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Disadvantageous collusion and government regulation
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International Journal of Industrial Organization 26 (2008) 168 – 185 www.elsevier.com/locate/econbase
Disadvantageous collusion and government regulation Tay-Cheng Ma ⁎,1 National Kaohsiung University of Applied Sciences, Taiwan Received 27 July 2006; received in revised form 10 October 2006; accepted 24 October 2006 Available online 5 December 2006
Abstract The semi-collusion model indicates that when firms collude on outputs and compete on capacities, cartel members may be worse off. Why do rational firms choose such kind of disadvantageous collusion? In order to solve the puzzle, this article uses Taiwan's flour cartel case to investigate firms' incentives and finds that government regulation seems to be the primary reason to create such a predicament. © 2006 Elsevier B.V. All rights reserved. JEL classification: L13 Keywords: Semi-collusion; Cournot equilibrium; Two-stage game
1. Introduction Standard analysis in industrial organization suggests that oligopolistic firms are better off colluding rather than competing in the product market, but this line of argument ignores the effects of competition in other, non-production activities. While collusion in a product market concerning short-run variables such as price or quantity may be feasible, collusion in long-run variables such as investment in capacity is often difficult.2 For this reason, Matsui (1989), Mitchell (1993), and Fershtman and Gandal (1994) consider a two-stage game model in which firms compete on capacities in the first stage and collude on outputs in the second stage, and they refer to such behavior as semi-collusion. They further assume that the cartel allocates market shares according to a firm's production capacity, which is the so-called ‘relative capacity’ sharing ⁎ 5F., No.5, Lane 16, Taishun St., Da-an District, Taipei City 106, Taiwan. Fax: +886 2 23694772. E-mail address: [email protected]. 1 Present affiliation: Department of Economics, Chinese Culture University. 2 Brander and Harris (1984) indicate that even in cases of overt collusion, which include Germany's cement cartel in the 1920s and 1930s, and the Texas oil industry in the 1930s, firms find it very difficult to collude in capacity. 0167-7187/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2006.10.009
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rule. In this setting, they show that cartel members would add capacity in an effort to increase their market shares in the second stage. This leads to a larger capacity than that for a non-cooperative regime. Furthermore, if the capital price is not too cheap, then the first-stage overinvestment may be large enough to make the overall semi-collusive equilibrium profits be less than the noncooperative equilibrium profits. The firms henceforth are better off not colluding. These models imply that rational firms would not choose this kind of market-sharing rule to enforce collusion, since it might reduce their profits. This raises an interesting question. Why does the literature still show several examples of industries in which firms colluded on output, but not in capacity, such as the plastics and aluminum industries during the 1950s3 as well as the Japanese cartels during the 1960s?4 This article tries to investigate the puzzle by focusing on the impact of government regulation on a cartel's sharing rule. Taking institutional and regulation factors into account, I use a unique set-up of Taiwan's flour cartel and focus on two fundamental problems that a cartel faces: the decision on capacity investment and the distribution of monopoly rents. This involves an antitrust case brought by Taiwan's Fair Trade Commission (TFTC, hereafter) against the Taiwan Flour Industry Association (Association, hereafter), which was alleged to have colluded in the market for years until the Association was found to be guilty in 2000. TFTC sanctioned that the flour firms had restricted competition and constituted concerted behavior prohibited under Articles 7 and 14 of the Fair Trade Law. TFTC also released a report on its inquiry into pricing behavior in Taiwan's flour market. This report provides detailed data on prices, outputs, and costs as well as a great deal of qualitative information which is valuable in interpreting the data. The information is derived directly from the working of a real-world cartel. The most interesting part of this cartel case is that the industry has maintained an extremely high level of excess capacity, such that its capacity utilization rate stayed at the level of around 40%–50% for more than 20 years. The TFTC report indicates that the cartel adopted a ‘relative capacity’ sharing rule, leading to excess capacities. Extra capital expenditures are so high that the collusive profits are even smaller than the non-cooperative profits. Why did rational flour firms choose such kind of disadvantageous market-sharing rule? The evidence shown in this paper indicates that this marketsharing rule is imposed and regulated by the government. Government regulation seems to be the most plausible explanation for these irrational behaviors in Taiwan's flour market. In this article Section 2 sets out some stylized facts about Taiwan's flour market. Section 3 explains some characteristics of the dataset. Sections 4 and 5 try to obtain cost and demand information to infer market conduct. In Section 6 these estimates, along with the data on cost and capacity, are used to check if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits. Section 7 concludes. 2. Taiwan's flour market TFTC (2001) indicates that Taiwan's flour industry is made of 32 firms; the leading 11 firms controlled about 70% of market sales between 1994:1 and 1999:1. The implied Herfindahl index during this time was quite low: only 417–530. There was also a remaining fringe of 21 firms with a total of 30% market share. This kind of structure hardly supports any oligopolistic behavior in the industry. However, government regulation provided a feasible environment for collusion.
3 4
See Scherer (1980, pp. 370–371). See Matsui (1989, pp. 454–455).
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The history background could be traced back to the regulation period. Taiwan is a riceproducing country and rice protection was the top priority of her agricultural policy in the 1980s. Since flour is a substitute of rice, the regulation body – Taiwan's Ministry of Economic Affairs (MOEA, hereafter) – had to control wheat imports so as to protect rice farmers. In order to regulate wheat imports, MOEA authorized the Flour Industry Association to have the sole license to import wheat from abroad. Since Taiwan does not grow its own wheat, this arrangement made the Association the only supplier of wheat materials. These regulations had been effective until the government decided to liberalize the economy under pressure from both international society and domestic researchers in 1992. After the deregulation, flour firms still held the consensus to monopolize the market until the TFTC prohibited them from collusion in 2001. 2.1. Excess capacity TFTC data show that the industry maintained an extremely low capacity utilization rate at around 40% between 1994:1 and 1999:1, which is much lower than the level of 80% for the whole manufacturing industry during the same period. Table 1 shows that most flour firms had capacity utilization rates below 50% except firms 10 and 11. Although TFTC does not expose the names of the firms in order to protect their privacy, Ma (2005, pp. 110–111) writes: …readers familiar with Taiwan's flour market can easily identify these two firms as Uni-President Enterprises and LienHwa Company. These two firms are separately owned by integrated food-processing conglomerates with a portfolio of businesses spanning the downstream users in the industry, and some of their products are used within the conglomerates and not traded in the market. Thus, all flour firms had a similar extent of excess capacity with respect to sales to groceries. The flour cartel could be characterized as a two-stage game in which firms first choose capacity levels non-cooperatively and then in a second stage choose their outputs cooperatively. As to the market-sharing rule, TFTC (2001) indicates that flour firms adopted a ‘relative capacity’ sharing rule in the cooperative regime. This means that sales volume for an individual firm was proportional to the size of its plant when there was excess capacity. In this setting, firms adopt a focal rule such that the capacity resolved in the first stage determines both the collusive profits to be divided in the second stage and the way those profits will be divided. Thus, capacity plays a Table 1 Firms' production, market share, and cost (1994–1998, yearly averages) Firm
1 2 3 4 5 6 7 8 9 10 11
Item Production (tons)
Market Share(%)
Capacity (tons)
Utilization Rate (%)
33,760 33,853 34,564 35,507 36,543 36,913 39,265 41,199 53,629 53,713 110,412
4.68 4.69 4.79 4.92 5.01 5.11 5.39 5.71 7.43 7.44 15.30
100,980 114,000 87,120 90,000 94,900 109,500 80,784 86,400 98,940 69,677 128,986
33.43 29.70 39.67 39.45 38.51 33.71 48.61 47.68 54.20 77.09 85.60
Notes: The figures are the yearly averages between 1994 and 1998 for each firm. Firms are ranked by their production. Source: TFTC (2001).
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double role: (1) It gives colluders a stronger bargaining position in their negotiation about cartel quotas. The more capacity the firm builds in the first stage, the higher the output quotas it shares in the second stage. (2) Firms with huge excess capacity can punish deviators more harshly, so that deviations are less likely to occur.5 Hence, excess capacity is used as a credible threat to enforce collusion, and the collusive output was sustained as equilibrium in every demand state. The literature has been quite careful to investigate the second role of excess capacity in policing the collusion.6 In contrast, the argument of this paper concerns not the second role, but the first one. Instead of stressing the relation between excess capacity and sustainability of the cartel, I investigate how excess capacity gave colluders a stronger bargaining position in their negotiation about cartel quotas. This involves two issues about semi-collusion: the decision on capacity investment in the first stage as well as its impact on profits in the second stage. The essence of this semi-collusion is explained as follows. 2.2. The second stage (product stage) The flour industry's profit should theoretically be much better than the average level, because firms collude to monopolize the market. However, a survey conducted by the MOEA shows that the industry's mark-up percentage was merely 1.95% in 1998 which was lower than 7.65% for the whole manufacturing industry, 10.68% for the food processing industry, 4.67% for the edible oil industry, 6.42% for the bakery industry, and 18.08% for the noodle processing industry. Why did collusion yield such a low profit? 2.3. The first stage (capacity stage) The puzzle could be investigated through the channel in which the market sharing rule had an effect on capacity investment and capital expenditure. Since the cartel allocated market share according to a firm's production capacity and cartel members uncooperatively decided on how much capacity to install, after taking the share rule into account, it is inevitable for firms to add capacity in an effort to increase their market shares. This unavoidably created excess capacity in the second stage.7 Furthermore, if the capital prices were not too cheap, then the first-stage overinvestment may be large enough to make the overall semi-collusive equilibrium profits smaller than the non-cooperative equilibrium profits. This raises another puzzle. Why did rational firms choose such kind of market-sharing rule and enforce a collusion which may have reduced their profits? 2.4. Market-sharing rule The evidence shows that this disadvantageous market-sharing rule is exogenously given by the government. During the regulation period, the government had to set up a rule of game for the 5
Conversely, when the level of excess capacity is low, a cheater need not worry much about retaliation since the industry cannot easily expand production by any significant amount. 6 Recent game theoretic contributions, such as Osborne and Pitchik (1983, 1986) and Davidson and Deneckere (1990), emphasize that the correlation between excess capacity and collusion is positive rather than negative. Empirical works by Rosenbaum (1989) and Ma (2005) also indicate that the correlation between a firm's excess capacity and other firms' outputs is negative. 7 Firms invest in this excess capacity not for future production, but rather as an investment to enhance their bargaining power in the negotiations concerning the division of the collusive profits.
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Association to distribute import quotas. Some economists suggested that quota rights should be granted to millers through a competitive bidding so as to allocate the wheat materials to the most efficient firms. However, the policy adopted by the MOEA was to allocate the wheat quotas according to a firm's relative capacity.8 This policy reflected Taiwan's economic needs at that time. In the 1980s Taiwan's trade surplus took up more than 10% of GDP, showing that her investment was much lower than domestic savings. Thus, the MOEA considered this rule as a good policy to stimulate domestic capital investment as well as to reduce the trade surplus. However, at the industry level, this policy encouraged overinvestment and created excess capacity.9 2.5. A non-binding import quota Another interesting question is whether the wheat import quota is binding. If this were the case, then both competitive and perfectly coordinated oligopolists produce the same quantity at the same price, because firms could not produce even the monopoly amount in the product market due to the import quota on their inputs. Thus, there was probably little need to collude and there was no reason to believe that the specific conduct (competition or collusion) in the product market had any effect on overall output. However, Ma (in press) indicates that the import quota was basically non-binding. This proposition is based on the following facts regarding the conflicts between regulation and competition. The quantity of the wheat import quota was jointly determined by the Commodity Price Supervisory Board (CPSB, hereafter)10 and the Agricultural Council to ensure the attainment of the target of rice production.11 In most cases, the yearly quantity of import quota was decided at the end of the previous year. Then, the Flour Industry Association distributed import quotas among member firms according to their capacities. According to Ma (in press), more often than not, wheat imports needed to sustain rice protection were less than the quantity needed to uphold the joint-profits maximization. In that case, the Association would propose to increase wheat imports by arguing that quotas were not enough to stabilize the flour price. On the other hand, wheat import restrictions inevitably led to an upward pressure on flour prices. Since the main mission of the CPSB is to stabilize the commodity prices, these extra procurements, the so-called “special quotas”, were rarely rejected by the CPSB. This allowed firms to influence the setting of the import quota and to achieve an optimal quantity of wheat imports to maximize their jointprofits. The previous inference is supported by the empirical evidence of Ma (in press), who uses a p-tobit model to show that import quota was basically non-binding during the regulation period. Thus, one can safely claim that flour price (or quantity) was set under the regime of collusion for any individual firm facing the import quota. After the quotas were taken off in 1992, flour firms still held the consensus to monopolize the market by collusion. Given the durability of capacity, the sharing rule is still being used in the post-regulation period. According to TFTC (2001), innovation rarely happened in flour 8
Note that Taiwan does not produce any wheat. Import quotas decide firm's production volumes and profits. After the regulations were revoked in the early 1990s, the capacity created by policy shocks was used as a credible threat to discipline the cartel members, since firms could easily dump a large amount of output on the market to punish the cheaters. 10 The Commodity Price Supervisory Board is a subordinate office under Taiwan's Ministry of Economic Affairs. Its mission is to stabilize the commodity prices. 11 Note that flour is a substitute of rice. The government had to restrict wheat imports so as to reduce flour production and to protect local rice production. 9
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production such that the capacity is long-lived. It takes at least 10–15 years to depreciate the capacity build in the past. My data set comprises a period (1994–1998) after the import quotas were taken off, whereas excess capacity still exists in industry. Given the same level of excess capacity built in the first stage, most firms' profits under the regime of semi-collusion are still more than those under the regime of non-cooperative competition.12 This provides rationality that the cartel still colludes in the second stage and uses the same sharing rule even the import quota system was abolished. 3. Some advantages of the dataset Empirical evidence on the correlation between excess capacity and semi-collusion is weak.13 The main reason is that researchers have difficulty in getting an ideal case to study the essence of the cartel. For instance, Schmalensee (1987, p. 352) summarizes three potentially important constraints on collusion: First, it is rarely trivial to reach a collusive agreement, and this task is likely to be harder when costs differ than in the symmetric case, because firms' preferred prices differ. Second, collusion requires not only that an agreement be reached, but that it be stable against cheating. Finally, potential entrants may provide an effective check on collusion. Nevertheless, Taiwan's flour cartel provides an ideal empirical setting in which firms could conduct collusion without these constraints. This allows economists to conduct their experiments in a designated environment exactly like a scientific laboratory. The reasons are listed as follows. 3.1. Costs are constant and equal in the product market While there are 3 different grades of flour, output is homogeneous across millers for any given grade. The flour is shipped in bags to grocers who in turn package the flour for final users without any identification of the manufacturers. Thus, the inter-brand competition is trivial. Price therefore tends toward uniformity, and flour firms compete in quantity. The production technology of flour is quite simple and the millers utilize a common technology. Wheat is transformed at a fixed, and generally accepted, coefficient into flour. As TFTC (2001) notes, the production of 1 kg of flour needs on average 1.37 kg of wheat. This coefficient remains constant over the sample period. In the 1980s, the MOEA used to set up a Wheat Stabilization Fund (WSF, hereafter) and announced “wheat standard prices”. If a firm's wheat import cost was higher (or lower) than the standard price, then the WSF disbursed (or collected) price differences. Thus, the wheat cost was nearly the same across millers. Since flour is homogeneous across firms, wheat is the main input to produce flour,14 wheat is transformed into flour at a fixed coefficient, and the wheat cost is similar across firms, this article deals with a symmetric collusive scheme in the product stage (second stage). 3.2. Absence of price wars Bresnahan (1989) reviews some cartel cases and finds that the cartel should be expected to fall apart and to restructure, such that data on collusive industries typically show both periods of cooperation and periods of price wars. This uncertainty leads to a time-varying conduct parameter 12 13 14
See Fershtman and Gandal (1994) for details. See Davidson and Deneckere (1990, p. 525). Wheat cost takes up about 75% of flour price.
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Fig. 1. Quarterly price and the average wheat cost of the flour firms. Source: TFTC (2001).
in empirical studies. Unless the collusion is sustained as the equilibrium in every period, Bresnahan's argument means that the estimated conduct parameter could not measure market power correctly in most cases.15 However, this article investigates an implausible cartel case in which price wars never occurred among the cartel members,16 such that Friedman's trigger strategy equilibrium is sustained in every period. Fig. 1 shows the flour price and average wheat cost of the industry. Obviously, price–cost margins were quite stable over the sample period.17 Price fluctuations were mostly brought about by the variations in wheat costs. Since a firm's conduct was constant over the sample period, one can safely claim that the estimated conjectures could be used to measure the average collusiveness of conduct. 3.3. No entry threats The production of flour does not involve enormous investment and sophisticated marketing channels, such that the entry is quite simple. However, a quota system instituted by the Association seemed to rule out entry almost completely. Since millers' wheat materials had to be imported from abroad and were subject to the high cost of transport, TFTC indicates that firms had to use a 50,000-ton vessel to carry wheat for each voyage so as to achieve economies of scale. However, this scale was far beyond the material needs of a single firm. Thus, the flour firms had to procure and to convey wheat jointly through arrangement of the Association. This import scheme allowed the Association to block entry by not permitting new entrants to join the procurement group through the quota system previously mentioned. Ma (2005, p.111) writes this point of view as follows: Since 1990, there has been only one entrant (Global Flour Company) that joined the industry in 1998, and it was a joint venture of several incumbent flour firms in southern 15 Collusive behaviors generally happen in the market where interactions are repeated. Traditionally, IO economists use estimated conjectures to investigate firms' collusive behaviors. However, the repeated game is dynamic, while the conjectural variation model is clearly static. Hence, there might be a potential bias when the dynamic behaviors are investigated based on estimates from a static model. 16 In the working of this real-world cartel, excess capacity was used to discourage cheating behavior as previously mentioned. See Ma (2005) for details. 17 The mean value of the price–cost margins is 0.25 and the standard deviation is 0.03.
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Taiwan. The 20% tariff rate for the flour itself was also too high to allow for imports. Thus, the collusive behavior of the incumbents was not influenced by the threat of new entry for years. The fringe producers likewise could not expand their outputs to destroy the collusion scheme, since they could not find partners to import wheat jointly from abroad under the boycott of the Association. The only possibility for breaking up the cartel is that there are a significant number of firms with excess capacity jointly importing wheat from the U.S. However, this way of doing business might dump a large amount of output on the market such that they have to worry about prices collapsing. 4. Model This section considers a market for a homogenous product in which firms first choose capacity levels non-cooperatively and then in a second stage choose their outputs cooperatively. The model allows for a wide range of oligopoly outcomes and uses conjectural variation to measure the degree of market power. The structure of this two-stage game is similar to Fershtman and Gandal (1994). In contrast to this model, however, they assume perfect collusion and equal cost such that their conclusions correspond to a special case of this model. 4.1. Demand and cost structure I begin by specifying a quantity-setting game in which each flour firm faces an inverse market demand of the form: P ¼ a*−bQ þ CZ;
ð1Þ
where P is the flour price, Q is the quantity demanded, and Z is a vector of exogenous variables P affecting demand. There are n firms in the market, each firm producing qi, such that Q ¼ ni¼1 qi is Pn the industry output, and q−i ¼ j pi qj ¼ Q−qi is the combined output of the other firms. In the first stage (long-run), firms can vary their cost through the adjustment in capacity. However, in the second stage (short-run), cost relies only on a variable input, which is determined by the quantity produced,18 given the capacity determined in the first stage. Thus, the cost structure can be specified as follows: Ci ¼ cqi þ ri ki ;
ð2Þ
where c = MC = AVC, which does not change with the output and is identical across firms, Ci is total cost, ri = λiPK, λi represents the rental cost of the services of a dollar worth of capacity, P K is the price of capacity, and ki is the production capacity of firm i.19 Because wheat is the main variable input in the production of flour, is transformed into flour at a fixed coefficient, its price is exogenously determined in the international market and is identical across firms for the sake of the WSF, and flour production is operating within the range of huge excess capacity, the assumption of a constant and identical c seems reasonable. Capacity (ki) is viewed as a surrogate for a long-run quantity decision, which is relatively inflexible in the short. No plant can be pushed beyond its capacity limits. Capacity thus serves as a 18
The cost in the second stage can be considered as the short-run variable cost. Formally, I should write the variables in the form of xit, which denotes the observation of variable x for firm i in period t. However, no confusion should result from omitting t in order to keep the notation uncluttered here. 19
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proxy for the scale of production by placing an upper bound on any firm's output level. A firm with capacity ki can produce up to ki units of product at constant marginal cost. In the case of excess capacity, the investment in the first stage does not have an effect on the marginal cost in the second stage. The only effect of ki on a firm's profits is to give it a stronger bargaining position in its negotiation about cartel quotas. A firm invests in this excess capacity not for future production, but rather as an investment to enhance its share in the division of the collusive profits. 4.2. Competition in both stages Under the Cournot conjecture hypothesis, Kreps and Scheinkman (1983) show that the equilibrium of the two-stage game is the same as the Cournot equilibrium of the induced quantity game in which the capacity level is equal to the production level. Thus, it is straightforward to show that firm i's output (or capacity) is given by: na−
qi;cournot ¼ ki;cournot
n X
ri a−ri i¼1 − ; ¼ b bðn þ 1Þ
ð3Þ
where a = a⁎ +Γ Z − c. The industry output can be obtained by adding the outputs of all firms: na − Qcournot ¼ Kcournot ¼
n X
ri
i¼1
bðn þ 1Þ
:
ð4Þ
Finally, the profit of the industry can be obtained as:
½a þ ð X r −ðn þ 1Þr Þ X n
i
n
Pcournot ¼
i¼1
i¼1
bðn þ 1Þ2
2
i
:
ð5Þ
4.3. Semi-collusion (cooperation in the second stage) In the regime of semi-collusion, firms choose their capacities non-cooperatively in the first stage, but collude in the second stage. As is standard, the model is solved backwards beginning from the second stage in which a certain degree of collusiveness exists in the market. Firm i chooses quantity to maximize profits. max PðQÞqi −Cðqi jki Þ: qi
ð6Þ
Solving the first-order condition yields the price-cost margin at the industry level:20 P−c 1 ¼ ½a þ ð1−aÞH; P e 20
See Martin (1993, pp. 499–500).
ð7Þ
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P where a ¼ AqAq qq is the conjectural elasticity,21 e ¼ bQ is the price elasticity of demand, and H is the Herfindahl index of market concentration, the sum of squares of the market shares of flour firms. Eq. (7) encompasses much of static oligopoly theory. For perfect collusion or monopoly α = 1, for −1 Bertrand competition a ¼ n−1 , and for the case of Cournot behavior, α = 0. Finally, by multiplying both sides of Eq. (7) by PQ, the profit of the industry in the second stage is −i
i
i
−i
P2 ¼ b½a þ ð1−aÞHQ2 :
ð8Þ
Eq. (8) shows that industry profit increases with the conjectures and market concentration. 4.4. Semi-collusion (competition in the first stage) In the first stage, the market shares are allocated according to the firms' relative capacities such that each firm is allocated k þkik of collusive profits. Here, k−i is the sum of the capital stocks of the i −1 other firms. As in Matsui (1989) and Fershtman and Gandal (1994), the only effect of ki on a firm's profits is to maximize its share of industry profits.22 The more capacity the firm builds in the first stages, the higher the output quotas it shares in the second stage. Given this collusive technology, the profit function of firm i in the first stage is: pi ¼ ðki ; k−i Þ ¼
ki b½a þ ð1−aÞHQ2 −ri ki : ki þ k−i
The corresponding first-order condition is: 2 Q b½a þ ð1−aÞH ðK−ki Þ ¼ ri ; K where K = ki + k−i is the industry's capacity. Rewrite Eq. (10) as: 2 Q ri : ¼ K b½a þ ð1−aÞHðK−ki Þ
ð9Þ
ð10Þ
ð11Þ
Note that firms have different rental costs of capital (ri = λiPK), even if they face identical and constant marginal cost (c) in the second stage. This specification allows firms to have different choices in the investment stage. Assume that capacity costs are sufficiently small so that: n X i¼1
ri b
aðn−1Þ½a þ ð1−aÞH : ½1 þ a þ ð1−aÞH
ð12Þ
Under this assumption, the Appendix shows that the semi-collusive equilibrium is characterized by excess capacity. Semi-collusion yields lower equilibrium profits than when firms compete non-cooperatively in both stages. 21
Theoretically, one should let each firm have distinct conjectures. However, this arrangement exhausts the available degrees of freedom. Since this article is only interested in the existence of oligopolistic interdependence, it is sufficient to evaluate the aggregate output response of the other firms anticipated by firm i. Thus, by following Genesove and Mullin (1998) and Roller and Sickles (2000), the model assumes αi = α such that the conjectural elasticity is the same across flour firms. 22 Note that marginal production cost (c) in the second stage does not change with the capacity.
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5. Econometric application 5.1. Functional specification The empirical implementation of the above model involves the simultaneous estimation of the demand Eq. (1) and the first-order conditions (7) and (10). The linear demand function corresponding to Eq. (1) is specified as follows: P ¼ a*−bQ þ dPrice þ ey þ m1 ;
ð13Þ
1 where P is the deflated flour price, Price is the deflated rice price, y is per capita realPincome, 2 and ν 1P rice qi is the error term. Note that P as well as y are exogenous. Since e ¼ and H ¼ Q , Eqs. (7) bQ and (10) can be rewritten as:
" P ¼ c þ bQ a þ ð1−aÞ
Xqi 2 Q
# þ m2i ; and
# Xqi 2 Q2 ri ¼ b a þ ð1−aÞ ðK−ki Þ þ m3i ; K Q
ð14Þ
"
ð15Þ
where νi2 and νi3 are error terms. P P11 Using these functional forms, I substitute Q ¼ 11 i¼1 qi and K ¼ i¼1 ki into Eqs. (13)–(15), and estimate this system of three equations — which endogenize P, q, and k by using the nonlinear three-stage least squares so as to avoid simultaneity bias caused by the endogeneity. The parameters to be estimated are a⁎, b, d, e, and α. 5.2. Data The primary data source is the survey carried out by TFTC (2001). The sample covers the quarterly data of 11 major flour firms in the period from 1994:1 to 1999:1. Since one of these firms did not enter into the market until 1998, we have 215 observations. While the data has some advantages previously mentioned, its main drawback is that it relates only to 5 years and 1 quarter. However, the collusion began at least from 1991. Thus, the data cover only, at most, half of the affected period, and there are no non-cartel periods represented therein. Nevertheless, this paper still hopes to draw some strong conclusions, in particular to the role of excess capacity in this twostage game. 5.3. Estimates and interpretation of parameters This subsection estimates the model by using non-linear three-stage least squares. The covariance matrix is corrected for conditional heteroscedasticity and serial correlation.23 The results are reported in Table 2. Column A shows that most variables are significant except income coefficient e. This might reflect the fact that flour is a necessity such that its expenditure does not 23
See White (1980).
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Table 2 Coefficients estimates (non-linear three-stage least squares estimates) Parameters to be estimated
(A)
(B)
a⁎ b d e α
−2.317⁎ (− 2.629) 0.024⁎ (4.692) 0.152⁎(12.695) 0.0001 (0.255) 0.827⁎ (4.181)
−2.424⁎ (−3.046) 0.023⁎ (7.331) 0.154⁎ (16.426) 0.869⁎ (6.461)
Notes: Number of observations = 215. The figures in brackets are t values. ⁎ denotes that the estimate is significant at the level of 1%.
change with income.24 In the subsequent simulation analysis, we still stay with the empirical results that include income as an explanatory variable and use the figures in column A as the baseline specification. Table 2 also indicates that estimated parameters conform to the theory. Both the own-price coefficient b and the cross-price coefficient d have the expected sign. A further consistency check shows that the own-price elasticity of demand, which is evaluated at the sample mean, is 3.4. Since the stylized facts indicate a certain degree of collusiveness existing in the flour industry, it follows that firms must price in the elastic part of their linear demand schedules. A point elasticity of demand above unity therefore is consistent with the theory. 5.4. Evidences of collusion The empirical results present some evidences to suggest that collusion existed among firms. The estimated conjectural elasticity (α ˆ ) is 0.83, which is significantly different from − 1/10 (0) as perfect competition (symmetric Cournot) predicts. Although α ˆ is less than the level of the perfect collusion (1), the evidence still suggests that millers did exercise market coordination to a certain extent. According to Davidson and Deneckere (1990), perfect collusion can be sustained only if the cost of capacity is zero such that firms can carry considerable capacity to support the monopoly price in the unconstrained semi-collusive equilibria. However, in the real world, capital price cannot be zero. Thus, our excess capacity could only support some prices between the Cournot level and the monopoly level, but not the monopoly price.25 5.5. Conduct parameter vs. measurement of market power — a test of robustness Our model basically uses the estimated conjectures to investigate firms' behaviors. However, a number of objections have been raised against this methodology. For instance, Corts (1999) argues that α ˆ typically mismeasures the level of market power if industry behavior corresponds to a dynamic oligopoly game.26 According to the Corts critique, α ˆ underestimates the degree of market power if demand shocks are not fully persistent, and it may fail to measure any market power whatsoever when demand shocks are completely transitory. Conversely, the more persistent demand 24
Thus, its income elasticity is near to zero. Davidson and Deneckere hence referred to these equilibria as constrained semi-collusive equilibria. There is generally a continuum of constrained semi-collusive equilibria. 26 The repeated game with trigger strategies is dynamic, while the conjectural variation model is clearly static. Hence, there might be a potential bias when the dynamic payoff is calculated based on estimates from a static model. 25
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Table 3 Dickey–Fuller and Phillips–Perron Tests Test
Variable
Dickey–Fuller (with 0 lags) Dickey–Fuller (with 4 lags) Phillips–Perron (with 0 lags) Phillips–Perron (with 4 lags)
Price
y
Critical values⁎
− 1.70 − 1.49 − 1.79 − 1.77
− 1.49 − 1.54 − 1.58 − 1.84
− 2.65 − 2.67 − 2.65 − 2.65
⁎The critical values are at the 10% significance level. These test statistics all have a non-standard distribution, and these distributions depend upon the number of lags.
shocks become, the more accurate α ˆ can measure market power. Thus, α ˆ can accurately estimate market power in case demand shocks are fully persistent. The Corts critique could be explained by the essence of the efficient supergame equilibrium. Under the equilibrium, the supply Eq. (7) must guarantee a quantity that balances current gains to deviation against discounted future profit losses that would result from the deviation. For instance, a higher Price increases market demand for flour, which induces the short-term gains to deviation. If the demand shocks were persistent, then the observations of a higher Price would indicate an increased probability of observing high future demand states.27 This leads to higher future collusive gains such that the expected future losses resulting from punishment for a current deviation will increase. Thus, a higher Price increases both current gains to deviation and future losses from punishment simultaneously. This makes q less responsive to Price such that θˆ is robust to changes in Price (demand shocks).28 In order to test the degree of persistence of the demand shocks, both Dickey–Fuller and Phillips–Perron tests are performed to judge if the demand shocks are persistent. The evidence in Table 3 shows that, at the 10% significance level, one cannot reject the null hypothesis that demand shocks are fully persistent. Thus, one can safely claim that the estimated conjectures could be used to measure the average collusiveness of conduct. 6. Disadvantage collusion This section uses the TFTC data to simulate if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits as Matsui (1989) and Fershtman and Gandal (1994) predict.29 6.1. Simulation The demand information used to simulate equilibrium profits under different regimes is obtained from the empirical results of column (A) in Table 2. Thus, the demand function could be written as: P ¼ −2:317−0:024Q þ 0:152Price þ 0:0001y þ residuals:
27
In the case of fully persistent, the value of Price may provide perfect information about future demand states and may therefore change the expected discounted future profit losses incurred by punishment. 28 Conversely, if demand shocks are intertemporally independent, then higher Price increases short-term gains to deviation, but expected future losses do not change. Firms have to increase q in the current period so as to offset this increased incentive to deviate. 29 The lower semi-collusive profits resulted from overinvestment in the first stage.
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Table 4 Quarterly average gains and losses from adherence and deviation Firm
1 2 3 4 5 6 7 8 9 10 11
(1)
(2)
(3)
(4)
(5)
(6)
(7)
πi,cournot (1000 NT$)
πi,semi-collusion (1000 NT$)
(1)–(2) (1000 NT$)
Excess capacity (tons)
P KKi / Pqi
πexcess i,cournot (1000 NT$)
(2)–(6) (1000 NT$)
13,813 27,663 4744 15,222 8976 8564 36,075 11,597 29,622 50,675 3784
10,837 4714 1299 4768 1286 6502 16,223 342 21,971 51,755 12,684
2976 22,948 3445 10,453 7690 2063 19,852 11,255 7652 − 1080 − 8900
10,380 (9th) 20,037 (1st) 16,805 (3rd) 14,589 (4th) 11,328 (7th) 11,300 (8th) 13,623 (5th) 18,147 (2nd) 13,139 (6th) 4644 (10th) 3991 (11th)
1.36 (9th) 3.11 (1st) 1.73 (6th) 2.19 (3rd) 1.90 (4th) 1.59 (7th) 1.86 (5th) 2.88 (2nd) 1.57 (8th) 0.90 (10th) 0.88 (11th)
9022 5106 − 6689 1262 − 2057 2749 14,106 − 8,427 18,774 48,158 2342
1814 − 391 7989 3507 3343 3753 2117 8769 3196 3596 10,342
Notes: The figures in brackets denote the ranks of the variable values.
Substituting the means of Price and y into the equation can get the estimates of flour prices under different levels of industry output as: Pˆ ¼ a− ˆ ˆbQ ¼ 9:704−0:024Q:
ð16Þ
The TFTC data contain P, qi, c, and ri. One can put this information together to check if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits. The paths of equilibrium profits could be obtained as follows. 1. Insert a, b, c, and ri into Eqs. (3) and (4) to solve a firm's qi,cournot as well as industry's output Qcournot for each quarter during the period of 1994:1–1999:1. Find the values of Pcournot and πi,cournot by substituting Qcournot into Eq. (16). 2. Use Eq. (A1) to calculate the simulated paths of quantity and price under the regime of semicollusion Qsemi-collusion and Psemi-collusion. Calculate overall semi-collusive (first stage) profits πi,semi-collusion by using Eq. (9). 3. It is well known that the monopoly output can be written as Qmono ¼ ða−rÞ=2b. As an approx1 X11 imation, I plug r ¼ r , a, and b into this formula and get the paths of Qmono and Pmono. i¼1 i 11 One has to make sure that the actual industry output conforms to the semi-collusive path. Davidson and Deneckere (1990) propose that perfect collusion cannot be sustained, because r N 0. The simulated evidence seems to support their argument. During the sample period, the simulated value of quarterly average industry production under a semi-collusion regime (11 dominant firms) is 133,847 metric tons, which is quite near to actual quantity of 117,152 metric tons. This figure is higher than the prediction of the perfect collusion model (90,817 metric tons), and much lower than the Cournot quantity (213,396 metric tons).30 This evidence suggests that the semi-collusion equilibrium quantity is closer to the perfectly collusive level than it is to the Cournot level. It also 30
In the Davidson–Deneckere model, any output between the Cournot level and the monopoly level can be sustained as an equilibrium.
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indicates that the conjectural variation model explains the actual output path better than the Cournot strategy does. 6.2. Disadvantageous collusion Columns (1) and (2) in Table 4 report the quarterly average profits under regimes of semicollusion and non-cooperative Cournot, respectively.31 Evidently, for most firms, the overall semi-collusive equilibrium profits are much smaller than the non-cooperative equilibrium profits. These firms are better off not colluding. The two exceptions are firm 10 and firm 11. As previously mentioned in Section 2, these two firms have relatively small excess capacity such that they do not have to undertake heavy capital expenditure. This argument is supported by column (5), which shows that their capital–sales ratios ðPK Ki =Pqi Þ are much lower than the ones of other firms. 6.3. Decision not to collude in the second stage is not credible Although overall semi-collusive equilibrium profits may be low, it is important to note that for a given choice of variables in the first stage, such as the policy-induced excess capacity in our case, the firms are better off colluding in the second stage.32 In order to verify this argument, column (6) calculates the firms' profits, given that policy-induced excess capacity already exists in the first stage and firms produce Cournot quantity in the second stage. 33 pexcess i;cournot ¼ Pcournot qi;cournot −cqi;cournot −ri ki;semicollusion
Here, ki,semi-collusion is the capacity determined under the regime of semi-collusion in which excess capacity exists. Column (7) indicates that, given the same level of excess capacity, most firms' profits under the regime of semi-collusion are more than that under the regime of noncooperative competition.34 Thus, given the capacity determined in the first stage, semi-collusion still induces positive monopoly rents in the second stage. However, these gains have to be tradedoff against the superfluous expenditure on capacity. The size of this inefficiency depends on the level of capacity that is installed, which is a function of the incentives to gain a bigger share of profits. It is import control that conclusively imposes an inefficient market-sharing rule, which creates incentives for firms to build up excess capacity in the first stage. While collusion in the second stage yields lower overall profits for the sake of heavy capital expenditure, the decision not to collude must be accompanied by some types of deregulation in the first stage, otherwise the firms will wish to renegotiate and the decision not to collude in the second stage will not be credible. 7. Conclusion In the collusive regime, firms have to bargain on how to divide the monopolized profits. The literature generally uses the ‘relative capacity’ sharing rule and proposes that each firm's sales P For instance, profits for firm i are computed by 1=21 21 t¼1 ðpi;semicollusion;t Þ. This conforms to the spirit of subgame perfection. 33 Note that πi,cournot = Pcournot qi,cournot − cqi,cournot − riqi,cournot. 34 Firm 2 is the outlier, because its excess capacity and capital expenditure are so high that it cannot take advantage of collusion in the second stage. 31 32
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volume is proportional to the size of its plant. For instance, Fershtman and Gandal (1994, p. 145) demonstrate this point of view: We find it attractive, because there is a large body of ‘anecdotal evidence’ that cartels use such a rule in setting output quotas. In order to test the feasibility of this kind of market-sharing rule, this article uses Taiwan's flour cartel case to investigate its impact on firms' investment decisions and their profit paths. The evidence shows that firms have to overinvest so as to increase their market shares, since the cartel allocates market shares according to firms' production capacity. This inevitably creates excess capacity. Furthermore, if the capital price is not too cheap, then the overinvestment may be large enough to make the overall semicollusive profits smaller than the non-cooperative profits. Under such cases, the rational firms are better off not colluding. Why did rational flour firms choose such kind of disadvantageous market-sharing rule? Like conventional wisdom, in our case the key point still lies on the fact that this market-sharing rule is imposed and regulated by the government. Government regulation seems to be the primary reason to create such a predicament. It is thus seen that ‘anecdotal evidences’, in which the relative capacity sharing rule is commonly used by cartels, cannot be validated in the real world, except when a regulation shock happens which seriously distorts the mechanism to collude as this article mentions. Hence, regulators should be careful in the enforcement of the regulation. Appendix A. Semi-collusion vs. competition A.1. The industry carries excess capacity in the semi-collusive equilibrium Proof. By plugging Eq. (1) and e ¼ P=bQ into the first-order condition in the second stage, Eq. (7), one can express the industry's equilibrium output and profit as: a Q¼ ; and ðA1Þ b½1 þ a þ ð1−aÞH P2 ¼
a2 ½a þ ð1−aÞH b½1 þ a þ ð1−aÞH2
:
ðA2Þ
On the other hand, Eq. (8) and the first-order condition in the first stage, Eq. (11), shows that the equilibrium capacities for the individual firm and industry are: ki ¼ K−ri K¼
K2 ; and P2
ðA3Þ
ðn−1ÞP2 P : ri
Finally, using Eq. (12), one can obtain K N Q.
ðA4Þ □
A.2. Semi-collusive equilibrium profits are lower than Cournot equilibrium profits Proof. Summing Eq. (9) over i and using ki and K, one can write the industry's profit function in the first stage as: " P 2 # n X r 2 P1 ¼ P2 − ri ki ¼ P2 ð2−nÞ þ ðn−1Þ P i 2 ; ðA5Þ ð ri Þ i¼1
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while the equilibrium profit in the non-cooperative case is given by Eq. (5). Using Eq. (12), a comparison of Eqs. (5) and (A5) shows that equilibrium profits are lower under the semi-collusive setting. □ Appendix B. Data description and construction⁎ Variables
Number of observations
Mean
Standard error
Minimum
Maximum
P (NT$) c (NT$) Q (1000 tons) H P rice (index) ri (NT$) P KKi / Pqi
215 214 215 215 215 215 211
9.64 7.30 192.59 475.52 96.46 1.54 1.88
0.70 0.78 18.92 34.72 3.77 0.63 0.78
8.90 6.79 159.90 417.38 89.66 0.66 0.76
11.04 9.45 228.42 530.90 100.00 3.13 3.92
⁎All the data are taken from the TFTC (2001) dataset, except Price. (1) P is the average weighted price of three types of flour sold in the market. The weights are the sale volumes. P is deflated by GNP deflator. (2) c is the wheat cost to produce 1 kg of flour. (3) Q = Σqi is the industry output where qi is the output of firm i. (4) si = qi / Q is the market share. (5) ri = λiPK is the cost of capacity. (6) Price is the index of rice price, which is taken from Commodity Price Statistics reported by the Directorate-General of Budget, Accounting and Statistics, Executive Yuan, Taiwan. (7) PKKi / Pqi is the capital–sales ratio, where PKKi is the cost of fixed assets, and Pqi is total sale of firm i. References Brander, H., Harris, R., 1984. Anticipated Collusion and Excess Capacity, mimeo, University of British Columbia. Bresnahan, T., 1989. Empirical methods for industries with market power. In: Schmalensee, R., Willig, R. (Eds.), Handbook of Industrial Organization II. Elsevier Science Publishers, Amsterdam, pp. 1001–1055. Corts, K., 1999. Conduct parameters and the measurement of market power. Journal of Econometrics 88, 225–227. Davidson, C., Deneckere, R., 1990. Excess capacity and collusion. International Economic Review 31, 521–541. Fershtman, C., Gandal, N., 1994. Disadvantageous semicollusion. International Journal of Industrial Organization 12, 141–154. Genesove, D., Mullin, W., 1998. Testing static oligopoly models: conduct and cost in the sugar industry. Rand Journal of Economics 29, 355–377. Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcome. Bell Journal of Economics 14, 326–337. Ma, T., 2005. The collusive equilibrium in a quantity-setting supergame: an application to Taiwan's flour industry. Review of Industrial Organization 27, 107–124. Ma, T., in press. Import quotas, price ceilings and pricing behavior in Taiwan's flour industry, Agribusiness. Martin, S., 1993. Advanced Industrial Economics. Blackwell, Cambridge. Matsui, A., 1989. Consumer-benefited cartels under strategic capacity investment competition. International Journal of Industrial Organization 7, 451–470. Mitchell, S., 1993. The welfare effects of rent-saving and rent-seeking. Canadian Journal of Economics 26, 660–669. Osborne, M.J., Pitchik, C., 1983. Profit-sharing in a collusive industry. European Economics Review 22, 59–74. Osborne, M.J., Pitchik, C., 1986. Price competition in a capacity-constrained duopoly. Journal of Economic Theory 38, 238–260.
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Roller, L., Sickles, R., 2000. Capacity and product market competition: measuring market in a puppy-dog industry. International Journal of Industrial Organization 18, 845–865. Rosenbaum, D., 1989. An empirical test on the effect of excess capacity in price setting. International Journal of Industrial Organization 7, 231–241. Scherer, F.M., 1980. Industrial Market Structure and Economic Performance, 2nd ed. Houghton, Boston. Schmalensee, R., 1987. Competitive advantage and collusive optima. International Journal of Industrial Organization 5, 351–367. TFTC, 2001. The concerted behaviors in the oligopolistic market: a case study on the flour industry. Research Report 9002 Taiwan Fair Trade Commission (in Chinese).
International Journal of Industrial Organization 26 (2008) 168 – 185 www.elsevier.com/locate/econbase
Disadvantageous collusion and government regulation Tay-Cheng Ma ⁎,1 National Kaohsiung University of Applied Sciences, Taiwan Received 27 July 2006; received in revised form 10 October 2006; accepted 24 October 2006 Available online 5 December 2006
Abstract The semi-collusion model indicates that when firms collude on outputs and compete on capacities, cartel members may be worse off. Why do rational firms choose such kind of disadvantageous collusion? In order to solve the puzzle, this article uses Taiwan's flour cartel case to investigate firms' incentives and finds that government regulation seems to be the primary reason to create such a predicament. © 2006 Elsevier B.V. All rights reserved. JEL classification: L13 Keywords: Semi-collusion; Cournot equilibrium; Two-stage game
1. Introduction Standard analysis in industrial organization suggests that oligopolistic firms are better off colluding rather than competing in the product market, but this line of argument ignores the effects of competition in other, non-production activities. While collusion in a product market concerning short-run variables such as price or quantity may be feasible, collusion in long-run variables such as investment in capacity is often difficult.2 For this reason, Matsui (1989), Mitchell (1993), and Fershtman and Gandal (1994) consider a two-stage game model in which firms compete on capacities in the first stage and collude on outputs in the second stage, and they refer to such behavior as semi-collusion. They further assume that the cartel allocates market shares according to a firm's production capacity, which is the so-called ‘relative capacity’ sharing ⁎ 5F., No.5, Lane 16, Taishun St., Da-an District, Taipei City 106, Taiwan. Fax: +886 2 23694772. E-mail address: [email protected]. 1 Present affiliation: Department of Economics, Chinese Culture University. 2 Brander and Harris (1984) indicate that even in cases of overt collusion, which include Germany's cement cartel in the 1920s and 1930s, and the Texas oil industry in the 1930s, firms find it very difficult to collude in capacity. 0167-7187/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ijindorg.2006.10.009
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rule. In this setting, they show that cartel members would add capacity in an effort to increase their market shares in the second stage. This leads to a larger capacity than that for a non-cooperative regime. Furthermore, if the capital price is not too cheap, then the first-stage overinvestment may be large enough to make the overall semi-collusive equilibrium profits be less than the noncooperative equilibrium profits. The firms henceforth are better off not colluding. These models imply that rational firms would not choose this kind of market-sharing rule to enforce collusion, since it might reduce their profits. This raises an interesting question. Why does the literature still show several examples of industries in which firms colluded on output, but not in capacity, such as the plastics and aluminum industries during the 1950s3 as well as the Japanese cartels during the 1960s?4 This article tries to investigate the puzzle by focusing on the impact of government regulation on a cartel's sharing rule. Taking institutional and regulation factors into account, I use a unique set-up of Taiwan's flour cartel and focus on two fundamental problems that a cartel faces: the decision on capacity investment and the distribution of monopoly rents. This involves an antitrust case brought by Taiwan's Fair Trade Commission (TFTC, hereafter) against the Taiwan Flour Industry Association (Association, hereafter), which was alleged to have colluded in the market for years until the Association was found to be guilty in 2000. TFTC sanctioned that the flour firms had restricted competition and constituted concerted behavior prohibited under Articles 7 and 14 of the Fair Trade Law. TFTC also released a report on its inquiry into pricing behavior in Taiwan's flour market. This report provides detailed data on prices, outputs, and costs as well as a great deal of qualitative information which is valuable in interpreting the data. The information is derived directly from the working of a real-world cartel. The most interesting part of this cartel case is that the industry has maintained an extremely high level of excess capacity, such that its capacity utilization rate stayed at the level of around 40%–50% for more than 20 years. The TFTC report indicates that the cartel adopted a ‘relative capacity’ sharing rule, leading to excess capacities. Extra capital expenditures are so high that the collusive profits are even smaller than the non-cooperative profits. Why did rational flour firms choose such kind of disadvantageous market-sharing rule? The evidence shown in this paper indicates that this marketsharing rule is imposed and regulated by the government. Government regulation seems to be the most plausible explanation for these irrational behaviors in Taiwan's flour market. In this article Section 2 sets out some stylized facts about Taiwan's flour market. Section 3 explains some characteristics of the dataset. Sections 4 and 5 try to obtain cost and demand information to infer market conduct. In Section 6 these estimates, along with the data on cost and capacity, are used to check if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits. Section 7 concludes. 2. Taiwan's flour market TFTC (2001) indicates that Taiwan's flour industry is made of 32 firms; the leading 11 firms controlled about 70% of market sales between 1994:1 and 1999:1. The implied Herfindahl index during this time was quite low: only 417–530. There was also a remaining fringe of 21 firms with a total of 30% market share. This kind of structure hardly supports any oligopolistic behavior in the industry. However, government regulation provided a feasible environment for collusion.
3 4
See Scherer (1980, pp. 370–371). See Matsui (1989, pp. 454–455).
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The history background could be traced back to the regulation period. Taiwan is a riceproducing country and rice protection was the top priority of her agricultural policy in the 1980s. Since flour is a substitute of rice, the regulation body – Taiwan's Ministry of Economic Affairs (MOEA, hereafter) – had to control wheat imports so as to protect rice farmers. In order to regulate wheat imports, MOEA authorized the Flour Industry Association to have the sole license to import wheat from abroad. Since Taiwan does not grow its own wheat, this arrangement made the Association the only supplier of wheat materials. These regulations had been effective until the government decided to liberalize the economy under pressure from both international society and domestic researchers in 1992. After the deregulation, flour firms still held the consensus to monopolize the market until the TFTC prohibited them from collusion in 2001. 2.1. Excess capacity TFTC data show that the industry maintained an extremely low capacity utilization rate at around 40% between 1994:1 and 1999:1, which is much lower than the level of 80% for the whole manufacturing industry during the same period. Table 1 shows that most flour firms had capacity utilization rates below 50% except firms 10 and 11. Although TFTC does not expose the names of the firms in order to protect their privacy, Ma (2005, pp. 110–111) writes: …readers familiar with Taiwan's flour market can easily identify these two firms as Uni-President Enterprises and LienHwa Company. These two firms are separately owned by integrated food-processing conglomerates with a portfolio of businesses spanning the downstream users in the industry, and some of their products are used within the conglomerates and not traded in the market. Thus, all flour firms had a similar extent of excess capacity with respect to sales to groceries. The flour cartel could be characterized as a two-stage game in which firms first choose capacity levels non-cooperatively and then in a second stage choose their outputs cooperatively. As to the market-sharing rule, TFTC (2001) indicates that flour firms adopted a ‘relative capacity’ sharing rule in the cooperative regime. This means that sales volume for an individual firm was proportional to the size of its plant when there was excess capacity. In this setting, firms adopt a focal rule such that the capacity resolved in the first stage determines both the collusive profits to be divided in the second stage and the way those profits will be divided. Thus, capacity plays a Table 1 Firms' production, market share, and cost (1994–1998, yearly averages) Firm
1 2 3 4 5 6 7 8 9 10 11
Item Production (tons)
Market Share(%)
Capacity (tons)
Utilization Rate (%)
33,760 33,853 34,564 35,507 36,543 36,913 39,265 41,199 53,629 53,713 110,412
4.68 4.69 4.79 4.92 5.01 5.11 5.39 5.71 7.43 7.44 15.30
100,980 114,000 87,120 90,000 94,900 109,500 80,784 86,400 98,940 69,677 128,986
33.43 29.70 39.67 39.45 38.51 33.71 48.61 47.68 54.20 77.09 85.60
Notes: The figures are the yearly averages between 1994 and 1998 for each firm. Firms are ranked by their production. Source: TFTC (2001).
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double role: (1) It gives colluders a stronger bargaining position in their negotiation about cartel quotas. The more capacity the firm builds in the first stage, the higher the output quotas it shares in the second stage. (2) Firms with huge excess capacity can punish deviators more harshly, so that deviations are less likely to occur.5 Hence, excess capacity is used as a credible threat to enforce collusion, and the collusive output was sustained as equilibrium in every demand state. The literature has been quite careful to investigate the second role of excess capacity in policing the collusion.6 In contrast, the argument of this paper concerns not the second role, but the first one. Instead of stressing the relation between excess capacity and sustainability of the cartel, I investigate how excess capacity gave colluders a stronger bargaining position in their negotiation about cartel quotas. This involves two issues about semi-collusion: the decision on capacity investment in the first stage as well as its impact on profits in the second stage. The essence of this semi-collusion is explained as follows. 2.2. The second stage (product stage) The flour industry's profit should theoretically be much better than the average level, because firms collude to monopolize the market. However, a survey conducted by the MOEA shows that the industry's mark-up percentage was merely 1.95% in 1998 which was lower than 7.65% for the whole manufacturing industry, 10.68% for the food processing industry, 4.67% for the edible oil industry, 6.42% for the bakery industry, and 18.08% for the noodle processing industry. Why did collusion yield such a low profit? 2.3. The first stage (capacity stage) The puzzle could be investigated through the channel in which the market sharing rule had an effect on capacity investment and capital expenditure. Since the cartel allocated market share according to a firm's production capacity and cartel members uncooperatively decided on how much capacity to install, after taking the share rule into account, it is inevitable for firms to add capacity in an effort to increase their market shares. This unavoidably created excess capacity in the second stage.7 Furthermore, if the capital prices were not too cheap, then the first-stage overinvestment may be large enough to make the overall semi-collusive equilibrium profits smaller than the non-cooperative equilibrium profits. This raises another puzzle. Why did rational firms choose such kind of market-sharing rule and enforce a collusion which may have reduced their profits? 2.4. Market-sharing rule The evidence shows that this disadvantageous market-sharing rule is exogenously given by the government. During the regulation period, the government had to set up a rule of game for the 5
Conversely, when the level of excess capacity is low, a cheater need not worry much about retaliation since the industry cannot easily expand production by any significant amount. 6 Recent game theoretic contributions, such as Osborne and Pitchik (1983, 1986) and Davidson and Deneckere (1990), emphasize that the correlation between excess capacity and collusion is positive rather than negative. Empirical works by Rosenbaum (1989) and Ma (2005) also indicate that the correlation between a firm's excess capacity and other firms' outputs is negative. 7 Firms invest in this excess capacity not for future production, but rather as an investment to enhance their bargaining power in the negotiations concerning the division of the collusive profits.
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Association to distribute import quotas. Some economists suggested that quota rights should be granted to millers through a competitive bidding so as to allocate the wheat materials to the most efficient firms. However, the policy adopted by the MOEA was to allocate the wheat quotas according to a firm's relative capacity.8 This policy reflected Taiwan's economic needs at that time. In the 1980s Taiwan's trade surplus took up more than 10% of GDP, showing that her investment was much lower than domestic savings. Thus, the MOEA considered this rule as a good policy to stimulate domestic capital investment as well as to reduce the trade surplus. However, at the industry level, this policy encouraged overinvestment and created excess capacity.9 2.5. A non-binding import quota Another interesting question is whether the wheat import quota is binding. If this were the case, then both competitive and perfectly coordinated oligopolists produce the same quantity at the same price, because firms could not produce even the monopoly amount in the product market due to the import quota on their inputs. Thus, there was probably little need to collude and there was no reason to believe that the specific conduct (competition or collusion) in the product market had any effect on overall output. However, Ma (in press) indicates that the import quota was basically non-binding. This proposition is based on the following facts regarding the conflicts between regulation and competition. The quantity of the wheat import quota was jointly determined by the Commodity Price Supervisory Board (CPSB, hereafter)10 and the Agricultural Council to ensure the attainment of the target of rice production.11 In most cases, the yearly quantity of import quota was decided at the end of the previous year. Then, the Flour Industry Association distributed import quotas among member firms according to their capacities. According to Ma (in press), more often than not, wheat imports needed to sustain rice protection were less than the quantity needed to uphold the joint-profits maximization. In that case, the Association would propose to increase wheat imports by arguing that quotas were not enough to stabilize the flour price. On the other hand, wheat import restrictions inevitably led to an upward pressure on flour prices. Since the main mission of the CPSB is to stabilize the commodity prices, these extra procurements, the so-called “special quotas”, were rarely rejected by the CPSB. This allowed firms to influence the setting of the import quota and to achieve an optimal quantity of wheat imports to maximize their jointprofits. The previous inference is supported by the empirical evidence of Ma (in press), who uses a p-tobit model to show that import quota was basically non-binding during the regulation period. Thus, one can safely claim that flour price (or quantity) was set under the regime of collusion for any individual firm facing the import quota. After the quotas were taken off in 1992, flour firms still held the consensus to monopolize the market by collusion. Given the durability of capacity, the sharing rule is still being used in the post-regulation period. According to TFTC (2001), innovation rarely happened in flour 8
Note that Taiwan does not produce any wheat. Import quotas decide firm's production volumes and profits. After the regulations were revoked in the early 1990s, the capacity created by policy shocks was used as a credible threat to discipline the cartel members, since firms could easily dump a large amount of output on the market to punish the cheaters. 10 The Commodity Price Supervisory Board is a subordinate office under Taiwan's Ministry of Economic Affairs. Its mission is to stabilize the commodity prices. 11 Note that flour is a substitute of rice. The government had to restrict wheat imports so as to reduce flour production and to protect local rice production. 9
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production such that the capacity is long-lived. It takes at least 10–15 years to depreciate the capacity build in the past. My data set comprises a period (1994–1998) after the import quotas were taken off, whereas excess capacity still exists in industry. Given the same level of excess capacity built in the first stage, most firms' profits under the regime of semi-collusion are still more than those under the regime of non-cooperative competition.12 This provides rationality that the cartel still colludes in the second stage and uses the same sharing rule even the import quota system was abolished. 3. Some advantages of the dataset Empirical evidence on the correlation between excess capacity and semi-collusion is weak.13 The main reason is that researchers have difficulty in getting an ideal case to study the essence of the cartel. For instance, Schmalensee (1987, p. 352) summarizes three potentially important constraints on collusion: First, it is rarely trivial to reach a collusive agreement, and this task is likely to be harder when costs differ than in the symmetric case, because firms' preferred prices differ. Second, collusion requires not only that an agreement be reached, but that it be stable against cheating. Finally, potential entrants may provide an effective check on collusion. Nevertheless, Taiwan's flour cartel provides an ideal empirical setting in which firms could conduct collusion without these constraints. This allows economists to conduct their experiments in a designated environment exactly like a scientific laboratory. The reasons are listed as follows. 3.1. Costs are constant and equal in the product market While there are 3 different grades of flour, output is homogeneous across millers for any given grade. The flour is shipped in bags to grocers who in turn package the flour for final users without any identification of the manufacturers. Thus, the inter-brand competition is trivial. Price therefore tends toward uniformity, and flour firms compete in quantity. The production technology of flour is quite simple and the millers utilize a common technology. Wheat is transformed at a fixed, and generally accepted, coefficient into flour. As TFTC (2001) notes, the production of 1 kg of flour needs on average 1.37 kg of wheat. This coefficient remains constant over the sample period. In the 1980s, the MOEA used to set up a Wheat Stabilization Fund (WSF, hereafter) and announced “wheat standard prices”. If a firm's wheat import cost was higher (or lower) than the standard price, then the WSF disbursed (or collected) price differences. Thus, the wheat cost was nearly the same across millers. Since flour is homogeneous across firms, wheat is the main input to produce flour,14 wheat is transformed into flour at a fixed coefficient, and the wheat cost is similar across firms, this article deals with a symmetric collusive scheme in the product stage (second stage). 3.2. Absence of price wars Bresnahan (1989) reviews some cartel cases and finds that the cartel should be expected to fall apart and to restructure, such that data on collusive industries typically show both periods of cooperation and periods of price wars. This uncertainty leads to a time-varying conduct parameter 12 13 14
See Fershtman and Gandal (1994) for details. See Davidson and Deneckere (1990, p. 525). Wheat cost takes up about 75% of flour price.
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Fig. 1. Quarterly price and the average wheat cost of the flour firms. Source: TFTC (2001).
in empirical studies. Unless the collusion is sustained as the equilibrium in every period, Bresnahan's argument means that the estimated conduct parameter could not measure market power correctly in most cases.15 However, this article investigates an implausible cartel case in which price wars never occurred among the cartel members,16 such that Friedman's trigger strategy equilibrium is sustained in every period. Fig. 1 shows the flour price and average wheat cost of the industry. Obviously, price–cost margins were quite stable over the sample period.17 Price fluctuations were mostly brought about by the variations in wheat costs. Since a firm's conduct was constant over the sample period, one can safely claim that the estimated conjectures could be used to measure the average collusiveness of conduct. 3.3. No entry threats The production of flour does not involve enormous investment and sophisticated marketing channels, such that the entry is quite simple. However, a quota system instituted by the Association seemed to rule out entry almost completely. Since millers' wheat materials had to be imported from abroad and were subject to the high cost of transport, TFTC indicates that firms had to use a 50,000-ton vessel to carry wheat for each voyage so as to achieve economies of scale. However, this scale was far beyond the material needs of a single firm. Thus, the flour firms had to procure and to convey wheat jointly through arrangement of the Association. This import scheme allowed the Association to block entry by not permitting new entrants to join the procurement group through the quota system previously mentioned. Ma (2005, p.111) writes this point of view as follows: Since 1990, there has been only one entrant (Global Flour Company) that joined the industry in 1998, and it was a joint venture of several incumbent flour firms in southern 15 Collusive behaviors generally happen in the market where interactions are repeated. Traditionally, IO economists use estimated conjectures to investigate firms' collusive behaviors. However, the repeated game is dynamic, while the conjectural variation model is clearly static. Hence, there might be a potential bias when the dynamic behaviors are investigated based on estimates from a static model. 16 In the working of this real-world cartel, excess capacity was used to discourage cheating behavior as previously mentioned. See Ma (2005) for details. 17 The mean value of the price–cost margins is 0.25 and the standard deviation is 0.03.
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Taiwan. The 20% tariff rate for the flour itself was also too high to allow for imports. Thus, the collusive behavior of the incumbents was not influenced by the threat of new entry for years. The fringe producers likewise could not expand their outputs to destroy the collusion scheme, since they could not find partners to import wheat jointly from abroad under the boycott of the Association. The only possibility for breaking up the cartel is that there are a significant number of firms with excess capacity jointly importing wheat from the U.S. However, this way of doing business might dump a large amount of output on the market such that they have to worry about prices collapsing. 4. Model This section considers a market for a homogenous product in which firms first choose capacity levels non-cooperatively and then in a second stage choose their outputs cooperatively. The model allows for a wide range of oligopoly outcomes and uses conjectural variation to measure the degree of market power. The structure of this two-stage game is similar to Fershtman and Gandal (1994). In contrast to this model, however, they assume perfect collusion and equal cost such that their conclusions correspond to a special case of this model. 4.1. Demand and cost structure I begin by specifying a quantity-setting game in which each flour firm faces an inverse market demand of the form: P ¼ a*−bQ þ CZ;
ð1Þ
where P is the flour price, Q is the quantity demanded, and Z is a vector of exogenous variables P affecting demand. There are n firms in the market, each firm producing qi, such that Q ¼ ni¼1 qi is Pn the industry output, and q−i ¼ j pi qj ¼ Q−qi is the combined output of the other firms. In the first stage (long-run), firms can vary their cost through the adjustment in capacity. However, in the second stage (short-run), cost relies only on a variable input, which is determined by the quantity produced,18 given the capacity determined in the first stage. Thus, the cost structure can be specified as follows: Ci ¼ cqi þ ri ki ;
ð2Þ
where c = MC = AVC, which does not change with the output and is identical across firms, Ci is total cost, ri = λiPK, λi represents the rental cost of the services of a dollar worth of capacity, P K is the price of capacity, and ki is the production capacity of firm i.19 Because wheat is the main variable input in the production of flour, is transformed into flour at a fixed coefficient, its price is exogenously determined in the international market and is identical across firms for the sake of the WSF, and flour production is operating within the range of huge excess capacity, the assumption of a constant and identical c seems reasonable. Capacity (ki) is viewed as a surrogate for a long-run quantity decision, which is relatively inflexible in the short. No plant can be pushed beyond its capacity limits. Capacity thus serves as a 18
The cost in the second stage can be considered as the short-run variable cost. Formally, I should write the variables in the form of xit, which denotes the observation of variable x for firm i in period t. However, no confusion should result from omitting t in order to keep the notation uncluttered here. 19
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proxy for the scale of production by placing an upper bound on any firm's output level. A firm with capacity ki can produce up to ki units of product at constant marginal cost. In the case of excess capacity, the investment in the first stage does not have an effect on the marginal cost in the second stage. The only effect of ki on a firm's profits is to give it a stronger bargaining position in its negotiation about cartel quotas. A firm invests in this excess capacity not for future production, but rather as an investment to enhance its share in the division of the collusive profits. 4.2. Competition in both stages Under the Cournot conjecture hypothesis, Kreps and Scheinkman (1983) show that the equilibrium of the two-stage game is the same as the Cournot equilibrium of the induced quantity game in which the capacity level is equal to the production level. Thus, it is straightforward to show that firm i's output (or capacity) is given by: na−
qi;cournot ¼ ki;cournot
n X
ri a−ri i¼1 − ; ¼ b bðn þ 1Þ
ð3Þ
where a = a⁎ +Γ Z − c. The industry output can be obtained by adding the outputs of all firms: na − Qcournot ¼ Kcournot ¼
n X
ri
i¼1
bðn þ 1Þ
:
ð4Þ
Finally, the profit of the industry can be obtained as:
½a þ ð X r −ðn þ 1Þr Þ X n
i
n
Pcournot ¼
i¼1
i¼1
bðn þ 1Þ2
2
i
:
ð5Þ
4.3. Semi-collusion (cooperation in the second stage) In the regime of semi-collusion, firms choose their capacities non-cooperatively in the first stage, but collude in the second stage. As is standard, the model is solved backwards beginning from the second stage in which a certain degree of collusiveness exists in the market. Firm i chooses quantity to maximize profits. max PðQÞqi −Cðqi jki Þ: qi
ð6Þ
Solving the first-order condition yields the price-cost margin at the industry level:20 P−c 1 ¼ ½a þ ð1−aÞH; P e 20
See Martin (1993, pp. 499–500).
ð7Þ
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P where a ¼ AqAq qq is the conjectural elasticity,21 e ¼ bQ is the price elasticity of demand, and H is the Herfindahl index of market concentration, the sum of squares of the market shares of flour firms. Eq. (7) encompasses much of static oligopoly theory. For perfect collusion or monopoly α = 1, for −1 Bertrand competition a ¼ n−1 , and for the case of Cournot behavior, α = 0. Finally, by multiplying both sides of Eq. (7) by PQ, the profit of the industry in the second stage is −i
i
i
−i
P2 ¼ b½a þ ð1−aÞHQ2 :
ð8Þ
Eq. (8) shows that industry profit increases with the conjectures and market concentration. 4.4. Semi-collusion (competition in the first stage) In the first stage, the market shares are allocated according to the firms' relative capacities such that each firm is allocated k þkik of collusive profits. Here, k−i is the sum of the capital stocks of the i −1 other firms. As in Matsui (1989) and Fershtman and Gandal (1994), the only effect of ki on a firm's profits is to maximize its share of industry profits.22 The more capacity the firm builds in the first stages, the higher the output quotas it shares in the second stage. Given this collusive technology, the profit function of firm i in the first stage is: pi ¼ ðki ; k−i Þ ¼
ki b½a þ ð1−aÞHQ2 −ri ki : ki þ k−i
The corresponding first-order condition is: 2 Q b½a þ ð1−aÞH ðK−ki Þ ¼ ri ; K where K = ki + k−i is the industry's capacity. Rewrite Eq. (10) as: 2 Q ri : ¼ K b½a þ ð1−aÞHðK−ki Þ
ð9Þ
ð10Þ
ð11Þ
Note that firms have different rental costs of capital (ri = λiPK), even if they face identical and constant marginal cost (c) in the second stage. This specification allows firms to have different choices in the investment stage. Assume that capacity costs are sufficiently small so that: n X i¼1
ri b
aðn−1Þ½a þ ð1−aÞH : ½1 þ a þ ð1−aÞH
ð12Þ
Under this assumption, the Appendix shows that the semi-collusive equilibrium is characterized by excess capacity. Semi-collusion yields lower equilibrium profits than when firms compete non-cooperatively in both stages. 21
Theoretically, one should let each firm have distinct conjectures. However, this arrangement exhausts the available degrees of freedom. Since this article is only interested in the existence of oligopolistic interdependence, it is sufficient to evaluate the aggregate output response of the other firms anticipated by firm i. Thus, by following Genesove and Mullin (1998) and Roller and Sickles (2000), the model assumes αi = α such that the conjectural elasticity is the same across flour firms. 22 Note that marginal production cost (c) in the second stage does not change with the capacity.
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5. Econometric application 5.1. Functional specification The empirical implementation of the above model involves the simultaneous estimation of the demand Eq. (1) and the first-order conditions (7) and (10). The linear demand function corresponding to Eq. (1) is specified as follows: P ¼ a*−bQ þ dPrice þ ey þ m1 ;
ð13Þ
1 where P is the deflated flour price, Price is the deflated rice price, y is per capita realPincome, 2 and ν 1P rice qi is the error term. Note that P as well as y are exogenous. Since e ¼ and H ¼ Q , Eqs. (7) bQ and (10) can be rewritten as:
" P ¼ c þ bQ a þ ð1−aÞ
Xqi 2 Q
# þ m2i ; and
# Xqi 2 Q2 ri ¼ b a þ ð1−aÞ ðK−ki Þ þ m3i ; K Q
ð14Þ
"
ð15Þ
where νi2 and νi3 are error terms. P P11 Using these functional forms, I substitute Q ¼ 11 i¼1 qi and K ¼ i¼1 ki into Eqs. (13)–(15), and estimate this system of three equations — which endogenize P, q, and k by using the nonlinear three-stage least squares so as to avoid simultaneity bias caused by the endogeneity. The parameters to be estimated are a⁎, b, d, e, and α. 5.2. Data The primary data source is the survey carried out by TFTC (2001). The sample covers the quarterly data of 11 major flour firms in the period from 1994:1 to 1999:1. Since one of these firms did not enter into the market until 1998, we have 215 observations. While the data has some advantages previously mentioned, its main drawback is that it relates only to 5 years and 1 quarter. However, the collusion began at least from 1991. Thus, the data cover only, at most, half of the affected period, and there are no non-cartel periods represented therein. Nevertheless, this paper still hopes to draw some strong conclusions, in particular to the role of excess capacity in this twostage game. 5.3. Estimates and interpretation of parameters This subsection estimates the model by using non-linear three-stage least squares. The covariance matrix is corrected for conditional heteroscedasticity and serial correlation.23 The results are reported in Table 2. Column A shows that most variables are significant except income coefficient e. This might reflect the fact that flour is a necessity such that its expenditure does not 23
See White (1980).
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Table 2 Coefficients estimates (non-linear three-stage least squares estimates) Parameters to be estimated
(A)
(B)
a⁎ b d e α
−2.317⁎ (− 2.629) 0.024⁎ (4.692) 0.152⁎(12.695) 0.0001 (0.255) 0.827⁎ (4.181)
−2.424⁎ (−3.046) 0.023⁎ (7.331) 0.154⁎ (16.426) 0.869⁎ (6.461)
Notes: Number of observations = 215. The figures in brackets are t values. ⁎ denotes that the estimate is significant at the level of 1%.
change with income.24 In the subsequent simulation analysis, we still stay with the empirical results that include income as an explanatory variable and use the figures in column A as the baseline specification. Table 2 also indicates that estimated parameters conform to the theory. Both the own-price coefficient b and the cross-price coefficient d have the expected sign. A further consistency check shows that the own-price elasticity of demand, which is evaluated at the sample mean, is 3.4. Since the stylized facts indicate a certain degree of collusiveness existing in the flour industry, it follows that firms must price in the elastic part of their linear demand schedules. A point elasticity of demand above unity therefore is consistent with the theory. 5.4. Evidences of collusion The empirical results present some evidences to suggest that collusion existed among firms. The estimated conjectural elasticity (α ˆ ) is 0.83, which is significantly different from − 1/10 (0) as perfect competition (symmetric Cournot) predicts. Although α ˆ is less than the level of the perfect collusion (1), the evidence still suggests that millers did exercise market coordination to a certain extent. According to Davidson and Deneckere (1990), perfect collusion can be sustained only if the cost of capacity is zero such that firms can carry considerable capacity to support the monopoly price in the unconstrained semi-collusive equilibria. However, in the real world, capital price cannot be zero. Thus, our excess capacity could only support some prices between the Cournot level and the monopoly level, but not the monopoly price.25 5.5. Conduct parameter vs. measurement of market power — a test of robustness Our model basically uses the estimated conjectures to investigate firms' behaviors. However, a number of objections have been raised against this methodology. For instance, Corts (1999) argues that α ˆ typically mismeasures the level of market power if industry behavior corresponds to a dynamic oligopoly game.26 According to the Corts critique, α ˆ underestimates the degree of market power if demand shocks are not fully persistent, and it may fail to measure any market power whatsoever when demand shocks are completely transitory. Conversely, the more persistent demand 24
Thus, its income elasticity is near to zero. Davidson and Deneckere hence referred to these equilibria as constrained semi-collusive equilibria. There is generally a continuum of constrained semi-collusive equilibria. 26 The repeated game with trigger strategies is dynamic, while the conjectural variation model is clearly static. Hence, there might be a potential bias when the dynamic payoff is calculated based on estimates from a static model. 25
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Table 3 Dickey–Fuller and Phillips–Perron Tests Test
Variable
Dickey–Fuller (with 0 lags) Dickey–Fuller (with 4 lags) Phillips–Perron (with 0 lags) Phillips–Perron (with 4 lags)
Price
y
Critical values⁎
− 1.70 − 1.49 − 1.79 − 1.77
− 1.49 − 1.54 − 1.58 − 1.84
− 2.65 − 2.67 − 2.65 − 2.65
⁎The critical values are at the 10% significance level. These test statistics all have a non-standard distribution, and these distributions depend upon the number of lags.
shocks become, the more accurate α ˆ can measure market power. Thus, α ˆ can accurately estimate market power in case demand shocks are fully persistent. The Corts critique could be explained by the essence of the efficient supergame equilibrium. Under the equilibrium, the supply Eq. (7) must guarantee a quantity that balances current gains to deviation against discounted future profit losses that would result from the deviation. For instance, a higher Price increases market demand for flour, which induces the short-term gains to deviation. If the demand shocks were persistent, then the observations of a higher Price would indicate an increased probability of observing high future demand states.27 This leads to higher future collusive gains such that the expected future losses resulting from punishment for a current deviation will increase. Thus, a higher Price increases both current gains to deviation and future losses from punishment simultaneously. This makes q less responsive to Price such that θˆ is robust to changes in Price (demand shocks).28 In order to test the degree of persistence of the demand shocks, both Dickey–Fuller and Phillips–Perron tests are performed to judge if the demand shocks are persistent. The evidence in Table 3 shows that, at the 10% significance level, one cannot reject the null hypothesis that demand shocks are fully persistent. Thus, one can safely claim that the estimated conjectures could be used to measure the average collusiveness of conduct. 6. Disadvantage collusion This section uses the TFTC data to simulate if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits as Matsui (1989) and Fershtman and Gandal (1994) predict.29 6.1. Simulation The demand information used to simulate equilibrium profits under different regimes is obtained from the empirical results of column (A) in Table 2. Thus, the demand function could be written as: P ¼ −2:317−0:024Q þ 0:152Price þ 0:0001y þ residuals:
27
In the case of fully persistent, the value of Price may provide perfect information about future demand states and may therefore change the expected discounted future profit losses incurred by punishment. 28 Conversely, if demand shocks are intertemporally independent, then higher Price increases short-term gains to deviation, but expected future losses do not change. Firms have to increase q in the current period so as to offset this increased incentive to deviate. 29 The lower semi-collusive profits resulted from overinvestment in the first stage.
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Table 4 Quarterly average gains and losses from adherence and deviation Firm
1 2 3 4 5 6 7 8 9 10 11
(1)
(2)
(3)
(4)
(5)
(6)
(7)
πi,cournot (1000 NT$)
πi,semi-collusion (1000 NT$)
(1)–(2) (1000 NT$)
Excess capacity (tons)
P KKi / Pqi
πexcess i,cournot (1000 NT$)
(2)–(6) (1000 NT$)
13,813 27,663 4744 15,222 8976 8564 36,075 11,597 29,622 50,675 3784
10,837 4714 1299 4768 1286 6502 16,223 342 21,971 51,755 12,684
2976 22,948 3445 10,453 7690 2063 19,852 11,255 7652 − 1080 − 8900
10,380 (9th) 20,037 (1st) 16,805 (3rd) 14,589 (4th) 11,328 (7th) 11,300 (8th) 13,623 (5th) 18,147 (2nd) 13,139 (6th) 4644 (10th) 3991 (11th)
1.36 (9th) 3.11 (1st) 1.73 (6th) 2.19 (3rd) 1.90 (4th) 1.59 (7th) 1.86 (5th) 2.88 (2nd) 1.57 (8th) 0.90 (10th) 0.88 (11th)
9022 5106 − 6689 1262 − 2057 2749 14,106 − 8,427 18,774 48,158 2342
1814 − 391 7989 3507 3343 3753 2117 8769 3196 3596 10,342
Notes: The figures in brackets denote the ranks of the variable values.
Substituting the means of Price and y into the equation can get the estimates of flour prices under different levels of industry output as: Pˆ ¼ a− ˆ ˆbQ ¼ 9:704−0:024Q:
ð16Þ
The TFTC data contain P, qi, c, and ri. One can put this information together to check if the overall semi-collusive equilibrium profits are smaller than the non-cooperative equilibrium profits. The paths of equilibrium profits could be obtained as follows. 1. Insert a, b, c, and ri into Eqs. (3) and (4) to solve a firm's qi,cournot as well as industry's output Qcournot for each quarter during the period of 1994:1–1999:1. Find the values of Pcournot and πi,cournot by substituting Qcournot into Eq. (16). 2. Use Eq. (A1) to calculate the simulated paths of quantity and price under the regime of semicollusion Qsemi-collusion and Psemi-collusion. Calculate overall semi-collusive (first stage) profits πi,semi-collusion by using Eq. (9). 3. It is well known that the monopoly output can be written as Qmono ¼ ða−rÞ=2b. As an approx1 X11 imation, I plug r ¼ r , a, and b into this formula and get the paths of Qmono and Pmono. i¼1 i 11 One has to make sure that the actual industry output conforms to the semi-collusive path. Davidson and Deneckere (1990) propose that perfect collusion cannot be sustained, because r N 0. The simulated evidence seems to support their argument. During the sample period, the simulated value of quarterly average industry production under a semi-collusion regime (11 dominant firms) is 133,847 metric tons, which is quite near to actual quantity of 117,152 metric tons. This figure is higher than the prediction of the perfect collusion model (90,817 metric tons), and much lower than the Cournot quantity (213,396 metric tons).30 This evidence suggests that the semi-collusion equilibrium quantity is closer to the perfectly collusive level than it is to the Cournot level. It also 30
In the Davidson–Deneckere model, any output between the Cournot level and the monopoly level can be sustained as an equilibrium.
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indicates that the conjectural variation model explains the actual output path better than the Cournot strategy does. 6.2. Disadvantageous collusion Columns (1) and (2) in Table 4 report the quarterly average profits under regimes of semicollusion and non-cooperative Cournot, respectively.31 Evidently, for most firms, the overall semi-collusive equilibrium profits are much smaller than the non-cooperative equilibrium profits. These firms are better off not colluding. The two exceptions are firm 10 and firm 11. As previously mentioned in Section 2, these two firms have relatively small excess capacity such that they do not have to undertake heavy capital expenditure. This argument is supported by column (5), which shows that their capital–sales ratios ðPK Ki =Pqi Þ are much lower than the ones of other firms. 6.3. Decision not to collude in the second stage is not credible Although overall semi-collusive equilibrium profits may be low, it is important to note that for a given choice of variables in the first stage, such as the policy-induced excess capacity in our case, the firms are better off colluding in the second stage.32 In order to verify this argument, column (6) calculates the firms' profits, given that policy-induced excess capacity already exists in the first stage and firms produce Cournot quantity in the second stage. 33 pexcess i;cournot ¼ Pcournot qi;cournot −cqi;cournot −ri ki;semicollusion
Here, ki,semi-collusion is the capacity determined under the regime of semi-collusion in which excess capacity exists. Column (7) indicates that, given the same level of excess capacity, most firms' profits under the regime of semi-collusion are more than that under the regime of noncooperative competition.34 Thus, given the capacity determined in the first stage, semi-collusion still induces positive monopoly rents in the second stage. However, these gains have to be tradedoff against the superfluous expenditure on capacity. The size of this inefficiency depends on the level of capacity that is installed, which is a function of the incentives to gain a bigger share of profits. It is import control that conclusively imposes an inefficient market-sharing rule, which creates incentives for firms to build up excess capacity in the first stage. While collusion in the second stage yields lower overall profits for the sake of heavy capital expenditure, the decision not to collude must be accompanied by some types of deregulation in the first stage, otherwise the firms will wish to renegotiate and the decision not to collude in the second stage will not be credible. 7. Conclusion In the collusive regime, firms have to bargain on how to divide the monopolized profits. The literature generally uses the ‘relative capacity’ sharing rule and proposes that each firm's sales P For instance, profits for firm i are computed by 1=21 21 t¼1 ðpi;semicollusion;t Þ. This conforms to the spirit of subgame perfection. 33 Note that πi,cournot = Pcournot qi,cournot − cqi,cournot − riqi,cournot. 34 Firm 2 is the outlier, because its excess capacity and capital expenditure are so high that it cannot take advantage of collusion in the second stage. 31 32
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volume is proportional to the size of its plant. For instance, Fershtman and Gandal (1994, p. 145) demonstrate this point of view: We find it attractive, because there is a large body of ‘anecdotal evidence’ that cartels use such a rule in setting output quotas. In order to test the feasibility of this kind of market-sharing rule, this article uses Taiwan's flour cartel case to investigate its impact on firms' investment decisions and their profit paths. The evidence shows that firms have to overinvest so as to increase their market shares, since the cartel allocates market shares according to firms' production capacity. This inevitably creates excess capacity. Furthermore, if the capital price is not too cheap, then the overinvestment may be large enough to make the overall semicollusive profits smaller than the non-cooperative profits. Under such cases, the rational firms are better off not colluding. Why did rational flour firms choose such kind of disadvantageous market-sharing rule? Like conventional wisdom, in our case the key point still lies on the fact that this market-sharing rule is imposed and regulated by the government. Government regulation seems to be the primary reason to create such a predicament. It is thus seen that ‘anecdotal evidences’, in which the relative capacity sharing rule is commonly used by cartels, cannot be validated in the real world, except when a regulation shock happens which seriously distorts the mechanism to collude as this article mentions. Hence, regulators should be careful in the enforcement of the regulation. Appendix A. Semi-collusion vs. competition A.1. The industry carries excess capacity in the semi-collusive equilibrium Proof. By plugging Eq. (1) and e ¼ P=bQ into the first-order condition in the second stage, Eq. (7), one can express the industry's equilibrium output and profit as: a Q¼ ; and ðA1Þ b½1 þ a þ ð1−aÞH P2 ¼
a2 ½a þ ð1−aÞH b½1 þ a þ ð1−aÞH2
:
ðA2Þ
On the other hand, Eq. (8) and the first-order condition in the first stage, Eq. (11), shows that the equilibrium capacities for the individual firm and industry are: ki ¼ K−ri K¼
K2 ; and P2
ðA3Þ
ðn−1ÞP2 P : ri
Finally, using Eq. (12), one can obtain K N Q.
ðA4Þ □
A.2. Semi-collusive equilibrium profits are lower than Cournot equilibrium profits Proof. Summing Eq. (9) over i and using ki and K, one can write the industry's profit function in the first stage as: " P 2 # n X r 2 P1 ¼ P2 − ri ki ¼ P2 ð2−nÞ þ ðn−1Þ P i 2 ; ðA5Þ ð ri Þ i¼1
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while the equilibrium profit in the non-cooperative case is given by Eq. (5). Using Eq. (12), a comparison of Eqs. (5) and (A5) shows that equilibrium profits are lower under the semi-collusive setting. □ Appendix B. Data description and construction⁎ Variables
Number of observations
Mean
Standard error
Minimum
Maximum
P (NT$) c (NT$) Q (1000 tons) H P rice (index) ri (NT$) P KKi / Pqi
215 214 215 215 215 215 211
9.64 7.30 192.59 475.52 96.46 1.54 1.88
0.70 0.78 18.92 34.72 3.77 0.63 0.78
8.90 6.79 159.90 417.38 89.66 0.66 0.76
11.04 9.45 228.42 530.90 100.00 3.13 3.92
⁎All the data are taken from the TFTC (2001) dataset, except Price. (1) P is the average weighted price of three types of flour sold in the market. The weights are the sale volumes. P is deflated by GNP deflator. (2) c is the wheat cost to produce 1 kg of flour. (3) Q = Σqi is the industry output where qi is the output of firm i. (4) si = qi / Q is the market share. (5) ri = λiPK is the cost of capacity. (6) Price is the index of rice price, which is taken from Commodity Price Statistics reported by the Directorate-General of Budget, Accounting and Statistics, Executive Yuan, Taiwan. (7) PKKi / Pqi is the capital–sales ratio, where PKKi is the cost of fixed assets, and Pqi is total sale of firm i. References Brander, H., Harris, R., 1984. Anticipated Collusion and Excess Capacity, mimeo, University of British Columbia. Bresnahan, T., 1989. Empirical methods for industries with market power. In: Schmalensee, R., Willig, R. (Eds.), Handbook of Industrial Organization II. Elsevier Science Publishers, Amsterdam, pp. 1001–1055. Corts, K., 1999. Conduct parameters and the measurement of market power. Journal of Econometrics 88, 225–227. Davidson, C., Deneckere, R., 1990. Excess capacity and collusion. International Economic Review 31, 521–541. Fershtman, C., Gandal, N., 1994. Disadvantageous semicollusion. International Journal of Industrial Organization 12, 141–154. Genesove, D., Mullin, W., 1998. Testing static oligopoly models: conduct and cost in the sugar industry. Rand Journal of Economics 29, 355–377. Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcome. Bell Journal of Economics 14, 326–337. Ma, T., 2005. The collusive equilibrium in a quantity-setting supergame: an application to Taiwan's flour industry. Review of Industrial Organization 27, 107–124. Ma, T., in press. Import quotas, price ceilings and pricing behavior in Taiwan's flour industry, Agribusiness. Martin, S., 1993. Advanced Industrial Economics. Blackwell, Cambridge. Matsui, A., 1989. Consumer-benefited cartels under strategic capacity investment competition. International Journal of Industrial Organization 7, 451–470. Mitchell, S., 1993. The welfare effects of rent-saving and rent-seeking. Canadian Journal of Economics 26, 660–669. Osborne, M.J., Pitchik, C., 1983. Profit-sharing in a collusive industry. European Economics Review 22, 59–74. Osborne, M.J., Pitchik, C., 1986. Price competition in a capacity-constrained duopoly. Journal of Economic Theory 38, 238–260.
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