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Oligopolistic Market Structure in the Japanese Pistachio Import Market

1Department of Agricultural Economics, University of Kentucky, 302 Barnhart Building, Lexington, KY 40546, USA

Citation Information: Journal of Agricultural & Food Industrial Organization. Volume 11, Issue 1, Pages 87–99, ISSN (Online) 1542-0485, ISSN (Print) 2194-5896, DOI: 10.1515/jafio-2013-0005, September 2013

Publication History

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Iran is the major producer of pistachio nuts in the world. Iran dominated the international pistachio export markets until 1982, when a new competitor, the United States, emerged in the international markets. Currently, both Iran and the United States are major pistachio exporters to Japan. In this study, we address the following empirical question: Is the Japanese pistachio import market best characterized by Cournot or Bertrand duopoly competition or some other form of game? We use two historical data sets on pistachio prices and quantities imported by Japan from Iran and the United States and estimate the demand functions for these two main exporters. Considering two different strategic variables, quantity and price, full information maximum likelihood (FIML) resulted in different estimates. We used normalized likelihood ratio statistics for the model comparison. Having proper game-specific nonlinear-equation restrictions enabled us to form six alternative models. The model that best fit the data was the Stackelberg model with US quantity leadership.

Keywords: oligopolistic markets; Cournot model; Bertrand model; Stackelberg model; likelihood ratio tests; pistachio nuts; Japan

JEL Codes: Q17; F12; C72


Iran dominated international pistachio markets for a long time. Iran was the major producer and exporter of this commodity in the world until 1982, when a new competitor, the United States, emerged in the international markets and took over the majority of Iran’s traditional export markets, mainly in Europe, Japan, and other countries. Pistachio nuts are a heterogeneous commodity, and the quality of Iran’s pistachios, especially in terms of taste, differentiates this commodity in the international markets. This study investigates the possibility of oligopolistic behavior by these two main competitors in the Japanese import market.

Pistachio trees grow naturally in dry and desert climate areas and are native to Iran, Syria, Turkey, Greece, Turkmenistan, Pakistan, and Afghanistan. Pistachio trees were first introduced into the United States in 1954, but the industry was not commercialized until 20 years later. During this time, the United States was mainly importing pistachios from Iran (Zheng 2011). Iran and the United States export quantity, value, and unit price are compared in Figures 1, 2 and 3, respectively, for the period 1961–2008. The shock of Iran’s revolution in 1979 and the aflatoxin food safety incident in 1997, in which European countries rejected a large shipment of pistachios from Iran, helped the United States establish a strong rivalry with Iran in international pistachio markets.

Figure 1

Total export quantity of Iran and United States 1961–2008.

Figure 2

Total export value of Iran and United States, 1961–2008.

Figure 3

Total export unit value of Iran and United States, 1961–2008.

Historical data during the period of 1982–2008 show that the pistachio market in the world changed from a monopoly by Iran to a duopoly formed by Iran and the United States. This duopoly dominated the world markets in the 1980s, but a dramatic change occurred in the 1990s and since then US pistachios have gradually penetrated the international markets. After 1998, a year after the aflatoxin contamination case of an Iranian shipment to Europe, these changes started to catch up with Iran. Japan, one of the traditional markets for Iran’s pistachios, is a good example of this change in the market. According to Japan’s customs’ statistics, a dramatic decline in Japan’s total import affected Iran more than other exporters. Japan’s total import from Iran dropped from almost 7,500 tons in 1995 to 240 tons in 2010; meanwhile, the United States experienced a steady increase in its total export quantity. Figure 4 shows the change in the world market share for Iran and the United States during 1961–2008. The decreasing trend of Iran’s share is more obvious after the food safety incident in 1997. Figure 5 shows Japan’s total import quantity of pistachios.

Figure 4

Market shares of Iran and United States, 1961–2008.

Figure 5

Japan total pistachio import quantity from Iran, United States, and the world.

This change can be seen in market shares as well. Iran was providing between 80 and 90% of Japan’s pistachio imports in the 1980s and 1990s. As Figure 6 shows, after 1998, Iran’s market share dropped drastically and by the end of 2010, the United States became the main exporter of pistachio nuts to Japan. Zheng, Saghaian, and Reed (2012) address factors affecting such dramatic changes. They investigated structural games played by the two main exporters during this period.

Figure 6

Iran and United States market shares in Japan’s pistachio import market.

The focus of this research is the interesting empirical question of whether the Japanese pistachio market is best characterized by either Cournot or Bertrand duopoly competition or some other form of game. To be effective, the choice of policy instruments depends highly on the strategic variables and the importance of knowing the international market structure and subsequently identifying the optimal policy. International commodity markets are characterized by price or quantity competition and product differentiation. An understanding of the form of the strategic interaction is important if realistic models are to be developed with which to analyze international trade and trade policy in commodities (Carter and MacLaren 1997).


There are several studies on collusive and non-collusive behavior in international commodity markets. Gasmi, Laffont, and Vuong (1992) proposed a methodology for the study of market conduct combining game theoretic considerations and tests for non-nested hypothesis. In order to have structural econometric modeling, they started from the specification of firms’ demand and cost functions, which determine firms’ payoffs. Then, they introduced behavioral assumptions describing different market situations through the consideration of some simple equilibrium paths and their relevant first-order conditions. An econometric model then forms each hypothesized market structure. Since these models are non-nested generally, they use the test statistic suggested by Vuong (1989) for non-nested hypotheses to assess relative performance of competing models. Applying this methodology, Gasmi, Laffont, and Vuong (1992) analyzed collusive behavior in a soft drink market using an empirical methodology. They considered price and advertising as strategic variables. Besides Nash and Stackelberg behaviors, they studied collusion on both of those strategic variables, collusion on one variable and competition on the other; they used data on Coca-Cola and Pepsi-Cola markets for the period 1968–1986 and estimated cost and demand functions using full information maximum likelihood. Their empirical results suggest that there exists some tacit collusive behavior in advertising between these two companies while such behavior on prices is not supported by the data.

Carter and MacLaren (1997) used the same methodology to study the Japanese market for imported beef. The United States and Australia are the main beef exporters to Japan. They considered six non-collusive and non-nested models with price and quantity as strategic variables. Based on the test statistics, the model that fit the data best was a Stackelberg model with price leadership by Australia. Saghaian and Reed (2004) also studied the Japanese beef market to examine market power among the exporters. They used disaggregated beef by cuts and form. They estimated a residual demand model for the main four competitors: Australia, the United States, Canada, and New Zealand. They found that the highest markup of the price over marginal cost belongs to US frozen ribs, which is the only indication of market power by US exporters. Although market share of Australia and New Zealand differed a great deal, both enjoyed some degree of market power due to their close proximity to the Japanese markets and the freshness of their products.

Zheng, Saghaian, and Reed (2012) studied international pistachio markets, especially factors affecting the variations of US exports. They evaluated the US role in world production and trade of pistachios and considered the impact of market conditions and food safety shocks. Their results showed that advanced technology and a reputation for higher food safety standards are the great advantages of US pistachio producers in order to improve their international market shares.

Theoretical models

Price model

If price is assumed to be the strategic variable, according to Carter and MacLaren (1997), export demand function for Iran (ir) and the United States (us) would be: where qi is the quantity of pistachios imported by Japan from country i and pk is the price in yen of the country k’s pistachio exports with k = i,j while y is the Japanese per capita income, and s and s are the unknown parameters.

The profit function for exporter i is given by: where ci represents the marginal cost of the ith exporter. Although some studies like Carter and MacLaren (1997) and Gasmi, Laffont, and Vuong (1992) included specific exogenous variables which account for cost of production, other works such as Saghaian and Reed (2004) and Goldberg and Knetter (1999) suggested the use of a bilateral exchange rate as ideal cost shifter in the international setting since the variation in exchange rate would shift cost of exporters in target market.

In the case of Bertrand–Nash equilibrium (pbir, pbus), the first-order conditions for profit maximization are given by: By substituting the reaction function for the United States, pus = Rus(pir), into the profit function for Iran and maximizing with respect to pus, the Stackelberg leader equilibrium (psirir, psirus), in which Iran is assumed to be the leader, is obtained. The condition for this equilibrium is given by: replacing the subscript ir(us) with us(ir) would give us the equilibrium for the case that the United States is the leader.

Quantity model

If the strategic variable is quantity, the inverse demand function for each country would be: where s and s are unknown parameters. Exporters demand function now is: Therefore, unique Cournot–Nash equilibrium, (qcir, qcus), is: Similar to the Bertrand case, Stackelberg leader equilibrium (qsusus, qsusir), in which the United States is assumed to be the leader, follows the same rule, i.e., substituting the follower, Iran, reaction function (defined in terms of quantity) into the profit function of the leader and maximizing with respect to qus. Thus, the Stackelberg equilibrium with the United States as the quantity leader is given by: In case Iran is the Stackelberg leader in quantity, equilibrium has the same form but subscripts should be changed from us(ir) to ir(us). So, there are six alternative models (see the Appendix A for the six functional forms) – namely, Bertrand (eqs [1] and [3]), Stackelberg in price (eqs [1], [3.1], and [3.2]), Cournot (eqs [4] and [6]), as well as Stackelberg in quantity (eqs [4], [6.1], and [6.2]) – that can be presented in a general linear simultaneous equation form as follows: where uits are jointly normally distributed error terms by assumption with covariance matrix . Furthermore, s represent the intercept in eqs [1] and [4]; and respectively. To obtain the econometric structure of each game, some game-specific nonlinear-equation restrictions should be imposed on λs that are given in Table 1.

Table 1

The structure of matrix [7] for each model, M1 through M6.

Accordingly, (Vuong 1989) the likelihood ratio (LR) statistics can be a good test for model selection. A good property of this test is that neither of the competing models needs to be specified correctly. For each pair of models (Mf, Mg), we can calculate the LR statistic normalized by: where and are the estimated residuals and covariance matrix for model Ms, s = f,g. The resulting normalized statistic is asymptotically distributed normal under the null hypothesis of equal fit (Gasmi, Laffont, and Vuong 1992). Using the standard normal distribution at some significance level and relevant critical value c, if the normalized LR is smaller than c in absolute value, we cannot reject the null hypothesis and therefore we cannot discriminate between the two models. On the other hand, if the calculated test statistic is greater than +c we conclude that Mf is better while normalized LR less than –c implies that Mg is significantly better.

Data description and empirical results

Data description

Two data sets, annual and quarterly (see the Appendix B), were used separately to estimate and compare the models. Annual data on Japan’s import of pistachios from Iran and the United States are used from 1988 through 2010, forming a total of 23 observations. To deal with possible problems due to low number of observations in the annual data set, quarterly data were also obtained from the same sources for the second quarter of 1992 until the end of 2011, which expanded the data set to 79 observations. Total value of import data for each country of origin was obtained from Japanese customs data set, and unit prices were computed from that information. Data on exchange rates were obtained from the Research and Statistics Department in the Bank of Japan, and Japan’s per capita GDP was obtained from IMF International Financial Statistics.

Table 2 presents the descriptive statistics of the data used for the model estimation. From 1988 until 2010, on average Japan imported nearly 3,000 tons of pistachio nuts from Iran each year, with the average value of 1.6 billion Yens and unit price of 700 thousands Yens per ton. Average annual volume of imports from the United States in the same period was 1,500 tons, valued at one billion Yens. Unit price for US pistachio was 610 thousand Yens per ton. GDP per capita of Japan during the study period was 3.7 million Yens.

Table 2

Descriptive statistics of model variables.

Empirical results

Eq. [7] is estimated for each of the six models with the two sets of annual and quarterly data, using the full-information maximum likelihood estimator in SAS, which allowed us to impose nonlinear restrictions presented in Table 1. The results for price and quantity models are presented in Tables 3 and 4, respectively.

Parameter estimates for the price models (comparing annual with quarterly data).

Parameter estimates for the quantity models (comparing annual with quarterly data).

The own-price coefficients, and , for all the models in Table 3 have the expected negative sign with both annual and quarterly data sets. is significantly different from zero for the Bertrand and the Stackelberg models with US price leadership, while is statistically significant for the Bertrand and the Stackelberg models with Iran price leadership, in both data sets. Although the magnitude of estimated coefficients is smaller using the quarterly data set, comparing the two sets of results does not show much qualitative differences. Table 4 presents estimation results for the three quantity models using both annual and quarterly data sets.

It is important to note that in Tables 3 and 4 several variables are not statistically significant, raising some doubts about the overall validly of the results. However, these results are consistent with the results in Carter and MacLaren (1997) and Gasmi, Laffont, and Vuong (1992), and the key variables including own prices in the demand equations are statistically significant and have signs consistent with the theory. The competing models have simple specifications because the focus is not merely to estimate the demand equations, but to get to the LRs for each equation. Gasmi, Laffont, and Vuong (1992) emphasize that the competing models do not need to be correctly specified in order for the LR tests to be valid. The possible misspecification problem has also been addressed by both Carter and MacLaren (1997) and Gasmi, Laffont, and Vuong (1992). Carter and MacLaren (1997) note that there is a possibility that the best of the models specified may not be the correct model since the actual behavior of the market may differ from the choice of the game-theoretic equilibrium.

The own-price elasticities of demand, at the average point of the annual data set for Bertrand model for Iran and the United States are –0.94 and –1.24 for the annual data and –0.97 and –1.22 using the quarterly data, respectively. Same elasticities for the Stackelberg model with Iran’s leadership are –0.72 and –1.26, and for the US leadership they are –0.95 and –4.18 with the annual data. Considering estimated coefficients using quarterly data, own-price elasticities for the Stackelberg model with Iran’s leadership are –1.86 and –1.22 for Iran and the United States, respectively. These elasticities for the model with the US leadership are –0.97 and –1.48. Log-likelihood statistics are very close to each other for the models using similar data sets. Likelihood function for the third model has a smaller absolute value. Income elasticities for Iran’s pistachio for these three models are 2.28, 2.07, and 2.34 with the annual data, respectively, which shows that Iranian pistachio is a luxury commodity, and for US pistachio are –1.73, –3.3, and –3.48. The negative sign for US pistachio income elasticity implies that an increase in Japanese income makes them switch to a more luxurious good, i.e., Iranian pistachio.

Although it seems that the results of quantity models, in term of statistical significance and parameter signs, are not as good as price models, the Cournot model has the highest likelihood statistics in absolute value among all those six models, using both data sets. In the quantity models, similar to the price models, we expected to get a negative sign on income parameters for US pistachio demand equations, indicating the substitution of lower quality (taste) good with more luxurious one.

Results for the model comparison based on the normalized LR statistics are presented in Table 5. Each column shows two sets of statistics based on the type of data used for the estimation. Apart from a slight difference in magnitude of the statistics, overall the results are the same using annual and quarterly data sets. To calculate the statistics, the model in the row is subtracted from the model in the column. Hence, a negative sign implies that the model in the column is preferred to the model in the row. Models included in rows are M1 through M5, while the models in columns are M2 through M6. For each comparison of models, we have two sets of statistics, considering annual and quarterly data. Overall, the table consists of five rows and ten columns of statistics.

Table 5

Normalized LR statistics.

Considering 0.05 level of significance, the critical values of the standard normal variable would be –1.96 and 1.96 for the annual data set. All price models (M1, M2, and M3) are significantly better than the Cournot model (M4) because the LR statistics are positive for both annual and quarterly data sets (see values in column 5 and 6). The quantity Stackelberg models (M5 and M6) are also preferred to the Cournot model (M4) because the LR statistics are negative and statistically significant (–11.91 and –4.90 for the annual data set, and –17.36 and –19.52 for the quarterly data set, respectively). Using the annual data sets, the difference between models M6 and M4 is statistically significant at the 5% significance level, but the difference between M6 and models M1 and M3 would be statistically significant at the 20% significance level. M6 is better than M5 because of the negative LR statistics for both annual and quarterly data set, although not statistically significant. All in all it seems that M6 is preferred to all the other models within this data set, because of the negative LR statistics in the last column. Also, none of the price models has statistical significance superiority to the other price models.


Applying policies like country of origin labeling, food safety issues, and quality factors like taste, differentiates goods more and more in the international food markets. This is evidence of imperfect competition in global markets. In a specific agricultural commodity like pistachio nuts, oligopolistic competition is more likely because there are two major producers and exporters in the world. In order to have a proper trade policy intervention, it is appropriate to characterize oligopolistic markets by the games that exporters play and the price or quantity strategic variables they choose.

In this research, we investigated such competitive behavior for the Japanese pistachio import market. Six non-nested models were estimated for which price was the strategic variable in the first three models and quantity in the remaining models. According to the statistical methods used, the price models fit the data better than quantity models. The model which best fits the data was Stackelberg with the US quantity leadership (M6).

In that situation, the United States, as the leader, plays a game similar to capacity accumulation game, and then it would increase investment to force Iran to restrict its own quantity, leading to a greater market share for the United States. Here the United States might benefit from first mover advantage. This market structure is similar to a Cournot game when one of the players chooses to play aggressive to increase market share for every output choice of the rival. The result would be the rightward shift in its reaction function, moving the equilibrium to the southeast, as shown in Figure 7. In this figure, firm 2 produces less than what it used to produce relative to the previous equilibrium situation.

Figure 7

Firm 1 decides to play “Tough” in a Cournot market.Source: Besanko et al. (2010).

However, any leader–follower Stackelberg game (with either Iran or the United States as the leader) in such a market structure requires the assumption of perfect information (i.e., Iran as the follower in this case would observe the quantity chosen by the leader.) Otherwise, the game would be reduced to a Cournot competition (Tirole 1988). Figure 8 elaborates the difference between Cournot and Stackelberg equilibrium in which firm 1 is the leader. Assuming Ri as the reaction function of firm i (i = 1,2), point C shows the Cournot equilibrium while point S shows Stackelberg equilibrium. Outcome of each firm in Cournot and Stackelberg equilibrium is depicted by qci and qsi, respectively. Normally, Stackelberg total outcome is higher than Cournot total outcome, which results in a lower price in the market.

Figure 8

Cournot and Stackelberg equilibrium.

In comparison to Cournot games, sequential output decisions in a model of leaders and followers can result in higher social welfare. This is due to having smaller deadweight losses in leadership models in comparison with Cournot models since concentration is less in the former (Economides 1993).

Production costs and product differentiation can play a significant role in decisions for strategic interactions. According to van Damme and Hurkens (1999), leadership of a country can be continued as long as the production costs of the follower are higher than the leader. As a matter of fact, the United States is much more productive and has a much higher yield per acre than Iran (Zheng, Saghaian, and Reed 2012). Thus, Iran, by reducing its relative production costs, and/or using product differentiation could potentially regain the lost market share in the Japanese pistachio import market.

Overall, since under general conditions in Stackelberg games, quantity competition is less competitive than price competition (Dastidar 2004), there is a possibility of collusive behavior in this market structure. Tacit collusion in this market is comparable to a Bertrand game where a firm decides to play the “soft” strategy, and charges a higher price for every price level picked by the rival. This is shown in Figure 9. Firm 1 moves its reaction function rightward, resulting in higher prices for both firms. Both firms benefit from firm 1’s soft play and increase profits. Thus, including non-competitive games to the analysis help explain tacit collusion possibilities in the Japanese pistachio nut import market. More research is required to address these issues thoroughly.

Figure 9

Firm 1 decides to play “soft” in a Bertrand model.Source: Besanko et al. (2010).

Bertrand model (M1)

Stackelberg model with Iran price leadership (M2)

Stackelberg model with the US price leadership (M3)

Cournot model (M4)

Stackelberg model with Iran quantity leadership (M5)

Stackelberg model with the US quantity leadership (M6)

The annual data set.

The quarterly data set.


Journal Paper Number 13-04-067 of the Kentucky Agricultural Experiment Station. The authors would like to thank the editor and anonymous referees for their insightful comments.


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