Blowin in the Wind: Sequential Markets, Market Power and Arbitrage

Transcription

1 Blowin in the Wind: Sequential Markets, Market Power and Arbitrage Koichiro Ito Boston University and NBER Mar Reguant Stanford GSB and NBER May 4, 2014 Preliminary and incomplete, comments welcome PLEASE DO NOT CITE OR CIRCULATE Abstract We study strategic behavior of wind farms in electricity markets, and examine their dynamic adjustments through sequential markets. Wind production is uncertain and volatile, with the degree of uncertainty being reduced over the day. Therefore, sequential forward markets can improve market efficiency through information updating. However, pre-existing distortions such as market power and limited arbitrage may distort incentives to reveal accurate production forecasts. By using micro-level data in the Spanish electricity market, we show that wind farms exploit a forward market price premium, overstate their production over 20% at the day-ahead market, and only slowly adjust their commitments to expected production, increasing the dynamic inefficiencies from wind misplanning. Consistent with the premium being driven by market power, wind farms that have market power do not exploit the price premium, whereas competitive fringe farmers do the arbitrage. Our results show how pre-existing distortions can have unintended consequences in the market, making the integration of wind power even more challenging. s: ito@bu.edu, mreguant@stanford.edu. We thank Simon Board, Severin Borenstein, Ryan Kellogg, Chris Knittel and Matt White, as well as participants at the Stanford IO lunch, UCEI Energy Camp, POWER Conference on Energy Research and Policy, IFN Stockholm, SITE Stockholm, University of Gothenburg, UCLA, MIT, TSE, PSE and École Polytechnique. 1

2 1 Introduction Renewable energy is growing fast around the world and is expected to have further faster growth in the next decade. Globally, renewable power, including hydropower, is expected to rise to 25% of gross power generation in 2018 (IEA 2013). Even if we exclude hydropower generation, the share of non-hydro renewable power is forecasted to be doubling, to 8% of gross generation in 2018, up from 4% in 2011 and 2% in One of the reasons for the fast growth in renewable energy is a growing amount of public funds from many countries to promote renewable energy. In the US, for example, the federal government and many state governments have adopted policies to promote the development of various renewable energy technologies for generating electricity. However, recent studies in economics argue that non-hydro renewable energy, such as wind and solar power generation, creates new challenges to the regulation and market design of energy markets (Joskow, 2011; Borenstein, 2012). First, renewable energy is intermittent in the sense that its output is volatile and uncontrollable, driven by meteorological conditions. For example, wind and solar generation is affected by wind speed, wind direction, cloud cover, and other weather characteristics. As a result, renewable energy generally cannot provide a stable and continuous amount of electricity to a grid system. This intermittency contrasts with traditional power generation, as nuclear, coal or gas plants can provide stable and continuous amounts of electricity. Second, it is generally impossible to predict the exact amount of production from renewable energy beforehand, creating substantial uncertainty in production. Uncertainty in production is particularly problematic in electricity markets because electricity is not a commodity that can be easily stored, and therefore market operators need to ensure that demand and supply are balanced at any given time of the day. As the share of renewable energy grows, these two problems become a central problem for regulators and market participants. However, there is a limited number of studies that investigate firms behavior in renewable energy generation, and that examine what economic policies or mechanism designs can mitigate this problem. In this paper, we investigate how market mechanisms can mitigate the uncertainty problems of renewable energy. Several mechanisms have been introduced in electricity markets to mitigate the effects of wind uncertainty. In particular, as more intermittent renewable sources are introduced, penalties for last minutes changes in production due to production uncertainty have been progressively introduced. For example, this is the case of Spain and Texas, where initially only very small (or none) of these costs were borne by the wind farms, but they have gradually been made part of their compensation scheme. Additionally, wind farms are often allowed to participate in the regular market for electricity suppliers, 2

3 bidding in forward and real-time markets, which take place in sequence. These sequential markets enable wind farms to update their commitments over time, potentially enabling them to use the latest information available on wind forecasts. However, their participation in these markets also creates challenges. In particular, these sequential markets are often not well arbitraged. 1 The lack of arbitrage, due to institutional restrictions on how arbitraging is made in the market, creates opportunities for wind farms to exploit these differences, making integration of wind even more challenging. We present a model to formalize the economic forces that are at play when designing these mechanisms. We model the dynamic optimization of wind farms in sequential markets. We show that, at the last minute and given adequate deviation prices, firms have an incentive to report accurately. If sequential markets are efficient, their presence is also consistent with the minimization of the costs of integration. However, sequential markets in electricity markets are oftentimes not well arbitrage due to a combination of institutional restrictions and market power (Borenstein et al., 2008). We show that, in our model and in the presence of market power on the sellers side, such institutional constraints give raise to a day-ahead premium: markets that happen earlier in time tend to have larger prices. In the presence of such pre-existing distortions, wind farms have incentives to distort their forecasts earlier in the day (i.e., overselling wind at higher prices early in the day), increasing the apparent costs of renewable energy. We empirically test these theoretical predictions by investigating wind farms responses to these economic incentives in the Spanish electricity market. Our empirical analysis is based on a rich set of micro-data on bidding behavior and electricity production by wind farms. We collect hourly marginal prices at each of the auctions, which allows us to get a sense of the expectations that wind farmers may have on prices. Second, we also collect hourly unit-level information on wind planned production. Finally, we also measure hourly unit-level final output as well as hourly equilibrium deviations, which allows us to get a sense of the degree of uncertainty in this market. These unusually detailed micro-data at the unit level allow us to investigate wind farms responses to the incentive mechanisms that are created by the regulators. In the Spanish electricity market, we find that there is a systematic day-ahead price premium. That is, forward prices are systematically higher than real-time prices. As a result, wind farms can gain the premium if they overbid in earlier markets. They can oversell at a high price, and buy back the energy at a lower price. We empirically examine the bidding behavior of wind farms in the sequential markets, and find evidence of significant asymmetries in how wind farms adjust their output over the day. In line with the theoretical predictions, wind farms systematically offer more production early in the day, compared to what they finally produce. It is only as time goes by and through adjustments in the sequential markets, that their scheduled 1 See, for example, Borenstein et al. (2008) for a discussion in the context of California. 3

4 quantity and actual production quantity come close. As suggested by our model, a positive price premium in the day-ahead market can be driven by the interaction of restrictions on arbitrage and market power. We find evidence that market power is a significant driver of the day-ahead premium. First, the day-ahead premium correlates with other variables that affect the incentives and ability to exercise market power, such as total forecasted demand and the elasticity of residual demand (McRae and Wolak, 2014). Second, if the premium is really driven by market power, wind farms with market power should behave very differently than fringe wind farms. Consistently, we observe very different behavior between small wind farms and wind farms with the incentive and ability to exercise market power. The contributions of the paper are twofold. First, we contribute to the existing literature measuring the costs of integrating intermittent sources of production, in line with Gowrisankaran et al. (2013). Whereas previous work assessing the costs of integrating renewable energy has relied on simulation approaches, we are able to measure these costs directly in a market with a very large penetration rate of wind production. The reduced form quantification costs that we do are related to Cullen (2013), who measures the environmental benefits of wind also looking at actual wind production data. Different than previous work, we emphasize the difficulties of integrating wind due to its uncertain nature, rather than its volatile patterns. Second, we follow previous work documenting the lack of arbitrage in electricity markets (Borenstein et al., 2008; Jha and Wolak, 2013). We build a dynamic model to explain the presence and sign of price premium in forward and real-time markets, and show that the patterns in the data are consistent with the hypothesis of market power on the sellers side. Whereas several papers have documented market power in the context of electricity markets (Wolfram, 1998, 1999; Borenstein et al., 2002; Reguant, 2014), our empirical exercise stands as one that is particularly clean. To first order, running a wind farm is costless, so in the short run, the marginal cost of a wind farm is observed. Therefore, systematic differences across fringe and integrated wind farms are likely to be driven by strategic behavior. Our results have several policy implications. Our analysis suggests that wind farms engage in substantial price arbitrage in the electricity market, which could have potential benefits, as documented by Saravia (2003) and Jha and Wolak (2013). In Spain, there are restrictions on the amount of arbitrage, inducing systematic price differences. Wind farms could be acting as defacto financial arbitrageurs. However, having wind farms perform such arbitrage also comes at costs. In particular, adjusting production output at power plants at the last minute is more costly than planning well in advance, due to the presence of dynamic costs in this industry. These biases in planned wind could further difficult its integration in the electricity grid. Therefore, it is important to keep in mind pre-existing distortions in electricity markets when designing 4

5 mechanisms to accommodate new technologies such as wind and solar, which are becoming increasingly ubiquitous. This paper proceeds as follows. In Section 2, we describe a model of sequential markets, taking into account production uncertainty. In Section 3, we explain institutional background and data, putting special emphasis on the performance of sequential markets and the apparent lack of full arbitrage, which appears to be driven by institutional restrictions and market power. Section 4 shows how wind farms respond to the presence of these incentives and further builds the case for market power. Section 5 analyses the costs arising from these distortions, and Section 6 concludes. 2 Model We develop first a model of sequential markets in the electricity wholesale market. Several aspects of firms behavior can affect prices in sequential markets, such as information updating or risk aversion, among others. In this paper, we focus on market power as a particularly important channel Sequential Markets Let s consider a model in which planning can be done at two different stages: market 1, which is the dayahead market; and market 2, which is the real-time market. For simplicity, and given that our main focus is on the role of market power, we consider a setting in which there is no uncertainty. 2 One potential reason that can make prices in both markets to depart are institutional restrictions on the amount of arbitrage. Institutional restrictions often impose that the first market (day-ahead) needs to plan for all expected demand. Given that all energy is traded in the first market, subsequent sequential markets are mostly a market for reshuffling. Furthermore, re-trading is limited to production units, which have capacity constraints. For this reason, the first market clears most of the volume and firms tend to have larger market power (if they are net sellers, they sell larger quantities), and buyers tend to have larger monopsony power. Consider a monopolist facing a residual demand in sequential markets. We consider the case in which the monopolist owns traditional power plants, and therefore its production is not stochastic and can be allocated in advance through sequential markets. 3 We discuss the incentives for wind farms in the next section. The 2 This is an important simplification. We plan to extend the model to a setting with uncertainty in future drafts. 3 We abstract from the role of the monopolist in helping compensate last minute wind deviations, as the main goal of the model is to give intuition on the sign of price premia in sequential markets. We also abstract from the monopolist owning both traditional power plants and wind mills. We plan to further explore these issues in future work. 5

6 problem of the price-setting firm becomes, max Q 1 Π = E[p 1 (Q 1 ) Q 1 + p 2 (Q 1, Q ) Q C(Q 1 + Q ) I 1 ], s.t. Q Q 2 Q 1 : max Q 2 E[p 2 (Q 1, Q 2 Q 1 ) (Q 2 Q 1 ) C(Q 2) I 2 ]. We include a cost of production associated with power generation through conventional sources of energy (coal and gas). When thinking about the problem, it is important to keep in mind that, in the first stage, the firm cannot commit to a particular quantity for the second stage, and therefore the strategies need to be consistent with profit maximization at each stage. To gain intuition, we consider a simplified example with linear residual demand, constant marginal costs c and no uncertainty. Demand is inelastic and fixed, given by A. 4 In our model, A represents the total forecasted demand, which is cleared in the day-ahead market. In the forward market, the residual demand is given by a constant intercept and slope, given by D 1 = A b 1 p 1. One potential interpretation of this residual demand is that it is the inelastic demand A minus the willingness to produce by fringe suppliers, which are willing to produce as long as p 1 is above their marginal cost c(q) = q/b 1. In the second market, demand is still fixed and equal to A. Although the production of A has already been fully allocated in the forward market, the second market allows players to re-shuffle their allocations. Therefore, the purpose of the market is for firms to adjust their commitments. 5 Assume that fringe players are willing to adjust their production with slope b 2. Then, the residual demand is given by D 2 = b 2 (p 1 p 2 ). If p 2 is below p 1, fringe firms reduce their output and the monopolist increases production. For the special case of b 1 = b 2, the interpretation is that fringe suppliers are willing to move along their original supply curve. We will also consider the case in which b 2 < b 1, which would imply that fringe suppliers are less willing to adjust their output in real time. This is consistent with adjustment being more costly as the time of delivery comes closer, which is a feature of electricity markets as well as many other industries. 6 We provide a full derivation of equilibrium prices and quantities, as well as proofs of the results, in the appendix, together with some numerical examples. For the purposes of the empirical exercise, Result 1 summarizes some useful comparative statics. Result 1. Assume that the monopolist is a net seller in this market (i.e., Q 2 > 0). Then, 4 An elastic demand can be easily included by modeling demand as A α 1p 1. 5 In practice, the real-time market can also adjust the total demand (up or down), but this is a very minor share of total demand. 6 In the context of electricity markets, Hortaçsu and Puller (2008) find evidence that the supply curve of fringe suppliers is relatively inelastic at the real-time market, which could be explained by a lack of sophistication or other adjustment costs. 6

7 p 1 > p 2 ; p 1 p 2 is increasing with A, decreasing with b 1, and increasing in b 2 ; if b 2 = b 1, Q 1 = Q; If b 2 < b 1, Q 1 > Q. The intuition behind the result is that, the monopolist exercises market power in both markets in equilibrium. For the simple case of constant marginal costs, it needs to put the same markup in both stages for the equilibrium to be consistent with profit maximization under each stage. However, and given an elastic downward slopping residual demand, this does not necessarily imply that prices equalize. In particular, fringe suppliers set a high price in the first market, and then reduce their commitments in the second market. The results of a day-ahead price premium are analogous to those in the literature considering a monopolist engaging in clearance sales (Lazear, 1986). In the first stage, the monopolist benefits from selling the good to a set of naïve consumers, while in the second stage, it sells the good to consumers with lower valuations. Consumers buying in the first period would have benefited from buying in the second period at a lower price. In our setting, we have assumed that demand is not elastic and, by construction, is all planned for already in the first market (A). The downward slopping residual demand comes from the presence of fringe suppliers. In our setting, fringe suppliers sell more in the first market, at a better price, and then buy back part of their commitments from the monopolist in the real-time market at lower prices. Therefore, individually, fringe suppliers find the strategy profitable. However, the equilibrium still leaves room for arbitrage. Full arbitrage Given that p 1 > p 2, competitive fringe suppliers could oversell even more at the first market. In such case, fringe suppliers would need to offer production below cost in the first market. The residual demand would no longer be given by total demand minus the marginal cost curve of fringe producers. We consider the case in which fringe suppliers compete for these arbitrage opportunities to the point at which p 1 = p 2. Abstracting from changes in the slope of the residual demands (b 1, b 2 ), consider an arbitrageur that can shift the residual demand horizontally at the forward market, by financially taking a position to sell (shift to the left), and buy back the same quantity at the real-time market, so that D 1 = A b 1 p 1 s, and D 2 = b 2 (p 1 p 2 ) + s. 7 If the costs of arbitraging are relatively small and the arbitrageurs market is competitive, s will be chosen so that p 1 approximates p 2. 7 Virtual bidders in markets such as MISO and California engage in these type of commitments. 7

8 Result 2. Assume that the monopolist is a net seller in this market and arbitrageurs are competitive so that, in equilibrium, s is such that p 1 = p 2. Then, Q 1 decreases with s and Q increases with s; p 1 will be lower with s and p 2 will be higher with s; s reduces total output by the monopolist. Limited arbitrage In practice, however, s might not be chosen so that prices equalize, due to some institutional constraints. For example, it is common in some electricity markets to limit participation to power plants. Therefore, an arbitrageur cannot take a purely financial position in the market unless it is backed up by an actual power plant. Suppose that arbitrage is limited by the capacity of fringe suppliers, K. The most an arbitrageur can overbid is K minus the actual production by fringe players at the end of the market (e.g., bp 2 for the case when b 1 = b 2 ). 8 This implies that the constraint to arbitrage will be most binding in situations in which demand is large or, more generally, if fringe suppliers are producing close to their capacities. Result 3. Assume that arbitrageurs can at most take a position equal to the unallocated fringe capacity. Then, price differences (p 1 > p2) are more likely when K is lower, all else equal; holding the capacities of fringe players K fixed, price differences (p 1 > p2) are more likely when A is large and when b 1 or b 2 are lower; when b 1 = b 2, price differences will arise whenever the monopolist is pivotal, i.e., if K < A. The intuition of the result is that the more market power the firm has (e.g., more demand relative to capacity or less elastic fringe supply curves), there might be price premia in hours of high demand the presence of capacity constrained arbitrageurs. 9 8 There might also be some implicit regulatory understanding that firms should not depart too much from their actual wind production during the sequential markets, even if there is potential for financial arbitrage. In such case, the constraints to arbitrage would be more binding. 9 Another explanation on why arbitrage might not be complete can be the presence of market power on the arbitrageurs side. For an arbitrageur, profits are made as long as p 1 > p 2. Therefore, there is an optimal limited amount of arbitrage in equilibrium. We plan to characterize the equilibrium of this alternative case in future drafts. 8

9 2.0.2 Incentives to Wind Farms We consider the incentives for wind farms in these sequential markets. A wind farm needs to choose quantity committed at each of the two markets, q w 1 and qw 2. Given that wind farms have uncertain and exogenous output at the last stage, it is unclear what its incentives at the last market are, for a given p 2. For example, one could imagine that it would be tempting for a wind farm to overclaim its wind production submitting a very high q w 2 and receive the market price on an unreasonable amount of output that never materializes. To avoid these incentive problems, it is important to emphasize that additional mechanism are put in place to incentivize wind farms to report accurately at the last minute. These mechanisms concern only only wind farms or other generators with intermittent resources. To provide incentives for wind farms to report accurate production at the last minute, electricity markets with a substantial presence of wind resources (e.g., Texas or Spain) have introduced penalties to deviations between the quantity of wind planned in the last market (q2 w ) and the actual measured output by the wind farm. For our purposes, we assume that the wind farm has strong incentives to submit its expected wind production at the last market. This pins down the equilibrium quantity in the second market, and given the penalty mechanism, q w 2 E[qw ]. 10 What should the wind farm do regarding q1 w? In the context of the electricity market that we study, the price in the sequential market (p 2 ) tends to be lower than the price in the first (day-ahead) market (p 1 ), at least in expectation, for most days and hours. If such differences are sustained, and E[p 1 ] > E[p 2 ], then the incentives in the first stage will be to overstate wind production, i.e., q w 1 > qw 2. In the context of the previous example, wind farms would be acting as financial arbitrageurs and setting s = q w 1 > qw 2 > 0. Result 4. If p 1 > p 2, a wind farm will have an incentive to overestimate its wind production in the first stage. As explained above, even in the presence of systematic differences, firms might be constrained in their ability to underbid or overbid. Clearly, a firm can at most underbid to the level of claiming to have zero wind available. Similarly, and given the restrictions in the market that we study, a firm can at most claim to produce up to the capacity of its wind farm. However, this constraint will be less important for wind farms 10 In the past, we have explored the implications of the penalty design in greater detail. We found that a wind farm does not have an incentive to commit its expected production, but actually to be slightly conservative and understate its forecast, due to non-linearities in the penalties. In the empirical section, we find that the economic incentives of the traditional sequential markets modeled here drive the biggest effects in bidding behavior, and therefore we have decided to reduce the specific institutional details regarding the penalties, which we provided in previous drafts. 9

10 than other production units, as wind farm seldom produce at full capacity due to limitations in how wind speed and wind patterns can be harvested. Wind farms and market power The prediction of wind farm behavior is contingent on its degree of market power. In particular, we have assumed that the wind farm has incentives to act as a de facto financial arbitrageur, as opposed to acting as a monopolist. However, if the wind farm has substantial generation, or it is integrated within a company with other sources of energy production, the result does not necessarily hold. The incentives of the wind farm are no longer to arbitrage price differences in these markets, but to equalize markups, as the monopolist in our previous example. Result 5 summarizes the predictions for those wind farms with market power. Result 5. If p 1 > p 2, a firm that, has market power as a net seller in the first stage, and is not setting the price with wind at the margin, will have no incentive to overestimate its wind production in the first stage. If wind is setting the price at the margin, the firm will have an incentive to underestimate wind production in the first stage. We explore the testable implications from Results 1-5 in the empirical section. Before, we give some more detail on the particularities of wind production and uncertainty, as well as how it is being regulated in the Spanish electricity market. 3 Institutions and Data 3.1 Overview In recent years, wind generation has been growing significantly in Spain. Figure 1 shows the annual evolution and total installed wind capacity in Spain from 1998 to The total capacity was only 713 MW in 1998 and grew to 22,785 MW in As of 2012, Spain is the fourth country in terms of installed wind capacity, only after the United States, Germany and China. Wind energy was the system s third technology in 2012, with a generation of 48,156 GWh, and a cover of the electrical demand of 17.4%. In fact, it is not uncommon that wind power generates more than a third of electricity consumption in some days of the year. Therefore, the Spanish case appears a particularly good case study for a market with a large presence of uncertain wind production. 10

11 Figure 1: Wind capacity evolution in Spain This figure shows the annual evolution and total installed wind capacity in Spain from 1998 to The uncertainty in wind generation is substantial. In Figure 2, we use data from the Spanish wind farms and show deviations between actual and planned wind generation one hour in advance. The average deviation is around 150MWh, with a standard deviation of around 690MWh. Taking into account that average wind production is around 4,800MWh during this period, with a standard deviation of roughly 2,800MWh, these are significant fluctuations in output. 11 To examine the effects of this uncertainty in the market and the performance of current mechanisms to address it, we collect data for the Spanish electricity market, between 2009 and Data for the Spanish electricity market are publicly available at the System and Market Operator websites. 12 We focus on data related to wind farm behavior and their participation in day-ahead and sequential markets. 3.2 Sequential Markets The Spanish electricity market is organized in a centralized fashion, with a day-ahead market and up to seven intra-day markets. Suppose that firms want to offer electricity to be produced at a certain hour of the next day. The first chance for them to bid is the day-ahead market. They submit their bidding strategies 11 Interestingly, the differences and their standard deviations have been going down over time, specially for the public wind forecast provided by the system operator, at the same time as wind production has been increasing. 12 See their respective websites, and 11

12 Density 0 2.0e e e e Net Deviations Wind (MWh) Figure 2: Deviations Distribution for Wind in Real-Time This figure shows the distribution of the deviations between scheduled and actual production from wind generation. 12

13 all at once and production for each hour is auctioned simultaneously. Therefore, the day-ahead market is a set of twenty-four simultaneous uniform auctions. 13 Roughly 80% of the electricity allocated in centralized markets is sold through this day-ahead market. In the intra-day markets, producers and consumers can bid as they do in the day-ahead market, to adjust their committed production in previous markets. For example, if firms realize that they want to generate hourly electricity that is less than their assigned quantity in the day-ahead market, they can purchase the difference in an intra-day market. In each of the intra-day markets, the intra-day marginal price is determined by a uniform price auction as well. Figure 3 shows the timetable of the day-ahead and intra-day markets. The day-ahead market clears at 10 am of the day before electricity is to be produced. The first intra-day market opens at 4 pm and closes at 5:45 pm. Firms bid for each hour of 28 hours (from 9 pm through midnight for the next day). In the second intra-day market, firms bid for each hour of 24 hours (from 1 am through midnight for the next day). Similarly, firms can bid in the third, fourth, fifth, and sixth intra-day markets. The seventh intra-day market is technically part of the first intra-day market of the next day. In the last market, firms commit their production. 14 As a result, firms have multiple chances to adjust for their scheduled production for a given hour of the day. For example, consider generation at nine p.m. for the next day. For this generation, firms can put a bid in the day-ahead market and in the first through seventh intra-day markets. Therefore, they have up to eight chances to adjust their generation. Firms have no more chance to adjust their committed quantity after the last market. If their actual production deviates from the final commitment, they have to buy back (if too little energy is produced) or sell (if more energy is produced) at special deviation prices. Even though we do not focus on how those markets are designed, in practice it will imply that wind farms have an incentive to reduce their departures between planned and actual production at the last stage. We collect hourly marginal prices at each of these markets, which allows us to get a sense of the expectations that wind farmers may have on prices. We also collect hourly allocated wind quantities, to track adjustments to output during the day. Finally, we also measure hourly unit-level final output as well as hourly equilibrium deviation prices, which allows us to get a sense of the expected deviation prices that firms face. We complement data on hourly outcomes with details on the ownership, location and feed-in tariffs perceived by wind farms. 13 In reality, the auction takes the form of a modified uniform auction, as explained in Reguant (2014). 14 Note that the last market is not necessarily the seventh intra-day market. For example, the third intra-day market is the last market for hours between 4 am and 7 am (see Figure 5). 13

14 Transaction*Time Day4ahead%Market 10:00 Intra4day%1 Intra4day%2 Intra4day%3 Intra4day%4 Intra4day%5 Intra4day%6 Intra%7 Hour%of%Energy%Delivery :00 21:00 1:00 4:00 8:00 12:00 16:00 Figure 3: Sequential Markets in the Spanish Electricity Market This figure describes the timeline of the sequential markets in the Spanish Electricity Market. For a given hour of their production, firms can bid in the day-ahead market and multiple intra-day markets. They also face costs for their deviations between the final commitment and actual production. 14

15 3.3 Evidence of Lack of Arbitrage One institutional feature that we have highlighted in the theoretical framework is the potential lack of arbitrage in electricity markets. 15 In Spain, there are two features that restrict arbitrage. First, on the supply side, only power plants can arbitrage. The extent to which they can arbitrage is limited by the capacity constraints in their units (upper bound) and not producing at all (lower bound). Second, the system operator clears roughly all forecasted demand in the day-ahead, as it is crucially important in electricity markets to balance demand and supply in real-time. Therefore, demand participants, who could potentially arbitrage with less restrictions on their amount of arbitrage, have barely an effect on total traded quantity. Finally, systematic differences between day-ahead quantities and final quantities have at times been scrutinized, potentially acting as an additional feature restricting firms from engaging in arbitrage. 16 These features can introduce systematic price differences in sequential markets. In our setting, we find that prices in the day-ahead market tend to be larger than in subsequent markets. Figure 4 shows average market prices across hours for each of the main markets to buy and sell electricity (day-ahead and seven intra-day markets). The figure indicates that there is a positive day-ahead price premium, i.e., the day-ahead prices are higher than intra-day market prices. This is particularly true for the last intra-day market (e.g., Intra-day market 5 for hours 12 to 15). Table 1 shows that the fact that the average price premium is positive is not an artifact of some price outliers, and thus the difference is systematic. This is particularly true for the hours in the afternoon and the evening, in which the median day-ahead premium is above one Euro/MWh in many hours of the day and across sequential markets. At night hours, the median day-ahead premium is zero, but the distribution of differences is systematically shifted to the right, still giving a positive day-ahead premium on average. [Table 1 about here] 4 Evidence of Market Power and Arbitrage Our theory suggests that market power in a forward market can create forward market price premium relative to the prices in spot markets. This is particularly important for electricity markets because planners have to clear the majority of energy in the forward market. This constraint results in significantly large infra- 15 See (Borenstein et al., 2008) for a description of similar issues in the context of California. 16 For example, during the implementation of the RD 3/2006, the regulator imposed some constrained on day-ahead market prices, but not intra-day prices. Firms reacted by withholding either supply or demand from the day-ahead market, and clearing a substantial amount of net power in the intra-day markets. Both supply and demand withholding was investigated by the monitoring agency. 15

16 55 50 Euro per MWh Hour Intra 1 Intra 2 Intra 3 Intra 4 Intra 5 Intra 6 Intra 7 Day ahead Figure 4: Market Clearing Price in the Day-ahead and Intra-day Markets This figure shows the average market clearing price (Euro per MWh) in the day-ahead and intra-day markets. Dayahead market tends to exhibit prices that are on average larger than in the subsequent sequential markets. 16

17 marginal quantity in the forward market. The theory suggests that the larger infra-marginal quantity, the larger the market power becomes, which is likely to increase the forward market price premium. We first test this prediction by exploiting the variation in demand in the Spanish wholesale electricity market. Given the existence of the price premium, firms that do not exercise market power in the forward market have an incentive to arbitrage. In particular, wind farms are likely to have this incentive because they have no physical adjustment cost for arbitraging. However, the incentive can be different for wind farms that are owned by integrated incumbent firms that have other types of power plants, because these firms are the ones that exercise market power in the forward market. To test this hypothesis, we estimate the price arbitrage of wind farms and investigate whether the arbitraging is systematically different between wind farms owned by competitive fringe firms and integrated incumbent firms. 4.1 Forward-Market Price Premium and Market Power Figure 4 shows that there is systematic forward market price premium on average. However, in the distribution of the day-ahead price premium, we find substantial variation across days and hours. What drives the price premium? In this section, we examine if the price premium is associated with market power in the day-ahead market. Define the price premium by p h = p hda p hf I. p hda and p hf I are the market clearing prices at the day-ahead market and at the final spot market for the delivery of energy at hour h. Similarly, define the price premium in log by lnp h = lnp hda lnp hf I. We run an OLS regression: p h = α + βdemand h + γb 1 + φx h + u h (1) where Demand h is the demand forecast by the system operator and X h are the control variables. b 1 is the slope of the residual demand that is defined in the previous section. Because we observe unit-level bidding data for each hour, we can obtain b 1 by calculating the local slope of the actual residual demand curve for incumbent firms. [Table 2 about here] Table 2 shows evidence that the forward market price premium is associated with the demand forecast. Column 1 indicates that an 1% increase in demand is associated with an increase in the price premium by a 1.29 percentage point. Column 2 implies that an 1% increase in the slope of the residual demand curve (more elastic demand) is associated with a decrease in the price premium by a 2.54 percentage point. The regression results are robust to control variables, including year-by-month fixed effects. Our regressions 17

18 provide useful information about the correlation between the price premium and demand as well as the slope of residual demand. In the future, we explore this point further by using techniques in the literature of auctions in wholesale electricity markets such as McRae and Wolak (2014). 4.2 Wind Farms and Arbitrage Our theory suggests that information updating through sequential markets might not be the only reason why wind farms might want to participate in sequential markets. If there are pre-existing distortions in these markets that prevent the prices from being efficient, firms may no longer have incentives to report accurate forecasts of their final production, specially early in the day, when they still have several opportunities to correct their position. In this section, we investigate whether wind farms respond to these financial incentives. To examine this question, we analyze how wind farms update their positions (i.e. commitments on how much they produce for a given hour) in the eight sequential markets: the day-ahead market and the seven successive intra-day markets. 17 For example, consider production for hour h on January 2 in First, firms bid in the day-ahead market (January 1). Their bidding supply curve and the market clearing price determine the commitment for production for hour h on January 2. Between the day-ahead market and the actual delivery hour, the firm has at most seven intra-day markets where they can update the committed quantity by selling or purchasing quantities. Our objective is to examine how firms change their positions for committed outputs for a given delivery hour h throughout the eight markets. To measure the changes in positions in market s, we define: lnq jhs = lnq jhs lnq jh,final, (2) where q jhs is wind farm j s output for hour h in market s for s = 1,..., 7 (the seven intra-day markets). The final output, q jh,final, is the actual output quantity that is produced by unit j. Firms bid their supply curve for h = 1 to 24 in the day-ahead market, the first intra-day market, and the second intra-day market. In the third, forth, fifth, sixth, and seventh intra-day market, firms bid their supply curve for h = 4 to 24, h = 7 to 24, h = 11 to 24, h = 15 to 24, and h = 20 to 24, respectively. That is, firms have more than one chance to bid for all hours. 17 There is a congestion market between the day-ahead market and the fist intra-day market, in which the market operator makes an adjustment for congestion. Because we do not find a systematic difference in output between the day-ahead and congestion market, in this section we focus on the day-ahead and seven intra-day markets. We discuss the role of congestion in the next section. 18

19 Because electricity generation of wind farms is affected by random shocks in weather, one expects that the final output sometimes deviates from the output that is committed in market s. However, as far as the forecasting error has mean zero and wind farms plan for their best available forecast, the change in output defined in (2) should be zero in expectation for each h in each market s. To test this hypothesis, we estimate the following equation by OLS, separately for each market s: 24 lnq jhs = α h I h + ɛ jhs, (3) h=1 where I h is a dummy variable for hour h. Therefore, this equation estimates the mean of lnq jhs for each hour. If firms do not systematically schedule wind production that is different from their final output, one would expect α h = 0. Table 3 presents the estimation results of equation (3). We include all data from January 2009 to December Column 1 shows evidence that wind farms systematically overbid in the day-ahead market for all hours. Moreover, they overbid more for later hours. For example, they overbid by 26% on average for the production for hour 24. Column 2 presents that wind farms adjust for some of the overbidding in the first intra-day market. Particularly, for hours between 1 to 11, the difference between the output in the first intra-day market and the final output is nearly zero. However, for hours between 12 to 24, wind farms still overbid in this market. Column 3 shows a similar tendency. Wind farms do not systematically overbid for earlier hours in the second intra-day market, but they overbid for later hours. We observe similar behavior in the rest of the intra-day markets: wind farms systematically overbid for later hours. Alternatively, we can look at the table horizontally. For example, the estimates for hour 24 in the last row of the table indicate that wind farms overbid by 26% on average in the day-ahead market, about 11% in the first intra-day market, between 3-7% in the second and fifth intra-day markets, and the overbidding approaches to zero in the final sequential markets. [Table 3 about here] In addition to the mean of the overbidding, we also examine its distribution. In Table 4, we focus on the second intra-day market to more closely examine the distribution of lnq jhs. We calculate percentiles of lnq jhs for the second intra-day market relative to the final output that wind farms actually produce. For the first four hours, nearly all observations are zero, which again provides evidence that in the last market, nearly all wind farms bid the exact quantity that they actually produce. In contrast, we find clear asymmetry in the distribution for hours from 5 to 24, and specially after 8. The distribution is skewed toward overbidding. 19

20 Finally, the distribution gets wider in later hours, which is consistent with the adjustment for forecasting errors, because wind farms get better forecasts for earlier hours and relatively noisy forecasts for later hours. [Table 4 about here] Overall, we find that wind farms systematically overbid in earlier markets of the sequential markets. This overbidding behavior is crucial for the system operator of wholesale electricity markets. System operators have to adjust any unbalance between supply and demand, and it is more costly to request for adjusting the unbalance in closer hours to the actual transaction. Why do wind farms have the systematic overbidding? As explained above, this overbidding is consistent with price arbitrage between the day-ahead and intra-day markets. As a result, wind farms can gain the premium if they overbid in forward markets. If this is the case, we should expect wind farms to engage in more overbidding in those days in which a larger price premium is expected. We test this hypothesis by estimating the price arbitrage of wind farms. Consider a regression, q jhda = α + β p hda + γx h + u h, (4) where q jhda is the overbidding of wind farm j in the day-ahead market relative to the final spot market for hour h and p hda is the day-ahead price premium. The coefficient of interest β tells us how much additional overbidding can be caused by an increase in the price premium by 1 Euro/MWh. The OLS estimates of this regression are likely to be biased because of reverse causality; overbidding by wind farms affects the price premium. We expect that the overbidding by wind farms in the day-ahead market lowers the day-ahead price premium, which implies that the OLS estimates will be biased downward. To address this problem, we use demand forecast as an instrument. From Table 2, we know that the price premium and the demand forecast have strong correlation. That is, we have a strong first stage relationship. Our identification assumption is that the demand forecast can be excluded from the second stage regression. That is, the overbidding behavior of wind farms is not affected by the demand forecast itself other than the channel through the price premium. In addition to the regression in levels, we also run this regression by using the log difference terms: lnq jhda = α + β lnp hda + γx h + u h, (5) where β can be interpreted as the price elasticity of arbitrage. Table 5 shows the regression results in Logs (Panel A) and in levels (Panel B). As we expect, the OLS 20

21 regressions in column 1 produce estimates biased downward. The OLS estimates imply that wind farms overbid less when the day-ahead price premium is large. Once we use our instrument, the instrumental variable regressions produce estimates with the expected sign. In the log specification, the estimates imply that the price elasticity of arbitrage is 2.55 with the full set of control variables. That is, when there is an 1% increase in the day-ahead market price relative to the final spot market price, wind farms bid 2.55% more in the day-ahead market relative to the spot market. Similarly, the regression result in column 4 in Panel B implies that when there is an increase in the day-ahead market price relative to the final spot market price by 1 Euro/MWh, wind farms bid MWh more in the day-ahead market relative to the spot market. [Table 5 about here] Finally, we find the negative coefficient for wind forecast for both regressions, although including wind forecast does not change much the coefficient on the price premium. We interpret that the negative coefficient implies that wind farms have more ability in price arbitrage when there is less forecasted wind, because there will be larger differences between their maximum capacity and actual ex-post production quantity. On the other hand, when there is substantial wind blowing, the actual production of wind farms approaches to their maximum capacity. In this case, there is limited quantity that can be sold in the day-ahead and purchased back in the spot market, which makes it difficult for wind farms to do price arbitrage. 4.3 Wind Farms and Market Power The previous section focuses on the overall responses of wind farms. In this section, we examine heterogeneity in the response, particularly focusing on the ownership of wind farms. In the Spanish electricity market, some wind farms are owned by incumbent firms that own other types of power plants such as thermal power plants. In contrast, other wind farms are owned by competitive fringe firms that own only wind farms. Do incumbent firms, competitive fringe firms, or both do the price arbitrage in the sequential markets? Our Results 4 and 5 in the theory section suggest that one should observe different behavior between these two sets of agents. If incumbent firms have market power and wind is at the margin, strategic firms could have an opposite incentive and therefore withhold wind. In Table 6, we test this question by estimating overbidding for incumbents and competitive fringes. The table shows evidence that the overbidding is statistically significant for competitive fringes. In contrast, incumbents do not reveal such behavior. We find precisely estimated zero coefficients for the overbidding for incumbents. The standard errors imply that we reject both small positive and negative overbidding. This 21

22 result supports our hypothesis that competitive fringes have large incentives to do the price arbitrage, while incumbents do not have such incentives. [Table 6 about here] Figure 5 graphically shows the estimates for competitive fringe firms in Panel A and incumbent firms in Panel B separately for each hour and market. Each point shows the mean of the overbid ratio relative to the actual final output. Panel A shows that fringe firms overbid in most hours and markets. The figure also shows discontinuous jumps at hour 12, 16, and 21. The discontinuous jumps are consistent with the market structure. For example, consider hours 12 to 15. For these hours, wind farms have five chances to bid their supply curve for exactly the same hours of their production. The figure suggests that they overbid most in the first intra-day market, moderately overbid in the second to fourth intra-day markets. However, they do not systematically overbid in the fifth intra-day market, which is the last market that they can bid. This is because they face deviation costs if their final output is less than their final bid. Similarly, for hours 16 to 20, they overbid in the first to fifth intra-day markets. There is no systematic overbidding in the sixth market, which is the last market for these hours. In contrast, Panel B shows that there is almost no significant overselling by incumbent firms. The difference between their commitment in the forward markets to the spot market is at most 2 percent. This evidence is consistent with our theoretical prediction that incumbent firms do not have incentive to pricearbitrage if they have market power in forward markets. We explore details of this evidence by regression analysis in the following section. Does this finding imply that incumbent firms have zero price elasticity of arbitrage? To test this hypothesis, we estimate the instrumental variable regression in (5) for competitive fringe firms and incumbent firms separately in Table 7. Column 4 in Panel A implies that the price elasticity of arbitrage is 3.60 for the wind farms owned by competitive fringe firms. This elasticity is larger than the overall elasticity for all wind farms (elasticity = 2.55) that is presented in Table (4). In contrast, columns 2 to 4 in Panel B indicate that for wind farms that are owned by incumbent firms, we cannot reject the null hypothesis that the price elasticity is zero. This finding is notable because all wind farms have almost zero physical adjustment costs to do price arbitrage, regardless of the ownership of the wind farms. Therefore, the results provide strong evidence that competitive fringe wind farms take advantage of price arbitrage, while incumbent wind farms do not arbitrage.this is because they are likely to be the agents who exercise market power in the day-ahead market, and therefore have incentives to withdraw their bids in the day-ahead market. [Table 7 about here] 22