertainty results in “parallel shifts” rather
than “pivots” in residual demand. If this assumption is violated, it is possible that the set of ex post
optimal price-quantity points is a “cloud” of points that cannot be connected by an increasing
supply function. If this were the case, a profit-maximizing firm’s solution to the (ex ante) expected
profit maximization problem may not be the set of ex post optimal price-quantity points. That is,
testing whether firms maximize ex post profits as we did would not be informative about whether
firms maximize ex ante profits. Because ex ante profitability is a more accurate measure of bidder
performance, we employ several testing strategies that do not impose restrictions on the relationship
between uncertainty and residual demand. All of these tests suggest that the “additively
separable in private information” restriction does not drive our findings of foregone profits.
Best-response to previous rival bids. First, we test whether firms could significantly increase
profits by using a simple bidding rule that utilizes only information available to traders at the time
of bidding. The bidding rule we employ is a naive best response to recent rival bidding.
As discussed in Section 2, traders have access to the aggregate bid function with a two day
lag. Using their own bids from the past, traders can calculate the aggregate bids by rivals in the
recent past.28
To construct the naive best-response of firm i for upcoming day t, we
(i) use aggregate bids and own bids for day t − 3 and calculate aggregate rival bids on day t −
3;
(ii) assume rivals use the t − 3 bid schedule on upcoming day t;
(iii) calculate ex post optimal bid function for various realizations of day t total balancing
demand.
This algorithm uses only information available to firms when bids are submitted. We view
this bidding rule as fairly unsophisticated—it uses only a small fraction of the information
available to traders and it would be simple to program as an add-in to the trading interface
used by the generators. We calculate producer surplus under “naive best-response” bidding and
compare to producer surplus under actual bidding. If uncertainty causes the ex ante expected
profit-maximizing bid to differ from ex post optimal bids, the actual profitability should be much
closer to the naive best-response benchmark.
Results are shown in columns 2 and 4 of Table 1. Across all firms, naive best response
profits are substantially higher than actual profits and very close to ex post optimal profits. The
28
Note that individual firm bid data are only available (to firms and analysts) with a six-month lag, so firms are
unable to use Proposition 1 in real time to estimate rival firms’ contract quantities and resolve some of their uncertainty.
Some of rivals’ uncertainty stems from variation in QCit . We find that balancing contract positions by a firm varies across
time; for example, the standard deviation of QCit is 449, 161, and 7 for Reliant, Calpine, and Guadalupe, respectively.
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performance of actual bidding is significantly below the naive best-response benchmark for all
firms except Reliant. In fact, most bidders’ measure of Percent Achieved rises very little when
compared against the naive best-response benchmark. Naive best-response profits are very close to
ex post optimal profits–the former average $1193 and the latter average $1204. This suggests that
our findings of foregone profits do not arise from the additive separability restriction. Moreover,
this is consistent with the additive separability restriction. The results in columns 4 and 5 reveal
that a firm’s conditioning on RDt−3 instead of RDt leads to negligible profit losses. Thus, under a
profit metric, the shifts in RD are purely parallel.
We also test the restriction of how uncertainty affects residual demand using a Generalized
Method of Moments (GMM)-based approach inspired by Wolak (2003a). we allow for a much
more general relationship between uncertainty and residual demand, and derive first-order
conditions for the choice of each bid point. These conditions yield moment conditions that
are zero in expectation under the null of expected profit maximization. The results indicate that,
except for Reliant, firms in this market violate the first-order optimality conditions that need to
hold for expected profit maximization. Details are in Hortac¸su and Puller (2005).
Testing additive separability. Because we can estimate bidders’ (private information) contract
positions, we also investigate whether the additive separability restriction holds in the data.
According to this restriction, assuming that the firm’s and its competitors’ marginal costs are
unaffected, exogenous shifts in a bidder’s contract position (QC) should affect the intercept of the
bid function, but not the slope.
To operationalize this test, we first fit a linear function to each day’s bid function and calculate
a slope term. The linear specification yielded excellent fit especially in the price range between
$0 and $30. We also used a linear specification to calculate the slopes of bidders’ daily marginal
cost functions (intercepts change very little during the sample period).
Optimal bids can depend on (the parameters of) competitors’ marginal cost schedules in
complex ways. Unfortunately, incorporating every competitor’s marginal cost parameters in a
regression specification would exhaust degrees of freedom rapidly. Therefore, instead of using
competitors’ marginal cost slopes and intercepts as control variables, we use the slope of the
(realized) residual demand curve seen by each bidder (we do not use the intercept, as this
is the uncertain part of residual demand not seen by the bidder). Note that, under additive
separability, this residual demand derivative can be seen as a “sufficient statistic” encoding
changes in competitors’ costs.
The first regression in Table 2 reports the panel regression of the bid function slope on the
estimated contract quantity, controlling for residual demand and (own) marginal cost variation,
along with a linear time trend and bidder fixed effects. Although the coefficient on contract
quantity is statistically significant at the 5% level and positive, the economic significance of
this correlation is not large, as the amount of variation in bid function slope that is explained by
changes in contract quantity is small. Specifically, the average standard deviation of daily contract
quantities (across firms) is 338, and multiplying this by the coefficient estimate 0.001 leads to
only 4.2% of the average bid function slope in the sample (which is 8.0).
In the second column of Table 2, we repeat the regression in the first column, but also
control for auction fixed effects, which can be interpreted as factors (common across bidders) that
bidders take into account when formulating their bids, but not explicitly taken into account by our
simplified econometric specification. This specification yields a weaker (both economically and
statistically) relationship between contract quantities and bid function slope. Note that accounting
for the auction fixed effect leads to a dramatic increase in the coefficient on residual demand slope,
which, in theory, should be an important determinant of bid functions. This latter fact is suggestive
of an omitted variables problem in the first regression, which is ameliorated by the fixed effect
specification.
In Table 3, we report the results of the first regression in Table 2 estimated at the bidder
level. We display the results for those bidders who submit their own bid schedules, and do not use
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TABLE 2 Testing Additive Separability: Panel Regressions
Bid Fn Slope Bid Fn Slope
Contract quantity .0010 .00049
(.0003)∗
(.00031)
Slope of residual demand −.002 .38
(.004) (.01)∗∗
Slope of marginal cost .129 .075
(.017)∗∗
(.011)∗∗
Time trend .000044
(.000033)
Bidder fixed effects Y Y
Auction fixed effects N Y
Observations 2254 2254
R2
.70 .79
Dependent variable is the slope of each bidder-auction’s bid function using a linear fit. Sample includes all bidders in
2001. The slope and intercept of the bid function, residual demand function, and marginal cost are based on a linear fit
of the bid points between $0 and $30.
∗
Significant at 5%.
∗∗
Significant at 1%.
an intermediary “qualified scheduling entity” (QSE).29
Reliant, the most successful bidder (in
terms of ex post and ex ante profit maximization), appears to conform to the additive separability
restriction–changes in contract quantity do not have a statistically significant effect on the slope
of Reliant’s bid function. The next most successful bidder in terms of ex post profit maximization,
City of Bryan, also satisfies this restriction. Although TXU violated additive separability during
its first month of bidding, we fail to reject additive separability in its subsequent bidding patterns.
In contrast, additive separability appears to break down for Calpine and City of Austin; however,
the amount of variation in bid function slope explainable by shifts in contract position is less than
20% in both of these cases. The violation of additive separability is strongest for LCRA; variation
in contract quantities can explain 50% of the variation in bid function slope.
These tests indicate that the additive separability restriction holds on average across the
bidders, and that there is heterogeneity across bidders in terms of how close they come to
satisfying this restriction. The heterogeneity pattern affirms that the theoretical restriction might
be a good approximation to reality; bidders who appear to perform well both from the ex post
and ex ante profit maximization benchmarks (especially Reliant, who performs best) come close
to satisfying additive separability.
5. Explaining deviations from optimal bidding
This Section investigates explanations for the observed deviations from static profit
maximization and the considerable heterogeneity across firms in terms of performance. We
explore whether the observed deviations are driven by characteristics of the firms such as the
firm size, the firm type (e.g., investor-owned utility versus municipal utility), and the generation
technology. We find that the most significant determinant of performance is the size of the
stakes that each firm has in the balancing market, which suggests there are scale economies to
participation in the balancing market auctions. Finally, we document evidence of a modest degree
of learning by the small firms.
Participation costs and scale economies in bidder performance. We consider the
hypothesis that small firms might not have sufficiently large dollar stakes to justify the fixed
cost of participating in the balancing market. To do this, we first have to clarify what we mean
29
We discuss this sample further in Section 5.
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HORTAC¸ SU AND PULLER / 105
TABLE 3 Testing Additive Separability: Individual Bidders
Percent Achieved Bid Fn Slope
Reliant 79 −.00081
(.0029)
City of Bryan 45 −.0025
(.0014)
TXU (first month) .021
(.013)
TXU (after first month) 39 .0025
(.0013)
Calpine 37 .0044
(.0018)∗
City of Austin 30 .0055
(.0015)∗∗
LCRA 25 .0136
(.0014)∗∗
City of Garland 13 .0011
(.0007)
South TX 3 .0014
(.0006)∗
The reported coefficients are the coefficients of each firm’s contract quantity. Unreported control variables include the
slope of the marginal cost and residual demand functions, and a time trend.
∗
Significant at 5%.
∗∗
Significant at 1%.
by “participation.” We find that many firms forego profits because their bid functions have a
large range of prices at which quantity offered is zero. For example, in Figure 2, Guadalupe is
not offering to supply additional INC energy until the price reaches $33 nor offering to reduce
production until price is $11 despite the fact that one of its units can INC and DEC at a marginal
cost of $28. These bid patterns effectively price the bidders out of the market for plausible
realizations of residual demand (in fact, as Table 1 shows, some firms at the bottom of this table
are almost always priced out of the market). In separate calculations, we find that the six firms
with the highest measures of Percent Achieved are called to produce balancing power in 67% of
the actions. In contrast, the other firms are called to produce in only 31% of auctions, despite the
fact that it is ex post optimal to produce in 89% of the auctions.
An interpretation of these bid patterns is that it does not pay for the small firms
to bid the optimal markup even if this optimal markup would allow them to profit from
incrementing/decrementing their power generation, or “participating” in the balancing market
much more often. This interpretation is plausible if it is costly for these firms to calculate the
optimal markup.
The fixed and variable costs of running a trading operation are likely not to be trivial.
One market participant suggested that even a simple bidding operation would require an upfront
expenditure of $3 million with annual operating costs of $1 million, and that most sophisticated
trading operations could be much more expensive. The magnitude of these costs is not trivial
compared to the “money-left-on-table” figures reported in Table 1.30
Another component of this
“fixed cost of participation” is institutional. ERCOT only allows certified companies, QSEs, to
submit bids in the balancing market. All other firms have to route their bids through a QSE,
or contract with a QSE to conduct their bidding operations. This suggests that only firms with
greater dollar stakes may find it optimal to incur the fixed costs of becoming a QSE.
The presence of such fixed costs leads to substantial heterogeneities in bidding behavior—
not just in outcomes, but also in the strategies that are being used. Many bidders do not make
30
An annual expenditure of $1 million corresponds to $114 per hour for one year of operations (365 days, 24
hours), without correcting for the fact that the hour we are analyzing is a peak hour.
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full use of the strategy space available to them, but rather use coarse-grained bidding strategies.
The bid rules allowing 40 price-quantity points afford generators a large degree of flexibility in
bidding. However, none of the bidders make full use of the 40 bid points that they can use to
trace out their optimal bidding functions. Among the firms serving as their own QSE, the firm
earning the greatest fraction of ex post profits (Reliant) also uses the largest number of bid points,
averaging 22.2 points per bid schedule. None of the other firms use more than 13 points on
average. Apparently, traders choose not to formulate refined bid strategies with desired quantities
for many potential realizations of the market clearing price.
One explanation for such “coarse-grained” bidding strategies is provided by Kastl (2006a).
In Kastl’s model of bidding in Czech treasury auctions, there is an explicit marginal cost of
submitting a price-quantity point. Thus, “coarse” bids are constrained optimal, and can depart
significantly from bids that can comprise a larger number of points. Although the cost of adding
bid points may explain a portion of the foregone ex post profits, it appears the majority of foregone
profits is not due to bidding constraints. To see this, suppose that there were a cost to adding bid
points that restricted firms to submitting the number of bid points that we observe them using
(rather than 40). For example, TXU uses an average of 12.6 bid points. We calculate naive bestresponse
(NBR) profits using 12 equally spaced prices between 10 and 40. Note that because the
12 price points are fixed rather than chosen optimally, we will understate best-response profits and
thus overstate Percent Achieved. Even relative to this “constrained” benchmark, TXU’s Percent
Achieved is only 60%. Performing the same exercise for Calpine (using 7 points) yields a Percent
Achieved of 45%.31
Even conditional on paying the fixed cost of becoming a QSE, scale economies still appear
to matter. This is clearly seen in Figure 3, which displays the relationship between bidding
performance and size for generation firms that act as their own QSE. Our measure of performance
is the percent of ex post optimal profits, calculated in the manner described in Section 4. Our
measure of stakes in the balancing market is the volume of sales under ex post optimal bidding
(using other size measures, such as actual volume of sales, or firms’ total capacity, yields similar
patterns). There is a positive relationship between Percent Achieved and optimal sales volume.
The figure includes the fitted linear relationship, which is positive and marginally significant
when all firms are included. When Bryan is excluded, the relationship is even stronger and highly
significant.
We now examine the extent to which stakes are correlated with performance for the broader
sample of firms in a regression context, along with other firm-specific factors that we believe
might affect performance. We regress each firm’s measure of Percent Achieved on a measure of
stakes in the balancing market––the volume of sales under ex post optimal bidding (SIZE). Also
included are firm-level covariates on firm type (independent/merchant power producer, municipal
utility, and investor-owned utility) and whether the firm acts as its own bidder (OWNBIDDER).
Finally, we include dummy variables for whether the firm’s generation technology is at least
50% comprised of two technologies that are less flexible to quick changes in output (COAL and
COMBINED-CYCLE).
Results are reported in Table 4. The baseline regression in column 1 yields a result that
is consistent with the “scale hypothesis:” a 1000 MW increase in sales is associated with a 52
percentage point increase in Percent Achieved.
Column 2 suggests that a “corporate governance”-based explanation is not borne out by
the data. Controlling for size and technology, the performance of municipal utilities appears
to be slightly (2.5 %–4.8%) better than that of investor-owned utilities, although the regression
coefficient is not statistically significant at conventional levels. Moreover, merchant firms actually
seem to be the weakest performers.
31
We also used a similar approach to get a lower bound on the implied cost of using an additional bid point. To do
this, we calculated TXU’s NBR profits using 12 versus 13 bid points (we kept the 12 equally spaced points constant, and
varied the 13th point to maximize TXU’s profit). TXU’s incremental profit gain from adding the 13th bid point was $1.59.
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FIGURE 3
PERFORMANCE VS. STAKES IN BALANCING MARKET FOR FIRMS SERVINGS AS THEIR OWN
BIDDING ENTITIES
Percent Achieved is the percent of possible producer surplus achieved relative to not bidding, as defined in section 4 and
reported in column 1 of Table 1. Volume of optimal output is the mean of the absolute value of quantity sales under
ex-post optimal bidding, as reported in column 6 of Table 1. We restrict this analysis to firms that serve as their own
bidding entities because we can best measure “stakes” of a bidding entity by focusing on firms that serve as their own
bidders.
We also find that the technology mix of a firm does not appear to affect its performance on the
balancing market. In column 3, we add measures of technology type and find that owning a large
fraction of coal and combined-cycle generation units does not negatively impact performance.
We can best measure scale effects if we focus on those firms that choose to establish their
own bidding operation rather than those that outsource. In column 4, we control for whether
the firm performs its own bidding and allow the effect of SIZE to vary by OWNBIDDER status.
Larger stakes are associated with higher performance for firms that serve as their own bidders. For
firms that perform their own bidding, a 1000 MW increase in optimal sales volume is associated
with an 86 percentage point increase in Percent Achieved.
Moreover, if one were to view the choice to serve as their own bidder as a revealed preference,
then the threshold volume of sales where it becomes profitable to construct an in-house bidding
operation rather than to outsource is 71 MW (= (−.071/.001)). The results are similar when we
control for firm type and technology (column 5). A 1000 MW increase in optimal sales volume
is associated with an 97 percentage point increase in Percent Achieved and the threshold size for
ownbidding is 163 MW.
Explanations of deviations from static profit maximization, other than scale economies, do
not have strong empirical support. Explanations based on risk preferences are ruled out by the
fact that the first-order condition of optimality (equation(2)) does not depend on the curvature of
the utility function. Collusion appears to be unlikely because the heterogeneity in bid patterns is
consistent with a collusive coalition that includes the small but not the large players, a possibility
we believe to be unlikely. Engineering-based explanations such as unmeasured adjustment costs
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TABLE 4 Relationship between Profitability and Firm Characteristics
(1) (2) (3) (4) (5)
Size (MW) .00052 .00047 .00035 −.00015 −.00035
(.00031)∗
(.00026)∗
(.00028) (.00025) (.00024)
Size∗
OwnBidder .00101 .00132
(.00044)∗∗
(.00042)∗∗∗
OwnBidder −.071 −.215
(.111) (.109)∗
Merchant firm −.098 −.167 −.170
(.135) (.146) (.098)∗
Municipal .048 .025 .047
(.135) (.142) (.089)
Coal −.021 .043
(.113) (.120)
Combined-Cycle .082 .127
(.058) (.071)∗
Constant .100 .158 .200 .158 .262
(.054)∗
(.142) (.152) (.058)∗∗
(.098)∗∗
Observations 34 34 34 34 34
R2
.15 .28 .31 .34 .50
Dependent variable is the Percent Achieved for firm i over the entire sample as defined in Section 4. Parameters are
estimated by OLS. White standard errors are in parentheses. The excluded category for firm type is investor-owned
utililty.
∗
Significant at 10%.
∗∗
Significant at 5%.
∗∗∗
Significant at 1%.
or transmission constraints also appear implausible due to the periods we choose to analyze; for
a more detailed discussion, see our working article (Hortac¸su and Puller, 2005).
Learning. One might also expect bidders to gradually learn the rules of competition in
this market, and improve their bidding behavior over time. To explore this hypothesis further, we
examine whether there are any time trends in bidder performance.
Table 5 reports the results of a regression of individual bidder’s daily performance (measured
by the percentage of ex post profit achieved for that day) on a time trend and controls for seasonality
and the bidder’s ex post optimal generation in that period. The specification includes bidder fixed
effects to account for firm-level sources of variation. Notice that, for the entire sample of firms, the
estimated coefficient for the time trend is positive, and indicates a 3 percentage point improvement
in performance for every 100 days (or roughly 10% over a year). It is interesting to note that this
time trend is not significant (though of the same estimated magnitude) for the top six bidders. For
the rest of the firms, the time trend in performance is strongly significant.
Thus, our data support a learning hypothesis, although the rate of learning in this market
strikes us as being rather slow (especially compared to rates of learning reported in laboratory
experiments).32
Firms in this market face a considerable amount of uncertainty, which may slow
bidders’ ability to infer optimal decision rules from their experiences. Moreover, several bidders
have told us that they do not have the resources to perform detailed “ex post” analyses that will
enable them to assess how successful their bidding has been, and that they view our exercise as
providing useful information in this regard.
32
It is difficult to make a direct comparison between “rounds” in the laboratory and “days” in electricity markets.
However, if we are willing to equate rounds with days, bidding behavior appears to converge (in percentage profit terms) to
theoretical predictions quicker in many laboratory experiments. See Kagel (1995) for examples from auction experiments.
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TABLE 5 Evolution of Performance and Learning
All Firms Top 6 Firms Non-Top 6 Firms
Days before opening of market .00031 .00033 .00028
(.00010)∗∗
(.00029) (.00009)∗∗
Volume optimal output (GWh) .16 .25 .09
(.06)∗∗
(.10)∗
(.06)
Off-peak season .01361 −.04437 .03164
(.01892) (.03799) (.01885)
Constant .02330 .21053 −.01441
(.03030) (.07503)∗∗
(.02886)
Observations 9765 2103 7662
R2
.25 .18 .11
The dependent variable is the Percent Achieved for firm i on day t. Model includes firm fixed effects. Parameters are
estimated by OLS. White standard errors in parentheses.
∗
Significant at 5%.
∗∗
Significant at 1%.
6. Quantifying efficiency losses
Inefficiencies arise in electricity markets when the bids do not lead to least-cost production.33
In a balancing market, firms bidding above marginal cost on the INC side may not be called upon
to produce despite the fact they have low-cost generators. Similarly, firms bidding below marginal
cost on the DEC side may not be called to reduce production even if they have high-cost plants
operating.
We measure the cost of production in the balancing market implied by actual bids and
compare those costs to the production costs under various counterfactual bidding behaviors. Our
benchmark for efficiency is competitive bidding, which is an equilibrium under an alternative
market design—the multi-unit Vickrey auction. We calculate the production costs if firms instead
were to bid their marginal cost functions. These calculations suffer from one data limitation—the
generation data are incomplete for a few of the smaller firms. This does not affect our ability
to analyze bidding behavior for the remaining firms but prevents us from calculating efficient
dispatch for many days in our sample. Therefore, these measures of efficiency loss should be
interpreted with caution for they only represent a fraction of our sample period.
Results are shown in Table 6. The average hourly dispatch costs in the balancing market
are $29,874 under actual bidding and $23,571 under marginal cost bidding, implying that actual
production costs are 27% higher than least-cost production.
We can decompose the welfare losses into the two major sources of inefficiency. The first
source of inefficiency is the strategic exercise of market power—large firms face steeper residual
demand functions and thus have incentives to bid steeper than marginal cost. This may result in
inefficient production when low-cost units are withheld from the market while higher-cost units
are called to generate.34
A second source of inefficiency is the behavior of small generators. As we have noted,
many of the smaller participants submit extremely steep bid functions—even though static profit
maximization suggests that they should bid very close to marginal cost. As a result, they are
33
Because total demand is perfectly inelastic, prices higher or lower than competitive levels do not cause suboptimal
levels of consumption. All inefficiencies are productive rather than allocative. For a more general discussion of the
efficiency properties of uniform price multi-unit auctions, see Ausubel and Cramton (2002).
34
Borenstein, Bushnell, and Wolak (2002) find the actual production costs to be 14% higher than competitive levels
in the California market in 2000. Mansur (forthcoming) refines the methodology and finds that production costs in the
PJM market exceed competitive costs by 3%–8%. Note that our analysis only calculates productive inefficiencies in the
balancing market for units that have already started and submitted day-ahead schedules.
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TABLE 6 Decomposition of Efficiency Losses from Observed Bidding Behavior
Bidding Counterfactual Average Production Cost
Actual bids for all firms $29,874
Strategic firms Bid MC, others bid actual $28,671
All firms bid MC (Vickrey auction) $23,571
Total efficiency losses $6,303
Strategic bidders $1,203
Nonstrategic bidders $5,100
Strategic firms are Reliant, TXU, Calpine, Brownsville, Bryan, and Tenaska Gateway Partners. The average production
cost is the hourly average of the absolute value of the cost of dispatch (either costs in INC hours or cost savings in DEC
hours) during uncongested weekdays for the 6–7 pm bidding hour.
often not called to produce despite the fact that it would be efficient to do so. This source of
inefficient production can arise from a variety of sources as we discuss above (e.g., fixed cost of
establishing a sophisticated trading operation). To the extent that the inefficiencies result from
scale economies, the fixed cost of setting up trading operations or outsourcing to power marketers
should be included in a complete welfare analysis.
To decompose the total amount of production inefficiency into these two components, we
separate the firms into two groups: “strategic” bidders who exercise market power optimally,
and “nonstrategic” bidders who bid excessively steep schedules that effectively minimize their
participation in the market. We first compute counterfactual generation costs in this market under
the assumption that strategic firms ignore their market power and bid competitively, that is, we
calculate what the total generation cost would have been if the strategic firms were bidding their
marginal costs. In this counterfactual, we assume that the nonstrategic firms continue to bid what
they are observed to bid, that is, that they do not respond to the (counterfactual) change in the
behavior of their strategic competitors.35
We assume that the three largest firms—Reliant, TXU, and Calpine––as well as the other
three firms in the top six in Table 1 (Brownsville, Bryan, and Tenaska) are strategic. We find
counterfactual dispatch costs when these six firms bid marginal cost and all other firms submit
their actual bid schedules. The difference in dispatch costs between this counterfactual bidding
strategy and the actual bids can be interpreted as the “efficiency loss due to market power.” The
remaining efficiency loss is due to nonstrategic firms that bid so as to not participate in the market.
Table 6 decomposes the efficiency losses. Again, the total efficiency loss due to misrepresentation
of marginal costs is on average $6303 per hour, or 27% of the total cost of efficient
generation in the balancing market. If the strategic firms were to bid their marginal costs, the
total efficiency loss would have been only $1203 less than the actual efficiency loss. This means
that most (81%) of the observed efficiency loss is due to the steep bid schedules submitted by the
nonstrategic bidders.
We should note, once again, that the above calculation relies on relatively few intervals (62
out of a total of 220 periods—the latter periods are especially prone to the missing data problem).
This calculation is largely based upon the first six months of the market’s operation. However,
this calculation points out that the observed deviations from static profit maximization are not
without economic consequence. In fact, they cause larger efficiency losses than the “near-optimal”
exercise of market power by the strategic firms. Submitting bid functions that are too steep not
35
Note that the “reverse” of this counterfactual, where we set nonstrategic bids equal to marginal cost and do not
allow strategic bidders to respond, would be less realistic, because our results show that the strategic bidders do respond
to changes in the residual demand they are facing. Counterfactuals involving the equilibrium response of strategic bidders
are complicated by the fact that multi-unit auctions can have multiple equilibria.
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HORTAC¸ SU AND PULLER / 111
only sacrifices producer surplus but also prevents technologically efficient firms from supplying
energy to the balancing market.
One would expect that these efficiency losses due to the nonstrategic firms’ behavior would
dissipate over time. Unfortunately, as we noted above, we face data limitations that prevent us
from conducting a long time series analysis, especially in the later part of the sample. However,
market forces are at play to reduce the inefficiencies. To the extent there are scale effects, the
small firms may outsource bidding decisions or consolidate bidding activities across plants. It
is noteworthy that there are a variety of power marketers and large energy trading firms that
offer energy asset management services to generators in ERCOT. Such outsourcing can increase
participation by nonstrategic firms and reduce inefficiencies without substantially increasing the
fixed cost of bidding expertise.
7. Conclusion
Our analysis of the ERCOT balancing market yields the following conclusions. The first
conclusion, we believe, is a comforting one for economic theory. In a marketplace that is marked
by considerable uncertainty and institutional complexity, two factors that may pose analytical
challenges for both the firms competing in the market and the economists who are observing
(and, in some cases, advising) them, firms with large stakes in the market behave close to
theoretical predictions of a strategic model of oligopolistic interaction. Indeed, as two empirical
industrial organization researchers who have previously utilized such models to infer supply and
demand parameters in other markets, we interpret the behavioral pattern displayed by Reliant as
good news for previous and future empirical work on oligopolistic markets. More specifically,
the confirmation of the basic predictions of the uniform-price share auction model is important,
as one could use this model to forecast bidder behavior in restructured electricity markets that
are being put into operation in many different parts of the world.
However, our results also suggest some amount of caution when analyzing and predicting
the behavior of smaller players in newly restructured markets. Smaller firms submit bids that
differ substantially from the benchmarks we construct for optimal bidding. This finding is not
inconsistent with rational economic behavior by these bidders, however. As argued in Section
5, “participation” in the balancing market may have nontrivial costs, and the behavioral pattern
across firms appears to confirm this hypothesis.
Our third result is that small firms’ deviations from optimal bidding is economically
important. In Section 6, we calculated that small firms’ bidding patterns led to the major portion
of losses in productive efficiency. This suggests interesting new avenues for market design that
explicitly take into account the strategic complexity, hence the participation costs, imposed by
proposed market mechanisms. Such a consideration may favor dominant strategy implementable
mechanisms, such as the Vickrey-Clarke-Groves (VCG) mechanism, over others. However, as
pointed out by Milgrom (2004), the VCG mechanism suffers from serious pitfalls of its own.
Nevertheless, we view theoretical research in this area to prove extremely fruitful for real-world
applications.
Appendix A
Proof of proposition 2. Given the additively separable form of the bidding strategies Si (p, QCi ) = αi (p) +
βi (QCi ), use the market clearing condition (1) above to represent the event {pc
t ≤ p | QCi , Si }, that is, there is excess
supply at p, conditional on firm i bidding Si at this price,
j=i
βj (QCj ) − ε ≥ D(p) − Si −
j=i
αj (p).
The left-hand side of this inequality can be labeled as a (bidder-specific) random variable, θi , that does not depend
on p, and the right-hand-side is a deterministic function of price. Let i (.) denote the cdf of θi and γ i (.) denote the pdf
(both conditional on the bidder’s contract quantity, QCi ). Given these,
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Hp(p, Si ; QCi ) =
∂
∂ p
Pr pc
t ≤ p | QCi , Si
=
∂
∂ p
Pr θi ≥ D(p) − Si −
j=i
αj (p)
=
∂
∂ p
1 − i D(p) − Si −
j=i
αj (p)
= −γi D(p) − Si −
j=i
αj (p)
∂
∂ p
D(p) − Si −
j=i
αj (p)
and
HS(p, Si ; QCi ) =
∂
∂Si
Pr pc
t ≤ p | QCi , Si
= −γi D(p) − Si −
j=i
αj (p)
∂
∂Si
D(p) − Si −
j=i
αj (p) .
Evaluating the derivatives gives
Hp (p,Si ;QCi )
HS (p,Si ;QCi )
= −[D (p) − j=i αj (p)]. Now, observe that with the above restrictions,
the residual demand function faced by firm i (for a given realization of the random variables {ε, QC−i , i =
1, . . . , N}), is given by
RDi (p, ε, QC−i ) = D(p) + ε −
j=i
αj (p) −
j=i
βj (QCj ) (4)
with derivative
RDi (p) = D (p) −
j=i
αj (p),
which yields the result in the proposition.
Note that in one other case where we can collapse the multiple stochastic terms into a scalar random variable, we
do not obtain the ex post optimality result. This is the case when Si (p, QCi ) = αi (p) + βi pQCi and ˜D(p) = D(p) + pε,
that is, private information and aggregate uncertainty leads to pure rotations of the residual demand curve. In this case,
the market clearing condition becomes θi = j=i βj QCj − ε ≥ 1
p
[D(p) − Si − j=i αj (p)], but Hs (p,Si )
Hp (p,Si )
= 1
RDi (p,ε,QC−i )
.
Q.E.D.
Appendix B
Data description. Hourly bid schedules by each bidder, or qualified scheduling entity (QSE), are from ERCOT.
QSEs occasionally bid for more than one firm. For example, in the South zone in 2001, the QSE named Reliant bid for
both Reliant and the City of San Antonio. We match the bid functions to all units for which the QSE bids. So for all units
owned by both Reliant and the City of San Antonio in the South in 2001, we match the bid function to the generation
data. However, interpretation of the results becomes problematic when an observed bid function represents the bids by
more than one firm. Because the results are some combination of two firms’ behavior, we will not interpret results in such
situations. We only interpret our results as firm-level behavior when at least 90% of all electricity generated by owners
using that QSE can be attributed to a single owner. We make one exception to this 90% rule—TXU generation, which
comprises 87% of the generation for TXU the QSE in North 2002.
We measure the variable costs of output using data on each unit’s fuel costs and the rate at which the unit converts
the fuel to electricity. For each 15-minute interval, we have data from ERCOT on whether a generating unit is operating,
its day-ahead scheduled generation, and its hourly available generating capacity. We measure the marginal cost of units
that burn natural gas and coal. For each unit, we have data on the fuel efficiency (i.e., average heat rate). Each unit is
assumed to have constant marginal cost up to its hourly operating capacity, an assumption that is common in the literature.
The ERCOT system is largely separated from other electricity grids in the country so there are virtually no imports.
Daily gas spot prices measure the opportunity cost of fuel for natural gas units. We use prices at the Agua Dulce,
Katy, Waha, and Carthage hubs for units in the South, Houston, West, and North zones, respectively. We assume a gas
distribution charge of $0.10/mmBtu. Coal prices are monthly weighted average spot price of purchases of bituminous,
subbituminous, and lignite in Texas, reported in Form FERC-423. Coal-fired plants in Texas are required to possess
federal emission permits for each ton of SO2 emissions. In order to measure average emission rates, we merge hourly
net metered generation data from ERCOT with hourly emission data from EPA’s CEMS to calculate each unit’s average
pounds of SO2 emissions per net MW of electricity output. The emissions each hour are priced at the monthly average
EPA permit price reported on the EPA website.
In order to deal with complications posed by transmission congestion, we restrict our sample to daily intervals
6:00–6:15 pm during which there is no interzonal transmission congestion during the 6–7 pm bidding hour. We believe
intrazonal (or local) congestion is likely to be rare during these intervals.
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We do not incorporate the possibility that some of the available capacity to INC in our data may be sold as reserves.
However, the amount of operating reserves procured are small as a fraction of total demand.
We measure the marginal cost of INCing or DECing from the day-ahead schedule of output. We account for the
fact that units cannot DEC down to zero output without incurring costs of startup and facing constraints on minimum
downtime. It is unlikely that revenue from the balancing market would be sufficiently lucrative to compensate a unit
for shutting down. Therefore, we assume that each operating unit cannot DEC to a level below 20% of its maximum
generating capacity.
References
ATHEY, S.C. AND HAILE, P.A. “Nonparametric Approaches to Auctions.” In J.J. Heckman and E. Leamer, eds., Handbook
of Econometrics, Vol. 6. New York: Elsevier, forthcoming.
AUSUBEL, L.M. AND CRAMTON, P. “Demand Reduction and Inefficiency in Multi-Unit Auctions.” Mimeo, Department of
Economics, University of Maryland, 2002.
BAJARI, P. AND HORTAC¸SU, A. “Are Structural Estimates of Auction Models Reasonable? Evidence from Experimental
Data.” Journal of Political Economy, Vol. 113 (2005), pp. 703–741.
BALDICK, R. AND NIU, H. “Lessons Learned: The Texas Experience.” In J. Griffin and S.L. Puller, eds., Electricity
Deregulation: Choices and Challenges. Chicago: University of Chicago Press, 2005.
——, GRANT, R., AND KAHN, E. “Theory and Application of Linear Supply Function Equilibrium in Electricity Markets.”
Journal of Regulatory Economics, Vol. 25 (2004), pp. 143–167.
BORENSTEIN, S., BUSHNELL, J.B., AND WOLAK, F.A. “Measuring Market Inefficiencies in California’s Restructured
Wholesale Electricity Market.” American Economic Review, Vol. 92 (2002), pp. 1376–1405.
BRESNAHAN, T. “Empirical Studies of Industries with Market Power.” In R. Schmalensee and R. Willig, eds., Handbook
of Industrial Organization, Vol. 1. New York: North Holland, 1989.
BUSHNELL, J.B. AND SARAVIA, C. “An Empirical Assessment of the Competitiveness of the New England Electricity
Market.” Working Article no. 101, Center for the Study of Energy Markets, University of California Energy
Institute, 2002.
——, MANSUR, E.T., AND SARAVIA, C. “Vertical Arrangements, Market Structure and Competition: An Analysis of
Restructured U.S. Electricity Markets.” American Economic Review, Vol. 93 (2008), pp. 237–266.
CRAMTON, P. “Competitive Bidding Behavior in Uniform-Price Auction Markets.” Proceedings of the Hawaii International
Conference on System Sciences, 2004.
CRAWFORD, G., CRESPO, J., AND TAUCHEN, H. “Bidding Asymmetries in Multi-Unit Auctions: Implications of Bid Function
Equilibria in the British Spot Market for Electricity.” International Journal of Industrial Organization, Vol. 25
(2007), pp. 1233–1268.
EINAV, L. “A Note on the Analogies between Empirical Models of Auctions and of Differentiated Product Markets.”
Mimeo, Department of Economics, Stanford University, 2004.
FABRA, N. AND TORO, J. “Price Wars and Collusion in the Spanish Electricity Market.” International Journal of Industrial
Organization, Vol. 23 (2005), pp. 155–181.
GENESOVE, D. AND MULLIN, W.P. “Testing Static Oligopoly Models: Conduct and Cost in the Sugar Industry, 1890–1914.”
RAND Journal of Economics, Vol. 29 (1998), pp. 355–377.
GREEN, R.J. “Increasing Competition in the British Electricity Spot Market.” Journal of Industrial Economics, Vol. 44
(1996), pp. 205–216.
—— AND NEWBERY, D.M. “Competition in the British Electricity Spot Market.” Journal of Political Economy, Vol. 100
(1992), pp. 929–953.
HENDRICKS, K. AND PORTER, R.H. “An Empirical Perspective on Auctions.” In M. Armstrong and R.H. Porter, eds.,
Handbook of Industrial Organization, Vol. 3. New York: Elsevier, 2007.
——,——, AND BOUDREAU, B. “Information, Returns, and Bidding Behavior in OCS Auctions: 1954–1969.” Journal of
Industrial Economics, Vol. 35 (1987), pp. 517–542.
HORTAC¸SU, A. “Mechanism Choice and Strategic Bidding in Divisible Good Auctions: An Empirical Analysis of the
Turkish Treasury Auction Market.” Mimeo, Department of Economics, University of Chicago, 2002a.
——. “Bidding Behavior in Divisible Good Auctions: Theory and Evidence from the Turkish Treasury Auction Market.”
Mimeo, Department of Economics, University of Chicago, 2002b.
—— AND PULLER, S.L. “Understanding Strategic Bidding in Restructured Electricity Markets: A Case Study of ERCOT.”
NBER Working Paper no. 11123, 2005.
JOSKOW, P.L. “Deregulation and Regulatory Reform in the U.S. Electric Power Sector.” In S. Peltzman and C. Winston,
eds., Deregulation of Network Industries: The Next Steps. Washington, DC: Brookings Press, 2000.
—— AND KAHN, E. “A Quantitative Analysis of Pricing Behavior in California’s Wholesale Electricity Market during
Summer 2000.” Energy Journal, Vol. 23 (2002), pp. 1–35.
KAGEL, J. “Auctions: A Survey of Experimental Research.” In J. Kagel and A. Roth, eds., Handbook of Experimental
Economics. Princeton, NJ: Princeton University Press, 1995.
C RAND 2008.
114 / THE RAND JOURNAL OF ECONOMICS
KASTL, J. “Discrete Bids and Empirical Inference in Divisible Good Auctions.” Mimeo, Department of Economics,
Stanford University, 2006a.
——. “On the Existence and Characterization of Equilibria in Private Value Divisible Good Auctions.” Mimeo,
Department of Economics, Stanford University, 2006b.
KLEMPERER, P.D. “Why Every Economist Should Learn Some Auction Theory.” In M. Dewatripont, L.P. Hansen, and
S.J. Turnovsky, eds., Advances in Economics and Econometrics: Invited Lectures to Eighth World Congress of the
Econometric Society. Cambridge: UK University Press, 2003.
—— AND MEYER, M.A. “Supply Function Equilibria in Oligopoly under Uncertainty.” Econometrica, Vol. 57 (1989),
pp. 1243–1277w.
MANSUR, E.T. “Upstream Competition and Vertical Integration in Electricity Markets.” Journal of Law and Economics,
Vol. 50 (2007), pp. 125–156.
——. “Measuring Welfare in Restructured Electricity Markets.” Review of Economics and Statistics, Vol. 90 (2008), pp.
369–386.
MCADAMS, D. “Partial Identification in Multi-Unit Auctions.” Mimeo, Sloan School of Management, MIT, 2006.
MILGROM, P.R. Putting Auction Theory to Work. Cambridge, UK: Cambridge University Press, 2004.
PULLER, S.L. “Pricing and Firm Conduct in California’s Deregulated Electricity Market.” Review of Economics and
Statistics, Vol. 89 (2007), pp. 75–87.
RUDKEVICH, A. “Supply Function Equilibrium in Power Markets: Learning All the Way.” TCA Technical Report no.
1299-1702, Tabors Caramanis and Associates, 1999.
SWEETING, A. “Market Power in the England and Wales Wholesale Electricity Market 1995–2000.” Economic Journal,
Vol. 117 (2007), pp. 654–685.
VISWANATHAN, S., WANG, J.J.D., AND WITELSKI, T. “Optimal Bidding in Multi-Unit Discriminatory Auctions.” Mimeo,
Fuqua School of Business, Duke University, 2002.
WANG, J.J.D. AND ZENDER, J.F. “Auctioning Divisible Goods.” Economic Theory, Vol. 19 (2002), pp. 673–705.
WILSON, R. “Auctions of Shares.” Quarterly Journal of Economics, Vol. 93 (1979), pp. 675–689.
——. “Architecture of Power Markets.” Econometrica, Vol. 70 (2002), pp. 1299–1340.
WOLAK, F.A. “An Empirical Analysis of the Impact of Hedge Contracts on Bidding Behavior in a Competitive Electricity
Market.” International Economic Journal, Vol. 14 (2000), pp. 1–39.
——. “Identification and Estimation of Cost Functions Using Observed Bid Data: An Application to Electricity Markets.”
In M. Dewatripont, L.P. Hansen, and S.J. Turnovsky, eds., Advances in Economics and Econometrics: Theory and
Applications, Eighth World Congress, Volume II. New York: Cambridge University Press, 2003a.
——. “Measuring Unilateral Market Power in Wholesale Electricity Markets: The California Market 1998 to 2000.”
American Economic Review, Vol. 93 (2003b), pp. 425–430.
WOLFRAM, C.D. “Measuring Duopoly Power in the British Electricity Spot Market.” American Economic Review, Vol. 89
(1999), pp. 805–826.
C RAND 2008.