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This paper introduces and tests Bid Function Equilibria (BFE) in the British spot market for electricity. BFE extend von der Fehr and Harbord's (1993) multi-unit auction model of wholesale electricity markets by allowing firms to have heterogeneous costs for different generating units. Pure-strategy equilibria in BFE predict asymmetric bidding by producers: a single firm (the “price-setter") bids strategically while other firms (“non-price-setters") bid their costs. We test for asymmetries in firms' bid functions in the British spot market between 1993 and 1995 and find strong empirical support for the theory. We conclude that BFE have important implications for the design and governance of electricity markets.

Within the United States and throughout the world, the deregulation of wholesale electricity markets is well underway. Despite the consensus that these markets can generally benefit from competition, concerns that deregulated energy markets are especially vulnerable to market power continue to persist (Borenstein et al., 2002).1 In the United States, the Federal Energy Regulatory Commission (FERC) has prescribed a universal wholesale market design which it hopes will be less susceptible to market power and manipulation.2 Despite the FERC's laudable intentions, there is concern over whether regulators have an accurate understanding of market equilibrium in these markets. In this paper, we introduce and test Bid Function Equilibria (BFE), a model of firm behavior in wholesale electricity markets. BFE were developed by Crespo (2001) to extend von der Fehr and Harbord's (1993) multi-unit auction model of wholesale electricity markets by allowing firms to have heterogeneous costs for the different generating units they control.3 This has the advantage of better reflecting the institutional reality of most wholesale electricity markets and clarifying the implications of multi-unit auction theory for firms' bid functions.4 The primary implication of BFE is that behavior is asymmetric: the firm that sets the clearing price (the “price-setter”) behaves strategically while all other firms (“non-price-setters”) bid close to their marginal costs. This has important implications for the nature of markups over costs (‘bid markups’) across firms in a wholesale market equilibrium. We test these implications in the England and Wales (E&W) spot market for electricity. Fig. 1 and Fig. 2 provide examples of asymmetric bidding in E&W data. They show the marginal costs and bids for each generating unit by each producer in the E&W market on two days: November 28, 1993 and October 19, 1995. Bids for the individual generating units have been aggregated as they would by the National Grid Company (NGC) to form an aggregate supply curve. Also shown is the maximum (across 24 half-hour periods) daily demand (load) on each day. In Fig. 1, National Power is the price-setter for the majority of high-demand periods. The top panel in the figure shows the aggregate supply curve at all loads while the bottom panel focuses on the aggregate supply curve near the maximum load. While all producers are bidding close to or below marginal cost for units far to the left of the maximum load, only National Power is bidding significantly above cost adjacent (and to the left) of the maximum load.5 The picture reverses, however, in Fig. 2. Here, PowerGen is the price-setter for the majority of high-demand periods and it is they, not National Power, that is bidding above costs to the immediate left of the maximum load. Our results use E&W data from January 1, 1993 to December 31, 1995 and demonstrate strong support for the theory. First, using variation in bids for individual generators across time, we find strong and persistent asymmetries when firms do and do not set prices. For example, the estimated effects of infra-marginal capacity, a key strategic factor, impact bids as predicted by BFE and are far stronger for the price-setting firm than for non-price-setting firms. We also use BFE to simulate market equilibria and find evidence of strong incentives to exploit capacity constraints in instances of high demand. When the potential costs of such strategies in the England and Wales market are incorporated, the theory predicts bid markups in periods of peak demand of 22–23%, very close to those estimated by Wolfram (1998) and Wolfram (1999) in the same market. Our findings have important implications both for the design of electricity markets and the mitigation of market power in these markets. First, BFE help explain the level of bid markups under conditions when the market is not capacity-contained. In these instances, while our estimates of markups are significant, they are less than 30% or more by which average costs of generation exceed marginal costs. This is true despite the relatively concentrated nature of the England and Wales market in the period we study. In instances of high demand, however, our results indicate the potential for exploiting capacity constraints. It is during these periods that the potential for, and consequences of, market power are the greatest. Priority should therefore be given to controlling market power during the extreme cases when one firm possesses incentives to exploit capacity constraints. Finally, simulations show that mitigation policies that target specific generating units (e.g. intermediate versus baseload capacity) can significantly enhance market performance. These results complement other research applying oligopoly models to wholesale electricity markets. In general, this research tends to take one of two approaches. The first approach assumes that firms can make continuous supply decisions. Schmalensee and Golub (1985) and Borenstein and Bushnell (1999), for example, analyze the potential for market power in wholesale electricity markets using a model of static Cournot competition. Fabra and Toro (2005) and Puller (2006) extend the Cournot approach to consider dynamic (tacitly collusive) equilibria. An alternative strand applies models of multi-unit auction theory, but with continuous bid functions. These models, developed by Klemperer and Meyer (1989) and denoted Supply Function Equilibria (SFE), were first applied to electricity markets by Green and Newbery (1992). Subsequent applications include Green (1996), Newbery (1998), Green (1999), Baldick, Grant, and Kahn (2004), Genc and Reynolds (2005), and Baldick and Hogan (2006). Models in this strand of the literature generally predict markups for all producers, whether or not they set the price. The second approach, characterized by von der Fehr and Harbord (1993), also builds models of multi-unit auctions, but acknowledges the discreteness inherent in electricity supply. von der Fehr and Harbord (1993), for example, build a model with N firms, each producing a given capacity kn at constant marginal cost cn and submitting bids to serve an inelastic market demand, d. This approach has since been extended to allow for elastic demand, within-firm cost heterogeneity, long-lasting bids, and repeat play (Brunekreeft (2001), Garcia-Diaz and Marin (2003), Fabra (2003), Fabra, von der Fehr, and Harbord (2006)).6 Of these, BFE is closest to the work independently developed by Garcia-Diaz and Marin (2003). They also allow for complete information, deterministic demand, and increasing step cost functions and find that pure strategy equilibria are characterized by firm asymmetries. Where we differ is in our uses of the model and our test of its implications on observational data. Garcia-Diaz and Marin (2003) compare equilibrium prices to Cournot prices (finding the former to be lower), show how equilibrium prices vary with aggregate demand elasticity, and analyze the consequences of mergers in an application modelled on the Spanish electricity market. We characterize equilibrium bid functions, test the implications of the theory using data from the England and Wales electricity market, and analyze the consequences of divestiture in an application modelled on that market. In all cases, our results are clearly complementary.7 Our results are also related to a large empirical literature analyzing wholesale electricity markets. Many studies, including Wolfram (1999) and Puller (in press), compare estimates of market power with that predicted by theory, while others, including Wolak (2000), Wolak (2003),Hortacsu and Puller (2006), and Sweeting (2005), analyze whether observed behavior is consistent with short-run profit maximization.8 These often find markups not only for the price-setter, but also for non-price-setters. In part, this can be explained by the necessity for firms in the E&W market to submit bid functions that are fixed for a day, a topic we discuss in Section 3.3. That being said, our results should not be interpreted too strongly– there is ample evidence in our data that both price-setters and non-price-setters bid above marginal cost– but rather that such incentives may be stronger for the price-setter than non-price-setters. Integrating the asymmetric implications of BFE with those of alternative theories of electricity supply would be useful. The remainder of this paper is organized as follows. Section 2 reviews the theoretical literature on multi-unit auction models of wholesale electricity markets and contrasts the results of these models with other approaches taken in the literature. Section 3 presents the theory in more detail and explores its implications for the England and Wales market. Section 4 describes the available data and Section 5 presents the econometric specification and results. Simulations of BFE are presented in Section 6, and Section 7 concludes.

The purpose of this paper is to provide an explanation of firm behavior in wholesale electricity markets. We do this by testing the implications of Bid Function Equilibria in the England and Wales spot market for electricity. The primary implication of BFE is the presence of asymmetries in bidding behavior between the firm that sets the clearing price (the price-setter) and all other firms (non-price-setters). Using data on bid functions between 1993 and 1995, we find strong empirical support for the theory. Strong and persistent asymmetries exist in bid functions consistent with strategic bidding by price-setters in a Bid Function Equilibrium. BFE have several important implications regarding the efficient regulation of wholesale electricity markets. First, it offers important insights into the tradeoff between short- and long-run efficiency in these markets. In a seminal paper, Christensen and Greene (1976) found that “technological change unrelated to increases in scale deserves the primary attribution for… declines in the cost of [electricity] production.” This discovery was used to promote competition in generation and ultimately the deregulation of electricity markets the world over. Today, there is a great deal of energy devoted to mitigating short-run market power, independent of the industry's long-run objectives. While our estimates of markups (on the order of 22–23%) are significant, they are less than the 30% or more by which average costs of generation exceed marginal costs. Given that fixed cost recovery is essential to promoting new efficient technologies, BFE support the conclusion that, under normal market conditions, markups are likely to be in a range that promotes fixed cost recovery without necessarily leading to above-normal profits. That being said, the frequency of corner solutions in the simulations, although less likely in today's less concentrated markets, highlights the importance of mitigating market power when one (“pivotal”) supplier has an incentive to exploit capacity constraints.48 Finally, if divestiture is being considered as a way to address market power, BFE indicate that targeting specific generating units (e.g. intermediate versus baseload capacity) can significantly enhance market performance. There are many possible extensions of this research. The most immediate application would be for use in other wholesale electricity markets. For example, in recent years there has been an emergence of a literature examining market power issues in the newer California deregulated market for electricity (Borenstein and Bushnell, 1999, Borenstein et al., 2002 and Wolak, 2000). Similar issues have arisen in the New England (NEISO), New York ISO (NYISO) and the Pennsylvania, New Jersey, and Maryland (PJM) markets (e.g. Mansur, 2005). Although BFE would have to be generalized to include idiosyncratic aspects of these markets, its basic features would remain. Even more promising is to address issues of market power during periods of high demand by incorporating Bid Function Equilibria in a structural model of short-run strategic availability decisions by generators. Similarly, the wealth of data and repeat nature of play in electricity markets provide ample opportunity to study explicit or tacit collusion in the market (e.g. Puller, in press and Sweeting, 2005). BFE would assist these efforts by characterizing outcomes in downstream stages (i.e. conditional on availability or as the punishment stage in a repeated game), enabling the analysis to focus on such higher-order strategic incentives.