Understanding strategic bidding in multi-unit auctions: a case study of the Texas electricity spot market.

[] 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 S[O.sub.2] 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 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 (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.

[FIGURE 2 OMITTED]

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

[[pi].sub.it] = [S.sub.it]([p.sup.c.sub.t])[p.sup.c.sub.t] - [C.sub.it] ([S.sub.it]([p.sup.c.sub.t])) - ([p.sup.c.sub.t] - [PC.sub.it])[QC.sub.it].

We calculate [[pi].sub.it] for three scenarios: (i) ex post optimal bidding ([S.sub.it] = [S.sup.XPO.sub.it]), (ii) actual bidding ([S.sub.it] = [S.sup.O.sub.it]), and (iii) bidding to avoid the balancing market (([S.sub.it] = 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 = [[pi].sup.Actual] - [[pi].sup.Avoid]/[[pi].sup.XPO] - [[pi].sup.Avoid],

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 (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)