Vertical integration and collusive incentives: an experimental analysis

International Journal of Industrial Organization 18 (2000) 471–496 www.elsevier.com / locate / econbase

Vertical integration and collusive incentives: an experimental analysis Charles F. Mason*, Owen R. Phillips Department of Economics and Finance, University of Wyoming, Laramie, WY 82071 -3985, USA Received 21 December 1994; received in revised form 31 December 1996; accepted 29 April 1998

Abstract We consider vertically related industries with multiple downstream markets; firms make simultaneous output choices in a repeated game. Upstream duopolists merge with producers in one of the downstream markets that also is a duopoly. Experimental duopoly markets are constructed to assess the effects of vertical integration upon outputs and profits. We find that integration raises outputs in both downstream and upstream markets, although only the upstream effect is statistically significant. Integrated profits are lower and consumer welfare is higher. The integrated markets tend to equilibrate more quickly.  2000 Elsevier Science B.V. All rights reserved. Keywords: Vertical integration; Merger; Market experiments JEL classification: L1; L22

1. Introduction Consider an intermediate good that is sold as an input in multiple downstream markets. The production of this good is dominated by a few sellers that simultaneously choose outputs. One of the downstream markets is oligopolized, and upstream firms integrate into this downstream market. This market structure may describe, for example, large gasoline refiners merging with airline companies,

* Corresponding author. Tel.: 11-307-766-2178; fax: 11-307-766-5090. 0167-7187 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 98 )00024-1

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movie studios acquiring theaters in major metropolitan areas, or manufacturers of a product integrating downward and becoming the major retailers in a certain geographic market. There exist a variety of reasons for outputs and prices to change in these markets as a consequence of such integration. We describe some of them. Before merging, it is well known that this vertical relation suffers from the ‘double marginalization’ problem.1 Downstream firms set a price above their marginal cost, which depends on the upstream price of the intermediate good. Profit maximizing upstream firms have already set a price for the input above their marginal cost; thus the input price is marked-up twice. By eliminating the dual markups, vertical integration should raise outputs and lower prices in both markets. In addition, integration can eliminate uncertainty in the vertical relation. If the upstream market is in a state of disequilibrium, or maintains only temporary equilibria, and downstream producers are risk averse, they would be inclined to produce less and correspondingly demand less of the input in a vertically separated structure (Carlton, 1979; Perry, 1982). The often cited reason for airlines merging with petroleum refiners is that airlines wanted more stable deliveries and prices of jet fuel (Businessweek, November 17, 1980). In the 1948 Paramount Pictures case (334 U.S. 131 (1948)), movie studios claimed they were merging with theaters in order to guarantee outlets for their films. Since the integrated firm has information unavailable to the nonintegrated firms, a more precise prediction of upstream and downstream prices and outputs can be formed after a merger. Integration is therefore capable of mitigating production uncertainties; outputs also should increase for this reason.2 On the other hand, a fully integrated market structure might facilitate greater levels of cooperation than a nonintegrated market structure, which might lower outputs. There is the persistent notion that if firms interact repeatedly over an indefinite number of periods, more collusive outcomes that raise prices and restrict outputs at both levels of production are possible as a result of the mergers (see

1

For a discussion of double-marginalization in the context of vertically related oligopolies, see Greenhut and Ohta (1979); Hay and Morris (1991); Perry (1989), or Tirole (1988). Since an increase in upstream output lowers downstream marginal cost, it raises marginal profit for the downstream firms. While upstream firms neglect this effect in a nonintegrated market structure, it is taken into consideration by vertically integrated firms. Thus, a unilateral merger raises the integrating firms’ combined profits (relative to the level without integration). However, as we note below, if more than one pair of firms becomes vertically integrated, industry profits may fall. 2 There can be more to this simple story. Crocker (1983) and Gal-Or (1992) show that vertical integration may take place to eliminate ‘opportunistic’ behavior by the downstream firm when it holds private information about its costs. The downstream firm may have an incentive to strategically distort reports of its true costs in order to boost profits on final sales. When firms are vertically separated this manipulation may go undetected by the upstream firm.

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Scherer, 1980, pp. 303–312). Enhanced cooperation, however, need not imply output reductions in all markets. The multimarket contact induced by vertical integration allows firms to use output increases in one market to facilitate output reductions in another in order to increase total profits (Bernheim and Whinston, 1990).3 Collusive incentives can therefore counteract incentives to increase outputs from eliminating double marginalization or reducing uncertainty. In a repeated game setting, the net effect of the vertical integration becomes an empirical issue. This paper studies the impact of mergers in vertically related markets. To keep the theory and empirics manageable we assume that before integration there are only two firms in an upstream X market, and two firms in a downstream Y market. An additional competitive Z market also uses the upstream product, so that the market demand for the upstream product can not be exactly inferred from downstream Y output. Moreover, the Y market is a small component of total demand for X, so that Y market firms know they have very little impact on upstream production decisions. We assume there are no vertical efficiencies in the technology and that costs are symmetric across rival firms. Upstream producers have no marginal costs, while downstream marginal costs are proportional to the input price. Given this stylized vertical relation, we are interested in the market effects when the two firms in X merge with the two firms in Y. To investigate how vertical integration changes outputs and prices we collect data from laboratory markets. Subjects acting as upstream or downstream producers choose outputs in a repeated game. In a control treatment, individuals participate in either an upstream duopoly market or a downstream duopoly market, but not both; we term this structure vertically linked. In a second treatment, corresponding to vertical integration, subject pairs make output choices in both the upstream and downstream market. To make our games mathematically equivalent to infinitely repeated games with discounting, we invoke a random stopping rule after 35 choice periods (Fudenberg and Tirole, 1989; Gibbons, 1992; Rasmusen, 1994). The use of a random stopping rule to mimic an infinite horizon super game is relatively common in experimental designs (Plott, 1989). The termination probability we use, 1 / 5, is small enough to support a wide range of collusive super

3 It is well known that more collusive outcomes are possible as part of a noncooperative equilibrium in a repeated game if firms play trigger strategies. While the quantitative effects of multimarket contact might well depend on the type of trigger used, the important qualitative effect is robust to the style of trigger used (Bernheim and Whinston, 1990, pp. 21–22). Phillips and Mason (1992) provide experimental evidence supportive of the Bernheim–Whinston model for conglomerate mergers. The situation is more complicated when oligopolists attempt to cooperate in an uncertain environment. In a model with uncertain demand and unobservable prices, Green and Porter (1984) show that firms abandon the collusive regime when price falls below some critical level. A corollary is that collusive outputs tend to be higher when prices are uncertain. In this case, vertical integration would alter the nature of a tacit agreement for two reasons, because of the mitigation of uncertainty and because of the newly introduced multimarket contact.

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game strategies, but large enough so that different sessions would be expected to have similar length and with similar average earnings.4 Comparing behavior in these two treatments, we find substantially larger levels of output in the upstream market and slightly greater outputs in the downstream oligopoly market under the vertically integrated structure. While the second of these effects is not statistically significant, the first is. If output in the X market rises significantly and output in Y only rises slightly, it can inferred that output in the Z market increases significantly. Overall, the hypothesis that vertically linked markets operate at levels identical to those in vertically integrated markets is rejected with great confidence. Moreover, integration lowers industry profits, and by an amount substantially larger than would be implied by the Cournot model. We also find that downstream markets tend to equilibrate more rapidly under integration compared to the linked control markets.5 This last observation is consistent with the perspective that integration allows firms to reduce upstream price uncertainty which facilitates convergence to downstream equilibrium. Taken as a whole, our results support the hypothesis that vertical integration increases total surplus. Indeed, we find that consumer surplus increases about 12% and total surplus rises 3% after integration. While it may be tempting to draw broad conclusions from these results, one must bear in mind that we are analyzing one specific parameterization in which data are gathered from experimental markets. Our discussion depends on a large alternative downstream market, and abstracts from a variety of institutional features that can influence the effect of vertical integration on output levels. For instance, we ignore effects related to technology and we do not delve into the vast literature on transactions costs and principal-agent problems. Nevertheless, we believe our results shed some light on the potential effects of vertical integration. The remainder of the paper is organized into five sections. In Section 2 we

4

The anticipated number of draws before the experiment will terminate after the random stopping rule is invoked (i.e., total length-35) follows a geometric distribution with parameter p51 / 5. The mean and standard deviation of this distribution are each 4; the probability that the continuation phase will last between zero and ten periods is roughly 90%. Even though the game will almost surely end in finite time, there is a positive probability of not stopping before any given period. Thus, a finite game with a random endpoint is mathematically equivalent to a game with an infinite horizon (Rasmusen, 1994, Chapter 4). Hence propositions generated from models with an infinite time horizon are testable with data from this experimental design. We selected the length of the initial phase to ensure a sufficient number of observations for the econometric analysis, as discussed below, and to facilitate subject learning. 5 While the theory underlying our design predicts instant convergence to the subgame perfect equilibrium, we neither expect nor observe this in the laboratory. Subjects need time to converge towards an equilibrium, because of learning, signalling, or other disequilibrium effects. Despite the fact that many of the observations from this initial phase are not equilibrium observations, Alger (1987) argues for their inclusion in data analysis, since they provide useful information about subjects’ ultimate tendencies.

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describe a simple model of two vertically related markets, which forms the basis of our experimental design. Section 3 provides a description of our experimental procedure and some summary results from the experiments. Econometric analysis of the data is discussed in Section 4, where we demonstrate the main findings of the paper. Concluding remarks are offered in Section 5.

2. A simple model of vertically related markets We consider the market for an intermediate good, labeled X, which is used as an input for final goods Y and Z. Output decisions in all markets are made simultaneously.6 Market Z is not modeled explicitly; its role enters through the market demand for the upstream product. There are two firms in the each of the X and Y markets. The vertical relation is such that upstream prices determine downstream costs, but downstream sales of Y do not uniquely determine upstream demand because of the other downstream market.7 We assume sellers in Y regard the price of the input as parametric, and sellers of X are not sensitive to the amount of the input they sell to market Y. The output choices made by subjects in the repeated game are discrete, so given that the Y market is small relative to the Z market, the strategic changes made in the Y market can only change X strategies in limited ways. While neglecting the effect of downstream producer actions on upstream price is a simplification, we argue in Appendix A that it does not significantly affect our analysis. The experimental markets we construct below present payoff tables to subjects that allow quantity choices based on the linear inverse demand curves

6

PX 5 150 / 19 2 5(x 1 1 x 2 ) / 76,

(1)

PY 5 (1800 2 15( y 1 1 y 2 )) / 289,

(2)

Bresnahan and Reiss (1985) argue that choices are made sequentially in the automobile market, with manufacturers selecting prices first and retailers selling the cars later. While this may be true, there is no reason to think it is ubiquitous. In the petroleum refining-airline example, neither side of the vertical relation has any greater ability to commit to future actions. In such an environment, the simultaneous choice scenario seems more realistic. 7 This aspect of our model distinguishes it from earlier oligopoly analyses, such as Greenhut and Ohta (1979) and Hamilton and Lee (1986), but it also finesses a difficult theoretical issue. If the upstream market sells to only one market we have a bilateral oligopoly. The equilibrium in such a market requires the resolution of a bargaining problem that is complicated by the possibility that players in each market may form a coalition to bargain against the coalition from the other market. To avoid this troublesome issue, we opted to include an additional downstream market. With this construct, downstream firms know they cannot dictate upstream behavior.

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where PX is the price of X, PY is the price of Y, seller i’s output in the X market is denoted by x i and its output in the Y market is y i , and sellers are labeled 1 and 2. We assume that Y is produced according to a fixed proportions constant returns to scale technology that uses 1 unit of good X for each 10 units of good Y. Hence, the marginal cost of Y is PX / 10. The marginal cost in market X is assumed to be zero. Finally, we imposed a fixed cost of 1300 / 19 for each seller in market X and 18330 / 289 for each seller in market Y.8 Table 1 summarizes outcomes associated with Cournot / Nash (CN) and symmetric joint profit maximizing (JM) behavior. Underlying derivations are contained in appendix A. The left half of the table displays outputs, prices, and profits for the two markets when the structure is vertically linked. The right half shows outcomes when the markets are vertically integrated. Assuming that levels of cooperation are consistent across markets when firms are integrated, we restrict attention to regimes where agents select the Cournot / Nash outputs or joint profit maximizing outputs in each market. One immediate observation is that vertical integration lowers industry profits if firms operate at Cournot / Nash equilibrium outputs before and after merger (from 99.18 to 93.76). This is consistent with recent work that has shown rivals could be better off if they committed to not integrating (Gaudet and Long, 1996; Hamilton and Mqasqas, 1996). However, in a one-shot game with a market structure that is very similar to ours, Gaudet and

Table 1 Model results

Y market behavior

CN

JM

8

Vertically linked X market behavior

Vertically integrated X market behavior

CN

JM

C

JM

x i 540 y i 538.31 Px 52.63 Py 52.25 pxi 536.84 pyi 512.75 x i 540 y i 528.31 Px 52.63 Py 53.29 pxi 536.84 pyi 522.25

x i 530 y i 537.6 Px 53.95 Py 52.34 pxi 550.00 pyi 59.43 x i 530 y i 527.6 Px 53.95 Py 53.38 pxi 550.00 pyi 518.49

x i 541.27 y i 538.20 Px 52.46 Py 52.26 pxi 533.28 pyi 513.60 n.a.

n.a.

x i 531.41 y i 528.19 Px 53.76 Py 53.30 pxi 549.74 pyi 519.06

The level of the fixed cost allowed us to locate the symmetric joint profit maximization and zero profit outcomes away from the corners of a payoff, and to retain a reasonably large separation between these two outcomes and the Cournot / Nash equilibrium, without making the payoff matrix unmanageably large. We wanted these features in order to avoid the appearance of focal points in the payoff tables.

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Long show that ‘it is always profitable for a pair of downstream and upstream firms to vertically integrate unilaterally, no matter what the other pair of firms does.’ Hence widespread integration may be the result of a prisoner’s dilemma.9 At the other extreme, if firms produce at the joint profit maximizing level, vertical integration raises industry profits (from 136.98 to 137.60), while lowering consumer prices as is typical when the double marginalization problem is eliminated. Ultimately, the effect of integration on profits will generally depend on the level of cooperation firms can achieve. Actual behavior in a vertical environment may not conform with theoretical predictions. Bounded rationality may limit subjects’ ability of to calculate best responses to rival behavior. Furthermore, even if one player attempts to infer a rival’s likely actions, he or she is unlikely to be sure of the rival’s rationality. For these reasons, we do not expect to see agents instantly computing, and then selecting outputs corresponding to, subgame-perfect equilibria. Nevertheless, there is good reason to believe that subjects’ play will converge to a Nash equilibrium of the repeated game, given sufficient time (Kalai and Lehrer, 1993; Mason and Phillips, 1996). Limited rationality has implications for the econometric analysis which we will discuss below, but it also underscores the potential that integration has for mitigating uncertainty. Agents in the upstream market may spend a good deal of time learning about their rival’s motivations. As a result there can be large variations in upstream price. Downstream players have no way of inferring the pattern of upstream prices in the linked design (indeed, upstream players are unlikely to have inferred this pattern), and hence they find themselves in a qualitatively uncertain environment. By contrast, vertically integrated firms have a good deal more control over the pattern of upstream price; moreover, by virtue of their multimarket contact one might anticipate more rapid learning, and correspondingly more rapid convergence to equilibrium. If this view is valid, reducing

9

The citation is from page 411; it refers to their later Proposition 4, on page 422. Like our model, Gaudet and Long’s has linear demand, constant costs, and fixed proportions downstream. Their model differs slightly from ours in that there is only one downstream market, and that upstream and downstream outputs are selected sequentially. This is designed to make their downstream firms price takers, which is similar in spirit to our assumption that the Y market is only a small part of the demand for X. Their result that merging is an equilibrium outcome is robust to industry size, and is a dominant strategy so long as there are equal numbers of firms upstream and downstream, with no more than four in each market. Gaudet and Long argue that this result obtains because the lower downstream costs that result from integration increase the degree of competition downstream, which more than offsets the benefits from mitigating the double marginalization effect. Hamilton and Mqasqas (1996) use a model that is similar to ours (although it allows for nonzero conjectural variations), and reach the same conclusions with Cournot conjectures. Finally, we observe that there may be no incentive to integrate if upstream firms can use nonlinear prices, e.g. through the inclusion of franchise fees, to extract downstream surplus (Bonanno and Vickers, 1988; Vickers, 1985; Tirole, 1988).

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uncertainty should result in more rapid convergence to equilibrium in both markets for a vertically integrated regime.

3. Experimental design and data We gather data from four experimental sessions, in which subjects make a series of choices in a repeated game. Two sessions have a linked market design and two sessions have a vertically integrated design. In the vertically linked design 24 subjects chose only an X or Y value, not both, in each period of the game. In the vertically integrated design 26 subjects chose both an X and a Y value in each period of the game. All subjects were recruited from undergraduate economic classes at the University of Wyoming. They reported to a reserved classroom with a personal computer at each seat. At the beginning of each session, instructions were read aloud as subjects followed along on their own copy. These instructions described a payoff table, where earnings are determined by the intersection of a row and column choice. In each period, each person was instructed to choose a row value. In either market X or Y, the row choice made by one player became the column choice for the other player. Questions about the instructions were taken and one practice period was held. In the practice period a monitor randomly chose a column value for all the subjects, who simultaneously chose a row value from a sample payoff table. This sample table was different from the X and Y tables used in the experiment. With both choices, profits from the intersection of a row and the monitor’s column were calculated and recorded by every subject. During the practice period we checked each subject to insure that they understood how to read the payoff tables and how to keep a record of their choices and earnings. Even though all choices were in a quantity-choosing market environment, the instructions were worded to simply tell the subjects they were simultaneously choosing a row value from a table identical to their counterpart. The upstream cost in the Y market was presented as an ‘adjustment factor’ in the form of an additional payoff table. Here the row value was the total X chosen by the upstream agents and the column was the Y subject’s choice. The adjustment table showed that the cost to downstream Y agents was lower the larger was the total X produced. For each market period earnings were written in a fictitious currency called tokens. At the end of the experiment tokens were exchanged for cash at the rate of 1000 tokens5$1.00 in the linked design, and 1000 tokens5$.75 in the integrated design. The personal computer at each of the subjects’ seats were linked to and networked by the University’s VAX cluster. The software automatically formed vertically related markets. In the linked design, subjects were arranged in groups of four, with two placed in an upstream X market and two placed in a downstream Y market. In the integrated design, subjects were arranged in groups of two, with each subject placed in both an X market and a Y market. Subjects were

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anonymously grouped, and grouped individuals were not in proximity to each other. Once everyone had made their choice, the computer screen reported back to each subject his or her choices, earnings, adjustment amount, and balance. Subjects wrote this information on a record sheet, and they could always double check the computer’s calculations from the payoff tables provided to them. Subjects also were informed of their rival’s choices and earnings. Finally, all participants knew that the experiment had a random endpoint, but would last at least 35 periods. Beginning with period 35, the software randomly generated a number between 0 and 100 at the end of the period. The experiment terminated the first time the random number did not exceed 20, so that the probability of continuing to the next period was 4 / 5. The first vertically linked session lasted 40 periods, while the second went for 37 periods. Each of the vertically integrated sessions terminated after period 35. The X and Y payoff tables were based on the inverse demand and cost conditions described above. Choices were rescaled in table X so that subjects were picking values between 1 and 22, with a choice of ‘1’ corresponding to an output of 28, and so on. Choices were rescaled in table Y so that subjects chose values between 1 and 27, with a choice of ‘1’ corresponding to an output of 25, and so on. Given this rescaling, and rounding to the nearest integer, the Cournot / Nash equilibrium choices are 13 in the payoff table for the linked X market and 14 for the linked Y market. The Cournot / Nash equilibrium choices in the integrated design are 14 for each market. In the linked design, the joint profit maximizing choice for the X market is 3. Assuming the X market price is set at the associated (monopoly) level, the joint profit maximizing choice for the Y market is 4. With vertical integration, the joint profit maximizing choices are 6 in the X market payoff table and 4 in the Y market. These laboratory markets do not show a great deal of movement in the equilibrium outputs after integration. The Y market Cournot / Nash and joint profit maximizing choices do not change at all and the Y market outputs differ by only one or two units. However, our focus is not on these designated equilibria, but on the choices, and therefore the level of cooperation, at which rivals eventually settle in the linked and integrated market structures. The payoff tables are designed to provide subjects with about ten discrete choice units between the Cournot / Nash and monopoly output levels. Summary statistics from our sessions are contained in Table 2. Here we present information on quantities and profits for each of the two markets under each of the two designs. To this end we tabulate average outputs based on the first 35 periods, and then for periods 26 to 35. We also include average industry profits for these two samples. Sample standard deviations for these averages are given in parentheses. Finally, to facilitate comparisons with theoretical predictions, we include information on subject pair’s choices and profits under the Cournot / Nash and joint profit maximum outcomes. These latter two columns are based on the predicted individual behavior in the CN / CN and JM / JM cells, in Table 1. Since

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Table 2 Summary statistics for paired behavior in vertically linked and vertically integrated markets

Vertically linked design

Vertically integrated design

Average X market output Average Y market output Average X market profits Average Y market profits Average total profits Average X market output Average Y market output Average X market profits Average Y market profits Average total profit

Periods 1–35

Periods 26–35

Cournot / Nash

Joint profit maximum

74.395 (0.585) 72.433 (0.566) 81.669 (1.220) 19.894 (1.032) 101.563 (1.389) 79.139 (0.357) 75.215 (0.396) 72.097 (0.941) 17.411 (0.741) 89.507 (1.442)

73.367 (1.163) 74.450 (0.899) 83.003 (2.202) 16.868 (1.897) 99.872 (2.339) 80.885 (0.734) 77.723 (0.745) 66.745 (2.023) 13.382 (1.148) 80.1177 (3.073)

80

60

76

54

73.6

100.0

25.5

37.0

99.1

137.0

82

62

76

56

66.6

99.4

27.2

38.2

93.8

137.6

subjects chose integers, and earned payoffs reported in tenths of cents, we round the individual outputs in Table 1 to the nearest integer, and profits to the nearest tenth of a cent, and then multiply by 2 to obtain predictions for the subject pair. These values provide some useful insights into the impact of integration. First, we note that average choices are noticeably smaller than the Cournot / Nash level in the linked markets, though this departure is more pronounced for the X market than for the Y market. Second, choices are larger in the integrated design than in the linked design, by an amount exceeding theoretical predictions from both the Cournot / Nash and joint profit maximizing models. This is true for both markets. The impact of the mergers is evidently more important in the X market than in the Y market, both numerically and statistically. Finally, average industry profits are dramatically smaller in the integrated design than in the linked design. The difference in industry profits, 12.056 over the first thirty-five periods, and 19.755 over the last ten periods, is markedly larger than the difference of 5.3 that is predicted by the Cournot / Nash model. While all of these effects appear large in comparison to the sample standard deviations, caution must be exercised here. The calculations in Table 2 implicitly treat each observation from each subject as a randomly generated, independent observation. By contrast, subject choices are likely to be generated by a more complex process, for example, a vector autoregressive process. It is well known

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that ignoring such time-dependency leads to biased estimates of the standard deviation, often under-estimating the true value. Since this would overstate the significance of our results we prefer to withhold judgment until we conduct an econometric analysis that takes this complexity into account. Before turning to such an analysis, we first summarize our data graphically. Fig. 1 illustrates the average choice for a subject pair in the integrated and linked X markets period by period. The solid line (XINT) shows average choices in the X integrated markets, and the dashed line (XLINK) is average choice behavior in the X linked market. We also include in the figure the Cournot equilibrium choice outputs (rounded to the nearest integer), which are the dashed line labeled xvin in the integrated design and the dotted line labeled xvln in the linked design. The horizontal axis in this figure is set at 60, which corresponds to the joint profit maximizing output in the linked design. It is apparent that subjects behave very differently in the X market between the two designs. Though average behavior is fairly similar in the early periods, the two plots diverge after period 15. Outputs are consistently lower than the Cournot level in the linked design throughout the session, while they trend upward over time in the integrated design. Fig. 2 reports average Y market outputs. Once again, the solid line (YINT) corresponds to the integrated structure and the dashed line (YLINK) to the linked structure. The Cournot equilibrium output (at the nearest integer choice) is indicated by the dotted line ynash; recall that Cournot outputs are the same in each treatment after rounding. The horizontal axis in this figure is set at 54, the joint

Fig. 1. Comparison of X market choices. Integrated vs. linked designs.

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Fig. 2. Comparison of Y market choices. Integrated vs. linked designs.

profit maximizing market for the linked design. In both designs, average Y market outputs start off well below the Cournot level, and rise over time to levels around the Cournot equilibrium. In the integrated design, average outputs in both markets tend to increase over the course of the experiment. Since an increase in X market output lowers downstream costs it might naturally cause average Y market outputs to increase. To further explore this connection, we graph average upstream output (the solid line labeled AVEX) and average downstream output (the dashed line labeled AVEY) in the vertically integrated design in Fig. 3. These plots display a very similar pattern, though it appears that changes in average X market outputs often precede changes in average Y market outputs.10

10

Formally, variable A is said to ‘Granger cause’ variable B if past values of A are valuable in explaining B (Jacobs et al., 1979). In the context of our vertically integrated design, X market outputs Granger cause Y market outputs if past X values are useful in explaining current Y values. The alternative hypothesis, that past X values are not useful in predicting current Y values, implies a parameter restriction in the context of Eq. (3) below. Thus, the hypothesis that X Granger causes Y is tested by asking if this parameter restriction is valid. In a longer version of this paper, we provide a formal statistical test of this hypothesis, and show that X choices Granger cause Y choices, but not conversely.

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Fig. 3. Comparison of integrated choices. X market vs. Y market.

4. Econometric analysis There are two hypotheses we wish to test. The first hypothesis is H1: average subject choices in the integrated and linked designs do not differ. The two-sided alternative to this hypothesis is that choices in the integrated design differ from choices in the linked design. If integration facilitates collusion, we would expect choices to be smaller in the former than the latter; if integration impedes collusion, the reverse is true. Results from tests designed to test this hypothesis will have obvious implications for differences in prices and profits between the market structures. The second hypothesis is H2: there is no significant difference in the time it takes subjects to converge to equilibrium in the integrated and linked designs. The two-sided alternative to this hypothesis is that convergence times differ between the two designs. Here we are addressing the stability of outcomes between the market types. We analyze the first hypothesis by regarding our database as a pooled cross-

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section / times-series sample, where the dependent variable is paired subject output. To analyze the second hypothesis, we conduct a time-to-failure analysis. Here the dependent variable is the time it takes a subject pair to converge to an equilibrium. For all tests the data set has at least 35 observations on 38 markets, where we interpret a market as a subject pair choosing either X or Y.11 In the linked markets subjects participate in only one market, while in the vertically integrated designs every subject makes choices in two markets. We refer below to ‘group 1’ as the set of subject pairs in the integrated experiments. Here there are 13 subject pairs with each pair operating in both the X and Y markets for a total of 26 markets. We label ‘group 2’ as the set of subject pairs in the linked experiments; there are 12 pairs in 12 markets.

4.1. Paired choice as the dependent variable The structural econometric model we estimate in order to test the first hypothesis is drawn from our earlier work (Mason et al., 1992; Phillips and Mason, 1992, 1996). We assume that each subject’s choice is dependent on his or her prediction of a rival’s imminent action, and that the game’s history is a key determinant of a subject’s prediction of the rival’s upcoming action. Subjects operating in the linked downstream market would also presumably try to predict the upcoming market choice in the upstream market. In both cases, predictions of upcoming choices would plausibly be based at least on the immediately preceding choice. In our model we allow for effects from the two preceding periods to influence current choices.12 We therefore posit the following relations for paired outputs: XY XX X Xit 5 b nX 1 m nXY Yit 21 1 m XX n Xit 21 1 u n Yit 22 1 u n Xit 22 1 ´ it ,

(3)

YY YX Y Yit 5 b nY 1 mnYY Yit 21 1 mYX n Xit 21 1 u n Yit 22 1 u n Xit22 1 ´it ,

(4)

where Xis (respectively, Yis ) represents the X (respectively, Y) market output chosen by subject pair i for period s5t, t21 or t22; n51 if pair i is in group 1 (integrated), and n52 if pair i is in group 2 (linked). The parameters mn jh measure 11 Our analyses make full use of the database. While many subjects appear to not reach equilibrium, they all are converging to a stable choice pattern. Our econometric model is designed to allow us to infer equilibrium behavior from the pattern of disequilibrium choices. This allows us to avoid the pitfalls associated with focusing on a limited number of periods (Alger, 1987). 12 While our past studies identified the second order autoregressive model as providing the best explanatory power, there are good reasons to expect ex ante that more than one lag ought to matter. These include subjects’ attempts at signalling collusive desires (Shapiro, 1980) and learning about the rival’s rationality (Kalai and Lehrer, 1993; Mason and Phillips, 1996). Cason and Friedman (1995) model subject behavior with a partial adjustment model, and also find past actions have a significant influence upon current behavior. One can then regard the second order lagged model as providing a parsimonious description of the evolutionary process.

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the impact of a small change in period t21 output in market h upon period t output in market j, for j, h[hX, Yj, n51 or 2. Similarly, the parameters un jh measure the impact of a small change in period t22 output in market h upon period t output in market j, for j, h[hX, Yj, n51 or 2. Notice that the various parameters are assumed to be the same for all subject pairs in a given design. Finally, we assume the disturbance term ´it k is serially uncorrelated.13 These relations are expected to hold without qualification for subjects in the integrated design. However, there is no reason to expect subjects in the upstream market of the linked experiments to be influenced by downstream market subject behavior, since downstream behavior has no effect on upstream profits. CorreYX spondingly, we impose the parameter restrictions mYX 2 5u 2 50 when estimating this system for the linked design. The first hypothesis has to do with the ultimate equilibrium values for the upstream and downstream markets; let us call these values X e1 and Y e1 for the integrated design and X e2 and Y e2 for the linked design. In constructing estimates of these values, we take the perspective that subject choices converge towards the true equilibrium over the course of the experimental session. Starting from Eqs. (3) and (4), estimates of the ultimate equilibrium values can be derived in terms of the parameters in the system above by substituting X en for Xis and Y en for Yis , s5t, t21, t22, assuming ´it X (Fomby et al., 1988). Solving the resultant matrix equations for X 1e and Y 1e , we obtain YY X XY XY Y X en 5 [(1 2 mYY n 2 u n )b n 1 ( m n 1 u n )b n ] /D;

(5)

Y ne 5 [( mnYX 1 u nYX )b nX 1 (1 2 m nXX 2 u nXX )b nY ] /D;

(6)

YY XX XX XY XY YX YX where D5[(12 mYY n 2u n )(12 m n 2u n )2( m n 1u n )( mn 1u n ) and n ine e dexes the group as 1 or 2. We note that the formulae for X n and Y n are continuous functions of the b s, m s, and u s so long as D ±0. It follows from Slutsky’s theorem 14 that X ne and Y ne can be consistently estimated by inserting consistent estimates of the b s, m s, and u s into Eqs. (5) and (6).

13 Because our regression model includes lagged dependent variables, the traditional Durbin–Watson statistic cannot be used to test for the presence of serial correlation (Fomby et al., 1988). One can, however, use Durbin’s h-statistic. Under the null hypothesis that the disturbance term in our regression model is not serially correlated, Durbin’s h-statistic is asymptotically distributed as a standard Normal random variable, and so one may infer significance of the test statistic by applying a t-test. In all the regressions reported below in Table 3, the h-statistic is small. Thus, we cannot reject the hypothesis that the ´it k are serially uncorrelated. 14 Slutsky’s theorem states that a continuous function f(u ) of a vector of parameters, u, can be consistently estimated by evaluating the function at a vector of consistent estimates of the parameters; see Fomby et al. (1988), p. 58, for further discussion. The variance of f(u ) can then be consistently estimated by the quadratic form g(u )9V(u )g(u ), where g(u ) 5 ≠f(u ) / ≠u and V(u ) is the associated maximum likelihood estimator of the covariance matrix for u (Fomby, Hill and Johnson, Corollary 4.2.2).

486

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To obtain estimates of the various parameters, and then test these hypotheses, we pooled the 26 paired choices for each period in the integrated experiments, and the 12 paired choices for each period in the linked sessions. In each case, we estimated the system of equations defined by (3) and (4) for all subject pairs in a given design, using ordinary least squares. The resultant parameter estimates are reported in Table 3. Using the estimates of X en and Y en allows us to estimate p eXn e and p Yn , the equilibrium profits in the X and Y markets under the two structures. Estimated equilibrium market outputs are numerically and statistically larger in the integrated design markets than in the linked design. This difference is Table 3 Regression results–paired choices Parameter

mnYX mn XX unYX un XX bnY mnYY mnYX QnYY un XY X en Y en

p eXn p eYn Total p R-squared Durbin’s h-statistics: a b

Integrated design point estimate 69.512 a (1.789) 0.073 (0.063) 0.080 (.057) 0.324 a (0.063) 20.081 (0.056) 63.245 a (1.789) 20.141 a (0.063) 0.309 a (0.057) 0.103 (0.063) 0.175 a (0.056) 79.686 b (0.625) 75.656 (0.732) 74.504 (1.619) 27.212 (1.608) 101.716 (2.282) 0.922 0.1997 (X), 1.5494 (Y)

Significant at better than 1% level. Significantly smaller than Cournot at better than 1% level.

Linked design point estimate 59.495 a (1.249) 0.377 a (0.059) – 0.322 a (0.060) – 56.376 a (2.174) 20.079 (0.060) 0.439 a (0.074) 0.026 (0.061) 0.288 a (0.074) 72.240 b (1.623) 75.157 (1.816) 90.144 (2.614) 24.461 (4.078) 114.605 (4.844) 0.960 20.5507 (X), 1.3265 (Y)

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statistically significant for the upstream (X) market, though not for the downstream (Y) market. To test the joint hypothesis that both equilibrium outputs are unaffected by integration, i.e., H0 : X 1e 5X 2e and Y 1e 5Y 2e , we use a likelihood ratio test. The resultant test statistic is distributed as a chi-squared variate with 2 degrees of freedom under the null hypothesis (Fomby et al., 1988). In this application the value of the test statistic is 18.424, which is significant at better than the 1% level. Thus, we reject the null hypothesis, and conclude that subject behavior in the linked and integrated designs is statistically different. Moreover, the increased X market output, 7.446, is large compared to the theoretically anticipated changes. Referring to Table 1, integration would raise upstream output by 2.82 units if firms were perfectly collusive, and by a smaller amount if they were not. One may calculate the standard error for X e1 2X e2 as 1.7392 so that the observed change produces a t-statistic of 2.56 when compared against the largest theoretically anticipated change. In light of the observation that steady-state outputs are higher in the integrated markets, total surplus is larger in our integrated design than in our linked design. At the estimated equilibrium quantities, total surplus rises from 717.81 in the linked design to 740.89 in the integrated design, an increase of 3.2%. Similarly, consumer surplus increases by 12%, from 318.25 in the linked to 357.42 in the integrated designs. At the same time, equilibrium industry profits are markedly smaller in the integrated markets than in the linked markets; this reduction in profits is both numerically and statistically significant. As we noted above, it is generally profitable for an upstream and downstream firm to merge in the Cournot model, even though industry profits are smaller in an integrated structure than in a linked structure; there is a prisoners’ dilemma aspect to vertical integration here. But the reduction in profits we observe is large compared to the reduction implied by the Cournot model.15

4.2. Time as a dependent variable If uncertainty regarding upstream prices is influencing behavior of downstream agents in nonintegrated markets, there is reason to believe that these downstream markets will be slower to converge to equilibrium than their counterparts in the integrated designs. It also is possible that subjects in integrated market structures can transfer learning across markets and reach stable choice patterns sooner. Thus integrated market structures may in general converge more quickly to equilibrium.

15

The reduction in industry profits is 12.889, which represents 11.25% of industry profits for vertically linked markets. It is also more than double the reduction of 5.3 implied by the Cournot model. The standard error for the difference between linked and integrated steady state industry profits is 5.354 (5[2.282214.844 2 ] 1 / 2 ), yielding a t-statistic of 2.407.

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In this subsection, we analyze trends towards equilibrium under the two market structures. Our approach to investigating speed of convergence is to compare the length of time it takes subject pairs to converge to within a certain proximity of their ultimate equilibrium across treatments. To put this concept into operation, we first m define Q M t as the largest choice from period t onward, and Q t as the smallest M choice from period t onward. Formally, Q t 5maxhQ s s>tj and Q m t 5minhQ s s> tj. Next, we let Dkt denote the range over which subject pair k’s choices vary from period t onward, i.e., Dkt 5Q tM 2Q tm . Then we say that a subject pair’s choices have nearly converged by period t if Dkt <4.16 The hypothesis we with to test is that there is no difference between the time it takes subjects in markets to nearly converge. The length of time it takes a certain event to first occur is typically referred to as a ‘lifetime’ or a ‘survival time’ (Lawless, 1990). In our application, a subject pair’s lifetime is the earliest choice period by which their choices nearly converge, unless they fail to nearly converge by the end of the experiment. In this latter case their lifetime has been censored, and for accounting purposes is entered as the final period of the experiment. We do not know the true period when such a subject pair would have nearly converged; rather, we only know that the true period is at least as large as the terminal period for their session. Table 4 summarizes the relevant information for our lifetime analysis. Column one reports the identify of the subject pair. With 26 subjects participating in the integrated design there were 13 pairs, with each pair choosing values in both X and Y. Thus, the X market output from subject pair ‘1’ determined the input costs for subject pair ‘1’ in the Y market, with the two subjects associated with subject pair ‘1’ in X being the same subjects in pair ‘1’ in Y. As each of the 24 subjects in the linked design was assigned to only one market, with 12 subjects in each of X and Y, there are 6 pairs in X and 6 pairs in Y. The X market output from subject pair ‘14’ determined the input cost for subject pair ‘14’ in the Y market, but in this treatment the subjects in the X pair are not the same individuals as the subjects in the Y pair. Column two indicates the treatment in which the session the subject pair participated. Column three gives the subject pair’s lifetime. Column four reports the period the experimental session ended for each subject pair. Column five indicates whether the pair failed to nearly converge by the end of the experimental session.

16 Of course, the use of 4 as a wedge between the largest and smallest choices is somewhat arbitrary. We selected this number because a deviation of 1 unit by an individual from an equilibrium choice was unlikely to greatly reduce his or her payoffs; correspondingly it seemed plausible that paired choices could be either 2 units larger or smaller than an equilibrium in any period, without reflecting a significant departure from a potential equilibrium. Even so, the point is that subjects are more likely to be ‘close’ to an equilibrium by any specified period in the integrated design than in the linked design, however one wishes to define closeness.

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Table 4 Data for lifetime analysis Market number / subject pair X Market 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Y Market 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Design

Lifetime

Terminal period

Censored?

Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Linked Linked Linked Linked Linked Linked

24 34 35 33 35 31 34 35 35 35 30 35 30 39 15 35 36 36 37

35 35 35 35 35 35 35 35 35 35 35 35 35 40 40 40 37 37 37

No No Yes No Yes No No Yes Yes Yes No Yes No No No No No No Yes

Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Integrated Linked Linked Linked Linked Linked Linked

35 33 35 34 34 30 34 35 35 35 34 35 31 40 37 37 37 37 37

35 35 35 35 35 35 35 35 35 35 35 35 35 40 40 40 37 37 37

No No Yes No Yes No No Yes Yes Yes No Yes No No No No No No Yes

Restricting attention to subject pairs whose lifetimes were not censored, we obtain an estimated lifetime of 32.2 in the linked design and 30.9 in the integrated design for the X market. The corresponding values for the Y market are 37 for the linked design and 32.9 for the integrated design. In both markets, we observe that

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Table 5 Duration analysis—Tobit regression model results Parameter

Estimated coefficient for X market

Estimated coefficient for Y market

b0

35.758 a (2.453) 21.045 (4.137)

34.640 a (0.7829) 4.615 a (1.367)

b1

Notes: standard errors in parentheses;

a

Significant at better than 1% level.

the average lifetime is smaller in the integrated design. It is also worth noting that slightly more than half of the pairs in the integrated design nearly converged before the end of the session (7 of 13 pairs). In the linked design, most subject pairs in the X market nearly converged (5 of 6 pairs) but relatively few subject pairs nearly converged in the Y market (2 of 6 pairs). It is also true that the linked sessions lasted longer than the integrated sessions, and of those subject pairs that nearly converged in the linked sessions, all but one did so after period 35. To assess the statistical importance of potential differences between the two designs, we consider the regression model fi 5 b 0 1 b 1 LINK i 1 ni ,

(7)

where fi is the observed lifetime for subject pair i, LINK i is a dummy variable taking the value 1 if subject pair i was in the linked sessions, and 0 otherwise, and ni is a disturbance term. In this context, the hypothesis of interest is b 1 50. Analysis of this regression equation is complicated by the fact that we do not observe the true lifetime for several of our observations. What we observe instead is the period at which the lifetime is censored. Correspondingly, our problem is one with a limited dependent variable; estimation of the parameters in Eq. (7) must take into account whether each observation is censored or not, and the period at which censoring occurs. One well known approach to such a problem is to use the Tobit regression model, which assumes the disturbance term in Eq. (7) follows a truncated normal distribution (see Greene, 1990, pp. 727–733). We report the results of the Tobit analysis for each of markets X and Y in Table 5.17 There are two key observations from these regressions. First, the estimated value of b 1 , the 17

We also considered two variations of Eq. (7). In the first variation, n follows an extreme value distribution, which is equivalent to assuming that lifetimes follow a Weibull distribution (Lawless, 1990, pp. 17–19 and 298–306). In the second variation, we assumed that lifetimes are lognormally distributed. The regression coefficients from these variations were quite similar, and corroborate the qualitative results reported in the text. In particular, the coefficient on LINK was significant and positive for the Y market (but not the X market) in both variations. One can also test the hypothesis that the distribution of lifetimes is identical for the two designs by nonparametric means. Here, the hypothesis is tested using a Wilcoxon rank test; under the null hypothesis the test statistic is distributed as a chi-squared variate with one degree of freedom (Lawless, 1990, pp. 423–425). Application of this test also corroborated the results reported in the text.

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coefficient on LINK, is not statistically important for the X market. Second, the estimate of b 1 for the Y market is significant and positive. We infer that subjects in the integrated Y markets nearly converge sooner than in the linked Y markets. On the other hand, convergence rates of X market choices in the linked and integrated designs do not differ significantly. We believe the change in the convergence pattern of the Y market comes from the reduced upstream price uncertainty in the integrated design.

5. Conclusion Our experimental analysis of vertically related markets yields a variety of results, some of which are unexpected. Subjects chose substantially larger outputs in upstream markets when placed in a vertically integrated structure. This is consistent with theory since integration allows firms to eliminate double marginalization. However, the increase in upstream output exceeds the theoretically anticipated change, by an amount that is statistically significant. At the same time, industry profits fell under integration. This is consistent with the noncooperative (Cournot) model, but again the change exceeds the theoretically predicted effect. Despite these lower profits, total surplus was larger in the vertically integrated markets, because of the marked increase in consumer surplus. We also find that downstream markets tend to stabilize more quickly in the integrated design than in the linked design. This may be the result of reduced uncertainty concerning upstream outputs, and the attendant reduction of uncertainty with respect to downstream costs. To the extent that agents are risk averse, this reduction in uncertainty provides an additional benefit to integration, which reinforces the increase in total surplus. Altogether, then, it appears that vertical integration had a procompetitive effect in our experimental markets. For roughly three decades following the Alcoa decision (United States v. Aluminum Co. of America, 148 F.2d 416 (2d Cir.1945), public policy was not sympathetic to vertical integration.18 More recently, antitrust authorities have been less sceptical of mergers. Indeed, the 1982 and 1992 revisions of the Department of Justice’s merger guidelines created a policy environment in which mergers are less likely to be challenged, unless there are obvious anticompetitive consequences. In particular, vertical mergers are subject to less scrutiny than in earlier days. Despite this change in policy perspective, there are still some concerns that

18

Manifestations of this philosophy in case law include U.S. v. E. I. duPont de Nemours and Co. (1957, 353 U.S. 586 ), Brown Shoe Co. v. U.S. (1962, 370 U.S. 294 ), and Ford Motor Co. v. U.S. (1972, 405 U.S. 562 ); see Williamson (1987) for further discussion. Public policy in the U.K. also appears to treat mergers more harshly than other forms of vertical restraints (Waterson, 1993).

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vertical mergers may facilitate collusion.19 This paper demonstrates that integration under highly concentrated conditions need not lead to higher prices, and as a consequence can benefit the consumer.

Acknowledgements We are grateful to Steve Polasky and to seminar participants at the Australian National University, Oregon State University, the University of Canterbury, and the University of Waikato for their remarks on earlier versions of this paper. Extensive comments by Robert Masson greatly improved the manuscript. This research is based on work supported by the National Science Foundation through the EPSCOR / WISE program under grant [RII-8610680. Funding was also received through the College of Business, University of Wyoming. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not reflect the views of these funding sources.

Appendix A

Derivation of equilibria In the following discussion, we let the inverse market demand curves be PX 5 a 2 bQ X ,

(A.1)

PY 5 a 2 b Q Y ,

(A.2)

for markets X and Y, respectively. Let f represent the number of X units required

19

This is evidenced by recent public remarks by Department of Justice officials:

‘ . . . under certain circumstances, a vertical merger may facilitate coordinated interaction with the merging parties’ rivals’ (Steven C. Sunshine, ‘Antitrust Policy Towards Telecommunications Alliances,’ address before the American Enterprise Institute, Washington D.C., 7 July 1994); ‘ . . . for a vertical merger to increase the chances of anticompetitive coordination, the upstream and downstream markets must be susceptible to the exercise of market power’ (Charles E. Biggio, ‘Merger Enforcement at the Antitrust Division,’ address before the Antitrust Law Committee, Chicago, Illinois, 15 May 1996). The head of the Bureau of Competition at the Federal Trade Commission expresses similar sentiments (Baker, 1996).

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to produce one unit of Y so that marginal cost is f PX in Y; marginal cost is zero in X. In the vertically linked structure the Cournot equilibrium output is a / 3b for each firm in market X, and the symmetric joint profit maximizing choice is a / 4b. Similarly, given an input price PX , the Cournot equilibrium output in market Y is (a 2 f PX ) / 3b ; the symmetric joint profit maximizing choice is (a 2 f PX ) / 4b. Since the Cournot equilibrium price in X is a / 3 while the joint profit maximizing price is a / 2, the Cournot output for each firm in the Y market is (3a 2 f a) / 9b if X market firms play Cournot and (2a 2 f a) / 6b if X market firms select the joint profit maximizing output. Similarly, the joint profit maximizing outputs for Y firms are (3a 2 f a) / 12b if X market firms play Cournot and (2a 2 f a) / 8b if X market firms select the joint profit maximizing output. Identifying the corresponding outcomes under vertical integration is a bit more complex. We first consider the Cournot equilibrium. One way to model behavior is to have firms choose an output for Y based on a transfer price equal to the marginal cost of X, and to also produce an amount of X to be sold to market Z. In light of the link between market demands in Y and Z and input demand for X, there are only two independent decisions (e.g., outputs in Z and Y or outputs in X and Y). We prefer to describe decisions in the two original markets, so as to keep the expositional simpler and to facilitate comparisons between the two market structures. Each firm i solves max[a 2 b(x i 1 x j )](x i 2 f y i ) 1 [a 2 b ( y i 1 y j )]y i , x i, y i

where the subscript j refers to the rival firm. The first order conditions for this problem yield 2x i 1 x j 5 a /b 1 f y i ;

(A.3)

2y i 1 y j 5 (a 2 f [a 2 b(x i 1 x j )] /b.

(A.4)

Since firm j’s optimality conditions are identical, we focus on the symmetric equilibrium. Let x I (respectively, y I ) represent the X (respectively, Y) market Cournot equilibrium outputs under vertical integration. Substituting x I for x i and x j and y I for y i and y j , and combining Eqs. (A.1) and (A.2), we obtain x I 5 (9ab 1 abf 2 1 3a bf ) / [(9b 1 2bf 2 )3b];

(A.5)

y I 5 (3a 2 f a) / [9b 1 2bf 2 ].

(A.6)

Next, we determine the symmetric joint profit maximizing outputs. These may be derived by setting x i 5x j 5x and y i 5y j 5y in the maximization problem above. The solution to this problem gives outputs x j mI and y j mI , which satisfy the first order conditions x j mI 5 a / 4b 1 f y j mI / 2;

(A.7)

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y j mI 5 (a 2 f [a 2 2bx j mI ]) / 4b.

(A.8)

Combining these equations yields x j mI 5 [a(2b 2 bf 2 ) 1 a bf ] / [2b(4b 2 bf 2 )]; y j mI 5 [a 2 f (a / 2)] / [4b 2 bf 2 )]

(A.9) (A.10)

Finally, the input demand from market Z can be inferred from Eqs. (1) and (2), along with the parameter f. Write this as Q Z 5 A2BPX . Since the Cournot equilibrium output levels in market Y are (a 2 f PX ) / 3b for each firm and each unit of Y requires f units of X, the derived demand from the downstream market is 2f (a 2 f PX ) / 3b. Combining these two sources of input demand, we obtain the market demand for X in the range of PX where both markets Y and Z demand positive amounts of X. This gives Q X 5 A 1 2af / 3b 2 (B 1 2f 2 / 3b )PX , or PX 5 (3Ab 1 2af ) /(3b B 1 2f 2 ) 2 [3b /(3b B 1 2f 2 )]Q X . Thus, we require a5(3Ab 12af ) /(3b B12f 2 ) and b5[3b /(3b B12f 2 )] in Eq. (A.1), or A5a /b22af / 3b and B51 /b22f 2 / 3b. Alternatively, we could regard the derived demand for markets Y and Z as given, and then determine the demand parameters for market X. Of course, both these approaches assume a specific form of behavior in the Y market, namely Cournot equilibrium choices. The nature of demand for X would be different if firms in market Y colluded, maximizing their joint profits. While there is a difference between the implied upstream market demand curve at these two extremes, the associated Cournot and collusive choices in the X market are sufficiently close under the two alternative Y market behaviors that they round to the same integer. As we use integer values in our experimental design, this means the experimental design does not depend on a specific behavioral model in market Y, even though the literal values for the underlying demand parameters in market Z (or, equivalently, market X) do depend on Y market behavior.

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