Analyzing firm behavior in restructured electricity markets: Empirical challenges with a residual demand analysis

Highlights

• We employ a residual demand analysis to analyze firm behavior in wholesale electricity markets.

• Residual demands can lead to non-monotonic best-response offer curves violating common bidding constraints.

• Firms could have recovered the majority of profits by employing a monotonic smoothing of the best-response offer curves.

Abstract

Using data from Alberta’s wholesale electricity market, we demonstrate the challenges that can arise when characterizing a firm’s unilateral expected profit-maximizing offer curve. We illustrate that the residual demand curves faced by firms can be highly non-linear, resulting in non-monotonic, downward sloping, optimal best-response offer curves violating common restrictions imposed on bidding behavior. This can have important implications on the conclusions drawn from such empirical analyses. We identify features of residual demand curves that can lead to these problems, providing guidance to researchers utilizing these methods. We find that a simplified monotonic smoothing of the unconstrained ex-post optimal offer curve can achieve the majority of the expected profits, offering an alternative to calculating the ex-ante expected profit-maximizing offer curve that can be computationally burdensome.

Introduction

The measurement of market power and evaluation of firm behavior is an important issue in concentrated wholesale electricity markets where firms interact repeatedly. Market power has been shown to lead to substantial market inefficiencies and rent transfers from consumers to producers (Borenstein, Bushnell, Wolak, 2002, Wolak, 2003a, Brown, Olmstead, 2017).¹ Further, evaluations of firm behavior have raised concerns of coordinated conduct (Sweeting, 2007, Brown, Eckert, 2021). These concerns have led to various market reforms and the implementation of policies to regulate the degree to which firms are able to bid above marginal costs (FERC, 2014, AUC, 2017).

The use of concentration measures to evaluate industry structure such as the Herfindahl–Hirschmann Index has been shown to be a poor measure of market power in electricity markets due to their inability to account for transmission constraints, elasticity of demand, and the intertemporal variation in firms’ abilities to exercise market power (Borenstein et al., 1999). This led to the proliferation of a literature that compares observed firm behavior to a perfectly competitive benchmark (e.g., Wolfram, 1999, Borenstein, Bushnell, Wolak, 2002, Brown, Olmstead, 2017). This literature often finds that firms exercise substantial market power elevating wholesale prices and resulting in large productive inefficiencies.

In addition, to address the possibility of coordinated conduct, there is a growing empirical literature that establishes methods to characterize a firm’s unilateral expected profit maximizing supply function (Wolak, 2000, Wolak, 2003a, Wolak, 2003b, Wolak, 2007, Wolak, 2010, Hortaçsu, Puller, 2008, McRae, Wolak, 2014, Mercadal).² While the details and methods differ across each study, these analyses utilize models that characterize a firm’s unilateral expected profit maximizing (best-response) supply function facing a stochastic residual demand function that represents market demand net of its rivals’ supply functions.³ Wolak, 2000, Wolak, 2003b and Hortaçsu and Puller (2008) discuss conditions under which the expected profit maximizing supply function can be characterized by finding the optimal price-quantity pair that maximizes a firm’s ex-post profit for any potential realization of residual demand. Hortaçsu and Puller (2008) utilize this methodology to map out each firm’s ex-post optimal offer curve and compare it to observed behavior in Texas’s electricity market. The authors find that large firms bid in a manner that is consistent with unilateral expected profit maximization, while smaller firms deviate from this benchmark.⁴ Mercadal (2018) extends this analysis to consider forward financial markets and transmission constraints.⁵

Wolak, 2007, Wolak, 2010, Wolak, 2015 discusses the potential for the ex-post optimal offer curve to be unobtainable in practice because of bidding restrictions (such as the requirement that firms submit monotonically non-decreasing supply functions). For example, Wolak (2015) notes through a graphical discussion that the ex-post profit maximizing offers may trace out a downward sloping offer curve. Wolak, 2003b, Wolak, 2007 present an econometric methodology to estimate the expected unilateral profit-maximizing offer curve subject to bidding restrictions imposed on firms’ offer curves. Notably, while these studies point out the potential for the ex-post optimal offer curve to violate practical constraints such as monotonicity, this literature does not consider the extent to which such violations will occur in practice, or the particular reasons and circumstances under which this is likely to occur. These questions, which are important to understand the practical limitations of employing ex-post offer curves and the need for a methodology to identify ex-ante expected profit maximizing supply functions, motivate the current paper.⁶${}^{,}$⁷

In this article, we utilize data from Alberta’s wholesale electricity market for a time period during which generating firms were alleged to have engaged in coordinated behavior.⁸ We focus our analysis on three firms that make up approximately 40% of the market, and consider the reasons and extent to which the ex-post optimal offer curves violate monotonic bidding restrictions.⁹

We show that a firm’s residual demand can be highly non-linear with large shelves and vertical portions; similar residual demand characteristics appear in Australia (Wolak, 2007), Italy (Bigerna et al., 2016), and New York (Benatia, 2018). We find that these features can result in profit functions that are non-concave with multiple local optima. We demonstrate that both the multiplicity of local optima and local convexity of residual demand can result in backward bending (downward sloping) ex-post best-response offer curves violating restrictions that supply functions must be monotonically increasing.¹⁰ We characterize conditions under which these problems will arise.

Within the restrictions of our empirical framework, we present evidence suggesting that two of the three large strategic firms in our sample bid in a manner that is inconsistent with the supply function that passes through the ex-post profit maximizing price-quantity pairs, whereas the third firm bids closely to this benchmark. However, because the ex-post optimal offer curve is often non-monotonic, these results could be driven in part by the fact that firms are unable to bid in a manner consistent with this benchmark. To investigate this possibility further, we construct alternative offer curves that represent a monotonic smoothing of the optimal offer curves. We document that two of the three firms earned expected profits considerably below those that would have been achieved by utilizing the simplified monotonically smoothed optimal offer curves. This suggests that the non-monotonicity of the ex-post optimal offer curves was not the key constraining factor for these two firms.¹¹

A finding that firms are not behaving according to the predictions of unilateral profit-maximizing behavior made by a particular model may be the results of restrictions of the model being used, as opposed to evidence of true deviations from unilaterally profit-maximizing behavior. While it is outside the scope of our analysis to relax every assumption of our framework, we consider several alternative explanations for why these firms may be deviating from the ex-post optimal offer curve by considering the impact of dynamic costs, misspecification in the estimated forward contract positions, and transmission congestion. These robustness checks do not change our conclusions.¹²

In addition, our paper assesses the extent to which a simplified monotonic smoothing of the ex-post optimal offer curve can capture potential expected profits when the ex-post optimal is unobtainable in practice (e.g., due to a violation of monotonicity). We find that employing the outer envelope of the ex-post optimal offers achieves the vast majority of available firm profits in our sample. Further, we argue why this simplified benchmark can serve as an initial conservative test for coordinated behavior in this setting.

Our analysis makes several contributions to the existing literature. First, our context represents an empirical illustration of the conditions under which a firm may not be able to achieve the full ex-post unilateral profit-maximizing profits due to monotonicity restrictions imposed in practice, and emphasizes the importance of accounting for such restrictions when considering whether firms are behaving unilaterally optimally. Second, we identify easily recognizable features of residual demand curves under which this issue is more likely to arise, providing guidance to researchers regarding whether non-montonicity concerns may be present in their particular empirical context. Third, our finding that the simplified monotonic smoothing of the ex-post optimal offer curve is able to achieve the majority of expected profits suggests a useful and practical alternative to the computationally and time-intensive derivation of the monotonically constrained ex-ante optimal offer curves.

Finally, there is a broader literature that analyzes the impacts of restrictions imposed on bidding behavior in multi-unit divisible goods auctions. Kastl, 2011, Kastl, 2012 and Holmberg et al. (2013) analyze the impact of restricting the number of steps in an agent’s bid function. Kastl (2012) and Woodward (2019) account for monotonic restrictions imposed on bidding in a theoretical framework. These studies demonstrate that these bidding restrictions can induce bidders to adjust the their bid functions impacting equilibrium outcomes. Our analysis contributes to this literature by providing additional empirical evidence on settings under which bidding restrictions and conditions on residual demand can induce agents to adjust their offers in multi-unit auctions.

The paper is organized as follows. Section 2 presents the theoretical foundations. Section 3 presents our main empirical application, data, methodology, and results. Several extensions of our main analysis are considered in Section 4. Section 5 concludes.