Defining electricity markets: an arbitrage cost approach

Resource and Energy Economics 23 (2001) 259–270

Defining electricity markets: an arbitrage cost approach Andrew N. Kleit∗ Department of Energy, Environmental, and Mineral Economics, The Pennsylvania State University, 2217 Earth Engineering Sciences, University Park, PA 16802-6813, USA Received 25 January 2000; received in revised form 23 January 2001; accepted 7 February 2001

Abstract Market definition is a crucial component of antitrust policy. There is, however, no universally accepted method of carrying out market definition. While several approaches have been presented in the literature, each has its share of drawbacks. This paper suggests that a modeling technique based upon the theory of arbitrage is well suited to answering this question. After the empirical approach is presented, it is used to calculate antitrust market definitions between electricity hubs in the American West. © 2001 Elsevier Science B.V. All rights reserved. JEL classification: Q41; L4 Keywords: Electricity; Market definition; Antitrust

1. Introduction In general, determining the proper methodology for conducting antitrust market definition is a recurring question in antitrust. In particular, restructuring of the electricity sector has brought new policy questions to this area. Today, many electricity firms at the generation level now compete, or will compete soon, in relatively unregulated markets. This, in turn, leads to those firms being more subject to antitrust enforcement. For example, should two electric utilities wish to merge, the merger can be subject to review by antitrust authorities for any potential anticompetitive effects (see, for example, Joskow (1999)). For such effects to be analyzed, however, a proper antitrust market definition must be constructed. There is, however, no universally accepted method of carrying out market definition. While several approaches have been presented in the literature, each has its share of drawbacks. This article suggests that a modeling technique based upon the theory of arbitrage is ∗ Tel.: +1-814-865-0711; fax: +1-814-863-7433. E-mail address: [email protected] (A.N. Kleit).

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well suited to answering this question. After the empirical approach is presented, it is used to calculate antitrust market definitions between electricity hubs in the American West. This article is organized as follows: Section 2 reviews the literature on antitrust market definition and discusses the problems involved in the approaches presented in the economic literature. Section 3 presents the arbitrage cost estimator and discusses how to apply its results to the definition of antitrust markets. It then discusses the data to be used in the empirical estimation. Section 4 presents the results of that estimation, and Section 5 has concluding remarks. 2. Market definition literature A market definition is required for an analysis of market power. For example, consider a merger between two competing firms. To analyze whether or not that merger would result in increased prices to consumers requires a definition of the relevant market. Under the joint Department of Justice/Federal Trade Commission approach, an antitrust market consists of all firms, whom, if they were controlled by a hypothetical monopolist, could raise price a “small but significant” amount. Generally, in practice, a “small but significant amount” implies a price increase of 5%. There are several approaches presented in the economic literature for how to conduct market definition. 1 (For an excellent review of this literature, see Kaserman and Mayo (1996, pp. 145–150)). Elzinga and Hogarty (1973) propose a test based on the percent of product flowing prior to the merger in or out of a defined region. This test has the advantage of requiring data that is often available to antitrust reviewers. The conceptual difficulty with this approach, however, is that it does not address what is likely to happen once the merger takes place and firms raise prices. In other words, it does not answer the question of what products would flow into a relevant area should a hypothetical monopolist raise price above current competitive levels. Scheffman and Spiller (1987) suggest using a residual demand approach. What this methodology does is to take a group of firms that is hypothesized to consist of an antitrust market, and then to estimate the demand curve facing this group. If the elasticity of demand facing this group would permit it to raise price profitably 5%, the group can be considered to be an antitrust market. The residual demand approach, however, has two basic problems. First, it has severe data demands, data demands that may not be feasible to meet during the heavy time pressure of an antitrust merger investigation. Second, as Froeb and Werden (1991) suggest, the residual demand approach works best for a market that is characterized by the Stackelberg model. For other market scenarios, the residual demand approach may not appropriate. There are a number of articles that adopt what may be termed the “market integration” approach to market definition. 2 These papers attempt to use the time series properties 1 Note that the discussion here involves largely geographic market definition. Similar issues are involved in product market definition. 2 There is a very large literature on market integration. See, for example, Weiner (1991) and Gulen (1999) in oil, Woo et al. in electricity, and de Vany and Walls (1995, 1996) and Spulber and Doane (1994) in natural gas. For a critique of this approach, see Kleit (1998).

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of prices in potentially related markets to determine if the two relevant areas are in the same antitrust market. These techniques, thus alleviate the data requirements of the residual demand approach. For example, Stigler and Sherwin (1985) calculate correlations of either price, the differences in price, or the differences in the logarithms of price, for several commodities between geographic areas. They assert that a high degree of correlation implies that the two geographic areas are in the same market. Stigler and Sherwin, however, do not define what level of correlation is sufficient for a market determination. In a variation of this approach, Slade (1986) runs a series of Granger causality tests on petroleum prices in cities across the United States. In general, her results imply that prices in cities in the southeastern US Granger cause each other, while linkages between other city pairs are weaker. From this, she concludes that the southeastern US can be considered an antitrust market in petroleum. Such approaches, however, have not been met with universal approval in the literature. In particular, Werden and Froeb (1993) suggest several difficulties with these techniques. First, there is the danger of spurious correlation. Assume, for example, that electricity prices in Markets A and B are both affected by the price of some common factor Z. If the variability of Z rises in the relevant time period, prices in Markets A and B would appear to be more correlated, leading to the potentially false inference that transaction costs between the two markets had declined. In other words, if input markets become more integrated, the time series approach could incorrectly show that the relevant commodity markets are also more integrated. 3 In general, Werden and Froeb point out that the previous attempts to analyze the time series properties of price do not fit well into the needs of modern prospective merger analysis. The joint Department of Justice/Federal Trade Commission Merger Guidelines (Department of Justice and the Federal Trade Commission, 1992), highlighting an approach that has been used successfully in enforcement agencies and courts, since the early 1980s, state that a geographic market is defined as “a region where a hypothetical monopolist . . . would profitably impose at least a small but significant and nontransitory” increase in price. 4 Thus, the Guidelines ask if transaction costs from another region are high enough so that they would allow a hypothetical monopolist to profitably raise price. Given this, what is at least theoretically required for market definition is an explicit value for the level of transaction costs. It also requires a “cut-off threshold”. A statistical level at which a market determination can be made, something that is missing from the Stigler and Sherwin (1985) analysis. 5

3 Conceptually, one could avoid this difficulty by regressing common cost factors out of market prices. Spulber and Doane (1994, p. 495), for example, attempt this by first running regressions of oil prices, the producer price index, and seasonal dummy variables on the price of gas in each region. They then found the correlations between regression residuals from each region. 4 Indeed, courts have explicitly rejected the use of price time series analysis to define markets in two major antitrust merger cases, Marathon Oil v. Mobil Corp., 530 F. Suppl. 315, 669 F.2d 378 (1981) and US v. Archer-Daniels-Midland Co., 856 F.2d 242 (1989). 5 Stigler and Sherwin (1985, pp. 582–583) make it clear they are not attempting to fit their methodology into the Merger Guidelines framework. According to them, the Merger Guidelines “market definition has one, wholly decisive, defect: it is completely non-operational.” Of course, the passage of time has served to refute this contention.

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Woo et al. (1997) attempt to address the question of how to determine the relevant transaction cost by estimating the equation Pjt = α + βPkt + εjt , for electricity markets in the western part of North America, where Pj t is the spot market price in market j at time t, Pkt the spot market price in market k at time t, β and α estimated coefficients and εj t the error term in the regression. Woo et al. (1997) assert that if β = 1, α represents the average transaction costs between markets j and k. They then present estimated transactions costs between markets. One can infer, however, problems with this analysis. In this approach, the term α represents the transaction costs from the low price market to the high price market. No attempt is made to infer the transaction costs of going from the high price market to the low price market. Further, consider two markets who have the same average price. In this case, α = 0. Yet that appears to be little reason to conclude that transaction costs between the two markets are zero. Thus, it still seems that there are open methodological questions about how to calculate market definition under the “hypothetical monopoly” test that is currently used, especially in circumstances where the available data is limited. It is with this in mind that the arbitrage cost estimator of Section 3 is presented.

3. Empirical methodology 3.1. The arbitrage cost model Given the discussion of market definition above, it appears that there is a need for a method for conducting market definition given serious data limitations. This section shows how the methodology of Spiller and Wood (1988a), modified to account for autocorrelation, exogenous effects on the cost of arbitrage, and other exogenous factors that affect price differences, can be used to meet this need. Here, we begin the presentation of the arbitrage (transaction) cost estimator of Spiller and Wood, which is based upon the theory of arbitrage. 6 With P1 equal the price of the good in area 1 and P2 equal the price of the good in area 2, let P = P1 − P2 . Without the threat of arbitrage, P is determined by the relationship

P N = α + ε,

ε ∼ N (0, σ 2 ).

(1)

where PN represents what the price difference would be without arbitrage, rather than the actual observed prices. Assume for the moment without loss of generality that P N > 0. Now consider the following: if the price of a good in Region 1 becomes “much” higher than the price of the good in Region 2, buyers in Region 1 will “arbitrage” the difference by buying the good in Region 2 and shipping to Region 1. This in turn limits the price 6 A similar model is presented in Spiller and Huang (1986). Other uses and extensions of the arbitrage approach appear in Sexton et al. (1991), Kleit and Palsson (1996), and Kleit (1998).

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differential between Region 1 and 2. The possibility for arbitrage is limited by the transaction or arbitrage cost of shipping the good from Region 2 to 1. Now define the arbitrage cost of shipping the good from Region 2 to 1 as T1 = T 1 + ε 1 ,

ε1 ∼ N (0, σ12 ), ε1 truncated below at − T 1 .

(2)

The reason for the truncation below is that T1 ≥ 0, as arbitrage costs cannot be negative. This in turn implies that T 1 7 is the mode of T1 , and the expected value of T1 is E(T1 ) = T 1 + E(ε1 ) = T 1 + σ1

f (−T 1 /σ1 ) , F (T 1 /σ1 )

ε1 ∼ N(0, σ12 ), ε1 truncated below at − T 1

(3)

where f ( ) is the density function of the normal distribution and F( ) is the cumulative normal distribution. Given the arbitrage cost, the price difference is truncated above at T1 . Thus, the price difference we observe is Y = minimum ( P N , T1 ).

(4)

Now assume P N < 0. Define the arbitrage cost of shipping the good from Region 1 to 2 as T2 = T 2 + ε2 ,

ε2 ∼ N (0, σ22 ), ε2 truncated below at − T 2

(5)

Again, T 2 is the mode of T2 , with the mean of T2 calculated as above. Given this, the price we will observe is Y = maximum ( P N , −T1 ).

(6)

The original Spiller and Wood model does not account of autocorrelation, which makes its results inefficient. Here, the Spiller and Wood framework is extended to adjust for the presence of autocorrelation. We, thus have an underlying series driven by N

PiN = α + ρ(E( Pi−1 ) − α) + ε,

ε ∼ N (0, σ 2 ),

(7)

N ) represents the expected value of the price where i is the subscript for time and E( Pi−1 difference without arbitrage in the previous period. Thus, ρ, −1 < ρ < 1, is our autocorrelation coefficient. 8 Given the above, we can construct the likelihood function. Let I = 1 if Y ≥ 0, 0 otherwise. There are two different ways by which we could observe a particular Y ≥ 0. The first is if Y = P N and Ti > P N . In this case, we are observing the non-arbitrage price difference, which is not constrained by arbitrage costs. The second

If T 1 < 0, 0 is the mode of T 1 . The same logic applies to T 2 below. N Recall that we do not directly observe Pi−1 , making it necessary to calculate an expected value. The expected value is calculated as follows: first, given Y the probability that the price series is truncated by arbitrage is calculated (see Spiller and Wood (1988b, pp. 889–890) for a description of how this is done). Then the expected value of the N relevant Ti is calculated, given Ti truncated below at Y (or −Y, as the case may be). Given this E( Pi−1 ) equals the probability of truncation times the expected value of Ti given truncation, plus one minus the probability of truncation times Y. 7 8

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possibility is that T1 = Y and P N > T1 . In this case, the price difference is constrained by arbitrage, and what we are observing is the arbitrage threshold. Thus, the likelihood of observing Y, given Y > 0 is equal to the likelihood P N = Y times the probability that T1 > Y plus the likelihood T1 = Y times the probability P N > Y . The likelihood of this occurring is 
N − α))/σ )) f (Y − (α + ρ(E( Pi−1 F ((T 1 − Y )/σ1 ) + L (Y ) = σ F (T 1 /σ1 )   
N ) − α) − Y ) (α + ρ(E( Pi−1 f ((Y − T 1 )/σ1 ) + F , (8) (σ1 F (T 1 /σ1 )) σ where again f is the probability distribution function for a normal, and F the cumulative distribution function. Now consider Y < 0. The likelihood of observing Y is similarly constructed 
N − α))/σ )) (Y − (α + ρ(E( Pi−1 F ((T 2 + Y )/σ2 ) − L (Y ) = σ F (T 2 /σ2 )   
N ) − α)) (Y − (α + ρ(E( Pi−1 f ((−Y − T 2 )/σ2 ) + F . (9) σ2 F (T 2 /σ2 ) σ The likelihood for the entire sample is, therefore, L(Y ) = IL+ (Y ) + (1 − I )L− (Y ).

(10)

In addition, this estimator can be used in situations where only one transaction cost is relevant. For example, if product moves only from market A to market B, the price in A is unlikely to be greater (a significant amount of the time) than the price in B. In this case, the arbitrage cost of shipment from B to A cannot be estimated. The arbitrage cost of shipping from A to B can be estimated, however, using the model above. Such estimator requires setting the relevant Ti at an arbitrarily high and the relevant σ i at an arbitrarily low level, and then estimating the remainder of the model (see the discussion of the Four Corners–Mid-Columbia estimation, Section 4 below). It is also possible to extend the Spiller and Wood model to estimate changes in arbitrage costs as a result of exogenous factors. Let Xβ i equal a vector of factors used to model transaction costs times the coefficients on those factors. Let the transaction costs to market i be T i = Xβi + εi ,

εi truncated below at − Xβi

In this paper, the X vector will consist of two variables: a constant (denoted in Table 1 as Tik ) and a variable measuring local weather conditions. 9 Given this specification, the expected value of E(Ti |Xβi , σi ) = Xβi + σi f (−Xβi /σi )/F (Xβi /σi ), as implied above in Eq. (3). 9

Day of week variables were attempted, but none were shown to be significant.

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In addition, we will also attempt to augment the Spiller and Wood model by attempting to determine the exogenous influences on mean differences (α) between markets. In this model, α = ZY, where Z is a matrix of explanatory variables and Y are the coefficients on those variables. Here, we will put two variables into the Z matrix, a constant and a weather variable. We now have four variables to be estimated in a maximum likelihood format, σ 1 , σ 2 , σ , and α, which were used in the original Spiller and Wood model. We must also estimate ρ, the degree of autocorrelation, β 1 and β 2 , the constant terms on and exogenous factors affecting arbitrage costs, and Z, the factors that affect mean differences between markets. 3.2. Application of arbitrage cost estimator to antitrust markets Under the joint Department of Justice/Federal Trade Commission Merger Guidelines approach, Region 2 is in Region 1s “antitrust market” if an anticompetitive price increase of 5% in Region 1 could be “defeated” by impacts from Region 2. Under the arbitrage approach, such imports will occur if 105% of the price in Region 1 is greater than the price in Region 2 plus the transaction cost of sending the good to Region 1. For this analysis, we will examine markets at their mean price. Let P 1 be the mean price in Region 1 and P 2 be the mean price in Region 2. Recall from above that the arbitrage cost of sending the good from Region 2 to 1 is T1 = T 1 + ε1 , ε1 ∼ TN(O, σ12 , −T 1 ). Given this, the probability that Region 2 is in Region 1 is Pr(P 2 + T1 < 1.05P 1 ) = Pr(T 1 + ε1 < (1.05P 1 − P 2 )) = Pr(ε1 < (1.05P 1 − P 2 − T 1 ))   ε1 (1.05P 1 − P 2 − T 1 ) = Pr < σ1 σ1 F ((1.05P 1 − P 2 − T 1 )/σ1 ) − F (−T 1 /σ1 ) = . 1 − F (−T 1 /σ )

(11)

where again F( ) is the cumulative normal distribution function (for a similar approach, see Kleit (1998)). Because in this model, the transaction costs are not constant over time, the probability of Region 2 being in Region 1s antitrust market will differ as the transaction cost variables change. Thus, the probability of Region 2 being in Region 1’s antitrust market reported will be the mean probability over the relevant data set. One additional point needs to be made. The 5% threshold of the Merger Guidelines is perhaps somewhat arbitrary. In light of the first point, it is possible to apply other percentage guidelines. If this is the case, and one is using an X percentage threshold, the above formula can be employed, simply replacing 1.05 by 1 + (X/100). 3.3. Data The price data used is the daily firm peak price in US dollars per megawatt hour (US$/MWh) from four western US trading hubs: the California–Oregon border (COB), the Four Corners “market” in the Southwest, the Mid-Columbia “market,” and the Palo

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Verte “market.” The data was obtained from Energy News Daily. The data is for 1998, and weekends and holidays are eliminated from the data set. The weather variables used are the degree heating/cooling days from either Sacramento or Los Angeles. The Sacramento data is applied to the COB and Mid-Columbia markets, as that is the weather region most likely to affect power flows from those two hubs. The coefficients on these two variables are expected to be positive, indicating that the higher the demand for power, the higher the strain on the transmission system, and therefore, the higher the transactions costs of shipping power. The Los Angeles degree day data is used for the Four Corners and Palo Verte markets, and again the coefficient is expected to be positive. To model the difference between prices (the α parameter) the difference between Sacramento and Los Angeles degree days is used.

4. Results Table 1 presents the results of the arbitrage estimation between the four trading hubs. In the first reported estimation, COB–Four Corners, T1 , measuring constant (untruncated) transactions costs from the Four Corners to COB, is US$ −61.85/MWh. However, due to the truncation effect, this does not imply that the actual arbitrage costs are negative, as derived above in Eq. (3). In particular, note that α 1 is relatively large, implying a large truncation effect. The constant untruncated transactions cost of shipments from the COB to the Four Corners is US$ 6.25/MWh. The coefficients on both the weather variables used for measuring transactions costs are insignificant, implying that degree days (here representing Sacramento for the COB and Los Angeles for Four Corners) did not have an important impact on arbitrage costs. The second estimation deals with the COB–Mid-Columbia pair. The constant untruncated transaction costs for both types of shipments are negative, though small in magnitude. The coefficients on degree days are both significant, though for shipments from Mid-Columbia to COB the coefficient is significant only at the 10% level (t-statistic = 1.91). In the COB–Palo Verte estimation, both constant untruncated transactions costs are significantly positive. The impact of degree days on the cost of shipping power from Palo Verte to COB is significant, while the coefficient on the cost of shipping power from COB to Palo Verte has only marginal significance (t-statistic = 1.51). For the Four Corners–Mid-Columbia estimation, no convergence could be reached on transaction costs from Mid-Columbia to the Four Corners. The model was reestimated as described in Section 3.1 to investigate only transaction costs from Four Corners to Mid-Columbia. Here the mean untruncated arbitrage costs are US$ 1.85/MWh, which is not significantly different from zero, and the coefficient on degree days (here in Sacramento) is positive and significant. The fifth estimation reported is Four Corners–Palo Verte. For shipments from Palo Verte to Mid-Columbia, constant untruncated arbitrage costs are estimated to be US$ −31.20/kWh. For shipments in the other direction, untruncated arbitrage costs are not significantly different from zero. The degree day variables are insignificant for shipments to Four Corners, and significant and positive for shipments to Palo Verte. In the Mid-Columbia–Palo Verte estimation, constant untruncated arbitrage costs from Palo Verte to Mid-Columbia are

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Table 2 Market definition results summarya To

From COB

COB

Four Corners

Mid-Columbia

Palo Verte

Four Corners 3.53 4.5% 98.5%

8.47 100.0% 100.0%

Mid-Columbia 17.53 77.8% 97.9% na

5.68 0.0% 93.2%

12.61 0.0% 0.0%

7.56 100.0% 100.0%

6.76 99.3% 100.0%

Palo Verte 12.43 0.0% 5.9% 1.28 100.0% 100.0% 14.96 0.0% 0.0%

10.50 100.0% 100.0%

a

Mean transactions cost in US$/MWh, market definition percentage at 5% threshold, market definition percentage at 10% threshold.

essentially zero, and in the reverse direction they are estimated to be US$ 7.29/MWh. The coefficient on degree days on transaction costs to Mid-Columbia is positive and significant. Note that 10 of the 11 degree day variables on transactions costs have the expected positive sign. Also, four of these variables are significant at the 5% level, and one more is significant at the 10% level. Table 2 attempts to put the results of Table 1 into the perspective of marsket definition, as described above in Section 3.2. The first number reported in any box is the relevant mean transaction costs from the hub listed above the box to the hub listed on the side of the box in US$/MWh. The second number is the estimated percentage of the time the “from” hub is in the “to” hub’s antitrust market, using a 5% price threshold. The third number is the estimated percentage of the time the “from” hub is in the “to” hub’s antitrust market, using a 10% price threshold. For example, the mean arbitrage cost of shipping from Four Corners to COB is estimated to be US$ 3.53/MWh. Using a 5% threshold, Four Corners is in COB’s antitrust market 4.5% of the time. Using a 10% threshold, Four Corners is in the COB market 98.5% of the time. In the reverse relationship, the mean cost of shipping electricity from COB to the Four Corners is US$ 8.47. COB is in the Four Corners market 100% of the time at both the 5 and 10% threshold levels. Using a 50% cutoff level, only Mid-Columbia is in the COB antitrust market at the 5% level. Mid-Columbia and Four Corners are in the COB antitrust market at the 10% threshold. For Four Corners, both COB and Palo Verte are in its antitrust market at the 5% level. None of the other three hubs are in Mid-Columbia’s antitrust market at the 5% level, and only COB is in it at the 10% level. All three other hubs are in Palo Verte’s antitrust market at the 5% threshold level. Table 3 presents the antitrust market definition results derived from the model used above without adjusting for autocorrelation (these results are, therefore, less efficient then

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Table 3 Market definition results summary not accounting for autocorrelationa To

From COB

COB

Four Corners

Mid-Columbia

Palo Verte

Four Corners

Mid-Columbia

9.17 4.8% 100.0%

6.97 100.0% 100.0%

8.75 100.0% 100.0%

na

5.71 0.0% 83.9%

13.77 0.0% 0.0%

8.96 100.0% 100.0%

6.80 100.0% 100.0%

Palo Verte 9.60 0.0% 96.3% 6.59 100.0% 100.0% 12.55 0.0% 0.0%

3.86 100.0% 100.0%

a

Mean transactions cost in US$/MWh, market definition percentage at 5% threshold, market definition percentage at 10% threshold.

the results previously presented). Most of the results are similar. There is some variance in the mean transactions for markets that are separated by smaller amounts. This is not surprising, as these parameters are estimated with somewhat less precision than the other transaction cost parameters. However, the antitrust market definitions are identical, with the exception of shipments from Palo Verte to COB, considered at the 10% level. 5. Conclusion Market power questions are coming to the forefront in the electric power industry, as that sector becomes more and more deregulated. The measurement of market power requires an appropriate methodology for undergoing market definition, in a process that often suffers from a lack of data for analysis. In this paper, the arbitrage cost estimator is presented as a method for conducting market definition analysis with extremely limited data requirements. The arbitrage cost estimator is then applied to pairwise comparisons between four electricity trading hubs in the American West. In the 11 pairwise comparisons conducted, six of the hubs were considered to be in the relevant antitrust market of the hub being analyzed using a 5% threshold, and eight of the hubs were in the antitrust market using a 10% price threshold. References de Vany, A.S., Walls, W.D., 1995. The Emerging New Order in Natural Gas. Quorom, Westport, CT. de Vany, A.S., Walls, W.D., 1996. The law of one price in a network: arbitrage and price dynamics in natural gas City Gate markets. Journal of Regional Science 36, 555–570. Department of Justice and the Federal Trade Commission, 1992. Horizontal Merger Guidelines, Antitrust and Trade Regulation Report, Vol. 62, p. 1559.

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Elzinga, K.G., Hogarty, T.F., 1973. The problem of geographic market in Antimerger Suits. Antitrust Bulletin 18, 45–81. Froeb, L.M., Werden, G.J., 1991. Residual demand estimation for market delineation: complications and limitations. Review of Industrial Organization 6, 33–48. Gulen, S.G., 1999. Regionalization in world crude oil markets: further evidence. The Energy Journal 20, 13–125. Joskow, P.L., 1999. Restructuring electric utilities: BG&E and PEPCO propose to merger. In: Kwoka, White (Eds.), The Antitrust Revolution: Economics, Competition, and Policy. Oxford, New York, pp. 89–115. Kaserman, D.L., Mayo, J.W., 1996. The Economics of Antitrust and Regulation. Dryden, New York. Kleit, A.N., 1998. Did open access integrate natural gas markets? An arbitrage cost approach. Journal of Regulatory Economics 14, 19–33. Kleit, A.N., Palsson, H.P., 1996. Is there anticompetitive behavior in the central Canadian cement industry? Testing transaction cost hypotheses. Canadian Journal of Economics 29, 343–356. Sexton, R.J., Kling, C.L., Carman, H.F., 1991. Market integration, efficiency of arbitrage, and imperfect competition: application to US celery. American Journal of Agricultural Economics 73, 568–580. Scheffman, D.T., Spiller, P.T., 1987. Geographic market definition under the US Department of Justice Merger Guidelines. Journal of Law and Economics 30, 123–147. Slade, M.E., 1986. Exogeneity tests of market boundaries applied to petroleum products. Journal of Industrial Economics 34, 291–303. Spiller, P.T., Huang, C.J., 1986. On the extent of the market: wholesale gasoline in the northeastern United States. Journal of Industrial Economics 35, 131–145. Spiller, P.T., Wood, R.O., 1988a. The estimation of transaction costs in arbitrage models. Journal of Econometrics 39, 309–326. Spiller, P.T., Wood, R.O., 1988b. Arbitrage during the dollar-sterling gold standard. Journal of Political Economy 96, 882–892. Spulber, D.F., Doane, M.J., 1994. Open access and the evolution of the US spot market for natural gas. Journal of Law and Economics 37, 477–518. Stigler, G.J., Sherwin, R.A., 1985. The extent of the market. Journal of Law and Economics 28, 555–585. Weiner, R.J., 1991. Is the world oil market ‘One Great Pool’? The Energy Journal 12, 95–107. Werden, G.J., Froeb, L.M., 1993. Correlation, causality, and all that jazz: the inherent shortcomings of price tests for antitrust market delineation. Review of Industrial Organization 8, 329–354. Woo, C.K., Lloyd-Zannetti, D., Horowitz, I., 1997. Electricity market integration in the pacific northwest. The Energy Journal 18, 75–101.