TESIS DE GRADO MAGISTER EN ECONOMIA. González Lira, Andrés

Transcription

1 PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE I N S T I T U T O D E E C O N O M I A MAGISTER EN ECONOMIA TESIS DE GRADO MAGISTER EN ECONOMIA González Lira, Andrés Diciembre, 2013

2 PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE I N S T I T U T O D E E C O N O M I A MAGISTER EN ECONOMIA Collusion, Cyclical Demand and Capacity Constraints: Evidence from the Chicken Industry in Chile Andrés González Lira Comisión Eugenio Bobenrieth Juan Pablo Montero José Miguel Sánchez Santiago, Diciembre de 2013

3 Collusion, Cyclical Demand and Capacity Constraints: Evidence from the Chicken Industry in Chile Andrés González Lira December 16, 2013 Abstract It is well known that cartels need to manipulate margins over the business cycle in order to enforce collusion amongst impatient firms, and that the specific evolution of these margins depends on the existence of capacity constraints. However, the literature has been largely silent about collusive pricing in presence of softer capacity constraints. We find that under a lax capacity constraint, the evolution of margins over the cycle depends on the degree of impatience of cartel s members; margins increase during booms when firms are patient and decrease when firms are impatient. This theoretical finding has relevant implications for empirical tests of collusion based on the observation of margins over the business cycle, which we discuss using an innovative test for collusion within the Chicken Industry in Chile. Department of Economics, Pontificia Universidad Católica de Chile. agonzal6@uc.cl. I would like to thank Juan Pablo Montero, Eugenio Bobenrieth and Jose Miguel Sanchez for their time and insightful comments. I would also like to express thanks for comments from seminar participants in IE-PUC and Mini-TOI Workshop. Suggestions from Raimundo Atal, Andrés Osorio, Jose Llodrá and Rodrigo Garcia in the editing process were very helpful. 1

4 1 Introduction In 2011, the Antitrust Authority of Chile presented a complaint against the nation s three main Chicken producers, 1 arguing that they coordinated production quantities since The case was considered one of the most important Antitrust cases in Chile due to the size of the alleged firms and the importance of chicken meat in Chilean diet. We utilize the fact that chicken meat sales move cyclically over a year to develop a theoretical framework for understanding how a cartel should behave in such circumstances, and we propose a simple and innovative empirical test to evaluate dynamic pricing over the business cycle. Economic theory is rich on collusive behavior with demand fluctuations. Rotemberg & Saloner (1986) find that cartels exposed to anticipated i.i.d. shocks will be induced to undertake countercyclical pricing policies - during booms cartels undercut margins in order to make deviations less profitable. This setting was extended by Haltiwanger & Harrington (1991), who introduce deterministic demand cycles instead of i.i.d. shocks and find that cartels, to sustain collusion, should avoid deviations mainly at maxiumum demand and just thereafter. Margins, therefore, should increase as peak demand approaches. 2 These theoretical insights provided fertile ground for empirical studies seeking to uncover collusive behavior. Borenstein & Sephard (1996) test the pricing behavior of the gasoline stations in the United States of America, finding that for deterministic demand cycles, margins increase either when the peak is approaching or when expected cost decreases. Rosenbaum & Sukharomana (2001) also study this behavior within the cement industry in Portland. They decompose demand fluctuations capturing booms and busts, and find that pricing policies differ during each period. 3 Based on the fact that the chicken industry in Chile presents a clear cycle, we test collusion using the hypothesis of Haltiwanger & Harrington (1991), and based on a theoretical model. We summarize the optimal pricing path during the business cycle for this specific (alleged) cartel. The fact that chicken demand has one large peak in a narrow time-frame (see Figure 1), encourages firms to deviate on and just after the peak, 4 Optimal collusive pricing (the price path that minimizes incentives for deviation) should show reduced margins in these periods, therefore margins before and after the peak should differ even as demand levels are equal. This theoretical effect suggests a simple test that compares margins before and after the peak. This method, new to this area, has important advantages over other previously used tests as it imposes less structure for expectations and trends of the cycle. 1 In size order: Agrosuper, Ariztía and Don Pollo. 2 The Present Value of Collusive Profits for equal demand levels change depending on the timing of the peak. 3 See also Rosenbaum & Yang (1998) and Gallet & Schroeter (1995). 4 Especially if the peak is considerably large. 2

5 Figure 1: Whole Chicken Sales ( ) Source: Agrosuper The empirical studies that support the Haltiwanger & Harrington (1991) hypothesis 5 find that margins increase when firms expect a high demand period in the near future. They impose non-trivial assumptions about how firms generate expectations for the future. Borenstein & Sephard (1996) find that margins from gasoline sales increase as the peak approaches (booms), assuming that agents expectations are generated by a VAR model. Rosenbaum & Sukharomana (2001) separate the cyclical trend from demand fluctuations using a Hodrick & Prescott (1997) filter, which is far from deterministic ex-ante. 6 Using demand fluctuations for whole chicken, 7 we propose a test for collusion based on a theoretical model that summarizes optimal pricing for this alleged cartel, and then compares margins before and after the peak. In particular, our results benefit from the considerable size of the demand peak shown in Figure 1. 8 The productive process of this industry depends mainly on the capacity of processing machines and breeding sheds. This industry anomaly could yield important insights regarding optimal collusive behavior due to the fact that the ability to deviate and produce more than the collusive quantity during the peak demand period is constrained, as are the 5 Which are based on forward looking behavior. 6 Expectations of future demand fluctuations are key to understand incentives in this context. 7 The Whole Chicken represents almost 60% of the Aggregate Sales and its cycle is very clear; sales between January to November are broadly at, but December shows a considerable peak, increasing 150% the weekly sales. 8 Notice that Sales of Christmas are 150% on average than a random week. The peak studied by Borenstein & Sephard (1996) is 30% more than the bottom of the cycle. Clearly the fact that the peak is bigger set more incentives to deviate and manipulate the pricing over the cycle more necessary. 3

6 punishments for deviations. None of the presented empirical papers deeply considers the production technology as an important factor in understanding the applicability of the test. The literature about collusion and capacity constraints is broad; Staiger & Wolack (1992) study the effect of capacity constraints in symmetric cartels, and find that the final effect is ambiguous: capacity constraints reduce incentives to deviate, as well as the ability of the cartel to retaliate against the cheat, so the final effect for collusion depends on the level of installed capacity. Fabra (2006) studies the effect of capacity constraints in an environment of cyclical demand, merging the analysis of Haltiwanger & Harrington (1991) and Satiger & Wolack (1992) assuming exogenous installed productive capacity. Fabra finds that capacity constraints affect the cartel stability during the cycle, and that the strength and timing of this affect depends on the restrictiveness of the capacity level. For a relaxed capacity level, the critical moment to sustain collusion is the peak and just after it. 9 However, for restrictive capacity constraints the critical moment is just before the peak. The intuition of this behavior is that for a very constrained output, production during the peak is tied to the capacity level, and there is no space to increase the output in order to deviate or retaliate, so deviation just before the boom delays punishments by one period. Knittel & Lepore (2006) study the behavior of a cartel in the described circumstances, including endogenous installed capacity constraints, delivering broadly similar results, depending on the marginal costs of installing capacity. The fact that the optimal pricing differs depending on the existence of capacity constraints certainly raises relevant doubts about the optimal collusive pricing testing mechanism. Principally, ignoring capacity constraints could lead to incorrect conclusions. We are interested in understanding optimal pricing when the capacity level is not completely strict - when producing more than the capacity level is feasible with increasing convex marginal costs. This topic has been ignored by theory, and is not far from the reality of other industries as well. As an example, consider a manufacturer of goods who is able to produce at a certain rate, but if an increase in that level of output is needed, he has to pay for extra labor hours. To face this issue we develop a theoretical model to understand the optimal pricing of a cartel in the context of a repeated Cournot game with cyclical demand, including the existence of different degrees of softness 10 of the capacity constraints. We find that for some range of convexity of marginal costs beyond capacity level there is no unique pricing behavior. In fact, we find that the margins increase as the peak approaches for patient firms (as in Haltiwanger & Harrington (1991)) and decrease for impatient firms, so that optimal pricing during the cycle depends on both the discount 9 As Harrington & Haltiwanger (1991). 10 By soft capacity constraints we mean the ability to produce more than the installed capacity, incurring in increasingly higher marginal costs. 4

7 factor and the convexity of marginal costs. This result is highly remarkable because previous literature focused solely on one of the industry specific forces (either high demand peaks or capacity constraints) but the blend of both delivers relevant implications for the applicability of an empirical analysis. Particularly we find that combinations of impatience and convexity of marginal costs that nullify both effects are very scarce, therefore empirical tests are applicable in the vast majority of cases. After addressing the theoretical model that summarizes the collusive pricing over the cycle in the context described above, we test the difference in margins before and after the peak and find no significant difference in the pricing. There are three possible hypothesis to explain these lack of results. First, the complaint is unsubstantiated and there was no collusive behavior within the Chicken Industry. 11 Second, there is collusive behavior but firms are very patient so Incentive Compatibility Conditions that assure discipline are not binding at any moment of the cycle. This hypothesis is feasible, but empirical studies of other industries that have less features 12 that would make Incentive Compatibility Conditions binding, find empirical support for the Haltiwanger & Harrington (1991) hypothesis. Third, firms are colluded but the combination of convexity of marginal cost and impatience nullify effects on pricing at any moment of the cycle, so no difference in margins between exists before and after the peak. This hypothesis will be shown to be highly unlikely. The paper is presented as follows: Section 2 introduces the model that summarizes the behavior of a cartel in the context explained above and discusses the main results based on Numerical Simulations, Section 3 presents the empirical application to test collusion based on the theoretical model of the Chicken Industry in Chile, and Section 4 concludes. 2 The Model 2.1 Basic Framework We consider an Industry with n 2 representative firms that interact in a infinitely repeated Cournot Game. The market demand is represented as P (Q t, α t ) = α t m Q t where Q t = n i=1 q it represents aggregate output, q it is the individual output of firm i at time t, and the cost function for each firm is C(q it ). The demand cycle will be represented: t [0, T ], with T defined as the duration of each cycle, we assume that the demand is equal (flat) over the cycle except in ˆt [0, T ] where α t = α t = α and ˆα > α, so: P (Q t, ˆα) > P (Q t, α) Q t 11 Or they are not coordinated to increase their profits. 12 Higher monitoring and punishments skills between firms. 5

8 The profit function in each period t is therefore: P (Q t, α ) = P (Q t, α) t, t ˆt (2.1) π i (q it, α t, t) = P (Q t, α t ) q it C(q it ) = (α t m ( Cartel Behavior n q it )) q it C(q it ) (2.2) If there is a cartel between the n firms, they would maximize the joint profits obtaining πit C = P (QC t, α t ) qit C C(qC it ) t. The optimal deviation from the cooperative quantity is represented by πt D (Q (i) t, α t ), 13 which can be obtained just one period. Following a deviation, firms compete in quantities, obtaining πt NC (Q t, α t ) through infinity. 14 δ [0, 1] represents the discount factor, so the supergame that summarizes the Incentive Compatibility Condition (ICC) that assures the cartel s sustainability for each period requires: 15 τ=0 π C τ (Q τ, α τ )δ τ π D τ (Q (i) τ, α τ ) + τ=0 i=1 π NC τ+1(q τ+1, α τ+1 )δ τ+1 (2.3) For the cartel to be sustainable there should exist a vector q that maximize profits and satisfies the ICC in each period. The maximization problem can be set as follow: τ=t π C τ (Q τ, α τ )δ τ t π D t (Q (i) t, α t ) + max q C t π C t = P (Q C t, α t )q C t C(q C it ) subject to: τ=t π NC τ+1(q τ+1, α τ+1 )δ τ t+1 t (0, ) The optimal vector q that results from the maximization problem is related to the specific moment in the cycle and it is repeated to infinity. 16 We assume πt D (Q (i) t, α t ) > πt C (Q t, α t ) > πt NC (Q t, α t ) t, so a cartel that is facing the last period of the game would be always willing to cheat, to anticipate that they would break the cartel as soon as they know that there is an end in the game; hereby the assumption of an infinite time horizon is needed. 13 Q (i) t is the aggregate collusive output of firms different than i adding the deviation output of i: Q (i) t = n j i qc jt + qit D 14 We are assuming that the maximum punishment that a cartel could reach is Cournot s Oligopoly quantities. There is a wide range of literature demonstrating that harsher punishment are efficient to make sustainable a cartel, we assume that the cartel is not sophisticated enough. 15 Imposing symmetry between firms implies that q it = q t i 16 Notice that for equal demands in different moments of the cycle, the only condition that change is ICC, because the present value of collusive profits and punishments change depending on how far is the Peak period. 6

9 Another important assumption of the model is that rents from deviations are bigger during the peaks. Defining: then: F (q C t (α t )) = [π D t (Q (i) t, α t ) π C t (Q t, α t )] F (q Cˆt (ˆα)) > F (qc t (α)) t ˆt To make the cartel sustainable, members will adjust q C t in order to manipulate F (q c t (α)): F (q c t ) q c t < 0, for q c [q D, q NC ] Specifically: F (q NC ) = 0 Deviation profits are more tempting during peaks (as in Rotemberg & Saloner (1986)). The cartel manipulates F (q C t (α t )) adjusting its collusive quantity (and profits) to avoid deviations. Rearranging the terms of the ICC (2.3) yields: τ=t δ τ t+1 (π C τ+1 π NC τ+1) (π D t π C t ) (2.4) The ICC (2.4) provides relevant intuition about what happens in periods of flat demand: As we assume that Collusive Rents are bigger during peak periods; [πt C (ˆα) πt NC (ˆα)] > [πt C (α) πt NC (α)] the Present Value of Collusive Rents for non-peak periods (left side of (2.4)) increases as the peak is approaching, and the cartel gets more sustainable, and does not need to significantly adjust the Collusive Quantity (and therefore profits) to avoid deviations. On the other hand, if the peak has just passed, the left side of (2.4) decreases so adjustments on the Deviation Rents (right side) are increasingly needed for the ICC to hold. This summarizes what Haltiwanger & Harrington (1991) described; for impatient firms the margins just before the peak are bigger than margins just after for equal levels of demand (α), and gives key insights on the determinants of the optimal collusive pricing over the business cycle. Another comment that should be considered before moving forward is that adjustments are needed for sufficiently impatient firms. Generally, collusion is easy to sustain when firms are patient because they place high value on future collusive profits. If firms are too patient (high δ) no adjustments are needed and the shape of margins during the cycle for this case will not show differences for equal levels of demand. Summing up, we have: 7

10 ˆ If δ ɛ (δ, 1) the ICC is relaxed all over the cycle; the collusive optimal pricing would be maximizing profits in every moment of the cycle. It is not necessary to adapt the quantities over the cycle to avoid deviations. ˆ If δ ɛ (δ, δ) there is at least a moment of the cycle that ICC is binding and adjustments from cartel members are needed. ˆ If δ ɛ (δ, 1) collusion could be sustainable. For very impatient firms (δ < δ), no collusion can be sustained so q t = q NC t t Capacity Constraints Harsh Capacity Constraints Capacity constraints warrant consideration as they could significantly alter the incentives of collusive behavior. First we assume that the constraint is absolutely harsh, meaning, beyond a certain level of output (k) the firm faces an infinite marginal cost so q t k. When demand fluctuates, the capacity level restricts peak output; in our model the peak and non-peak periods are remarkably different in terms of output level, thus we will concentrate solely on how capacity constraints affect the peak period. In a typical Cournot game q Ḓ (ˆα) > qnc(ˆα) > q (ˆα) so decreasing the capacity level affects the ability to deviate and t ˆt Cˆt the ability to punish. When capacity is not very restrictive, it does not alter the incentives as in the unconstrained case (Haltiwanger & Harrington (1991)). occurs when capacity is very restricted. The interesting case If, for instance k = q C (ˆα) = q NC (ˆα) = q D (ˆα) so [π D (ˆα) π C (ˆα)] = 0 and [π C (ˆα) π NC (ˆα)] = 0 during the peak, there is no chance to either deviate or punish, so profits are fixed and the incentives for both deviant and punisher are altered. Deviation gets more attractive in the period before the peak, because the punishment must be delayed by one period. Using the ICC (2.4), we find that the left side decreases as the peak is approaching so adjustments seems more necessary just before the peak - the opposite of the unconstrained case. The implications from this insight are very important if our goal is to empirically test collusive behavior. Another important issue to consider is that the critical value of discount factors (that need adjustments from ICC) decrease as the capacity is more constrained, so adjustments will be less necessary Softer Capacity Constraints Now we remove the condition of harsh capacity constraints (where the marginal costs are infinite beyond the capacity level k) and we allow increases of the output beyond k with 17 Notice that in the described Cournot Game would have δ = 0. 8

11 increasing Marginal Costs: C(q t ) = c q C(q t ) = C(q t ) = K(q t k) + c q, if q t k if q t > k (2.5) Assuming K (q t k) > 0, K (q t k) > 0 we summarize how harsh is capacity constraint (see Appendix A). The intuition is that Capacity Constraints (higher marginal costs beyond the capacity level) have a stronger effect on collusive, deviating or punishment outputs during peak periods instead of affecting the output (and therefore profits) during non-peak periods. Thus increasing output to avoid deviation affects profits differently in peak versus non-peak periods. This fact changes the optimal behavior of the cartel depending on how the ICC (2.4) evolves. For a very steep K (q t k), increasing the output for deviations gets too costly, and, also affects the non-cooperative (Cournot) equilibrium. While for some K (q t k) both deviation and collusive profits are more tempting during the peak, but for more impatient firms (where higher levels of outputs are needed to reduce incentives to deviate), the cost function affects profits non-linearly. Thus the profits of that period and the collusive rents turn out to be lower than non-peak collusive rents. The optimal pricing in this case would differ depending on the impatience of cartel members. For patient firms the collusive pricing would be similar to the results of Haltiwanger & Harrington (1991), but, when firms are impatient enough the only way to sustain collusion would be to set an optimal price path that decrease margins as the peak is approaching, as in Fabra (2006) and Knittel et al.(2006). This result has relevant importance for testing collusion in a cyclical demand environment and the conclusions are complex to evaluate. More details are presented in Appendix A 2.3 Numerical Simulations Unconstrained installed Capacity Following the described model, we simulate the behavior of a cartel with different discount factors, assuming a simplified world presented below: Model Specification: P (Q t ) = 100 m Q t t ˆt P (Q t ) = (2.6) P (Q t ) = ˆα m Q t for t = ˆt, ˆα > 100 Defining Q = q 1 + q 2 + q 3 (n = 3) C(q i ) = c q t 9

12 Assuming ˆα = 200, m = 1, c = 0 18 the collusive optimal pricing over the business cycle would be: Simulations of collusive pricing on the described Cournot Game yield important insights. As Rotemberg & Saloner (1986) proposed, the cartel must undercut its margins during the peaks when required by impatience of cartel members. This intuition was explained above. If the discount factor decreases further, the cartel should manipulate quantities to reduce collusive profits depending on the cycle period. As Haltiwanger & Harrington (1991) proposed, the cartel must set lower margins just after the peak, and is able to relax pricing as the peak approaches Harsh Capacity Constraints The Model is the same as the described above, with the addition of a capacity ceiling condition whereby production cannot exceed capacity level k. P (Q t ) = 100 m Q t t ˆt P (Q t ) = (2.7) P (Q t ) = ˆα m Q t for t = ˆt, ˆα > 100 C(q i t) = c q t Defining Q t = q 1t + q 2t + q 3t (n = 3) and k q it 18 These parameters will be maintained for the others simulations. 10

13 The idea is to switch the capacity level from a very relaxed to a very restricted level. We maintain the specifications in order to recognize how different levels of k make the cartel behave differently (following the analysis of Fabra (2006)). When the Capacity Constraint is severe, there is no space to deviate or to punish deviations so the profits from that period remain equal regardless of whether firms are in a collusive, deviating or punishment phase. Even though each of the non-peak periods has the same deviation and non-collusive profits (flat demand) it would be convenient for a firm to cheat just before the peak, because the punishment is delayed by one period. So in order for the cartel to be sustainable, it should avoid deviations especially in pre and post-peak periods by decreasing collusive (and deviation) margins. For less restricted capacity, the collusive pricing is similar to the unconstrained case (Figures 2.2 and 2.3). The existence of capacity constraints (either restricted or not) could modify the optimal collusive pricing 11

14 over the business cycle. However, in both cases the price paths over the cycle differ from the competitive case, so testing for Collusion in the context of harsh capacity constraints seems feasible Softer Capacity Constraints We observed that in the case of very harsh capacity constraints, cartel members lose the ability to deviate or punish deviations during the peak period, so margins over the business cycle take on a different shape than in the unconstrained case. Now we model the case when capacity constraints are not absolutely restrictive; i.e. production over the capacity-level is possible at an increasingly higher marginal cost. This fact is summarized by a parametric cost function that includes a parameter for convexity (in other words, the level of constraint) and an additional parameter for the level of capacity: P (Q t ) = 100 m Q t t ˆt P (Q t ) = (2.8) P (Q t ) = ˆα m Q t for t = ˆt, ˆα > 100 C(q t ) = c q t + exp(s(q t k)) s MC = c + exp(s(q t k)) ˆ c represents the constant Marginal Cost of each extra unit. ˆ k represents the installed capacity level. ˆ s summarize the severity of the capacity constraint (convexity). 19 In Appendix A different shapes of Costs are shown in detail. Here we only present the main results: 19 For simplicity we choose exponential costs to summarize the idea of constant marginal costs until the level k of capacity, beyond that level Marginal Costs increase as rapidly as we want adjusting s, the conclusions remain for different specifications as well. 12

15 We find that price paths behave similarly to the case where the Capacity Constraint is a hard ceiling when we impose steep Marginal Costs (s = 1) Keeping the constrained case k = 30 < q (ˆα), we now adjust the convexity of the cost Cˆt function to understand how pricing should behave in the transition to the unconstrained case (when Marginal Cost is flat). For a certain range of marginal cost convexity (for instance s = 0, 025) we find that the collusive pricing over the business cycle depends on impatience - for patient firms the margin increases as the peak approaches, but for impatient firms the opposite occurs. The convexity of marginal costs makes every extra unit of output during the peak more costly; for patient firms the quantity required to sustain collusion is lower (while at the same time facing lower marginal costs) than the quantity necessary to sustain collusion when firms are 13

16 impatient. This effect counterbalances the higher collusive profits from the peak, making them less attractive than the non-peak periods. For the same technology, the collusive pricing could differ over the cycle depending on the discount factor. This insight allows us to better understand the optimal pricing to be tested and the robustness of empirical studies in these circumstances. In summary, the evolution of margins over the cycle depends jointly on impatience and the harshness of capacity constraints. If our aim is to test collusion comparing margins before and after the peak, Figure 2.9 suggests testing whether the optimal brings us an idea when the optimal price either increases or decreases as the peak is approaching. Defining m after as the margin the period after the peak, and m before as the margin before the peak, we have: m = m after m before If margins increase as the peak is approaching (as Haltiwanger & Harrington (1991)) then m < 0, on the other hand, if margins decrease as the peak is approaching (as Fabra (2006) and Knittel & Lepore (2006)) then m > 0. In Figure 2.9 the capacity level k = q (ˆα) Cˆt is fixed such that increasing output beyond the optimal collusive quantity during the peak requires incurring higher costs for every extra unit of output. Figure 2.9: Optimal Collusive pricing by combinations of impatience and harshness of capacity constraints. 14

17 Figure 2.9 illustrates optimal collusive pricing over the cycle which depends on both, impatience and the convexity of marginal costs. We find that the margins should differ from those under competitive behavior for sufficient impatient firms, with harsh or soft capacity constraints (they should either increase or decrease as the peak is approaching). This set up is new for treatment of these kinds of problems, and allows us to move one step further toward understand the applicability of empirical tests that compare margins before/after peak demand periods. 3 Empirical Application: Testing Collusion Testing collusion based on theoretical hypothesis has been a frequent topic of empirical studies, In particular, the predictions from Haltiwanger & Harrington (1991) 20 have provided fertile ground to test for collusive behavior. Most of these papers impose structure to decompose the expectations of future demand as well as determine the cycle. Borenstein & Shephard (1996) study pricing policies of Gasoline Retailers in the United States, and test how expectations of booms of demand and future cost shocks affect contemporaneous pricing. They find evidence that supports the idea of tacit collusion; margins increase in boom periods and decrease when higher costs are expected. Rosenbaum & Sukharomana (2001) study pricing within the Cement Industry in Portland, Oregon using a HP filter in time series of sales they decompose the trend of demand movements, finding that the pricing for boom and bust periods differ, which supports the idea of collusive behavior. Rosenbaum & Yang (1998) study pricing over the demand cycles in the Aluminium Industry using a methodology similar to Borenstein & Shephard (1996) but their results differ for the expectations of cost shocks. 21 Broadly, the aim of this literature is to find some anticipation on margins around periods of the peak assuming different structures of expectations and information of agents to anticipate the trend of the demand. These papers have been broadly silent about some features of the industry that could affect analysis such as capacity constraints, asymmetries and the timing within the repeated game. It is certainly necessary to address these issues in an empirical test for collusion. In this paper we propose an empirical strategy that differs from the existing method by imposing less structure and taking advantage of the shape of the demand cycle. 22 compare margins from before and after the peak, excluding peak observations. We In line with the previous theoretical explanation, we find that, under collusion, margins should differ before and after the peak for impatient firms, especially if peaks are significantly 20 Margins for equal levels of demand differ depending on the location within the cycle. 21 See also Gallet & Schroeter (1995). 22 With one big peak, and even for the rest of the cycle. 15

18 big. We do not make assumptions about how agents anticipate the demand cycles 23 or the determinants of demand shifts. We use a descriptive methodology based on Regression Discontinuity Design, assuming that the demand before the peak is identical than after the peak (and we prove this assumption with falsification tests). Statistically significant differences in the pricing before/after the peak cannot be explained in the context of a competitive environment, and therefore would represent at least some tacit coordination between the members of the Industry. 3.1 Overview of the Chilean Chicken Market During 2011, the Chilean Antitrust Authority 24 filed a complaint against the three main Chicken Producers; Agrosuper, Ariztía and Don Pollo, arguing that they coordinated in quantities produced since 1995, in order to relax the competitiveness among them. The Chicken Producers rejected the complaint. The case took relevant importance in the public opinion because chicken represents a key factor in the Chilean diet. In this context testing if the industry shows any collusive pricing seems relevant based on the fact that they face cyclical demand fluctuations each year and also have physical capacity constraints for production. The Chilean Chicken Market has been evolving for many years with these three main actors sharing the domestic market 25 which together represents more than 85% of sales. 26 The Sales Channel to the final consumer is through Supermarkets, Stores and Industrial Sales, the three alleged firms use the same Sales Channel. Chicken demand can be divided in two main products; Whole Chicken and Cut up Chicken (mainly breast and legs) both present a peak every December. 27 More than a half of all sales come from the demand for Whole Chicken, which shows a very clear cycle during a year. Demand from January to November seems to be flat, but during December sales increases almost 35% over an average month. 28 The fact that the demand presents a clear cycle during the year allows us to contrast the behavior of a Cartel in this circumstances (described theoretically above) with the behavior of the alleged chicken Cartel industry. The composition of sales and the fluctuations of the demand are described in detail in Appendix B. An important feature of the Industry is the fact that the whole production process 23 Because they are highly deterministic in this Industry. 24 Fiscalía Nacional Económica 25 There is a considerable asymmetry between this three actors. Agrosuper has more than the 50%, Ariztía 18% and Don Pollo just 8%. This issue will be touch later. 26 Since the last few years there are some imports taking place specially coming from Argentina and Brazil, in the studied period ( ) imports and exports were not significant. 27 Explained by Christmas and the New Year s Evening sales. 28 The weekly fluctuations are much bigger. 16

19 of growing a chicken takes six weeks, forcing producers to make their strategic decisions in advance and extending the relevant timing of the game. In other words, if one of the companies decides to deviate from the quota it will increase its revenues for a significant period until the rivals are able to punish. This delay gives important incentives to deviate (higher deviation profits), therefore adjustment of the collusive quantity over the business cycle would be more necessary. This fact increases the likelihood of observing adjustments on margins over the business cycle in this industry, especially compared to other industries. In the market for gasoline, for instance, (tested by Borenstein & Shephard (1996)), deviation and retaliations do not last more than a week, because of the ease with which prices are monitored and adjusted. Another important feature from this market that makes it applicable for an empirical test is the remarkable asymmetry between the members of the alleged cartel. The biggest company has almost twice the installed capacity of the sum of the two other companies. The capability to retaliate deviations from the biggest player is reduced, and the biggest firm has more incentives than any other to deviate (high deviation profits and not hard retaliation from smaller firms). This issue also contributes to instability of the alleged cartel 29 and manipulation of the pricing over the business cycle becomes more necessary in this case. 3.2 Empirical Strategy The estimation is done by exploiting the difference in price for equal demand levels before/after the peak using a Regression Discontinuity Design that removes observations from the peak. The idea behind this method is to test the effect of a treatment for similar treated and not treated agents. In this case it is necessary to compare margins for equal demands before and after the peak, exploiting the fact that demand should be equal on either side of the peak. The advantage is that in a narrow window of time the other determinants of demand should not change significantly. This issue gives us an important empirical advantage compared with other studies mentioned before. It will not be necessary to impose more structure on the estimation. To begin testing, we remove observations from the 50th, 51st, 52nd and 1st weeks of the year, 30 in order to observe whether or not a significant difference in margins of Whole Chicken sales exists, as predicted in the theoretical models of cartel behavior. We focus our test on Whole Chicken because it presents less volatile prices and sales during the cycle, especially between January and November. The difference in margins before/after might 29 see Lambson (1994) and Compte et al. (2002). 30 Sales from weeks 50 and 51 show a considerable boom; almost 150% bigger than average weekly sales. We also remove observations from weeks 52 and 1, because sales show some satiety effect, and they decrease below the weekly average level, sales gets stable again after the 1st week. Results from the test do not change if observations from these weeks are included. 17

20 be found in other pieces as well, but the volatility hinders the test. We use data from 2000 to 2006 for two reasons. First, in that period exports and imports were not relevant for the industry 31, and second, the demand cycle was very clear in those years and the peak from December was still very considerable. The weekly data on prices and sales volume of Whole Chicken (and substitutes) are obtained from Agrosuper. 32 For marginal cost we use the price of Live Chicken (before processing), these prices are obtained from the Chilean Ministry of Agriculture, 33 and include the feeding and growing costs of fostering a chicken. 34 First we estimate the panel data of weekly observations of margins and sales from years 2000 to Results are shown in Table 4.1: 35 Table 4.1: Effect of before/after peaks on Margins and Sales Christmas ( ) Margin (18.24) Sales 44,749 (133,569) Observations 384 Note: Optimal Bandwidth (Kalyanaraman (2009)) was applied to evaluate significance in the discontinuity. No Covariates were controlled by *** p<0.01, ** p<0.05, * p<0.1 The parameter that summarizes the difference in both margins and sales pre and postpeak is not significantly different from zero either. Graphs are shown in Appendix C. Decomposing margins and sales by year we repeat the estimation for every year in order to understand how prices evolved over time. 31 After 2006 imports from Argentina and Brazil gained a relevant share of the market, especially in Whole Chicken sales. 32 We also have weekly data from the other firms, but in shorter series. Prices of Whole Chicken show no dispersion between firms. 33 None of the firms trade live chicken. 34 All prices are Nominal, we assume that inflation is not relevant in this narrow window of time. 35 Notice that we include quantities in the test because changes (before/after) in margins affect sales as well, if we find some difference it should be in both. 18

21 Table 4.2: Effect of before/after peaks on Margin and Sales by year (1) (2) (3) (4) (5) (6) (7) Christmas Christmas Christmas Christmas Christmas Christmas Christmas (2000) (2001) (2002) (2003) (2004) (2005) (2006) Margin ** *** *** (8.541) (5.679) (4.269) (1.217) (2.384) (24.12) (12.24) Sales -28, ,757-43, ,355** 17, ,916* 295,056*** (187,223) (115,709) (64,105) (76,559) (66,983) (70,028) (109,453) Observations Note: Optimal Bandwidth (Kalyanaraman (2009)) was applied to evaluate significance in the discontinuity. No Covariates were controlled by *** p<0.01, ** p<0.05, * p<0.1 The year 2006 (column (7)) presents the expected result (for the unconstrained cartel case). Margins fell by almost 10% after Christmas 2006, and the decline is statistically significant. The result is curious, however, because collusive pricing should be similar year after year. Studying the determinants of Whole Chicken demand we find that the only determinant with enough volatility in that period of time that could affect the demand of Whole Chicken is the price of substitutes. 36 In other words, if the price of substitutes changes in that period, the Whole Chicken demand is altered and the comparability between prices before and after the peak is invalid. This would undoubtedly hinder the estimation method. Using weekly observations of prices of Pork Leg and Whole Turkey as control covariates we repeat the estimation, obtaining: Table 4.3: Effect of before/after peaks on Margins and Sales Christmas ( ) Margin (14.43) Sales -24,669 (127,703) Observations 384 Note: Optimal Bandwidth (Kalyanaraman (2009)) was applied to evaluate the significance in the discontinuity. We controlled by covariates Whole Turkey price and Pork Leg price. *** p<0.01, ** p<0.05, * p< In Appendix C we test the stability of substitutes prices as we do for Whole Chicken margins, removing weeks 50th, 51st, 52nd and 1st, and we actually find that there are some significant changes. 19

22 Table 4.4: Effect of before/after peaks on Margin and Sales by year (1) (2) (3) (4) (5) (6) (7) Christmas Christmas Christmas Christmas Christmas Christmas Christmas (2000) (2001) (2002) (2003) (2004) (2005) (2006) Margin *** *** (8.147) (8.226) (4.380) (1.356) (2.463) (24.03) (9.896) Sales -35,969 99,186 9, ,912** 18, ,584** 771,346*** (183,687) (107,533) (69,778) (87,606) (66,951) (83,409) (270,878) Observations Note: Optimal Bandwidth (Kalyanaraman (2009)) was applied to evaluate significance in the discontinuity.we controlled by covariates Whole Turkey price and Pork Leg price. *** p<0.01, ** p<0.05, * p<0.1 Covariates in the discontinuity barely affect the pricing, and results presented in Tables 4.3 and 4.4 support the idea that there is not a stable pricing policy during the cycle that align incentives to avoid deviations. The fact that we don t find evidence of collusive behavior in margins raises doubts about the veracity of the complaint against the firms, since as discussed, pricing under collusion for impatient firms should show a consistent behavior. Still, is not possible to reject the hypothesis of collusion mainly for two reasons. First, adjustments on the pricing are only needed when impatience of firms requires, for patient firms no adjustments on pricing are necessary, and no effect might be found. However, as we showed, this industry has features, such as asymmetries and delay in the punishment that increases the critical discount factor and makes pricing adjustments over the cycle more necessary. Second, when firms are impatient and capacity constraints are binding, there is a positive likelihood to find no effect due to convexity of marginal costs, as shown in the theoretical model. There are some combinations of convexity and impatience which dilutes the effect, but the likelihood of having this level of convexity is negligible, although seems important to mention it. Falsification Tests and graphics are presented in Appendix C. 4 Concluding Remarks Haltiwanger & Harrington (1991) study collusive behavior with deterministic demand fluctuations, and find that the pricing should increase as peak demand approaches. Fabra (2006) and Knittel & Lepore (2006) add capacity constraints to the analysis, finding that pricing over the cycle depends on the level of installed capacity. Based on a theoretical model, we find that Softer Capacity Constraints can alter how a cartel sets optimal pricing during the cycle, and depending on firms impatience. For patient firms, margins increase 20

23 as the peak approaches (as in Haltiwanger & Harrington (1991)) and the opposite occurs for impatient firms using the same production technology. These findings bring new and interesting insights about optimal collusive pricing over the cycle, and the applicability of empirical tests in such circumstances. Predictions from Haltiwanger & Harrington (1991) have been broadly tested in literature on different industries, finding anticipation on the margins of demand peaks. These empirical studies impose structure to reveal the deterministic cycles of demands and expectations for the future demand cycles. We present a new empirical test based on deterministic demand cycles from the Chicken Industry in Chile, which were accused of Collusion. We test the pricing of Whole Chicken before and after the peak, and do not find evidence to support the collusion hypothesis. 21

24 References [1] Borestein, S. and Shepard, A. Dynamic Pricing in Retail Gasoline Markets. RAND Journal of Economics (1996) [2] Bos, I. and Harrington, J. E. Endogenous cartel formation with heterogeneous firms RAND Journal of Economics (2010) [3] Compte, O. Jenny, F and Rey, P. Capacity Constraints, Mergers and Collusion European Economic Review (2003) [4] Fabra, N. Collusion with Capacity Constraints over the Business Cycle International Journal of Industrial Organization (2006) [5] Fiscalia Nacional Economica. Requerimiento contra Agrosuper Agricola S.A. y otros (2011) [6] Gallet, C.A., Schroeter, J.R. The effects of the business cycle on oligopoly coordination: evidence from the US rayon industry. Review of Industrial Organization(1995) [7] Haltiwanger, J. and Harrington, J.E., Jr The impact of Cyclical Demand Movements on Collusive Behavior. RAND Journal of Economics (1991) [8] Hodrick, R. and Prescott E.P. Post-war Business Cycles: An Empirical Investigation Journal of Money, Credit and Banking. (1997) [9] Knittel, C. and Lepore, J. Tacit Collusion in the presence of Cyclical Demand and Endogenous Capacity Levels International Journal of Industrial Organization(2006) [10] Lambson, V. E. Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames Journal of Economic Theory. (1994) [11] Rosenbaum, D. and Sukharomana, S. Oligopolistic pricing over the deterministic market demand cycle: Some evidence from the US Portland cement industry International Journal of Industrial Organization(2001) [12] Rosenbaum, D. and Yang, S. P. The Effects Of The Business Cycle On Oligopoly Coordination: Evidence From The U.S. Aluminum Industry The Journal of Applied Business Research (2008) [13] Rotemberg, J.J and Saloner, G. A Supergame-Theoretic Model of Price Wars during Booms. American Economic Review(1986) 22

25 [14] Staiger, R. and Wolack, F. Collusive Pricing with Capacity Constraints in the presence of Demand Uncertainty, RAND Journal of Economics(1992) 23

26 Appendix A: Numerical Simulation (i) Cost Function By adjusting the capacity level and the convexity of the Marginal Cost function we are able to summarize the main features that we are interested in: the harshness of the capacity to produce and the level of it. We demonstrate that these two features drive incentives to set the optimal pricing over the business cycle: Costs: Adjusting Capacity (k): Costs: Adjusting Convexity (s): (ii) Variations on the Cost Function: Keeping the level of Convexity, we adjust the level of capacity: 24

27 As we increase the level of capacity k it looks more alike to the unconstrained case, as is expected. The opposite occur when we reduce the level k, It seems key to affect the Profit function from the peak period 25

28 Appendix B: Overview of the Chicken Demand (i) Aggregate Sales of Chicken Meat in Chile, divided by type of cut: Aggregate Sales by type 37 There is a clear peak of sales each December, for the different kinds of cut. Bur the Whole Chicken has the more clear (almost deterministic) cycle, and it broadly drives the aggregate peak. (ii) Firm s Market Share in Chile: 37 Source: Quiroz - APA 26

29 Appendix C: Empirical Issues (i) Regression Discontinuity of Margins and Sales before/after the peak ( ) Margins and Sales before/after the Peak Margins before/after the Peak 27

30 Margins before/after the Peak (ii) Falsification Tests We run a RD on a random week between January and November using the same methodology as the exposed collusion test. The results doesn t show jointly significant changes of margins and quantities. Table C.1: Discontinuity on week 14th removing weeks 15th-18th (1) (2) (3) (4) (5) (6) (7) (8) 14 th week 14 th week 14 th week 14 th week 14 th week 14 th week 14 th week 14 th week all years (2000) (2001) (2002) (2003) (2004) (2005) (2006) Margin * 12.98*** ** (21.14) (4.055) (11.80) (7.748) (3.885) (3.957) (5.461) (10.97) Sales 201,029-25, ,292** -1,660-24, ,934-58,201-96,132 (138,783) (110,139) (223,020) (210,231) (157,588) (144,352) (136,075) (132,562) Observations Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 We now repeat the RD test for Christmas peak for substitutes prices. The fact that prices of substitutes significantly change for Christmas would make necessary to control by them when testing collusion. 28

31 Table C.2: Effect of before/after Christmas on substitutes prices. (1) (2) (3) (4) (5) (6) (7) Christmas Christmas Christmas Christmas Christmas Christmas Christmas (2000) (2001) (2002) (2003) (2004) (2005) (2006) Whole-Turkey price *** ** ,309** (15.74) (22.16) (25.80) (34.73) (46.51) (309.7) (538.8) Pork-Leg price ** *** 102.5*** 114.9*** ** (44.32) (41.41) (34.01) (33.56) (49.99) (90.22) (50.59) Observations Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 29