Concentration, market imperfections, and interbranch organization in the Italian processed tomato supply chain

Čechura, Lukáš; Samoggia, Antonella; Jamali Jaghdani, Tinoush Article — Published Version Concentration, market imperfections, and interbranch organization in the Italian processed tomato supply chain Agricultural Economics Provided in Cooperation with: Leibniz Institute of Agricultural Development in Transition Economies (IAMO), Halle (Saale) Suggested Citation: Čechura, Lukáš; Samoggia, Antonella; Jamali Jaghdani, Tinoush (2024) : Concentration, market imperfections, and interbranch organization in the Italian processed tomato supply chain, Agricultural Economics, ISSN 1574-0862, Wiley, Hoboken, NJ, Vol. 55, Iss. 4, pp. 603-620, https://doi.org/10.1111/agec.12835 , https://onlinelibrary.wiley.com/doi/10.1111/agec.12835 This Version is available at: https://hdl.handle.net/10419/299878 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Received: 14 November 2022 Revised: 10 December 2023 Accepted: 21 March 2024 DOI: 10.1111/agec.12835 ORIGINAL ARTICLE Concentration, market imperfections, and interbranch organization in the Italian processed tomato supply chain Lukáš Čechura1Antonella Samoggia2Tinoush Jamali Jaghdani3 1Department of Economics, Faculty of Economics and Management, Czech University of Life Sciences Prague, Prague, Czech Republic 2Department of Agriculture and Food Sciences, University of Bologna, Bologna, Italy 3Department of Agricultural Markets, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), Halle (Saale), Sachsen-Anhalt, Germany Correspondence Tinoush Jamali Jaghdani, Department of Agricultural Markets, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), Halle (Saale), Germany. Email: [email protected] Funding information European Union’s Horizon 2020 research and innovation programme, Grant/Award Number: 727243 Abstract The increase in market concentration and market power in the food supply chain is an issue of concern globally. This study focuses on an analysis of market imperfections in the Italian processed tomato food supply chain by considering changes in its supply chain governance from 2006–2018. The identification of the degree of non-competitive behavior is based on the derived mark-down and mark-up models using the latest developments in stochastic frontier methodology. The estimated models reveal some degree of non-competitive behavior in the input as well as in the output processing market. However, in consideration of the results on the supply chain governance during the study period, we argue that the establishment of an Interbranch Organization (IBO) could create fairly stable long-term food supply chain relationships benefitting all IBO members and in particular farmers despite the significant change in concentration levels in the Italian tomato processing sector after 2015. KEYWORDS concentration rate, food chain, interbranch organizations, Italy, market imperfections, stochastic frontier analysis, tomatoes JEL CLASSIFICATION D43, D71, L11, L13, Q13 1 INTRODUCTION Farm input markets, agricultural commodity trading, processing segments, and the retail network of food supply chains have witnessed an increasing concentration across the globe (Clapp, 2021). The emergence of powerful food retailers, along with continued increases in concentration among food manufacturers, raises issues of bilateral oligopolies and countervailing power in wholesale markets (Sexton & Xia, 2018). Although increase in concentration does not necessarily lead to an exercising of market power (Crespi & MacDonald, 2022; Deconinck, 2021), the conThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2024 The Authors. Agricultural Economics published by Wiley Periodicals LLC on behalf of International Association of Agricultural Economists. cern is that upstream market power in food value chain can create higher costs for downstream firms and downstream market power can create lower prices received for upstream firms. Furthermore, the increasing concentration and consolidation among food manufacturers and retailers reduces the potential trading partners for many farmers to only one or a few (Fałkowski et al., 2017, ch1), which can potentially reduce the bargaining power of the producers. The creation of Producers’ Organizations (POs) is one of the possible ways to increase the bargaining power of scattered primary agricultural producers, as POs make Agricultural Economics. 2024;55:603–620. wileyonlinelibrary.com/journal/agec 603 604 ČECHURA et al. bulk purchases of agricultural commodities, give technical assistance and advice to their members, and sell collectively to processing industries under European Union (EU) Regulation 1308/2013 (Samoggia et al., 2022). This Regulation, which is also known as the “Common Market Organisation (CMO) Regulation”, addresses the lack of bargaining power for atomized primary agricultural producers and also tries to deal with agricultural production crises. When farmers and processors or traders in the supply chain join together, they can form Interbranch Organizations (IBOs). IBOs are organizations for governing the supply chain without being involved in production, processing or trade themselves. They promote dialogue, market transparency and a reference price streamlining process in their food industry. The above-mentioned discussion makes the measuring of the level of this concentration an important issue. Therefore, by focusing on tomato processing in Italy, we have decided to test these concentration changes in this food supply chain.1Italy was the third largest producer of processed tomatoes worldwide in 2020 (with 5166 million tons and +7.6% compared to 2019) after the USA (in particular California, with 10,258 million tons), and China (5800 million tons) (Tomato News, 2021b). In Europe, Italy (55.4%), Spain (25%), and Portugal (12%) are the European countries with the highest production volumes of processed tomatoes (European Commission, 2022). Italy is the second exporting country at the global level (23.6%) after China (26.3%). As such, it is the first exporting country of finished processed tomato products in the EU, followed by Spain (12.5%) and Portugal (8.2%) (Tomato News, 2021a). In this article, we focus on the analysis of market imperfections in the Italian processed tomato supply chain from 2006 to 2018. Our aim is to identify the degree of market imperfections in the input and output tomato processing market, conduct a concentration analysis of the main companies of tomato processors and/or processing associations, and evaluate the managerial governance of the tomato supply chain regarding the sustainability, integrity and resilience from a static as well as dynamic perspective. By focusing on the timeline of changes during 2006–2018 in the Italian tomato supply chain, we test the effects of higher coordination and higher consolidation on market imperfection. The shaping of an IBO in North Italy, which was started in 2007 and was officially recognized in 2011 at the regional level and in 2012 at the European level, is a sign of higher coordination and increased bargaining power. Furthermore, increase in the Concentration Rate (CR) of the tomato processing industry after 2014 is also a sign of higher consolidation. In light of these two fac1This selection has been done under the framework of the EU Horizon 2020, VALUMICS project with grant agreement No. 727243. tors, this study extends the research on the analysis of market imperfections. In particular, in order to fill the research gap identified by exploring the effects of the IBOs, this article addresses the following research questions: (1) what degree of non-competitive behavior of the food processors with respect to farmers and/or retailers could be observed? (2) can we observe the links between market failures and chain governance? and (3) is the supply chain becoming increasingly competitive or can an idiosyncratic development be observed? Our identification of the degree of non-competitive behavior is based on the derived mark-down and markup models using the latest developments in stochastic frontier methodology. Using a stochastic frontier analysis (SFA) to detect the degree of market power was first applied by Kumbhakar et al. (2012) for mark-up models. Another novelty of our study is the application of this approach in the analysis of a tomato supply chain through the decomposition of the one-sided error term in the markup and mark-down models within both the transient and persistent components along with the relation of relative mark-up and mark-down to the market power. In particular, we assume that market power comes from a company’s strategy and thus only the time-invariant (persistent) component of the mark-up and mark-down models can be associated with the bargaining power. We then provide the direct relationship between the relative mark-up/relative mark-down and the degree of market power. In Sections 2and 3, we will analyze the processed tomato sector in Italy, in addition to IBOs and the level of concentration. A literature review on market concentration and coordination is presented in Section 4, while the data and methodology are described in section 5and section 6 presents the main results. We provide a discussion and draw conclusions in the last two sections. 2 ITALY’S PROCESSED TOMATO SECTOR AND INTERBRANCH ORGANIZATION (IBO) Production of tomatoes for processing in Italy, as well as in Spain and Portugal, is locally concentrated. In Italy, the tomato processing sector is divided between a Northern production area (mainly the Emilia-Romagna region) with approximately 35% of total national production, and a Southern production area (mainly Campania and Apulia), which comprises approximately 30% of total national production (see Figure 1). In Italy in 2020, a total of 65,634 ha (+2% compared to 2019) were dedicated to the production of tomatoes for processing. About 2.74 million tons (53.1%) of processed tomatoes were produced in the Northern production area, and 2.42 million tons (46.9%) in the 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License ČECHURA et al. 605 FIGURE 1 Map of major tomato producing regions of Italy (Emilia-Romagna in the north and Apulia in the south). Source: Own elaborations, made with ggplot2 (Wickham, 2016), shapefile from GADM2, and tomato production data acquired from the Italian Statistics Office (ISTAT3). Centre-South production area (ANICAV, 2020). In particular, Italy is the leading exporter of canned tomatoes in the world, accounting for 76% of the global market share of the ten main exporting countries for the 2021/2022 season (Tomato News, 2021a). In 2007, Emilia-Romagna stakeholders encouraged the creation of the “District of Industrial Tomatoes” in order to prepare for the reduction in the levels of Common Agricultural Policy (CAP) support as part of the EU’s CAP reforms. The stakeholders active in this process were POs, processors, research centers and other local institutions (Donati et al., 2019; Mantino & Forcina, 2018). The territorial area of the district expanded to include other areas dedicated to the processing of tomatoes. 2Source: https://gadm.org/download_country.html. 3Source: https://www.istat.it/en/. The IBO was established and in 2011 it was officially recognized by the Emilia-Romagna Regional government, by EU authorities in 2012 and by the Italian Agriculture Ministry in 2017 (NIPTIO,42021b). Thus, the IBO is fully active only starting from 2011. The North of Italy progress in this regard led stakeholders in the South of Italy to establish an IBO for Southern Italy Tomato Processing in 2018, whichwasalsoeventually recognized by Italian authorities (NIPTIO, 2020). In Northern Italy around 20 tomato processing companies process 98.9% of the tomatoes produced in the area of the IBO for Northern Italy Tomato Processing (NIPTIO, 2021b). Tomato processing is concentrated 4NIPTIO refers to “OI Pomodoro da Industria Nord Italia” which can be translated as “North of Italy Processed Tomato Interbranch Organization”. 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 606 ČECHURA et al. in the province of Parma, with more than half of the private processing companies and half of the processing producers’ cooperatives located there (Mantino & Forcina, 2018). Tomato processing is carried out by both private companies (66% of processed tomatoes) and producers’ cooperatives (34% of processed tomatoes). The largest private processing companies are located in Parma and Piacenza, such as Mutti, Rodolfi, Greci Alimentari, and Emiliana Conserve. Some of these private companies still belong to the founding families (Mantino & Forcina, 2018). On the distribution side, around half of the processed tomatoes are sold to the food industry (47%), 36% to retail distribution, and 18% to HORECA5(NIPTIO, 2021a). The processing tomato supply chain of the IBO for Northern Italy Tomato Processing strives for a strong vertical and horizontal cooperation, both internally among IBO actors and with other supply chain stakeholders. Annual processed tomatoes are produced on a contractual basis agreed upon by IBO stakeholders at the beginning of the agronomic year. Moreover, the IBO stakeholders agree on the general rules that form the basis of a framework contract, which sets the tomato production and commercial relationships within the IBO for Northern Italy Tomato Processing, between producers, processors, and self-processing cooperatives. The framework contract includes an approximate and proposed price that is then renegotiated bilaterally by the chain actors, in particular the producer organizations and processing industries. The IBO allows for both vertical and horizontal integration in the tomato processing industry. It works as a neutral space where trade-offs between the clashing interests of producers and processors can be found. The IBO streamlines the negotiation of a reference price between producers and processors, helps the coordination of production planning in order to solve conflicting interests, and thus stabilizes the market. It also impacts the food chain both upstream (influencing policies and financing) and downstream (affecting crop planning). The price streamlining is a key aspect of IBO. The negotiation of the reference price of raw tomato to be processed and paid to producers by processors can take up to some months. The reference price is not a set minimum price, but a reference price agreed, mainly based on the historical prices paid in the past and through the analysis of past contracts. The reference price varies according to qualitative parameters specified in the framework contract, as agreed by all IBO’s companies. The two parameters affecting the final price are the level of “BRIX”, and the percentage of major and minor defects of the tomato to be processed. BRIX is a measure of the sugar content of a tomato. The higher the BRIX, 5HORECA refers to hotel, restaurant and cafè. the sweeter the tomato. Major defects are defects that significantly affect the quality of the tomato, such as bruises or rot. Minor defects are defects that do not significantly affect the quality of the tomato, such as small blemishes (Samoggia et al., 2022). 3 CONCENTRATION Another development in the Italian tomato processing sector has been the increase in the Concentration Rate (CR) after 2012. Table 1shows the top eight Italian firms and their share and concentration level in tomato processing in the last year of this study (2018). As can be observed, the CR of the top 1, 4, and 8 firms (CR1,CR4,andCR8) in 2018 was 11.6%, 39.8%, and 56.4%, respectively, although this picture was different before 2015. Figure 2shows the development of the CR for the top1,2,and4firms(CR1,CR2and CR4) for the 2006–2020 period. As can be seen, the CR dramatically changed after 2014. During this period, the annual amount of tomato processing did not vary a lot in Italy and the average annual tomato processing was 4.9 million tons with a coefficient of variation of 9.28% (Tomato News, 2021c). According to available information, in 2015, Agricoltori Riuniti Piacentini (A.R.P) merged with Casalasco; in 2017 COPADOR was taken over by Mutti (Tomato News, 2017); andin2018FerraraFoodswaspurchasedbyItaltom (Tomato News, 2018), which were some of the main merges since 2014. It must be mentioned that higher level of concentration in the food supply chain does not necessarily mean higher market power or price change (Dong et al., 2023). 4POS, IBOS, BARGAINING POWER AND MARKET IMPERFECTION There have been substantial amounts of research conducted on the presence of market power and a deviation from competitiveness. A general overview on these studies canbefoundinCrespiandMacDonald(2022), Deconinck (2021), and Sexton and Xia (2018). By considering the current governance of the Italian tomato processing supply chain, we focus on those studies that have analyzed the role of POs on increasing the bargaining power between actors of the supply chain and their effect on market imperfection. There is a general perception among both the public and policymakers that farmers’ share of the overall food value is unfairly low (Busch & Spiller, 2016; Samoggia et al., 2021) and the collective decisions of farmers in organizations such as POs can improve both market efficiency 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License ČECHURA et al. 607 TABLE 1 The top eight Italian firms and their share and concentration level in tomato processing in 2018. Rank Firm name Fresh tomatoes (1000 Tons) Firm share (%) Cumulative tomatoes processed (1000 Tons) Concentration rate (%) 1 Mutti 540 11.61 540 11.61 2Italtom 471 10.13 1,011 21.74 3 Conzorzio Casalasco 463 9.96 1,474 31.70 4Conserve Italia 377 8.11 1,851 39.81 5 La Doria 241 5.18 2,092 44.99 6Rodolfi Mansueto 220 4.73 2,312 49.72 7 Princes Industrie Alimentari 186 4.00 2,498 53.72 8Solana 125 2.69 2,623 56.41 Rest of Italy 2,027 Total Italy 4,650 Source: Conserve Italia, La Doria and Tomato News. FIGURE 2 Concentration rate for top the 1, 2, and 4 firms (CR1,CR2 and CR4) for the period 2006–2018. Source of data: Tomato News, La Doria annual reports, Mutti, Conserve Italia. and bargaining power (Sorrentino et al., 2018). The condition of atomized upstream suppliers of the supply chain and downstream concentrated or limited buyers of supply chains are discussed theoretically and through simulation by Mérel (2011) and Mérel and Sexton (2017). For instance, by considering the French Comté cheese market, Mérel (2011) argues that encouraging industry coordination may be socially desirable. The dairy farm cooperatives are one of the major agrifood POs that have been studied. By using the regional data of U.S. dairy cooperatives for the 2000–2007 period, Cakir and Balagtas (2012) have shown that cooperatives use the federal milk market ordering regulations to exercise their market power by having 9% mark-ups on farm milk prices. When such a cooperative is not available, the possibility of market power to be exercised by privately owned dairy processors is very high. The effect of cooperatives on market power in the Italian fruit and vegetable (F&V) and dairy supply chains have been tested by Lee and Van Cayseele (2022) for the 2007–2014 period. Compared to non-cooperatives, they found higher mark-ups for F&V processor cooperatives and lower mark-ups for F&V farmer and dairy processing cooperatives. To our knowledge, the effects of IBOs on bargaining power and market imperfection have not been empirically tested. The creation of IBOs can be justified by Sexton’s (2013) Modern Agricultural Market (MAM) concept. He argues that food processing firms consider their long-term relationship with agricultural producers (such as tomato or dairy farmers). From his point of view, before exercising market power, processing firms consider their capital cost investment, inelastic demand for agricultural products and transaction costs. Sexton argues that the processing firms need a reliable supply of agricultural products with certain characteristics to fulfil their output obligations (Sexton, 2013). Therefore, he argues that the coordination between agricultural producers and processors is beneficial for both and that IBOs are an example of such coordination. In this study, we look to the effect of the IBOs and, at the same time, the increasing concentration on market imperfection. Given the fact that market power comes from a company’s strategy having a long-term nature as Sexton argues, thus only the time-invariant (persistent) one-sided component of the mark-up and mark-down model can be associated with the bargaining power. From the empirical point of view, we have decomposed the one-sided error term in the mark-up and mark-down model within both the transient and persistent components to avoid upward biases of mark-up and mark-down components. Moreover, we use an estimation procedure that addresses three sources of potential endogeneity that 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 608 ČECHURA et al. are highly probable for our models: (i) unobserved heterogeneity; (ii) simultaneity of regressors with persistent and transient components; and (iii) correlation of regressors with the noise term. Finally, we provide a direct relationship between mark-up and mark-down components with a market power indicator. 5DATA AND METHODOLOGY 5.1 Data The data we use in the analysis is drawn from the Amadeus database,6created and produced by Bureau van Dijk. The database contains financial information for private companies across Europe and provides detailed information about (standardized) annual accounts, financial ratios, sectoral activities and ownership information. The panel dataset that we use in our analysis contains companies whose main activities are tomato food processing according to the NACE classification and desk research of each of the company websites. It is a panel dataset that represents the period from 2006 to 2018 and contains 97 companies that process only tomatoes or mainly tomatoes. The following variables are used in the analysis: Mark-down model: consists of cost share =material costs/revenue as a dependent variable and material costs, capital and labor as covariates. Material costs are used in the form of the total cost of materials and energy consumption per company. Revenue is represented as the operating revenue (turnover) of the companies and materials is the total costs of materials and energy deflated by the index of producer prices in the industry (2010 =100). This indicator is a relative rough approximation of the expenditure for raw agricultural materials. However, the fact that we are analyzing the tomato processing industry where agricultural raw materials constitute the bulk of the material costs, we assume that the approximation is acceptable. Labor is represented by the cost of employees deflated by consumer price index (2010 =100). Capital is the book value of fixed assets deflated by the index of producer prices in the industry (2010 =100). Mark-up model: consists of revenue share =revenue/costs as the dependent variable and output, normalized material costs and labor as covariates, while revenue is represented by the operating revenue (turnover) of a company and costs are the sum of the labor costs, materials costs and capital costs. Labor costs are represented by 6More information on the Amadeus database (since 2021 Orbis Europe) is provided at: http://www.bvdinfo.com. the costs of employees, material costs are the total costs of materials and energy consumption per company, and capital costs are calculated as the book value of fixed assets multiplied by the interest rate according to convergence criteria. Outputs are represented by the operating revenue (turnover) of a company and are deflated by the sectoral index of tomato processing prices (2010 =100). Material and labor are normalized by capital. For the case of the mark-down model, materials is the total costs of materials and energy deflated by the index of producer prices in the industry (2010 =100); labor is represented by the costs of employees deflated by the consumer price index (2010 = 100); and capital is the book value of fixed assets deflated by the index of producer prices in the industry (2010 =100). We reject producers with fewer than four observations (on average) to comply with the requirements of the Generalized Method of Moments (GMM) estimator. Furthermore, we decrease the problem with the use of unbalanced panel data this way. Finally, the GMM model estimates used input variables as instruments lagged up to two periods for the equation in levels and up to three periods for the equation in differences. We then use year dummies and the size variable for the mark-down model and year dummies for the mark-up model as additional instruments. Summary statistics of the main variables are provided in Table 2. Finally, the dependent variable and the covariates are logarithmically transformed and normalized by their mean in both models. 5.2 Theoretical models The mark-down and mark-up models are derived using the conjectural variation approach (e.g., Bresnahan, 1982; Muth & Wohlgenant, 1999). We follow the standard behavioral assumption about profit maximization. In this case, the Optimization Problem (OP) can be approached either as inputor output-market oriented. Input market-oriented OP—mark-down model 𝜋𝑖=𝑅(𝒑, 𝑥𝑖,𝒛 𝒊,𝑡 )−𝑤 𝑥.𝑥𝑖−𝒘 ′ 𝐳.𝒛𝒊(1) where 𝜋𝑖is the profit of ith processor, 𝑅(𝒑, 𝑥𝑖,𝒛 𝒊,𝑡)represents the revenue function depending on the vector of product prices (p), agricultural raw materials (𝑥𝑖), kth other inputs (𝑧𝑖,𝑘) and a time trend (𝑡) as an indicator of technical change. The symbol 𝑤𝑥and 𝒘𝒛are used for the corresponding factor prices, and the supply function of raw materials is: 𝑥=𝑔(𝑤𝑥,𝒔 )or 𝑤𝑥=𝑔 −1 (𝑥,𝒔)(2) 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License ČECHURA et al. 609 TABLE 2 Summary statistics of main variables (thousands of Euros). Variable Mean Standard deviation Minimum Maximum Operating revenue (Turnover) (R) 33,401.5 113,028.0 135.0 1,052,047.0 Total costs of materials and energy (M) 20,507.7 65,504.6 57.8 542,232.8 Costs of employees (L) 3112.2 12,024.1 .6 121,197.7 Book value of fixed assets (C) 12,025.4 46,711.2 1.3 465,413.9 Source: Own calculation from Amadeus data. where sis a vector of supply shifters and 𝑥= ∑𝐼 𝑖=1 𝑥𝑖 is the total supply of raw material (summing over I processors), or in terms of the inverse supply function 𝑤𝑥=𝑔 −1 (𝑥, 𝒔). Then, the first order condition for profit maximisation is: 𝜕𝑅 (𝒑, 𝑥𝑖,𝒛, 𝑡) 𝜕𝑥𝑖 −𝑤 𝑥−𝜕𝑔−1 (𝑥,𝒔) 𝜕𝑥 𝜕𝑥 𝜕𝑥𝑖 𝑥𝑖=0 (3) and after rearrangement: 𝑤𝑥(1+ Θ 𝜀𝑥)=𝜕𝑅 (𝒑, 𝑥, 𝒛, 𝑡) 𝜕𝑥 , where (4) 𝜀𝑥=𝜕𝑥 𝜕𝑔−1 (𝑥,𝒔) 𝑔−1 (𝑥,𝒔) 𝑥=𝜕lnx 𝜕ln𝑤𝑥 >0 In Equation (4), 𝜀𝑥denotes the price elasticity of the raw tomato supply and Θ=𝜕𝑥 𝜕𝑥𝑖 𝑥𝑖 𝑥is a conjectural elasticity capturing the degree of oligopsonistic market power (Bresnahan, 1989). The parameter range is 0 <Θ<1. Θ =0 corresponding to perfect competition, while Θ =1 characterizes a monopsonistic market.7Using Equation (4)and the relative mark-down measure (σ), we derive a direct relation between conjectural elasticity and relative markdown. In particular, the mark-down measures the percent deviation of factor prices from their Marginal Revenue Product (MRP)8as 𝜎=𝑀𝑅𝑃𝑥−𝑤𝑥 𝑀𝑅𝑃𝑥 . Substituting the factor cost with market power (𝑀𝑅𝑃𝑀𝑃 𝑥)and the factor cost under perfect competition (𝑀𝑅𝑃𝐶 𝑥=𝑤 𝐶 𝑥)into the relative 7Since prices of other inputs are assumed to be constant, their optimal level is given when the factor price is equal to the value of Marginal Revenue Product (MRP):𝑾𝒛=𝜕𝑹(𝒑,𝑥,𝒛,𝑡) 𝜕𝒛 . 8The relative mark-down is analogously defined to the Lerner index (Lerner, 1934) which measures the degree of oligopolistic power. The Lerner index gives the percent of the prices that are above marginal cost. The relative mark-down is correspondingly the percentage the factor price is below the value of the marginal revenue product. mark-down results in: 𝜎𝑀𝑃_𝐶=𝑀𝑅𝑃𝑀𝑃 𝑥−𝑤 𝐶 𝑥 𝑀𝑅𝑃𝑀𝑃 𝑥 = 1 (1+ Θ 𝜀𝑥) 𝜕𝑅 𝜕𝑥 −𝜕𝑅 𝜕𝑥 1 (1+ Θ 𝜀𝑥) 𝜕𝑅 𝜕𝑥 = 1 (1+ Θ 𝜀𝑥)−1 1 (1+ Θ 𝜀𝑥) =−Θ 𝜀𝑥 (5) That is, relative mark-down (𝜎𝑀𝑃_𝐶) is proportional (in absolute value) to the indicator of market power and can be directly computed when the supply elasticity (𝜀𝑥) and conjectural elasticity (Θ) are known. Or, if we know relative mark-down and supply elasticity, we may calculate conjectural elasticity. Finally, if the supply elasticity is unknown but supposed to be constant in the long run, we may use Equation (5) to investigate dynamics in conjectural elasticity in case that relative mark-down is estimated and vice versa. Moreover, the Equation (4) implies that: 𝑤𝑥=MR𝑃𝑥= 𝜕𝑅 𝜕𝑥 under perfect competition. This relation can further be expressed expanding both sides by 𝑥 𝑅as: 𝑤𝑥 𝑥 𝑅≤𝑀𝑅𝑃𝑥 𝑥 𝑅=𝜕𝑅 𝜕𝑥 𝑥 𝑅=𝜕𝑙𝑛𝑅 𝜕𝑙𝑛𝑥 =𝜕𝑙𝑛𝐷0 𝜕𝑙𝑛𝑥 (6) where the last equality comes from the duality of the revenue (R) and output distance (Do) functions (Shephard, 1970) and the inequality occurs when conjectural elasticity (Θ) is nonzero, that is, the situation with a certain degree of market imperfections. Output market-oriented OP—mark-up model The optimization problem can be introducedfor the output market in the analogical way. In this case, the profit function of processor (i)isgivenby: 𝜋𝑖=𝑝.𝑦 𝑖−𝐶(𝒘, 𝑦𝑖,𝑡 )(7) where pis a price of output, yiis the output of ith processor, wis a vector of input prices, and C(w,yi,t) is a cost function of processor (i) and time trend (t) for capturing technical change. The corresponding first-order condition for profit maximization is: 𝜕𝑓−1 (𝑦,𝒅) 𝜕𝑦 .𝜕𝑦 𝜕𝑦𝑖 .𝑦𝑖+𝑝−𝜕𝐶 (𝒘, 𝑦𝑖,𝑡) 𝜕𝑦𝑖 =0or (8) 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 610 ČECHURA et al. 𝑝. (1+ Ω 𝜀𝑝)=𝜕𝐶 (𝒘, 𝑦𝑖,𝑡) 𝜕𝑦𝑖 (9) where dis a vector of demand shifters, 𝜀𝑝=𝜕𝑦 𝜕𝑓−1(𝑦,𝑑) 𝑝 𝑦<0 stands for a demand elasticity of the final product and Ω= 𝜕𝑦 𝜕𝑦𝑖 .𝑦𝑖 𝑦is a conjectural elasticity. This conjectural elasticity provides information about the the degree of oligopolistic market power. In particular, the elasticity is in the interval Ω∈[0,1]where Ω =0 indicates competitive behavior and Ω =1 characterizes monopolistic power. Analogically to input market, Equation (9)canbeused to derive the relation between conjectural elasticity and the relative mark-up (φ) measured as the percent deviation of product price from the marginal cost: φ= 𝑃−𝑀𝐶 𝑀𝐶 (Kumbhakar et al., 2012).9That is, substituting the product price with market power (𝑝𝑀𝑃) and marginal cost under perfect competition (𝑝𝐶=𝑀𝐶 𝐶) into the relative mark-up results in: 𝜑𝐶_𝑀𝑃 =𝑝𝐶−𝑀𝐶 𝑀𝑃 𝑀𝐶𝑀𝑃 = 𝜕𝐶 𝜕𝑦 −1 (1+ Ω 𝜀𝑝) 𝜕𝐶 𝜕𝑦 1 (1+ Ω 𝜀𝑝) 𝜕𝐶 𝜕𝑦 = 1− 1 (1+ Ω 𝜀𝑝) 1 (1+ Ω 𝜀𝑝) =Ω 𝜀𝑝 (10) Equation (10)10 shows that the relative mark-up (𝜑𝐶_𝑀𝑃) is proportional (in absolute value) to the indicator of market power and can be directly computed when the demand elasticity and conjectural elasticity are known. On the contrary, if the relative mark-up and demand elasticity are known, we may calculate conjectural elasticity. Finally, if the demand elasticity is supposed to be constant in the long run, we may use Equation (10) to study dynamics in conjectural elasticity in case that relative mark-up is estimated and vice versa. Moreover, it follows from Equation (9) that: 𝑝≥ 𝜕𝐶(𝒘, 𝑦𝑖,𝑡) 𝜕𝑦𝑖 for Ω ∈ [0, 1], which can be expressed expandingbothsidesby 𝑦 𝐶as: 𝑝.𝑦 𝐶≥𝜕𝐶 (𝒘, 𝑦𝑖,𝑡) 𝜕𝑦𝑖 .𝑦 𝐶=𝜕𝑙𝑛𝐶 𝜕𝑙𝑛𝑦 =𝜕𝑙𝑛𝐷𝐼 𝜕𝑙𝑛𝑦 (11) where the last equality comes from the duality of the cost (C) and input distance (DI) functions (Shephard, 1970). 9The relation of the relative mark-up and Lerner index is: 𝐿=𝑃−𝑀𝐶 𝑃= 𝜑 1+𝜑 . 10 Note: using Lerner index in Equation (10) instead of relative mark-up results in: 𝐿𝐶_𝑀𝑃 =Ω 𝜀𝑝+Ω . 5.3 Estimation strategy The inequalities in (6)and(11) can be transformed to the equalities by adding a non-negative one-sided error terms, ufor the mark-down model and εfor the mark-up model (see Kumbhakar et al., 2012 for the mark-up model): 𝑤𝑥.𝑥 𝑅=𝜕ln𝐷𝑜 𝜕lnx −𝑢, 𝑢≥0and (12) 𝑝.𝑦 𝐶=𝜕𝑙𝑛𝐷𝐼 𝜕𝑙𝑛𝑦 +𝜀, 𝜀≥0 In Equation (12), ucaptures the mark-down and εthe mark-up. To estimate mark-down and mark-up for each firm we use stochastic frontier methodology from the efficiency literature (e.g., Kumbhakar & Lovell, 2000). Then, assuming that both the output and input distance functionshave translogform,theresultingmark-down(13) and mark-up (14) models, respectively, for one output is as follows11: 𝑤𝑥𝑥 𝑅=𝛽 𝑥+𝛽 xt𝑡+𝛽 xxlnx +𝜷 ′ 𝒛𝑥ln𝒛−𝑢and (13) py 𝐶=𝛼 𝑦+𝛼 yt𝑡+𝛼 yylny +𝜶 ′ 𝒙𝑦ln ∼ 𝒙+𝜀, where (14) ˜ 𝑥𝑗=𝑥 𝑗∕𝑥𝐽for j=1,...,J. The coefficients 𝜶and 𝜷in Equations (13)and(14)are actually the coefficients of the first order derivation of translog output and input distance functions, respectively, which is the reason for the notation structure of the coefficients. Kumbhakar et al. (2012) first applied the stochastic frontier approach in the estimation of the degree of market power in Equation (9). In our study, we adjust this approach in the following way: we use a system GMM estimator to address the endogeneity problem and to obtain unbiased parameters as well as error components. Then, we decompose a non-negative one-sided error term to the transient (time variant) and persistent (time-invariant) parts, that is, ui,t =μi,t +ηifor the mark-down model and εi,t =ςi,t +ψifor the mark-up model. Moreover, the intercept terms will be related to heterogeneity components to respect the different firm’s technologies. This conceptual distinction of the four components12 allows getting unbiased estimates of the one-sided error terms. In particular, since the market power is a product of firm strategy that 11 The detail information on output and input distance functions and the derivation of models (13) and (14) are provided in the Appendix. 12 The model specification is an analogy to the 4-component stochastic frontier model (Tsionas & Kumbhakar, 2014). 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. 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Agricultural Economics,55,603–620. https://doi.org/10.1111/agec.12835 APPENDIX A1: OUTPUT DISTANCE FUNCTION AND MARK-DOWN MODEL SPECIFICATION If we assume a joint-production process with the input vector 𝒙∈ℜ 𝐽 +to produce the output vector 𝒚∈ℜ 𝑀 +, then the production technology can be expressed by the output possibility set 𝑃(𝒙)={𝒚∶𝒙can produce (𝒚)} . The output possibility set is supposed to be closed, convex and bounded by the output isoquant Isoq 𝑃 (𝒙) = {𝒚 ∶ 𝒚 ∈ 𝑃(𝒙), 𝜆(𝒚) ∉ 𝑃(𝒙),𝜆 > 1} and the inputs as well as outputs are supposed to be strongly, or freely, disposable (for more reference see Kumbhakar & Lovell, 2000). Then, Shephard’s output distance function (Shephard, 1970)isa radial measure of the distance from output vector yto Isoq P(x): 𝐷𝑂(𝒙, 𝒚)=inf{𝜃>0∶(𝒚∕𝜃)∈𝑃(𝒙)} ,(A.1) where 𝜃measures the maximum degree of the proportional increase of yfor given x(Zhou et al., 2014). If we assume that the output distance function has a translog form, we can write20: ln 𝐷0=𝛽 0+𝛽 𝑡𝑡+1 2𝛽tt𝑡+𝛽 𝑥lnx +𝛽 xtlnxt +1 2𝛽xx(lnx)2 +𝜷 ′ 𝒛ln𝒛+𝜷 ′ 𝒛𝑡ln𝒛𝑡 + 1 2ln𝒛′𝑩𝒛𝒛ln𝒛+ln𝒛′𝜷𝒛𝑥lnx +𝜷 ′ 𝒚ln𝒚+𝜷 ′ 𝒚𝑡ln𝒚𝑡 + 1 2ln𝒚′𝑩𝒚𝒚ln𝒚+ln𝒚′𝜷𝒚𝑥lnx +ln𝒚′𝑩𝒚𝒛ln𝒛 (A.2) The first derivative of Equation (A.2) with respect to material inputs is: 𝜕ln𝐷0 𝜕lnx =𝛽 𝑥+𝛽 xt𝑡+𝛽 xx ln 𝑥 + 𝜷′ 𝒛𝑥 ln𝒛+𝜷 ′ 𝒚𝑥 ln 𝒚 (A.3) Using Equations (A.3)inrelation(6)21 we get: 𝑤𝑥𝑥 𝑅≤𝛽𝑥+𝛽 xt𝑡+𝛽 xx ln 𝑥 + 𝜷′ 𝒛𝑥 ln𝒛+𝜷 ′ 𝒚𝑥 ln 𝒚 (A.4) The output distance function is homogenous of degree 1 in outputs. Therefore, we impose homogeneity restriction by normalising all the outputs by one output to get the empirical representation of Equation (4)tobeestimated: 𝑤𝑥𝑥 𝑅≤𝛽𝑥+𝛽 xt𝑡+𝛽 xx ln 𝑥 + 𝜷′ 𝒛𝑥 ln𝒛+𝜷 ′ 𝒚𝑥 ln ∼ 𝒚(A.5) where  𝑦𝑚=𝑦 𝑚∕𝑦𝑀for m=1,...,M. 20 To follow the main body of the article, we split the vector of input x into: agricultural raw materials (x) and vector of other inputs (z). 21 To recall relation (6) from a main body of the article: 𝑤𝑥 𝑥 𝑅≤MR𝑃𝑥 𝑥 𝑅=𝜕𝑅 𝜕𝑥 𝑥 𝑅=𝜕lnR 𝜕lnx =𝜕ln𝐷0 𝜕lnx 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License ČECHURA et al. 619 For one output, (A.5) reduces to (homogeneity of degree 1 in outputs requires that βyx=0): 𝑤𝑥𝑥 𝑅≤𝛽𝑥+𝛽 xt𝑡+𝛽 xx ln 𝑥 + 𝜷′ 𝒛𝑥 ln 𝒛 (A.6) The inequality in (A.5) can be transformed to the equality adding a non-negative one-sided error term u: 𝑤𝑥𝑥 𝑅=𝛽 𝑥+𝛽 xt𝑡+𝛽 xx ln 𝑥 + 𝜷′ 𝒛𝑥 ln𝒛−𝑢, 𝑢≥0, (A.7) which is a representation of the mark-down model in Equation (13) in the main body of the article. APPENDIX A2: INPUT DISTANCE FUNCTION AND MARK-UP MODEL SPECIFICATION The production technology can be alternatively expressed by the input requirement set 𝐿(𝒚)={𝒙∶ 𝒙can produce 𝒚} , with the input vector 𝒙∈ℜ 𝐽 +to produce the output vector 𝒚∈ℜ 𝑀 +. The input requirement set is supposed to be closed, convex and bounded by the input isoquant Isoq 𝐿 (𝒚) = {𝒙 ∶ 𝒙 ∈ 𝐿(𝒚), 𝜆(𝒙) ∉ 𝐿(𝒚), 𝜆 < 1} and the inputs as well as outputs are supposed to be strongly, or freely, disposable (for more reference see again Kumbhakar & Lovell, 2000). Shephard’s input distance function (Shephard, 1970) is then a radial measure of the distance from output vector yto Isoq L(y): 𝐷𝐼(𝒚, 𝒙)=sup {𝜇>0∶(𝒚∕𝜇)∈𝐿(𝒚)} ,(A.8) where 𝜇measures the maximum degree of proportional reduction of xfor given y(Zhou et al., 2014). Assuming that the input distance function with one output has a translog form: ln 𝐷𝐼=𝛼 0+𝛼 𝑡𝑡+1 2𝛼tt𝑡2+𝛼 𝑦lny +𝛼 ytlnyt +1 2𝛼yy(lny)2 +𝜶 ′ 𝒙ln 𝒙 + 𝜶′𝒙𝑡 ln 𝒙𝑡 + 1 2ln𝒙′𝑨𝒙𝒙ln𝒙 +ln𝒙′𝑨𝒙𝑦lny, (A.9) the first derivative of equation (A.9) with respect to output is: 𝜕ln𝐷 𝐼 𝜕ln𝑦 =𝛼 𝑦+𝛼 yt𝑡+𝛼 yy ln 𝑦 + 𝜶′ 𝒙𝑦 ln𝒙(A.10) Consequently, using Equation (A.10)inrelation(11)22 22 To recall relation (11) from a main body of the article: 𝑝.𝑦 𝐶≥𝜕𝐶(𝒘,𝑦𝑖,𝑡) 𝜕𝑦𝑖 .𝑦 𝐶=𝜕lnC 𝜕lny =𝜕ln𝐷𝐼 𝜕lny we get: 𝑝⋅𝑦 𝐶≥𝛼𝑦+𝛼 yt𝑡+𝛼 yy ln 𝑦 + 𝜶′ 𝒙𝑦 ln𝒙(A.11) The input distance function is homogenous of degree 1 in inputs. Homogeneity is imposed by normalising all the inputs by one input. Therefore, the empirical representation of (A.11)is: 𝑝⋅𝑦 𝐶≥𝛼𝑦+𝛼 yt𝑡+𝛼 yy ln 𝑦 + 𝜶′ 𝒙𝑦 ln ∼ 𝒙(A.12) where  𝑥𝑗=𝑥 𝑗∕𝑥𝐽for j=1,...,J. Transforming inequality (A.12) to the equality by adding a non-negative one-sided error term 𝜀we get: 𝑝⋅𝑦 𝐶=𝛼 𝑦+𝛼 yt𝑡+𝛼 yy ln 𝑦 + 𝜶′ 𝒙𝑦ln ∼ 𝒙+𝜀, 𝜀 ≥0, (A.13) which is a representation of the mark-up model in Equation (14) in the main body of the article. APPENDIX A3: MARK-DOWN AND MARK-UP ESTIMATION WITHOUT COOPERATIVES Tables A3.1 and A3.2 provide the parameter estimates of the mark-down and mark-up models for the Italian tomato food processing sector without considering the cooperatives. Table A3.3 provides statistical characteristics of the relative mark-down and relative mark-up. The results of these estimations are approximately similar to the full models. TABLE A3.1 Markdown model without cooperatives. Variable Coefficient Standard deviation P-value t.000 .001 .577 ln_M .085 .011 .000 ln_L −.043 .012 .001 ln_C −.023 .009 .013 Constant .351 .028 .000 P-value AR(2) .04 .965 Hansen test of overid. restrictions: chi2(63) 69.53 .267 Number of observations: 893 Source: Own calculations. 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License 620 ČECHURA et al. TABLE A3.2 Mark-up model without cooperatives. Variable Coefficient Standard deviation P-value t.004 .002 .054 ln_y −.041 .015 .006 ln_nL .053 .034 .123 ln_nM −.069 .036 .056 Constant −1.871 .121 .000 P-value AR(2) .30 .766 Hansen test of overid. restrictions: chi2(96) 89.04 .680 Number of observations: 955 Source: Own calculations. TABLE A3.3 Summary statistics of mark-down and mark-up estimations without cooperatives. Mean Standard deviation Minimum Maximum Relative mark-down .217 .003 .000 .476 Relative mark-up .164 .003 .000 .619 Source: Own calculations. 15740862, 2024, 4, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/agec.12835, Wiley Online Library on [05/07/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License