Market Power and Vertical Integration in the Spanish Electricity Market PRELIMINARY AND INCOMPLETE Kai-Uwe Kühn and Matilde P. Machado.∗ University of Michigan, CEPR and Universidad Carlos III de Madrid
†
May 2004
Abstract The Spanish electricity market has two particularities: 1) the high concentration in the hands of two firms that hold around 80% of the market; 2) the high degree of vertical integration. The same firms buy from and sell electricity into a pool. We model the behavior of firms as competition in supply functions (a la Green and Newberry, 1991) taking into account both the vertical integration and the dynamic features involved in hydroelectrical generation. The different strategic effects we obtain from this model allow us to test the degree of market power of the two main firms through exogenous variations in their downstream demands that have different impact on the pool price. Our results suggest that the two largest firms in the Spanish market exercise market power.
∗
contact author e-mail:
[email protected] We particularly thank Daniel Ackerberg, Charles Brown, Luis Cabral, Trond Olsen and Juan Toro for comments on a previous version of the paper. Furthermore, we would like to thank Pedro Blás, Natalia Fabra, Miguel Angel Lasheras, and all participants at both the 4th CEPR conference in Empirical Industrial Organization and at the "Competition and Coordination in Electricity Industry" conference in Toulouse. Keywords: market power test, vertical integration, electricity markets, supply function equilibrium. JEL classification: L13,L41,L94. †
i
1
1
Introduction
In January 1998, the Spanish government liberalized the market for electricity generation and introduced a spot market for electricity. The basic design of this electricity spot market is similar to the previously deregulated UK market and even closer to the California electricity market that was deregulated at about the same time. It is well known that both deregulation experiments in the UK and California suffered from being susceptible to the exercise of substantial market power. Indeed, the lack of almost any elasticity of demand in electricity markets leads to extraordinarily large incentives to raise price relative to other markets. In the UK the issue of market power has already led to fundamental reforms and in California there have been widespread discussions on how to improve the system, for example, by introducing real time pricing on the user side. There are essentially four separate economic activities in electricity markets: generation, transmission, distribution and retailing (often called supply). With electricity liberalization transmission and distribution remained regulated because they are considered natural monopoly elements of the electricity system. Transmission and distribution services are payed at fixed per unit access prices. Most of the deregulation experiences liberalized generation imediately while retailing liberalization was gradual. The introduction of the spot market directly linked the two potentially competite activities: generation and retailing (see figure 3). By and large generation firms must sell their production in the spot market and retail and distribution firms must buy electricity from the spot market at the equilibrium price. One of the greatest concerns of post-liberalization has been market power of generation companies in the spot markets. The potential for market power, in the Spanish electricity market was considered a problem even before deregulation (see Kühn and Regibeau 1998, Arocena, Kühn and Regibeau 1999) since the two largest firms in the industry controlled about 75% of the generation (table 1 shows, that this legacy of concentration has remained essentially unchanged through 2001).
2
Besides the potential for market power in generation, table 1 also shows a unique feature of the Spanish electricity industry: the high degree of vertical integration into retailing (and distribution). Most deregulation experiments in fairly concentrated markets as in the UK and California have imposed vertical separation between generation and retailing activities in the belief that these would create incentives for entry into the industry.1 It was not clear then how vertical integration may affect the exercise of market power in electricity spot markets. Due to the high degree of vertical integration a high proportion of the payments made and received from the spot market are effectively pure transfers between retail and generation activities of the same companies. Does market power matter at all in such a setting? Does vertical integration increase or decrease the impact of concentration in generation? What would be the impact of entry into liberalized retail markets on spot market prices given the high degree of concentration in generation? Would vertical separation increase or decrease the efficiency in generation? Would it lead to substantial changes in the spot market price? All of these are important policy questions, especially in the face of repeated attempts to reorganize the Spanish electricity market. Our aim in this paper is to test for the exercise of market power when firms are present on both sides of the market with the use of only partial information. We develop and estimate a supply function 1
See Arocena et al. (1999) for such an argument.
Market Shares in the Spot Market Endesa (E. Viesgo not considered) Iberdrola Union Fenosa Hidro-Cantabrico E. de Viesgo Others REE (imports/exports)
Period: May Generation 45.05 28.72 12.55 6.63 3.45 0.9 2.73
- December 2001 total Retailing Distribution 38.42 38.31 38.90 39.15 13.54 14.97 5.86 6.30 0.97 1.27 1.95 .002 0.36 0
Table 1: Statistics for generation, retailing and distribution sold and bought in the spot market by each of the Spanish electric firms when adding generation by co-ownwership plants according to the fraction of the plant owned.
3
model to approximate the bidding strategies in the spot market and show that the way market power is exercised depends on whether firms are net demanders or net suppliers into this market at a particular instance in time.2 Net suppliers will underproduce as any normal oligopolist in order to raise the price received for the net electricity sold to the market. Net demanders, on the contrary, will overproduce due to an oligopsonistic incentive to reduce the price paid for the inframarginal units purchased from the spot market. In equilibrium, net demanders will overproduce while net suppliers will underproduce leading to excessive costs of generating electricity. Asymmetric asset holdings upstream and downstream, therefore, result in an inefficient allocation of generation assets. If firms always demanded as much as they generated they would not have incentives to act strategically, prices in the spot market would be the same as in a perfectly competitive market and production would be efficient. Market power can, therefore, only be identified and the efficiency of the market evaluated by taking the vertical structure of generation and retailing into account when analyzing a firm’s bidding decisions in the spot market. The systematic and varying degrees of vertical integration between the different electricity companies in our sample allows the identication of market power in the Spanish spot market. The use of a structural approach in this exercise allows us to make inferences about market power even in the absence of information on costs, financial contracts (which would modify the relevant marginal cost for a firm3 ), or information on the form of downstream negotiated retail contracts. In fact, the structural approach is crucial to devise the proper test of market power even if public information on the firm’s relevant marginal costs were available since market prices below marginal cost for some firms are consistent with the exercise of market power when firms are vertically integrated. The structural approach enables the identification and estimation of the firms’ marginal cost parameters which we will use to simulate relevant policy changes. Finally, our structural model has the advantage of nesting several alternative models e.g. perfect competition that are simultaneously tested in the data.
2 We have chosen the supply function model because it most closely resembles the true bidding structure of the market. It is therefore most appropriate for a structural estimation approach. However, it should be kept in mind that the qualitative features of the model would be retained by any other bidding model, for example one along the lines of Harbord and von der Fehr (1993). 3 See Wolak (2000) for a derivation and discussion of this result.
4
The test for market power we develop is also robust to including important idiosyncratic regulatory features of the Spanish electricity market that significantly change the incentives of the major players involved. The most important of these is a system of compensating “Costs of Transition to Competition” (CTCs). The payment of CTCs to generating companies is computed as a fraction set by law of the joint profit of distribution companies. These can be accommodated into the model by changing the definition of effective net demand positions in the market. While Table 1 suggests that Endesa is on average a net supplier and Iberdrola on average a net demander, a careful modelling of the CTC payments shows otherwise. As shown in Figures 1 and 2 the “relevant” measure of downstream demand suggests that Endesa should behave as a net-demander into the pool in81.5% of the times while Iberdrola should behave a net-supplier 54.5% of the times. This means that Endesa has, on average, an incentive to act similarly to a monopsonist and overbid generation assets into the spot market in order to lower the price on the net units purchased from the market. In contrast, Iberdrola’s is more likely to underprovide generation assets to the market in order to raise the price on the net electricity sold to the market. Using a data from the spot market bids from May to December 2001, we test three predictions from the theoretical model. First, the theory implies that the downstream demand realization should have systematic impact on the bidding strategy of the firm only if there is market power in the spot market. Second, firms should be producing up to a point where price exceeds marginal costs in states in which they are net suppliers and up to a point where price is below marginal costs in states in which they are net demanders. Third, Endesa should on average be producing at marginal costs exceeding price, while Iberdrola should be close to pricing at marginal costs on average. Not only we find evidence of exercise of market power by Endesa and Iberdrola but our model matches the data patterns remarkably well. We use our estimates of the relevant cost parameters to simulate price and efficiency gains induced by several potential changes in market structure. Preliminary results show that if Endesa and Iberdrola bid in their non-hydroelectrical generating units at marginal cost this would not change the average price substantially but would lead substantial efficiency gains of the order of magnitude of 6000 Euros per
5 hour. Although this is a small number it accrues to 144, 000.00 Euros a day. Supply function models of electricity markets have been estimated previously by Wolak (??). We are contributing to this literature by expanding on the theoretical work in Kühn and Machado (1998), which first explicitly modelled the vertical structure of the market, and exploiting the explanatory power of heterogeneous vertical integration for identifying market power in the spot market outcomes.4 Other work on supply function competition in electricity markets (e.g. Green and Newbery 1992, Green 1996) has focused on the calibration of alternative scenarios. Green (1996) has explicitly considered the impact of asymmetric holdings of generation assets on spot market prices. He shows that asymmetries in the distribution of generation assets between firms lead to higher prices in the spot market. His analysis is based entirely on the calibration of a supply function model to data of the UK electricity market. Unfortunately, the impact of asymmetries in the distribution of generation asset on spot market prices is difficult to test empirically due to the lack of variation in the distribution of those assets across firms5 . In contrast, there is much greater variation in the demand shares and therefore in the net-demand positions of different electricity companies than there is in capacities as figures 1 and 2 show. This allows us to identify the effects of structural changes empirically. The spirit of our exercise is very close to Wolfram (199?) in the sense that we are observing variations in infra marginal sales to determine the exercise of market power. In contrast to her work we are focused on the effects of vertical integration.
The rest of the paper is structured as follows. Section 2 describes a simple theoretical model that illustrates most of the qualitative strategic effects at play and derives the basic propositions. Section 3 describes the specificities of the Spanish electricity market. Section 4 adapts the basic model of Section 2 to the specificities of the Spanish one day ahead electricity spot market, allowing for the existence of a significant hydroelectric generating capacity and the regulatory rules that affect bidding incentives. We also describes the data used in this paper in this section. In Section 5 we show the estimation results perform our projection exercises to give a feel for the potential impact of market power on outcomes after 4 5
It has recently come to our attention that Ali Hortacsu and Steven L. Puller have in parallel to us done related work. Wolfram (1998) is a remarkable exception.
6
MWh
1766.44
-3757.02 1
time
5640
Evolution of Iberdrola's net-demand position
Figure 1: structural changes in the industry. Section 6 concludes. In the Appendix we discuss some of robustness issues and theoretical caveats that may influence the interpretation of our results and discuss the limits of projecting outcomes due to structural changes in the industry.
2
An Illustrative Model
The main feature of interest of the Spanish electricity market for our analysis comes from the fact that the major competitors are active both in generation and in retailing. This potentially generates market power both on the buyer and the seller side of the market. By the rules of the spot market virtually all electricity produced has to be sold into the spot market and retailers have to purchase all their electricity from the spot market. In this section we develop a simple duopoly model of supply function competition that has these characteristics. In section 4 we adapt this model to the idiosyncratic features of the Spanish electricity market. Yet, the basic mechanism driving the qualitative results of the extended model will be the same as in this illustrative model. Every generator i is integrated into downstream retailing. Demand from his customers is given by θi D(pi ). We assume that the final consumer price is predetermined by contract or regulation pi = p¯,
7
MWh
2975.18
-1505.52 1
time
5640
Evolution of Endesa's net-demand position
Figure 2: reflecting the idea that prices downstream are set less frequently than upstream. For ease of exposition we normalize D(¯ p) = 1. The demand parameter θi is randomly distributed on some interval [θ i , ¯θi ], where we allow for ¯θi = ∞. We will refer to it as the state of retailing demand for firm i. We allow θi to be correlated between firms. There is a set of signals about the state of retail demand of the form σ k = θl + εk , k = 1, ..., K, where l is either i or j, and E{εk } = 0. Each firm receives a subset of these signals denoted by Ii for firm i, which is firm i’s information set. For our model the only relevant signals are those which contain private information about the rival’s downstream demand. Hence, without loss of generality, we reduce the set of signals to one for each firm, where the signal for firm i has the form σ i = θj + εi .6 We assume that the distributions of the parameter vector (θi , θ j ) and the signal vector are such that the posterior for θi , i.e. E{θi | Ij } are linear in the signals observed.7 Firm i produces electricity with the total cost function Ci (qi ) = c0i qi + c1i
qi2 2.
A firm’s strategy set
consists of a set of supply functions of the form Si (π; Ii ), where Si is increasing and differentiable in π. For any information set Ii , this function specifies how much electricity the firm is willing to produce for all possible spot market prices π. Note that the signal about the firm i’s own demand would contain information about firm j’s demand if demands were correlated. We have chosen our formulation to make the model more transparent. 7 This implies that E{θi | θj } = E{θi } + ρ[θj − E{θj }], where ρ is the correlation coefficient between θi and θj . 6
8
The upstream generation market is run by a spot market operator who gets direct information about total market demand θ = θi + θj .8 He also receives the supply functions submitted by the two firms. He then sets the price π ∗ such that the market is cleared: θ = Si (π ∗ , Ii ) + Sj (π ∗ , Ij ).
(1)
An electricity generator obtains π ∗ Si (π ∗ , Ii )− Ci (Si (π ∗ , Ii )) of profits from selling electricity in the spot market. In addition he receives (¯ p − π ∗ )θi from distributing electricity to the end user for which he receives the price p¯ and pays the spot market price π ∗ . Firms maximize the joint profits from generation and retailing by simultaneously submitting their supply functions to the spot market operator taking the supply function chosen by the rival as given. Each firm will therefore perceive that a change in their supply function will affect the equilibrium spot market price the spot market operator sets via the market clearing condition (1). Maximizing profits over a function space is potentially a difficult problem to solve. Klemperer and Meyer (1989) have shown how to reduce such a problem by substituting in for the supply function of the firm from the market clearing condition. Then the problem can be solved by choosing an optimal price π for every realization of the uncertainty. Our model would be equivalent to theirs if all signals were common to both players so that there would be no private information.9 When there are private signals a firm will not only face whatever uncertainty exists in the total demand θ (as in Klemperer and Meyer), but will also be uncertain about the realization of the supply function of its rival.10 In order to use their techniques to solve the firm’s maximization problem and derive explicit equilibrium behavior, we will restrict attention in this paper to the analysis of equilibria 8
Assuming that the spot market is cleared on the basis of realized demand is a simplifying assumption allowing us to exposit the basic economic effect at play in the simplest way. In section 4 we will change this assumption to reflect the true structre of the Spanish spot market mechanism. As it will be clear later, the basic mechanism is still at work in that modified model. 9 Readers familiar with Klemperer and Meyer (1989) will note that in this case there would be no equilbirium in our model since we have assumed demand to be completely inelastic with respect to π. (see Section 6). 10 Formally, instead of analyzing Nash equilbria in supply functions we have to look at Bayesian Nash equilbria in our model.
9 in supply functions Si (π, Ii ) that are linear in all of their arguments: Si (π, Ii ) = s0i + s1i σ i + si π,
(2)
The intercept of the supply function has a deterministic component s0i and one component that depends on the signal observed. The latter corresponds to the signal that is observed by firm i privately. By restricting ourselves to linear supply functions we can generate a residual demand for firm i in the spot market that depends additively on a random shock as is the case in Klemperer and Meyer (1989). This residual demand for firm i is given by θ − Sj (π, Ij ) = θ − s1i [σ j − E{σ j | Ii }] − {Sj (π, Ij ) − s1i [σ j − E{σ j | Ii }]} Define the random variable ηi by η i ≡ θ − s1i [σ j − E{σ j | Ii }]. All the uncertainty faced by i in its residual demand is captured by the random variable η i . In other words, ηi is a sufficient statistic for the state of the spot market for firm i. For any given π we can therefore write the residual demand for firm i as η i − E{Sj (π, Ij ) | Ii }. Note that, for a higher η i , the demand curve shifts upward and the unique optimal quantity will lead to a higher equilibrium price. Because of this monotonicity we can express firm i’s problem simply as maximizing with respect to π for every possible realization of η i :
p − π]θi + π [ηi − E{Sj (π, Ij ) | Ii }] − Ci (ηi − E {Sj (π, Ij ) | Ii }) | Ii , η i } | Ii } , max E {E {[¯
π(ηi ,Ii )
(3)
Pointwise maximization of (3) yields the following first order condition for every η i −E{θ i | Ii , ηi } + Si (π, Ii ) − (π − c0i − c1i Si (π, Ii ))sj = 0
(4)
where we have substituted Si (π, Ii ) for η i − E{Sj (π, Ij ) | Ii } from the equilibrium condition. From this first order condition we immediately obtain our first result:
10 Proposition 1 Suppose firm j uses a linear supply function. Then, firm i in a state (Ii , η i ) will be producing at price exceeding marginal cost if and only if firm i is a net supplier of electricity in the spot market equilibrium. Furthermore, firm i prices on average below marginal cost if and only if it is on average a net demander.
Proof. It follows directly from (4) that Si (π, Ii ) −E{θi | Ii , η} > 0 ⇐⇒ (π − c0i − c1i Si (π, Ii )) > 0 and the same for the reverse sign. On average net supply to the market must be equal to the unconditional expectation E{Si (π, Ii ) − θi }. Since E{(π − c0i − c1i Si (π, Ii ))sj } = E{(π − c0i − c1i Si (π, Ii ))}sj by the linearity of j’s supply function, the same argument as before can be made for the unconditional expectations. Proposition 1 captures the essential strategic issue in this market. If a generator would expect to sell exactly as much into the spot market as he takes out of the spot market as a retailer, there would be no reason at the margin to increase or decrease production to influence the price. Any marginal change in production, to the first order, will only come down to a redistribution between the upstream and the downstream parts of the same business. When a firm expects to be a net supplier, then it has an incentive to hold back production, because this redistributes rents from net demanders to this firm. Holding back production results in a price increase from which the firm benefits on its net sales into the spot market. This is the standard oligopoly incentive to reduce production. The opposite is true for net demanders. A net demander has an incentive to overproduce in order to reduce the price paid on the net-purchases on the spot market. This is an oligopsony effect. It will make a net demander produce up to a point where price is below marginal cost. The reader should note that this effect does not depend on the supply function set up. Any model of the spot market that takes vertical integration into account will have the feature that incentives are driven by the net demand positions of the firms. The supply function model has the advantage of leading to an estimating equation that has few parameters and from which we can infer the structural parameters of the model.
11
Despite the fact that final consumer demand in our model is totally inelastic due to predetermined downstream prices (either due to contracts or to regulation), the interaction of oligopoly incentives for net suppliers and of oligopsony incentives for net demanders will lead to an important inefficiency in generation when there is significant market power: efficient units of production will be held back, while inefficient units will be bid into the market due to the oligopsony incentive. It is important to notice that in the absence of market power in the electricity spot market, the downstream demand positions should not matter at all. The firm would take the spot market price as exogenously given and not affected by its own choice of supply function. Maximizing (3) state by state would then simply generate a non-random linear supply function with slope of the marginal cost curve sci =
1 ci1 .
We can therefore conclude:
Proposition 2 A firm will condition its supply function on the state of downstream demand and on signals about demand in general only if it has market power in the electricity spot market.
To obtain more insight on the impact that the downstream distribution of retail demands has on the exercise of market power in the electricity spot market, we now analyze equilibrium behavior. We show that there exists a unique supply function equilibrium that is linear in price and the signals. To obtain such linearity in the best response of firm i to a linear supply function of firm j it is clear that we need E{θi | Ii , η i } to be linear. But ηi is just a linear function of θ and the signals that are privately observed by j. Our assumption on the linearity of posteriors then directly implies that E{θi | Ii , η i } takes the linear form: E{θ i | Ii , ηi } = λi0 + λi1 σ i + λiη ηi
(5)
First replace η i in equation (4) by Si (π, Ii ) + E{Sj (π, Ij ) | Ii } from the market clearing condition. This yields: −E {θi | Ii , Si (π, Ii ) + E{Sj (π, Ij ) | Ii }} + Si (π, Ii ) − (π − c0i − c1i Si (π, Ii ))sj = 0.
(6)
12 Now note, that (6) has to hold for all π, so differentiation with respect to π yields: −λiη (Si (π, Ii ) + sj ) + Si (π, Ii ) − sj [1 − c1i Si (π, Ii )] = 0
(7)
Equation (7) determines the slope of the supply function of firm i. Clearly, this only depends on the constants λiη and ci1 as well as on the slope of j’s supply function sj , which we have assumed to be linear. Hence, the slope of the optimal supply function of firm i will be a constant, independent of the signals received. Setting si = Si (π, Ii ) we can solve for the equilibrium slopes of the supply functions of firms i and j from the system of equations implied by (7). This yields: si =
2(λiη + λjη ) ci1 + cj1 + λiη λjη [ λci1 − iη
11
(8)
cj1 λjη ]
Note that the slope of the two firms are the same up to the expression [ λci1 − iη
cj1 λjη ].
This expression
determines the heterogeneity in the supply functions in equilibrium. To understand expression (8) it is useful to first consider a limit case: Suppose that firms observe no private signals of demand, i.e. ηi = θ and assume that θi and θ j are perfectly correlated. Then λi0 and λi1 in (5) are zero and λiη is simply given by the downstream market share of firm i, i.e. λiη + λjη = 1. In this case (8) is easily interpretable. If firms are symmetric, i.e. ci1 = cj1 and λiη = λjη = 12 , the whole expression collapses to si =
1 ci1 ,
the slope of the perfectly competitive supply function. Intuitively, with
completely symmetric firms, we must have a symmetric outcome. But then every firm will have a zero net supply position in equilibrium and market power effects are irrelevant. Now consider inducing an asymmetry in the demand position keeping costs symmetric. Clearly if firm i has the larger downstream market, λiη > λjη , firm i will have a steeper supply curve. Similarly, holding the demand side symmetric, i.e. λiη = λjη = 12 , the firm with the flatter marginal cost function will have a steeper supply function. The more efficient firm will want to expand output more strongly as a response to market shocks. Overall, we may get opposing effects from the downstream market share and the slope of the upstream cost function. Which firm has the steeper supply function will be determined by the relative size of with identical slopes of the supply functions, i.e. 11
ci1 λiη
=
cj1 λjη ,
ci1 λiη .
Note that even
the equilibrium response to demand shocks
Solving for sj and replacing it in the F.O.C we can then solve for s0i and s0j and finally then for price.
13
is distorted from that of perfect competition: For any given total production, the firm with the flatter marginal cost function does not produce enough, while the firm with the steeper marginal cost function produces too much. Unfortunately, the interpretation in terms of λiη as a market share breaks down in a more general setting with imperfect correlation or private signals. To see this, consider again the case of perfect correlation. But now we allow for private signals. In this case λiη
0. Together these constraints imply that bidding behavior of the firm only depends on its net-demand position. When these constraints are satisfied, proposition 1 holds and we find that firms set price below marginal cost iff they are net-demanders and price above marginal cost iff they are net-suppliers. Having the constraint a2 + a3 = 1 hold would also make alternative explanations for a3 > 0 implausible since 28
We discuss in the appendix that this assumption appears innocuous in the case of Endesa, but could be violated in the case of Iberdrola. 29 This is relevant important because formally the downstream and upstream part of the business are organized as separate companies which place “independent” bids.
29
none of those would necessarily imply that the incentives only depend on the net-demand position. Estimating equation (17) also gives us an estimate of the degree of market power of the individual generating firms. A natural measure of market power is the inverse of the slope of the residual demand function. This can identifed for all the models we discussed above as
1 S−i
=
1− a2 a1 .
It is straighforward to
see that this ratio would be zero under perfect competition. For any of the alternative models discussed above we can recover the parameters of the relevant marginal cost function from our estimating equation as:
a2 = c1i a1
(18)
and a0τ 1 b = −c0itτ + Dtτ . a1 S−i h
(19)
b∈Bi
Equation (18) identifies the slope of the marginal cost function. Equation (19) identifies the constant term of the adjusted marginal cost that is relevant for the theoretical test. There are a number of parameter restrictions which we can use as specification tests independently of the correct model. First, the coefficient on price a1 and the coefficient on hydroelectric production a2 should both be positive. Second, the estimated aggregate slope of the rivals’ supply function S−i
should be positive. Third, the model should approximate the average total production of rival firms by π, where π is the average spot market price and S 0−i can be estimated by the average electricity S0−i + S−i
bidded by rivals at price zero. Fourth, the coefficient c1i is overidentified. It can be obtained both by and a1 − 1/S−i c1i = a2 / a1 . If the model is well specified the estimated value of c1i should be c1i = 1/
(statistically) the same independently of the formula used.
30
4.5
The Data
We have data on supply and demand bids at the plant/unit level as well as the equilibrium price for all hours of the day from May until December 2001. This data was collected directly from the market operator web site ( www.omel.es). From information collected also from OMEL’s web page it is possible to obtain information about the type of generation plant (i.e. nuclear, hydroelectric) and the type of the demand bidding unit (i.e. distributor, supplier, pumping). We are also able to match each plant/unit with its proprietor i.e. Endesa Group, Iberdrola, Unión Fenosa, HidroCantábrico or Other. UNESA provided us with the daily hydroelectrical reserves by firm. We obtained temperatures for 4 hours a day for 50 weather stations across the country from the INM (Ministerio del Ambiente). The temperature data was crucial for the construction of valid instruments for the regressions in the next section. We take a practical approach and use the bids from the unregulated demand side of each firm condiu | I , π } needed in our estimation. To construct tional on the equilibrium price as the variable E{Ditτ it tτ r the variable αi E j E{Djtτ | Ijt } | Iit , π tτ we used the bids from the regulated demand. Moreover, to ej
ei
construct the variables S tτ and S tτ we also use the realizations of the special regime energy discharged into the distribution network over each calendar month. The data on the total energy sold under special regime by hour of the day was gathered in files taken directly from the OMEL’s web page for the period after June 29, 2001.30 In order to recover the two month of data since May 2001 we had to reconstruct the total special regime sales from the “programa diario base de funcionamiento” data. The “programa diario base de funcionamiento” is the plan for the next day after the daily market has cleared and after the special regime is included. By comparing this plan with the initial bids it is possible to perfectly infer the special regime sales.
30
The precise name of these files is: pdbf_tot_2001MMDD.xls where MM stands for the two digit month number and DD stands for the day of the month.
31
4.5.1
The Sale of Electra de Viesgo
Endesa sold generation plants, distribution, and retailing assets to a new entrant (ENEL) by spinning off Electra de Viesgo during the year 2001. Ownership was transferred only in January 2002, but the decisions to create Viesgo as a separate entity, which assets to assign to this new holding, and to sell off the holding were taken at the end of April 2001 (at the beginning of our sample).31 Viesgo was finally sold to the highest bidder ENEL in September 2001. Once the decision to sell Viesgo had been taken, the only way the Viesgo assets entered the profit function of ENDESA was through the payment received for Viesgo from the highest bidder. If the decision taken by ENDESA on its remaining assets in the four month period May through September 2001 were not expected to affect the sales price of Viesgo, we should treat Viesgo as a separate firm when analyzing ENDESA’s market behavior. We consider it as highly unlikely that the supply functions bid by ENDESA in the pool over this period would have a material influence on the expected present net value of the firm to any one of the bidders. That is simply not the level of detail that investment bankers would look at when deciding on recommendations for bids. For this reason we have excluded the output from generators and retailing demand from bidding units that were assigned to Viesgo from ENDESA’s supply and demand functions. However, we have also confirmed from the data that treating Viesgo as part of ENDESA does not change results significantly. If at all estimation results improve when excluding Viesgo.
5
Empirical Results (preliminary)
5.1
Selection of Instruments
The estimating equation (17) poses several endogeneity issues. For all alternative models discussed in Section 4.4, the major component of the error term is the shock to the marginal cost of the non-hydro 31
See ENDESA press release of April 28, 2001 at www.endesa.es/index_f4.html.
32 fully owned plants (εitτ ). These shocks are not observed to us but are observed by the firm when making its biding decisions. We consider these shocks to be the primary source of autocorrelation in the error term. Other components of the error term can only arise through misspecification of the model. The main source could come from our treatment of cross-ownership. If the jointly owned generating units are not either controlled by the firm or set inelastic supply functions (as proved in the appendix) then expected demand variables for firms with whom production is shared can appear in the error term. We will point out in our discussion below, where this will cause problems for our instruments. For Endesa we have confirmed that all jointly owned units effectively bid inelastic supply functions. For Iberdrola, in contrast, we have to assume that it controls two thermal plants it owns only to 50%. The production from these two thermal plants account on average for less than 6 percent of Iberdrola’s generation and for less than 1.5 percent of the market’s total production. The variables π tτ and hitτ are then clearly endogeneous since shocks to the marginal cost of non-hydro generation affect both the equilibrium price and the decision on how to optimally allocate production across hydroelectric and non-hydroelectrical plants. Moreover, if Endesa or Iberdrola have control over the production of co-owned plants then shocks to marginal cost should also lead to an optimal adjustment of production between the fully owned plants and the shared plants. Where this is not the case, we should still instrument for shared production because endogeneity could be caused by firms observing signals of the marginal costs of their rivals, which would have the effect of making such decisions correlated with the error term. The variable κn Sn is, therefore, is also treated as endogeneous. n∈Pi
For the spot market price we have a set of a priori excellent instruments: data on the amount of demand originating from end customers who are purchasing electricity at regulated prices, what we call regulated demand in the model, for each of the four main firms in the market. The regulatory regime leads to changes in the price of the end user at most once a year and end user prices are independent of prices in the electricity spot markets. For this reason, the regulated downstream demands can be considered exogenous. Clearly there cannot be any correlation with the marginal cost of firms. However,
33
all of these variables are highly correlated with the spot market price as regulated demand represents around 65 % of total demand in the spot market. From the point of view of the theory we would expect the disaggregated regulated demands to perform better as instruments for the spot price than the aggregated regulated demand. The disaggregated downstream regulated demands are highly correlated with the unregulated downstream demands for each of the firms. Relative movements in the downstream unregulated demand, in turn, lead to systematic movements in price because the price level is affected by relative net-demand positions. Hence, we would expect disaggregated regulated demands to contain more information about price movements than the aggreagted regulated demands. The only caveat to the quality of these instruments is the possibility that misspecification of the cross-ownership model leads to correlation between the error term and a competing firm’s regulated downstream demand. We discuss this possibility further below. Finding a good instrument for hydro-production is much more difficult. The amount of hydroelectricity that a firm decides to produce depends on the relative marginal costs of hydroelectric and non-hydroelectric production. An ideal instrument would, therefore, be uncorrelated with the nonhydroelectric marginal costs, but highly correlated with the shadow costs of hydroelectric production. There does not seem to be any good contemporaneous variable that would capture this idea. For this reason we have looked at various instruments that involve lags over decisions on hydro-electricity production. We consider a measure of the average hydro-electric production over time a preferable instrument to simple production lags in capturing variations in the shadow cost of hydro-production. The reason comes from the nature of relative cost variation in the production of hydro-electricity compared to the production of non-hydroelectricity. The short run marginal costs of hydro production do not appear to vary much and the overall shadow costs should not be expected to move significantly from day to day either, because they do not depend, for example, on rainfall on a specific day. Simple lags in hydro production may therefore contain more information about the previous period’s non-hydro marginal costs than about the shadow costs of hydro because day to day variation in relative production would be more
34
driven by non-hydro marginal costs which are relatively more volatile. Using an average, in contrast will smooth out day to day variations so that the averages are more driven by the slower moving variations in the shadow costs of hydroelectric production. An average would therefore be, a priori, a preferred instrument over simple lags. The most problematic variable for our estimation is the output from units with shared ownership essentially because of its low variability over the sample. This reflects the fact that over 90 percent of the joint production from the shared units comes from nuclear plants, which always bid all their capacity as base load and, therefore, have very low variability (except for variations that are caused by shut down due to maintenance). It is, therefore, hard to obtain precise estimates of the a4 parameter, whatever the instruments used. This problem is less severe for Iberdrola because the variability of production from shared plants is higher than Endesa’s due to the jointly owned coal plants that serve peak demands inducing higher variation. The choice of reasonable instruments for share production should then partially reflect the ownership composition of the jointly owned units. In cases where a firm does not control the joint output (and output decisions of the jointly owned units are approximately Cournot), any variable that drives the decisions of the firm that does control the output should be a reasonable instrument for the share variable. Some of our instruments for price, namely the regulated demands from rival firms should, therefore, help us identify the share coefficient in this case. For both Endesa and Iberdrola some of the jointly owned generating are controled by rivals and bid Cournot supply functions, therefore, we expect the disaggregated regulated demands to help identify the share coefficient. This constitutes an additional argument for the use of the disaggregated regulated demands instead of the total regulated demand as instruments in the estimating equation. On the other hand, when a firm does not control the joint output but the supply functions do not resemble Cournot strategies, problems arise with using the regulated demands of the rivals as instruments. Joint control (in form of decisions that are reached by bargaining, for example) would inevitably mean
35
that a term related with the downstream demand of the rival would show up in the error term. Usage of regulated demand of the rival would not be a valid instrument in this case. While this is not a problem for Endesa, it may be a problem for Iberdrola. Iberdrola shares two thermal plants with Union Fenosa at 50 percent ownership and these plants do not bid Cournot supply functions. If Iberdrola does not fully control the production from these thermal plants our estimating equation would be misspecified. However, as mention above, the production from these two thermal plants is such a small proportion of Iberdrola’s output that we do not think it will generate a significant bias. Nevertheless, this would imply that regulated demand from Union Fenosa would not be a valid instrument. Unfortunately, we have not found any instrument that would directly relate to the costs of the jointly owned units. The only other sensible instruments besides the disaggregated regulated demands available for the share variable appear to be lags of past production. Contrary to the case of hydro-electricity, there is no reason why an average should do better than straighforward lags. However, lags remain somewhat problematic due to autocorrelation that we should expect in shocks to the marginal cost term. We would expect endogeneity problems to be greater with a single day or two day lag of the variable than with a month average. It therefore seems to be much more difficult to find a good instrument. We have therefore tried a number of instruments including lagged shared production and lagged shared nuclear production. A further set of instruments comes from temperatures observed in different regions of Spain. These are potentially good instruments because they can be correlated with demand particularly the unregulated part of the downstream demand and, therefore, can help obtaining more precise estimates of the price and the share coefficient, a4 . The arguments above suggest that we should have a different instrumenting strategy for Endesa and Iberdrola. This leaves us with a large set of a priori plausible instruments. As the baseline for Endesa we have chosen all the disaggregate regulated demands (dis_EG, dis_IB, dis_UF and dis_HC) and the hourspecific average of hydro production over the month (EGhphour). For Iberdrola, we have chosen the
36
same except that we have left out the disaggregated regulated demand for Union Fenosa (dis_UF). As discussed above, the reason is due to the potential correlation between dis_UF and the error term for the case of Iberdrola due to the jointly owned thermal plants. Theoretically, our baseline should give us enough identification of the three endogeneous variables in the estimating equation. Indeed, for all these regressions the instruments where (conditionally) highly correlated with the endogenous variables that they were intended to instrument for (see table XXX). We tried to improve the baseline by adding as instruments other variables that satisfy our a priori criteria. First, 24 hour differences in temperatures (24-hour ∆temps) always have little impact on the point estimates of the parameters but reduce the standard deviation of the estimates. Hence, they are included in all reported regressions. One consequence of adding the temperature instruments is that the p-value of the Sargan test becomes very close to one. We believe that this is an artefact of 24-hour temperarture differences being a very large set of instruments. We do not take this test to be very informative. Second, for Iberdrola adding any of our a priori reasonable instruments for share production, namely 48-hour lags of shared production (sharIBLL) and 48-hour lags of shared nuclear production (SN_IBLL) left the coefficients on price, hydro production and Expected demand unchanged but greatly reduced the variance on the share coefficient and intercept terms (see table XXXX). Although, there is not a significant improvement in the p-value of the Sargan test, when temperatures are also included, the pvalue of the Sargan test does significantly increase when the temperature variables are excluded from the instrument set.32 For Endesa, all of the a priori plausible additional instruments for the share variable (e.g. sharEGLL and SN_EGLL) led to a dramatic fall in the p-value of the Sargan test and a negative point estimate for a4 . These two effects together strongly suggest that both of these instruments are correlated with the error term. In the case of Iberdrola we also attempted to add the Union-Fenosa (dis_UF) regulated demand as 32
Due to the uninformativeness of the p-values of the Sargan test when the 24-hour difference in temperatures are part of the instrument set, we consider, this comparison to be the relevant criterium.
37
an instrument. This had a dramatic impact on the p-value of the Sargan causing it to drop below 0.05 when temperatures were not part of the instrument set. This suggests that dis_UF is strongly correlated with the error term. As discussed this can arise because Iberdrola does not fully control generation units jointly owned with Union Fenosa. Alternatively, this correlation may be spurious because low demand periods in Union-Fenosa areas coincides with a partial shut down of a 100% owned nuclear plant of Iberdrola. We have also tried to replace the instruments EGhphour and IBhphour with the 48-hour lags and other moving averages of the hydroelectric production of Endesa and Iberdrola respectively.
5.2
Results
Tables 2 and 4 show the main estimation results of (17) for Endesa and Iberdrola, respectively. All regressions include month and hourly dummies (not shown in the tables). The estimation method used is two-step GMM with a weighting matrix given by the Newey-West procedure allowing for a maximum of 30 lags.33 In the appendix we present evidence of the autocorrelation in the estimating equations.34 In the appendix we also present the results of the first step GMM (or regular IV estimates) where standard deviations have been constructed according to the Newey-West procedure. For the case of Endesa in table 2 we show four different sets of IVs. They all use the disaggregated regulated demands (dis_EG, dis_IB, dis_UF, dis_HC) and except for IV1 the 24-hour differences in temperatures but they use different instruments for hydroelectricity: IV1 and IV2 use the hour-specific average over the calendar month of own hydroelectricity bid below equilibrium price in the daily market (EGhphour). IV3 uses an hour-specific average of own hydroelectricity bids below equilibrium price in the daily market over a thirty day period around the actual date (EGmovav3). IV4 is very similar 33 Robustness checks were made by increasing the number of lags to 50. Results did not change although standard deviations decreased slightly. 34 As we discuss in the appendix, the form of autocorrelation found in both Iberdrola and Endesa’s estimating equations is complex. The Newey-West procedure produces consistent estimates of the standard deviations under an unknown form of heteroskedasticity and autocorrelation.
38
but reduces the number of lags and forwards to 10 (EGmovav1). Finally, IV5 uses the 48-hour lag of hydroelectricity bid below the equilibrium price (EG_hpLL). For all IV sets, with or without temperature related instrumental variables, the p-value of the Sargan test was extremely high granting validity to our specifications.35 We should first check if the parameter estimates are consistent with all the alternative models proposed in Section 4.4. Namely, for any reasonable model nested in our estimating equation (??), the coefficient on price a1 should be positive as well as the coefficients on hydroelectricity production and shared production = (a2 and a4 ). Moreover, the estimate of the aggregate slope of the rivals’ supply function S−i
a1 a3
should
be non-negative and the two ways of identifying the slope coefficient of the marginal costs (c1i ) should result in similar estimates. The model should also do well in terms of matching the average of the rival’s production. As we can see from table 2, the OLS estimates for Endesa fail several of these consistency criteria. The estimated price coefficient (a1 ) is negative which is a clear sign of the endogeneity of price in this equation. The OLS estimate of the slope of the cumulative rivals’ supply function and the estimates of the slope of Endesa’s marginal cost, c1EN , are all negative because these are identified from the price coefficient. The OLS coefficient of the share production (a4 ) is also negative (although not statistically significantly different from zero) which is also inconsistent with any reasonable model. Lastly, the OLS prediction of the rival’s production (= 5112.5 MWh) is not within one standard deviation of the average rival’s production of Endesa. Given, the evidence of endogeneity and our discussion on reasonable IVs in Section 4.4 we should check if the IV estimates pass these basic checks on the parameter values. First, the estimates of the price coefficient, the share production coefficient, the slope of the rival’s supply function and the slope of Endesa’s marginal cost are now always positive for all sets of instrumental variables used. These 35
The Sargan-Hansen’s test is the following: −1 Z ζ ˜χ(s) ζZ (Z ΩZ)
is the Newey-West estimation of the variance-covariance matrix where s are the number of overidentfying restrictions and Ω of ζ.
39
parameters are, however, not always statistically different from zero due to the large standard deviations produced by the Newey-West procedure. Secondly, the estimates of the slope of the marginal cost are now not only positive but very similar for each IV set selected. Thirdly, the IV estimates match better the average production of the rivals, the estimated production is always within one standard deviation from the sample mean. The estimates in table 2 allow us to select which of the three models nested in the estimation equation (??) is rejected by the data. We can easily reject the competitive framework since a3 > 0 and a2 = 1 and both tests are significant at the 99% confidence level. We can also discard a model where there is market power in generation but where downstream profits are not taken into account by upstream generators since a3 > 0. In order for our theory to hold, we need a2 + a3 = 1, a2 = a4 , and a3 > 0. As we can see a3 = 1 and a3 > 0. Both of these tests are very from table 2, our IV estimations always produce a2 + powerful given the high precision of the estimates. With respect to the criteria a2 = a4 , our test has little power since a4 is very imprecisely estimated. We were able to increase the precision of all estimates and in particular get a more reasonable estimate of a4 with the introduction of the temperature related variables (24h ∆temps) as instruments (compare IV1 and IV2). Nonetheless, a4 remains quite imprecisely estimated. The reason is because all variables highly correlated with the shared production (e.g. 48-hour lag in nuclear production from shared plants) caused negative estimates of the share coefficient and significant changes in some of the other parameters. These two consequences were evidence of correlation between the instrument and the error term and, therefore, we have decided not to present these results. The imprecision of a4 makes it crucial to examine the first-stage estimation. We need to know where all instruments used are capable of identifying the share coefficient as well as the other endogeneous variables’ coefficients.36 The Wald test on whether the instruments are jointly zero in the first-stage regression of shared production does not rejects that null. However, when 24h ∆temps are not included as part of the instrumental variable set as in IV1 the p-value of the same test increases to 0.0072 clearly rejecting the null that the instrumental variables have no explanatory power. A comparison between the 36
The standard deviations of the first-stage regressions presented in table XXX (appendix) are computed using the NeweyWest procedure since the residuals are autocorrelated.
40
IV1 and IV2 show that indeed temperature related variables help identify the share coefficient as well as other coefficients. We think the high p-value of the Wald test for the first-stage of the shared production in IV2-IV5 is partly due to the high standard deviations produced by the Newey-West procedure. In addition, as explained in the appendix, we think that a2 = a4 should hold in the case of Endesa since the bids made by plants co-owned by Endesa are Cournot supply functions. Finally, we also checked that imposing a2 = a4 does not change the parameter estimates while it reduces their standard deviations specially in the case of the time dummies and constant term (see an example in table 3). In the bottom of table 2 we show the average value of the relevant estimated marginal costs over the sample period. According to the theory, since Endesa is on average a net-demander, the average marginal cost should be above the average price (35.2 Euros/MWh). The average of the estimated marginal cost support the theory (for all IVs) but its large standard deviation renders this test almost meaningless. We can also compute the percentage of times the theory holds when the firm is a net-demander and the percentage of times the theory holds when the firm is a net-supplier. These percentages are shown in the last two rows of table 2. It is important to notice that our identification of the marginal costs parameters implies that these percentages should be exactly 100 percent when the parameters of the model satisfy the equalities: a2 + a3 = 1 and a2 = a4.
37 Any
deviation from these equalities may cause a lower percentage
a3 is so close to 1 it seems that the deviation from 100 percent is in the last rows of table 2. Since a2 + probably mostly due to deviations from the equality a2 = a4 . Table 3 reproduces IV2 from table 2 in its first column and shows the estimation results when we impose each of the theoretical restrictions separately. Inmediately, one can see the effect of imposing the restrictions on the standard deviation of the price coefficient. Equally important (for our estimate of the average marginal cost) is the reduction in the standard deviation of the constant term coefficient. In its second column we see that once we impose the restriction a2 + a3 = 1, the estimated value of a4 is much 37
We are aware that the error term may contain some measurement error coming from the fact that we use realized bids data and realized average special regime energy instead of forecasts as was explained in the Data section. However, given the results obtained for the matching of the theory it seems that the term − ζatτ1 is a very good proxy for εctτ and that the magnitude of the potential measurement error is small.
41 a3 and this is reflected in an improvement in the percentages of observations in which closer to a2 = 1 − which the theory holds. When we impose a2 = a4 , the value of a2 + a3 improves only marginaly. In this case the percentage of times the theory holds when a net-supplier actually worsens but the theory now holds all the time for observations where Endesa is a net-demander which happens 81.5 percent of the times. When both restrictions are imposed, the theory has to hold all the time as shown in the last column of table 3. Notice as well that in the last column of table 3 the average of the estimated marginal cost is very precisely estimated and as predicted by theory significantly above the average price in the sample.38 Lastly, although the predicted average value of the rival’s production39 is closer to the sample average than OLS, we still underestimate the rival’s production level by roughly 1000 MW. The reason probably lies in the estimate of the intercept S0−i of the rival’s aggregate supply function. S0−i is the sample average of the amount bidded in by the rivals at zero price. Something that we need to check is if Endesa rivals bid any amount at prices very close to zero that can account for this differential. For the case of Iberdrola in table 4 we show also four different sets of IVs. They all use the disaggregated regulated demands of Endesa, Iberdrola and Hidro-Cantabrico (dis_EG, dis_IB, dis_HC) as instrumental variables. As explained in Section 4.4 we leave the regulated demand from Unión Fenosa out of the IV set because of evidence of correlation with the residuals. All IV sets in table 4 include as well an instrument related to hydroelectricity produced. IV1, IV2 and IV3 use the hour-specific average over the calendar month of own hydroelectricity bid below equilibrium price in the daily market (IBhphour) while IV4 uses 20 day hour specific average of future hydroelectricity bid below market price (IBmovav4). All except IV1 also include 48-hour lag nuclear production from shared plants weighted by ownership as an additional IV (SN_IBLL).40 Finally IV1, IV2 and IV4 include 24-hour differences in temperatures in some regions of Spain. The p-value of the Sargan test is always high including for IV2 where 24-hour 38 It is possible that the estimates of the marginal cost presented in table 2 are biased upwards since they conform much better with the predicted behavior when a net-demander than they do when a net-supplier. 39 In the computations of the rivals’ production we do not account for the production coming from plants where Endesa has a share. 40 48-hour lag of total production from shared plants weighted by ownership gives very similar results.
42
Table 2: Results of the total production regression for Endesa, using month and hour dummies, 2-step GMM E n d esa (V ie sg o ou t) — E lectricity U n its= M W h E n d og en eou s var= π, hEN , an d shared_ firms
π ( a1 ) hEN ( a2 ) Sh are d_ p la nts ( a4 ) E DEN ( a3 ) co n stant ( a0 ) a2 + a3 p-value o f H 0 : a2 + a3 = 1 p -va lu e of H 0: a2 = a4 p-value o f H 0 : a3 + a4 = 1 a = 1 (s.d.) S −EN a 3 S −EN × π
no bs AR2 Sa rga n test p -value p -va lu e W ald test π p -valu e W ald te st hEN p -value W a ld test Sh are d_ p la nts c 1EN = 1/ a1 − 1/S −EN
c 1EN = a 2 / a1 N on -E n d esa averag e pro d u ct. N on -E n d esa S −0 + S ×π −EN
C avera ge M C + % M εctτ > π if n et-d em an der C + % M εctτ < π if n et-su p plier
OLS
estim ate N W s.d . −18.40 3.17 0.513 0.039 −0.056 0.223 0.754 0.036 1846 609 1.267 2.80E − 18 0.011 0.17 −24.41
3.42
−874.10 5640 0.921
−0.013 0.004 −0.028 0.006 8041.2 1970.7 5112.5 −37.75 0 99.81
32.29
IV 1 (16 6) - IV s u sed E G h pm ea n, dis_ E G ,dis_ IB , d is_ U F ,dis_ H C estim ate N W s.d . 14.75 11.44 0.523 0.059 1.093 1.114 0.490 0.103 273.6 2665.1 1.014 0.877 0.600 0.583 30.08
IV 2 (120 )- IV s u sed : E G h pm ea n, dis_ E G ,d is_ IB ,d is_ U F , d is_ H C , 2 4h ∆tem p s estim ate N W s.d . 12.35 9.60 0.514 0.052 0.421 0.790 0.519 0.085 1870.5 1908.4 1.033 0.662 0.903 0.936
29.31
1077.42 5640 0.891 0.923 8.85E − 07 1.77E − 100 0.0072 0.035 0.020 0.036 0.027 8041.2 1970.7 7064.0 157.0
187.2 100 0
23.82
22.14
853.0 5610 0.900 0.999998 0.00016 5.11E − 109 0.330 0.039 0.024 0.042 0.032 8041.2 1970.7 6839.57 46.99
156.85 80.04 100
IV 3 (20 0)- IV s u sed : E G m ovav 3 d is_ E G ,d is_ IB ,d is_ U F , d is_ H C , 2 4h ∆te m p s estim ate N W s.d . 18.30 10.27 0.569 0.061 0.747 0.792 0.463 0.083 1458.0 1981.5 1.031 0.706 0.817 0.786 39.56
28.72
1416.88 4920 0.898 0.899 6.21E − 05 9.88E − 131 0.405 0.029 0.013 0.031 0.018 8041.2 1970.7 7403.45 80.11
115.36 100 0.76
IV 4 (19 8)- IV s u E G m ovav 1 d is_ E G ,d is_ IB ,d is d is_ H C , 24 h ∆t e estim ate NW 13.53 9.8 0.588 0.0 0.538 0.8 0.492 0.0 1808.9 201 1.080 0.295 0.950 0.970 27.51
24.
985.28 5160 0.903 0.966 1.29E − 05 7.27E − 102 0.500 0.038 0.0 0.043 0.0 8041.2 197 6971.85 66.56
153 100 43.34
differences in temperatures are not used as IVs granting confidence in all specifications presented in table 4. OLS estimates for Iberdrola are not as bad as the ones for Endesa. All coefficient estimates are positive including the price coefficient, the slope of the rivals’ aggregate supply function, and the estimates of the marginal cost slope. The two estimates of the slope of the marginal cost are also not statistically different from each other. The IV estimates also conform with these basic checks on the parameter estimates. Moreover, the two ways of identifying the slope of the marginal cost parameter render virtually the same value for all IV sets. The only caveat of the IV estimates seems to be the weak match of the rival’s average production of all IV sets with the exception of IV4. Similarly to the case of Endesa, the IV estimates can easily reject the competitive framework since a2 = 1 with 99% confidence level. Because a3 > 0 we know that generators take into account a3 > 0 and a3 = 1 and a2 = a4 cannot be rejected the downstream demand in their strategies. Finally, the null a2 + which together with a3 > 0 implies we cannot reject our model where what matters for the exercise
43
Table 3: Results of the IV4 regression for Endesa with restrictons on the parameters, 2-step GMM E n d esa
N o restriction s IV 2 (120 )
a2 + a3 = 1 IV 2 (12 0)
estim ate N W s.d . 12.35 9.60 0.514 0.052 0.421 0.790 0.519 0.085 1870.5 1908.4 1.033
a3 + a4
0.939
0.973
−
−
p -va lu e of H 0: a2 + a3 = 1 p-valu e of H 0: a2 = a4 p -va lu e of H 0: a3 + a4 = 1 c 1EN = 1/ a1 − 1/S −EN c 1EN = a 2 / a1 Sa rgan p -va lu e N o n-E nd esa avera ge h ou rly p ro du ction N o n-E n de sa S −0 + S −EN × π α i C a t SEN − hEN − shared_ firms M C + % M εctτ > π if n et d em a nd er C + % M εctτ < π if n et sup p lier
0.662 0.903 0.936
− − 0.972
0.678 − −
− − −
0.039 0.024 0.042 0.032 0.999998 8041.2 1970.7 6839.57 0.539 0.058
0.031 0.005 − − 0.9999993 8041.2 1970.7 7171.4 0.549 0.066
0.038 0.022 0.041 0.029 0.9999995 8041.2 1970.7 6875.5 0.539 0.057
0.031 0.005 − − 0.9999998 8041.2 1970.7 7174.78 0.549 0.067
156.85 80.04 100
−
N W s.d . 3.85 − 0.792 0.053 1952.9
46.69
122.40 88.34 100
e stim a te N W s.d. 12.74 9.26 0.517 0.048 − − 0.513 0.075 1647.0 413.7 1.030
a2 + a3 = 1, a2 = a4 IV 2 (1 20 )
π ( a1 ) hEN ( a2 ) Sh are d_ fi rm s ( a4 ) E DEN ( a3 ) co nsta nt ( a0 ) a2 + a3
46.99
estim ate 16.20 − 0.483 0.499 1870.6
a2 = a4 IV 2 (12 0)
64.92
44.03 100 53.73
e stim a te 16.22 − − 0.489 1801.0
−
51.05
N W s.d . 3.79 − − 0.047 177.78
5.09 100 100
of market power is firms’ net-demand positions. Notice that although in IV1 we do not include any instrument specifically related to the shared production, the precision of a4 is higher than for Endesa. This is likely due to the higher variance of Iberdrola shared production relative to Endesa’s. When we further include SN_IBLL in the IV set, the precision of a4 increases although the parameter’s point estimate is now farther away from a2 . This increase in precision reflects the high correlation between SN_IBLL and the shared production as is reflected in the decrease of the p-value of the Wald test in the first-stage regression. Iberdrola is slightly more often a net-supplier (54.5% of the times) than a net-demander. The theory predicts that the average marginal cost should be slighly below the average price (35.2 Euros/MWh). The estimates at the bottom of table 4 support the theory (for all IVs) but, although not as large as in the case of Endesa, the standard deviation is still large. If we perform the test for each observation conditional on the net-demand/net-supply position, we do poorly. For all IV sets the theory only holds when Iberdrola a3 is so is a net-supplier but fails to predict the actual behavior when it is a net-demander. Since a2 + close to 1 we think the deviations from the theoretical prediction have to do with the difference between a2 and a4 . Indeed in table 5 we show, for the case of IV1, that once we impose the restriction a2 = a4 the theory predicts the actual behavior 100 percent of the times when Iberdrola is a net-supplier and
44
Table 4: Results of the total production regression for Iberdrola, using month and hour dummies, 2-step GMM Ib e rd rola E lectricity U n its= M W h E n do gen eo us va r= π, hIB , an d shared_ firms
π ( a1 ) hIB ( a2 ) S ha red _ fi rm s ( a4 ) E DIB ( a3 ) co n stant ( a0 ) a2 + a3 p-value o f H 0 : a2 + a3 = 1 p -va lu e of H 0: a2 = a4 p-value o f H 0 : a3 + a4 = 1 a = 1 (s.d .) S −IB a 3 S −IB × π
no bs AR2 Sa rga n test p -value p -va lu e W ald π p -va lu e W ald hIB p -va lu e W ald S ha red _ fi rm s c 1IB = 1/ a1 − 1/S −IB
c 1IB = a 2 / a1 N o n-Ib erdro la averag e pro d u ctio n N on -Ib erd rola S −0 + S −IB × π C A verag e M C + % M εctτ > π if n et d em an der C + % M εctτ < π if n et su p plier
OLS
estim ate N W s.d . 16.38 2.44 0.771 0.039 0.907 0.155 0.302 0.031 132.2 326.1 1.073 0.035 0.348 0.162 54.16
11.11
1939.8 5640 0.934 − − − − 0.043 0.006 0.047 0.008 11082.2 1943.5 9910.0 76.92
26.12 100 0
IV 1 (2 18 )- IV s u sed : IB hp h ou r dis_ E G , dis_ IB d is_ H C ,24 h ∆tem ps estim ate N W s.d . 28.32 4.72 0.793 0.040 0.683 0.414 0.206 0.046 753.2 795.9 0.999 0.982 0.790 0.780 137.38
46.98
4920.22 5610 0.930 0.9999 2.08E − 44 1.45E − 129 0.343 0.028 0.004 0.028 0.006 11082.2 1943.5 12890.40 26.38
29.00 2.38 100
IV 2 (1 01 )- IV s used : IB h p ho u r dis_ E G , dis_ IB d is_ H C , SN _ IB L L e stim a te N W s.d. 27.85 5.16 0.790 0.043 0.554 0.208 0.218 0.045 980.7 422.0 1.008 0.888 0.236 0.262 127.95
45.32
4582.46 5592 0.930 0.730 2.91E − 44 1.77E − 135 1.77E − 18 0.028 0.004 0.028 0.006 11082.2 1943.5 12552.6 17.61
15.14 0 100
IV 3 (1 70 ) - IV s used: IB h ph o ur,24 h ∆tem ps d is_ E G , d is_ IB d is_ H C ,S N _ IB L L estim ate N W s.d . 28.61 4.72 0.791 0.040 0.597 0.173 0.210 0.043 904.2 349.1 1.001 0.985 0.244 0.247 136.29
45.11
4881.35 5586 0.929 0.9999 4.57E − 44 1.76E − 137 3.30E − 24 0.028 0.004 0.028 0.005 11082.2 1943.5 12851.5 20.51
12.21
IV 4 (2 72 )- IV s used : IB m ovav 4 ,2 4h ∆tem p s dis_ E G , dis_ IB d is_ H C , SN _ IB L L e stim a te N w s.d 21.19 5.26 0.756 0.039 0.516 0.164 0.262 0.047 1049.8 326.8 1.018 0.743 0.120 0.152 81.01
32.23
2901.45 5112 0.930 0.998 1.38E − 40 4.61E − 104 3.09E − 26 0.035 0.007 0.036 0.010 11082.2 1943.5 10871.63 12.71
0 100
15.25 0.04 100
85.9 percent of the times when net-demander. The restriction a2 = a4 seems to hold since the other parameters estimates hardly changed. Notice also the decrease in the standard deviation of the average estimated marginal cost as well as the increase in its value to 34.01 Euros/MWh just below the average price as the theory would predict. In the last column of table 5, once a2 + a3 = 1 is also imposed, we obtain even larger precision of the estimated marginal cost with no significant change in its value.
5.3
Efficiency Gains
In this subsection we use the estimated marginal costs to compute the efficiency gains that would accrue from a reallocation between Endesa and Iberdrola of the non-hydro total production from their 100% owned plants. Given that marginal costs are not the same in equilibrium, the net-supplier is producing too little and the net-demander is over producing, there would be gains from reallocating the production in order to equalize marginal costs. Tables 6 and ?? show the average hourly and total over the sample period of the efficiency gains in Euros from reallocating the non-hydroelectricity of the 100% plants between Endesa and Iberdrola. The estimates depend on which IV sets were used to compute the
45
Table 5: Results of the IV4 regression for Iberdrola with restrictons on the parameters, 2-step GMM Ib erd ro la
N o restriction s
a2 + a3 = 1
a2 = a4
a2 + a3 = 1, a2 = a4
IV 1 (2 18 )
IV 1 (2 18 )
IV 1 (218 )
IV 1 (2 18)
π ( a1 ) hIB ( a2 ) Sh are d_ fi rm s ( a4 ) E DIB ( a3 ) co nsta nt ( a0 ) a2 + a3
estim ate N W s.d . 28.32 4.720 0.793 0.040 0.683 0.414 0.206 0.046 753.20 795.93 0.999
estim ate 28.23 − 0.681 0.207 756.42
a3 + a4
0.889
0.888
−
−
p -va lu e of H 0: a2 + a3 = 1 p-valu e of H 0: a2 = a4 p -va lu e of H 0: a3 + a4 = 1 c 1IB = 1/ a1 − 1/S −IB c 1IB = a2 / a1 Sa rgan p -va lu e N on -Ib erd rola ave rage h ou rly p ro d uc tio n N on -Ib erd rola S −0 + S −IB × π α i C a t SIB − hIB − shared_ firms M C + % M εctτ > π if n et d em a nd er C + % M εctτ < π if n et sup p lier
0.982 0.790 0.780
− − 0.773
0.907 − −
− − −
0.028 0.004 0.028 0.006 0.9999 11082.2 1943.5 12890.40 −1.159 2.156 26.38 29.00 2.38 100
0.028 0.003 − − 0.99995 11082.2 1943.5 12857.89 −0.555 0.710 26.28 28.73 2.34 100
0.028 0.0039 0.028 0.0055 0.99996 11082.2 1943.5 13003.59 −1.136 1.903 34.01 6.04 85.85 100
−
N W s.d . 2.38 − 0.400 0.033 782.63
estim ate N W s.d . 28.30 4.69 0.793 0.040 − − 0.201 0.041 543.30 135.83 0.9940
estim ate 27.78 − − 0.204 530.60
−
N W s.d . 1.72 − − 0.031 76.52
0.029 −
0.002 − 0.99998 11082.2 1943.5 12837.14 −0.546 0.678 34.72 0.628 100 100
Table 6: Average hourly efficiency gains (Euros) from redistribution of production between IB and EG Ib erd ro la −→ E n d esa↓ IV 1 IV 2 IV 3 IV 4 IV 5
IV 1 (21 8) estim ate s.d. 6708 4172 6343 2823 3740 1353 3387 1637 9520 664473
IV 2 (10 1) e stim a te s.d . 6720 4139 6353 2791 3745 1329 3392 1614 9537 664465
IV 3 (1 70 ) estim a te s.d . 6703 4183 6336 2832 3727 1358 3373 1642 9522 664481
IV 4 (272 ) estim ate s.d. 6932 4055 6577 2748 4041 1334 3695 1608 9663 664372
marginal cost parameters. Depending on the combination of IV sets, the range for the the average hourly efficiency gain is between 3372.6 and 9663 Euros corresponding to a total over the sample from 1, 9021, 662 to 5, 4499, 046 Euros. These numbers are quite large and reflect a lower bound on the impact of market power. To estimate the real efficiency gains one would have to estimate the shadow costs for hydroelectricity and the costs of the shared plants. Standard errors were computed under the assumption that the error terms from Iberdrola and Endesa estimating equations are independent, in other words, assuming that the coefficient estimates of both equations are not related.41 We also construct a benchmark case where Endesa and Iberdrola produce a competitive amount of 41
Standard errors were computed by taking 10000 draws from the asymtpotic distribution of the parameter estimates of both Endesa and Iberdrola when a2 = a4 and a2 + a3 = 1 are imposed. The highest standard deviations occurred for Endesa IV1 (166) and Endesa IV5(157). For the case of Endesa IV1 there were parameter draws that led to optimal negative quantities. We decided to leave these draws out of the computation of the standard deviations. For Endesa IV5 (157) there were parameter drwas that led to negative c1EN . We decided to leave all these draws out ot the computation of the standard deviations. For all the other IVs we faced no such problems.
46
non-hydroelectrical energy coming from their 100% ownership plants. We assume, for simplicity, that the hydroelectrical bid functions from Endesa and Iberdrola remain constant as well as the bid functions of all other firms including the plants co-owned by Endesa and Iberdrola. We take the estimated marginal costs from the IV2 column for Endesa and IV3 column for Iberdrola when restrictions are imposed. The ratio between the price obtained in this benchmark and the sample price is on average 0.996. As table 7 shows the average prices over the sample period are very similar although the standard deviation is higher in the benchmark case. Indeed, the price ranges from [5.8, 121.1] in the benchmark case while it varies only between [14.5, 113.3] in the sample. The theory tells us that the benchmark should bring about an increase in production in periods where firms were net-suppliers in the sample and a reduction in production in periods when firms were netdemanders. Unfortunately, we cannot test the theory on the firms’ total production since our benchmark takes as given the bids from hydroelectric plants and jointly owned plants bids as given. Therefore, we will limit our analysis to the production of the non-hydro 100% owned plants. Table 8 shows the percentage of time the production from non-hydroelectric 100% owned plants increased or decreased in the benchmark case relative to the sample in periods where the firms are net-demanders and net-suppliers in the sample. As we can see, Endesa decreased production in 98% of the hours where it was a net-demander while Iberdrola decreased production only in 78% of these periods. On the other hand, Endesa increased production in 85% of the hours where it was a net-supplier and Iberdrola increased production in 83% of these periods. Overall, in the benchmark case, Iberdrola increases (slightly) the average production from its 100% non-hydro plants relative to the sample while Endesa decreases its production. Moreover, the impact of Endesa’s strategy in the market price is large. 96 percent of the times where the benchmark’s price is higher than the sample price corresponded to situations where Endesa is a net-demander in the sample. The decrease in its production in the benchmark case leads to higher benchmark prices relative to the sample.
47
Table 7: Statistics relating the benchmark case with the sample p ric e w eighted price Ib erdro la q uo ta E n d esa q u ota Tota l Su p ply IB su pp ly fro m 1 00 % n on -hy dro IB tota l su pp ly E G sup ply from 10 0% no n -hy d ro E G to tal sup p ly
B en ch m ark ave rage s.d . 35.96 14.24 37.68 − 12.31 2.85 25.77 4.09 20144 2971.2 2494 778 5540 967 5151 857 8541 1038
S a m p le avera ge s.d . 35.82 12.90 37.44 − 11.87 2.18 27.65 2.93 20326 3056.9 2414 592 5937 1262 5604 893 9219 1200
Table 8: Statistics relating the benchmark case with the sample N et d em an d p ositio n in th e sam p le net-d em an d n et-su p ply
6
P ro d uc tion from 10 0% ow n ed in B ench m ark rela tive to th e sam p le E n d esa Ib erd rola In crea se d ecrea se Inc rease D ecre ase 1.28 98.72 21.03 78.97 85.06 14.94 83.50 16.50
Conclusion
Indeed, the analysis immediately implies that the entry of unintegrated supply firms in the Spanish electricity market should lead to an increase in the electricity spot market price, since generating firms will overall shift towards being more net suppliers as they loose supply market share to the entrants. Perhaps surprisingly, this does not mean that the price increase induces inefficiencies. Indeed, when the spot market demand is extremely inelastic, as is still the case in electricity markets in the absence of real time pricing, the presence of net demanders will dominate leading to pricing below the competitive price. However, as demonstrated in California, the price may rise sufficiently that it is infeasible for unintegrated companies to profitably enter electricity supply markets. If the market power story that theory suggests were valid, it may in fact not be a good idea to enforce vertical disintegration in liberalized electricity generation markets.
References [1] Arocena, Pablo, Kühn, Kai-Uwe and Regibeau, Pierre (1999): Regulatory reform in the Spanish electricity industry: a missed opportunity for competition, Energy Policy, Vol. 27 (7), 387-399. [2] Borenstein, Severin and James Bushnell (1998): An Empirical Analysis of the Potential for Market
48
Power in California’s Electricity Industry, NBER Working Paper Series 6463. [3] Frankena, Mark W. (1997): Market Power in the Spanish Electric Power Industry, CSEN, Madrid Spain. [4] Green, Richard J. (1996):“Increasing Competition in the British Electricity Spot Market,” The Journal of Industrial Economics vol 44, No. 2, June 1996, pp 205-216. [5] Green, Richard J. and Newbery, David M. (1992): competition in the British Electricity Spot Market in Journal of Political Economy, 1992, vol 100 no 5. [6] Klemperer, Paul D. and Meyer, Margaret A. (1989): “Supply Function Equilibria in Oligopoly under Uncertainty,” Econometrica, vol 57, No. 6 pp 1243-1277. [7] Kühn, Kai-Uwe, and Pierre Regibeau (1998): “¿Ha llegado la Competencia? Un Análisis Económico de la Reforma del Sector Eléctrico en España,” Informes de IAE (CSIC). [8] Hendricks, Kenneth and Porter, Robert H (1989): Collusion in Auctions in Annales d’Economie et de Statistique No 15/16. [9] Wolak, Frank A. (2000): An Empirical Analysis of the Impact of Hedge Contracts on Bidding Behavior in a Competitive Electricity Market. Mimeo. [10] Wolfram, Catherine D. (1998): “ Strategic bidding in a multiunit auction: an empirical analysis of bids to supply electricity in england and Wales,” RAND Journal of Economics, Vol. 29 No. 4, Winter 1998, pp 703-725. [11] Wolfram, Catherine D. (1999): Measuring Duopoly Power in the British Electricity Spot Market, American Economic Review, September 1999. [12] Green, Richard and Newbery, David M. (1997): Competition in the Electricity Industry in England and Wales, Oxford Review of Economic Policy, vol. 13, No 1.
49
7
Appendix
7.1
Co-ownership
As mentioned in Section 3 co-ownership of generation plant is an important aspect of the Spanish electricity industry. Here we show how to adapt the estimation framework developed in section 4 to account for co-ownership. The identification of the structural parameters of the model is unaffected by the presence of co-ownership of generation plants. To keep notation to a minimum our analysis here focuses on a model without hydroelectric production. We also assume that there is only unregulated retailing and no special regime and that there is only one plant in which firm i has joint ownership. To simplify exposition we also assume that all retail contracts specify retail price p¯. The extension to the full model we estimate is straightforward. Denote by Si the production of plants owned entirely by firm i and C(Si ) the cost function of production from plants completely owned. Let l be a jointly owned plant with an ownership share of firm i given by αl . Production by plant l is denoted Sl and the cost of the plant is Cl (Sl ). For any given supply functions chosen for plant l, Sl (π, Iil ) and all other plants not co-owned by i, Sj (π, Itj ), the maximization problem for firm i can be written as:
Max E {E {(p − π)Ditτ (¯ p) + π(ηi − Sj (π, Ijt ) − Sl (π, Ilt )) − C(ηi − Sj (π, I−it ) − Sl (π, Ilt ))(20)
π(ηitτ ,Iit )
+αl [πSl (π, Ilt ) − Cl (Sl (π, Ilt ))] | ηitτ , Iit } | Iit } The first order condition is: p) | Iit }] + Si (π, Iit ) + αl E{Sl (π, Ilt ) | Iit } − (π − C (Si (π, Iit ))Sj −E{Ditτ (¯
(21)
+Sl −π(1 − αl ) + C (Si (π tτ , Iit )) − αl Cl (Sl (π, Ilt )) = 0 Note, that the second line in the first order condition (21) is zero in two cases. First, if firm i has control over the jointly owned plant it will cost minimize across the production of all plant. Then the term in
50
brackets is zero because margins must be equalized across plants for a firm that has control, i.e. π − C (Si (π tτ , Iit )) = αl [π − Cl (Sl (π, Ilt ))]. Second, the term is also zero if firm i does not have control but the strategy of plant l is a completely inelastic supply function (a Cournot strategy). This is true for all nuclear plants, which make up the bulk of the co-owned generation plants. Furthermore, we have verified in the data that this is also approximately true for all non-nuclear plants that are partially owned by Endesa. The condition fails for two traditional coal based thermal plants for Iberdrola. Iberdrola owns these at 50%. We will assume for the purposes of the estimation that Iberdrola controls the decisions of these plants so that the last term in (21) is zero for all firms in our sample. We will discuss below how we can test whether this assumption causes any problems in the estimation. Given that co-owned plants either are controled or are bid in with Cournot strategies the first order condition on price reduces to: −E{Ditτ (¯ p) | Iit } + Sˆi (π, Iit ) − (π − C (Sˆi (π, Iit ) − αl E{Sl (π, Ilt ) | Iit })Sj = 0 where Sˆi = Si + αl Sl , and an estimating equation: Sˆi (π, I−it ) =
1 −Sj c0i + Sj π + E{Ditτ (¯ p) | Iit } + Sj c1i αl E{Sl (π, Ilt ) | Iit } − εitτ } 1 + Sj c1i
(22)
This is an estimating equation where there is ownership weighted expected output on the left hand side. Expected output from jointly owned plants enters on the right hand side in exactly the same way hydro does in the estimating equation developed in the paper. Note that all parameters relevant to our analysis can still be identified. To estimate we will assume that E{Sl (π, Ilt ) | Iit } = Sl (π, Ilt ). This, in essence assumes that a co-owner of a plant will be assumed to know the supply function plant l bids at the time it makes its decision. Even if this is not true, the estimation error would not introduce a bias in the estimates we obtain.
51
Another issue that arises is that the output chosen by co-owned plants is endogenous and correlated with the error in the estimating equation. This is the same issue as with hydroelectricity, so that we would have to use instrumental variables for these outputs. Note, however, that the largest proportion of these outputs can be taken as being exogenous since nuclear plants are always bid in up to capacity. The more serious issues we have to address are: what happens when Cournot strategies for some of the co-owned plants are not as good an approximation to the true supply function as we think; and what happens if the assumption of that Iberdrola controls the 50% co-owned plants is invalid. Then the second term in (21) would appear in the error term of the estimating equation. To the extent that price appears in the error term this is not especially problematic because we are instrumenting for price in any case. However, the marginal cost difference may be correlated with the downstream demand position given that marginal cost difference will be determined by net demand positions of different plants. However, we can test for this problem easily. If our assumptions are wrong, the coefficient on αl Sl will exceed Sj ci1 . This would show up in that the coefficients on αl Sl and on downstream demand would not add up to 1. Hence, we can test in the data, whether our assumptions are violated or not.
7.2
First-Stage Estimates
Tables 9 and 10 show the first-stage estimates corresponding to the 2-step GMM estimates of section 5.
Table 9: Results of the first-stage estimation of IV2, using month and hour dummies E n d e sa (V iesgo o u t) — D ep . va ria ble= π
d is_ E G dis_ IB d is_ U F d is_ H C E G hp m ean 24 -h ou r ∆ tm p s ED_EN m o nth d u m m ies ho u r d u m m ies R2 AR2 ob s Wald te st p-valu e W a ld test
F irst-S tag e R egre ssion IV 2 (1 20 ) D ep . va ria ble= hEN D ep . va ria ble= Share
estim ate N W s.d 0.0011 0.00069 0.0032 0.00075 0.0027 0.00097 0.0019 0.00805 −0.0025 0.00077 yes 0.0049
0.0004
yes yes 0.823 0.822 5610 54.03 0.0002
estim ate 0.0791 −0.0221 0.0162 −0.3501 0.7318
N W s.d 0.0244 0.0270 0.0403 0.3252 0.0402
e stim a te 0.0236 −0.0248 0.0216 −0.4517 −0.0188
0.018
0.0304
yes 0.198
N W s.d 0.0130 0.0158 0.0195 0.1641 0.0107 yes
yes yes 0.877 0.875 5610 582.03 5.11E − 109
0.0076 yes yes 0.534 0.530 5610 24.33 0.330
52
Table 10: Results of the first-stage estimation of IV2, using month and hour dummies Ib e rd rola —
d is_ E G d is_ IB d is_ H C IB hp h ou r S N _ IB L L 24 -ho ur ∆ tm p s E D _ IB m onth d u m m ies h ou r d u m m ies R2 AR2 ob s W a ld te st p-valu e W ald test
7.3
D ep . va riab le π estim ate N W s.d 0.0022 0.0007 0.0062 0.0007 0.01597 0.0082 −0.0028 0.0007 − yes 0.0036
0.0004 yes yes 0.815 0.814 5610 266.37 2.08E − 44
F irst-S tag e R e gressio n IV (21 8) D ep . variab le D ep . va ria b le hIB Shared prod. estim a te N W s.d e stim a te N W s.d −0.0988 0.0659 0.0454 0.0194 0.2610 0.0484 −5.84E − 05 0.0193 0.6883 0.9093 −0.8935 0.2479 0.6315 0.0493 0.0133 0.0141 − − yes yes 0.3825
0.0314 yes yes 0.778 0.776 5610 676.14 1.45E − 129
0.0483
0.0124
yes yes 0.436 0.431 5610 23.02 0.343
F irst-S ta ge R eg ression IV (1 70 ) D e p. variab le D ep. variab le D ep . va ria b le π hIB Shared prod. estim a te N W s.d estim ate N W s.d e stim a te N W s.d 0.0062 0.0007 0.2638 0.0464 0.0004 0.0146 0.00210 0.0007 −0.0505 0.0622 0.0140 0.0149 0.01624 0.0084 0.0799 0.8021 −0.5432 0.1789 −0.00276 0.0007 0.6258 0.0468 0.0174 0.0120 0.0013 0.0023 −1.1040 0.2497 0.6945 0.0920 yes yes yes 0.0036
0.0004 yes yes 0.815 0.813 5586 267.45 4.57E − 44
0.3860
0.0289 yes yes 0.798 0.796 5586 717.27 1.76E − 137
0.0464
0.0110 yes yes 0.670 0.667 5586 166.63 3.30E − 24
1-step GMM estimates
Tables 11 and 12 shows the regular IV estimates or 1-step GMM where standard deviations were computed using the Newey-West procedure with maximum of 30 lags for Endesa and Iberdrola, respectively.
Table 11: IV results of the total production regression for Endesa, using month and hour dummies E n d esa (V iesgo o u t) — E lectricity U n its= M W h E nd og en eou s var= π, hEN , an d shared_ firms π ( a1 ) hEN ( a2 ) S ha red _ p la nts ( a4 ) E DEN ( a3 ) c on stant ( a0 ) a2 + a3 p-valu e of H 0: a2 + a3 = 1 p -value o f H 0 : a2 = a4 p-valu e of H 0: a3 + a4 = 1 a S = 1 (s.d.) −EN a 3 S −EN × π
n ob s AR2 S arg an te st p-value p -va lu e W ald te st π p-value W a ld test hEN p-value W a ld test S ha red _ p la nts c 1EN = 1/ a1 − 1/S −EN
c 1EN = a2 / a1 N on -E n d esa averag e pro d u ct. N on -E nd esa S −0 + S−EN ×π C avera ge M C + % M εctτ > π if n et-d em an d er C + % M εctτ < π if net-su p plie r
IV 1 (1 66) - IV s u se d E G h pm ea n , dis_ E G ,d is_ IB , dis_ U F ,d is_ H C e stim a te N W s.d . 14.53 11.45 0.527 0.060 1.024 1.131 0.490 0.103 460.2 2718.0 1.017 0.849 0.653 0.634 29.68
29.29
1062.82 5640 0.892 0.893 8.85E − 07 1.77E − 100 0.0072 0.035 0.021 0.036 0.028 8041.2 1970.7 7000.3 146.56
190.71 100 0
IV 2 (12 0)- IV s u sed : E G h pm ea n, d is_ E G ,d is_ IB ,d is_ U F , d is_ H C , 2 4h ∆te m p s estim ate N W s.d . 11.44 10.40 0.522 0.058 0.433 0.877 0.524 0.093 1790.6 2110.8 1.046 0.572 0.917 0.959 21.82
23.46
781.56 5610 0.901 0.999989 0.0002 5.11E − 109 0.330 0.042 0.030 0.046 0.041 8041.2 1970.7 6768.13 53.52
186.88 90.22 99.32
IV 3 (20 0)- IV s u se d: E G m ovav 3 d is_ E G ,d is_ IB ,d is_ U F , d is_ H C , 24h ∆tem ps estim ate N W s.d . 19.12 10.99 0.577 0.069 0.915 0.874 0.453 0.092 970.0 2161.1 1.030 0.736 0.691 0.664 42.24
32.14
1512.77 4920 0.895 0.771 6.21E − 05 9.88E − 131 0.405 0.029 0.012 0.030 0.018 8041.2 1970.7 7499.34 99.17
122.48 100 0
IV 4 (1 98)- IV s used: E G m ovav 1 d is_ E G ,dis_ IB ,dis_ U F , d is_ H C , 24 h ∆tem p s e stim a te N W s.d. 14.74 10.57 0.589 0.071 0.714 0.910 0.478 0.095 1401.6 2214.0 1.067 0.420 0.887 0.826 30.83
27.83
1104.19 5160 0.901 0.918 1.29E − 05 7.27E − 102 0.4997 0.035 0.020 0.040 0.028 8041.2 1970.7 7090.76 91.54
156.47 100 1.16
53
Table 12: IV results of the total production regression for Iberdrola, using month and hour dummies Ib e rd rola E lectricity U n its= M W h E nd og en ou s var= π, hIB , an d shared_ firms π ( a1 ) hIB ( a2 ) S h ared _ fi rm s ( a4 ) E DIB ( a3 ) c on stant ( a0 ) a2 + a3 p-value o f H 0 : a2 + a3 = 1 p -va lu e of H 0: a2 = a4 p-value o f H 0 : a3 + a4 = 1 a = 1 (s.d .) S −IB a 3 S −IB × π
no bs AR2 S arga n test p -value p -va lu e W ald π p -va lu e W ald hIB p -va lu e W ald S ha red _ fi rm s c 1IB = 1/ a1 − 1/S −IB c 1IB = a 2 / a1 N o n -Ib erdro la averag e pro du ction N on -Ib erd rola S −0 + S −IB × π C A vera ge M C + % M εctτ > π if n et d em an de r C + % M εctτ < π if n et su p plie r
8
IV 1 (2 18 )- IV s u sed : IB hp h ou r dis_ E G , dis_ IB d is_ H C ,24 h ∆tem ps estim ate N W s.d . 28.32 5.13 0.795 0.048 0.669 0.469 0.204 0.051 792.4 894.0 0.999 0.988 0.785 0.778 138.60
51.42
4963.9 5610 0.930 0.9997 2.08E − 44 1.45E − 129 0.343 0.028 0.004 0.028 0.006 11082.2 1943.5 12934.1 25.08
32.71 1.17 100
IV 2 (1 01 )- IV s used : IB h p ho u r dis_ E G , d is_ IB d is_ H C , SN _ IB L L e stim a te N W s.d. 27.92 5.23 0.799 0.049 0.566 0.212 0.213 0.046 963.7 424.4 1.012 0.835 0.243 0.283 130.97
47.04
4690.9 5592 0.929 0.594 2.91E − 44 1.77E − 135 1.77E − 18 0.028 0.005 0.029 0.007 11082.2 1943.5 12661.1 19.59
17.39 0 100
IV 3 (1 70 ) - IV s used: IB h ph o ur,24 h ∆tem ps d is_ E G , d is_ IB d is_ H C ,S N _ IB L L estim ate N W s.d . 28.15 5.23 0.799 0.051 0.582 0.202 0.210 0.046 943.5 413.7 1.008 0.889 0.261 0.295 134.26
IV 4 (2 72 )- IV s used : IB m ovav 4 ,2 4h ∆tem p s dis_ E G , dis_ IB d is_ H C , SN _ IB L L estim a te N w s.d 23.57 5.89 0.74366043 0.045 0.519 0.189 0.255 0.051 1041.5 391.8 0.999 0.986 0.211 0.222
48.51
4808.4 5586 0.929 0.9995 4.57E − 44 1.76E − 137 3.30E − 24 0.028 0.004 0.028 0.006 11082.2 1943.5 12778.6 20.15
92.35
38.52
3307.4 5112 0.929 0.990 1.38E − 40 4.61E − 104 3.09E − 26 0.032 0.007 0.032 0.009 11082.2 1943.5 11277.6
16.89 0 100
13.01
18.16 0 100
An extension of our basic model with elastic demand
Suppose you maintain all the assumptions in our model, except that the unregulated demand is generated by a downward sloping demand function. Assume that for firm i this is θi − bi π. (We assume that the lowest θi realization is way below the π that would choke off all demand. In our data set you could think of the highest price they are allowed to bid (or effectively bid), π ¯ and think of Di (π) = θi − bi π ¯ as the inelastic part of the demand). Aggregate demand in the spot market is: θ − bπ = i θi − ( i bi ) π. Suppressing all issues of regulated demands and costs of transition to competition, we can write down the maximization problem for firm i as:
max E E [¯ p − π]Di (π) + π ηi − bπ − E{Sj (π, Ij ) | Ii } π(ηi ,Ii ) j=i −Ci ηi − bπ − E{Sj (π, Ij ) | Ii } − hitτ − chi hitτ + δVi (Ht+1 , Ii(t+1) ) | Ii , ηi | Ii j=i
54
The first order condition becomes: p − π]bi − [π − Ci ](s−i + b) = 0 −Di (π) + Si (π, Ii ) − [¯
Si (π, Ii ) =
1 {−cio (s−i + b) + bi p¯ + (s−i + b−i )π + ci1 (s−i + b)hi + Di (π)} 1 + ci1 (s−i + b)
giving the estimating equation: Si (π, Ii ) = a0 + a1 π + a2 hi + a3 Di We identify: s−i + b−i =
a1 a3
and ci1
(s−i + b) a2 = s−i + b−i a1
We get that: 1 1 1 − a3 a2 − = = a1 s−i + b−i a1 a1 +b) So we get again that there are two apporoaches to identify ci1 s(s−i−i+b (which comes of course from the −i
theoretical restriction on the parameters on Di and hi . It follows that we get an upward bias in our estimation of the true slope of the marginal cost function given by: a2 a3 bi = ci1 bi > 0 − ci1 = ci1 a1 s−i + b−i a1 There is also a bias in the interpretation of the constant coefficient in marginal costs that we estimate:
−
a0 a1
(s−i + b) p¯bi − s−i + b−i s−i + b−i bi = ci0 − (¯ p − ci0 ) s−i + b−i = ci0
55 This one will be downward biased given that (¯ p − ci0 ) > 0 can be expected. Again, for small bi , this error will be small. How does it affect our predictions concerning net demand and supply positions and pricing below or above marginal cost? Note that from the first order condition: Di (π) − Si (π, Ii ) = −[π −
s−i + b bi (ci0 + ci1 (Si − hi )) − p¯](s−i + b−i ) s−i + b−i s−i + b−i
Substituting the parameters from the estimating regression we get: Di (π) − Si (π, Ii ) = −[π − (−
a0 a2 + (Si − hi ))] a1 a1
which is exactly the same as before. This means that the core test of the theory is independent of the biases in estimating the marginal cost parameters, because the appropriately modified marginal cost term that would be relevant for the prediction relies on the same coefficient estimates. This means that while our estimates of the marginal cost parameters may be biased, this bias is irrelevant for the test of our theory. We want to run exactly the same regression when we have slope in the demand functions.
