Price Coordination in Vertically Integrated Electricity Markets: Theory and Empirical Evidence.

• Author: Bosco, Bruno
• Position: Report - Statistical data

1. INTRODUCTION

   Recently restructured electricity markets work as multi-unit auctions (von der Fehr and Harbord, 1993; Wolfram, 1998). In such markets some operators dispose of the production capacity necessary to clear the market when competitors have already exhausted theirs and there is a portion of otherwise not matchable residual demand. These producers are generally called pivotal (1) and they are expected to sell at a monopolistic price on that residual demand, and so, fully exploit their market power. Yet, empirical evidence (Hortacsu and Puller, 2008; Wolak, 2003; Bosco et al., 2010, 2012, 2013) shows that asked prices recorded in wholesale electricity markets are well below the theoretical profit maximizing level, and this finding stimulated scholars to explore different possible reasons explaining this misalignment of theory and empirical outcomes. Among such possible reasons, forward contract obligations (de Frutos and Fabra, 2012; Ausubel and Cramton, 2010a), virtual power plant (VPP) (2) auctions (Ausubel and Cramton, 2010b) and firms' vertical integration (3) are the most discussed ones.

   Papers analyzing the behavior of vertically integrated firms in electricity markets (Bushnell et al., 2008) assume that their bids maximize the profit of the entire group. There is no evidence, however, on how independent firms belonging to the same group can coordinate their actions to achieve this goal. In this paper we look inside the black box of a vertically integrated firm and try to model--and then estimate--how the relationship between the producer and a seller belonging to the integrated group and operating in the same wholesale market affects the bidding behavior of the former. We assume that an electricity generator and a retailer belong to the same parent company and that they simultaneously sell and buy electricity in the wholesale auction. The retailer will resell the energy to final consumers who pay regulated prices. The parent company coordinates all activities and is interested in the group's net profit. We model this coordination by a simple Principal-Agent (P-A) model and explore the implications for electricity pricing and bidding conduct in a wholesale market. This coordination can be costly in terms of intra-group efficient allocation of resources and we show how generators' bidding behavior is affected by this cost. We also estimate empirically the magnitude of this effect for a vertically integrated firm which is a dominant player in the Italian wholesale market.

   The paper is organized as follows. Section 2 introduces the theoretical analysis and presents a bidding model of a vertically integrated supplier in a wholesale electricity market. Section 3 contains empirical results obtained for two vertically integrated Italian firms. We show that bid prices of suppliers are, at least for a sub-period of the sample, significantly affected by vertical integration according to the predictions derived by the theoretical model. Section 4 concludes.

2. THE MANAGERIAL INCENTIVE PROBLEM

   We model electricity transactions as they are organized in real-world markets. Electricity is exchanged in a wholesale market which works as a two-side auction: generators submit sale offers as price-quantity pairs while retailers bid to buy bulk electricity. The market operator orders bids (offers) in a non-increasing (non-decreasing) way and calculates the market equilibrium at the intersection of demand and supply. The clearing price, named SMP (System Marginal Price), is paid to all dispatched producers. Since retailers sell to their customers the electricity they have purchased wholesale, their profits are determined by the difference between the selling price (which is often regulated) and the SMP.

   Under textbook market conditions demand and supply would act independently and coordinate their decisions through the market. The electricity market however, is still characterized by the presence of vertically integrated firms. In fact there are producers and retailers which are legally separated but nonetheless they are under the control of the same parent company which faces the problem of profit allocation inside the group. This happens for example when one side of the market, typically the supply, enjoys a higher degree of market power with respect to the other side. Given the SMP rule, a high equilibrium price raises the profits of the generator but induces tight profit conditions for the retailer. For that reason we expect that the holding firm may wish to follow an "implicit" profit redistribution activity inside the group. To this end the parent tries to influence the bidding behavior of the branch endowed with the higher degree of market power to the advantage of the other branch. How this can be done depends upon the structure of the incentives existing inside the group. To explore this issue, in this Section we introduce a Principal-Agent model designed to describe the way in which the holding firm sets the right incentive for one branch to maximize group profits. The model is also used to obtain predictions on the bidding behavior to be subjected to empirical analysis.

   We assume that a group is composed by two operational firms, a generator G and a retailer R, and by a parent firm H which coordinates their activities. G and R are legally independent and compete on the supply and demand side respectively of a wholesale electricity market. G is assumed to maximize profits given its residual demand, y(p), defined as total market demand minus the other firms' supply when the price that it sets in the market equals p. (4) R buys a predetermined quantity x of electricity at the price p and it then sells x at a fixed regulated price p in the retail market. (5) H coordinates the two firms in order to maximize the entire group profits. H 's goal may not be in line with the goal of G since the latter may wish to maximize its own profits. In the model we allow for the possibility that H assigns a different weight to the (profit of) the two branches in its objective function. (6) The problem is therefore to introduce an incentive for G to set an asked wholesale price which will not destroy the retailer's profit opportunities. This situation is particularly compelling when supply conditions are such that the generator is a monopolist on the residual demand (pivotal generator) so that it could fix a price up to the market cap. For this reason we restrict our interest to a situation in which G is the only firm that is pivotal while competitors do not have sufficient capacity to be price-setter. (7)

   Assume there are no fixed costs and let [C.sub.G]= cy(p), be the cost of G, where c>0 is the constant marginal cost, whereas R has no costs apart fromp, i.e. the wholesale price. The model is characterized by asymmetric information between the holding firm H and the generator G. We model asymmetric information assuming that the marginal cost of production c is observed by G only and H assumes c to be a random variable having a cdf F(c). We assume that f(c) = F'(c) over [c,c] and that d[F(c)/f(c)]/dc is monotonically non-decreasing. The asymmetric information assumption can be justified on the grounds that the generator is a legally separated and an economically independent entity with respect to the holding firm. In this framework, a full ex-ante knowledge of cost conditions cannot be guaranteed and (the manager of) generator G has the incentive to conceal this information to the benefit of his own firm. (8) To implement a policy of profit maximization of the entire group H must therefore induce G to reveal his cost.

   We incorporate the managerial incentive into our problem as follows. (9) Assume that G is lead by a manager who, without other forms of incentive, would maximize the profit of his firm. This is defined by:

   [mathematical expression not reproducible] (1)

   where, as above, c indicates the constant marginal production cost of the producer, y(.) is the quantity and p(.) is the market price. The incentive for G to behave according to H's policy is obtained through a payment made to the manager and financed from G's profits. We define t as a direct payment made by H to the manager of G, who has utility given by:

   [mathematical expression not reproducible] (2)

   In (2) the manager weights, with parameter [beta], his personal reward and the company's profits. From (2) we can write t as a function of U:

   [mathematical expression not reproducible] (3)

   If the manager truthfully reveals the cost parameter c, then his maximal utility would be U and, by the Envelope Theorem, we can write the incentive constraint as

   [mathematical expression not reproducible] (4)

   Rewriting the generator's profits (1) using (3), we get

   [mathematical expression not reproducible] (5)

   where [[PI].sub.G] now has been rewritten net of t. Notice that the money transfer t given to the manager of G is paid out from G's own profits so that there are not intragroup...