Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model

Mantziaris, Stamatis; Rozakis, Stelios; Karanikolas, Paulos; Petsakos, Athanasios; Tsiboukas, Konstantinos Article Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics (BAE) Provided in Cooperation with: Firenze University Press Suggested Citation: Mantziaris, Stamatis; Rozakis, Stelios; Karanikolas, Paulos; Petsakos, Athanasios; Tsiboukas, Konstantinos (2024) : Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model, Bio-based and Applied Economics (BAE), ISSN 2280-6172, Firenze University Press, Florence, Vol. 13, Iss. 4, pp. 353-386, https://doi.org/10.36253/bae-14790 This Version is available at: https://hdl.handle.net/10419/321804 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. https://creativecommons.org/licenses/by/4.0/ Bio-based and Applied Economics BAE © 2024 Author(s). Open access article published, except where otherwise noted, by Firenze University Press under CC-BY-4.0 License for content and CC0 1.0 Universal for metadata. Firenze University Press | www.fupress.com/bae Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Citation: Mantziaris, S., Rozakis, S., Karanikolas, P., Petsakos, A., & Tsiboukas, K. (2024). Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model. Bio-based and Applied Economics 13(4): 353-386. doi: 10.36253/ bae-14790 Received: June 3, 2023 Accepted: September 2, 2024 Published: December 31, 2024 Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. Editor: Matteo Zavalloni Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Stamatis Mantziaris1,*, Stelios Rozakis2, Pavlos Karanikolas1, Athanasios Petsakos3, Konstantinos Tsiboukas1 1 Department of Agricultural Economics and Rural Development, Agricultural University of Athens, Greece 2 School of Chemical and Environmental Engineering, Technical University of Crete, Chania Crete, Greece 3 Department of Performance, Innovation and Strategic Analysis for Impact, Bioversity International, Rome, Italy *Corresponding author. E-mail: [email protected]) Abstract. Although the policy impacts on farms accumulate year by year, most farm decision models focus on short-term decisions, evaluating policies based on snapshots. Structural changes are gradually built; therefore, farm decision models should consider the sequences within the period under study. Multiyear data from the arable sector in Thessaly, Greece, have fed a newly developed farm-level recursive linear programming model mainly to simulate farm structural change dynamics. The proposed model incorporates new evidence on the strategic decision of arable crop farms regarding their remaining in the production system and farm expansion. Results reveal an evident gradual farmland concentration in relatively large farms, accompanied by a gradual expansion of the most profitable cropping activities, verifying the real-world survival strategy of farms. Keywords: farm structural change, land use change, recursive linear programming model, arable production system, Greece. JEL Codes: C61, Q12, Q18. 1. INTRODUCTION The declining number of surviving farms over time and the increase in average farm size generally signal the evolutionary process of structural change in the agricultural sector of developed economies (Plogmann et al., 2022), implying changes in the farm size distributions (Zimmermann and Heckelei, 2012; Saint-Cyr et al., 2019). Agricultural economists have shown great interest in describing structural change dynamics and understanding its drivers (Plogmann et al., 2022). Structural change is driven by various economic factors (Neuenfeldt et al., 2019), environmental factors and social drivers (RIRDC, 2007). Neverthe- 354 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. less, some authors (Wiborg, 1998; Plogmann et al., 2022) consider farm economic performance the primary driver of structural change since it somehow encloses all the above factors. Structural change is a normal evolutionary process in an economy (Goddard et al., 1993). Over time, rising agricultural productivity enabled the transfer of productive factors required for the development of other sectors of the economy (Balmann and Valentinov, 2016). However, structural change in the agricultural sector is usually correlated with public concerns, which are mainly expressed through public debates in two terms, firstly as “dying peasants” and secondly as “factory farming” (Balmann and Valentinov, 2016). Highlighting the first public concern, this may be because, generally, structural change hardly leads to Pareto Superior states (Balmann and Valentinov, 2016). From this perspective, Cochrane (1958) concludes that increased agriculture productivity positively affects only a limited number of innovative farms, while most farmers are affected negatively due to the following drop in agricultural commodity prices. Suppose we analyze this reasoning from the point of view of public policy; in that case, structural change may reduce the problem concerning the profitability of remaining farms but, on the other side, reduce the number of small farms and thus counters the equity goals of public society (Finger and Benni, 2021). Within this context, some authors consider the significant role of public policy in mitigating the consequences of structural change by pointing out that “much of the public policy agenda has clearly been established on a premise of optimality of a family farm structure” (Goddard et al., 1993: 486). However, implementing appropriate policy interventions presupposes providing detailed information (by policy analysts) on structural change in agriculture through evidence-based policy-relevant research to support evidence-based agricultural policy decision-making. The European Common Agricultural Policy (CAP) marks essential shifts in the context where farms operate, with significant reforms attempted every decade. Policy impacts on farms accumulate year after year, affecting the farm structures and, by extension, the well-being of rural communities, creating a ripple effect on the local economy. In this framework, modeling the dynamics of structural change adjustment (i.e., the change over time of farm numbers and farm size distribution) is highly desirable because it can provide policymakers and stakeholders with possible alternative scenarios of structural change adjustments, but it is still not widely used in policy analysis (Ciaian et al., 2013; Espinosa et al., 2016). Modeling exercises such as dynamic appraisals can support policy analysts in formulating public policies to obtain the “desired farm structure” considering the societal demands for equity (Finger and Benni, 2021). Two main methodological approaches incorporate structural change in agriculture: econometrics and simulation models (which aim to analyze farm structural change endogenously) (Espinosa et al., 2016; Zimmermann et al., 2009). Econometric models include Markov chains (Zimmermann and Heckelei, 2012) and various other regression approaches (Zimmermann et al., 2009). Simulation models include recursive programming models (e.g., Wiborg, 1998; Guinde et al., 2005; Henningsen et al., 2005; Offermann and Margarian, 2014; Djanibekov and Finger, 2018; Mittenzwei and Britz, 2018) and agent-based models (e.g., Balmann, 1997; Berger, 2001; Happe et al., 2008; Freeman et al., 2009; Bert et al., 2011; Troost and Berger, 2016; Beckers et al., 2018; Sun et al., 2022; Donati et al., 2024). As simulation models can endogenously capture farm structural change, they are considered suited to analyzing policy changes’ allocative and distributive effects on an agricultural production system (Guinde et al., 2005; Happe et al., 2008; Espinosa et al., 2016). Although agent-based models such as AgriPoliS (Balmann, 1997) are considered by various modelers the most comprehensive attempt at analyzing the impact of policies on structural change (e.g., Zimmermann et al., 2009), are characterized by greater complexity (e.g., Zimmermann et al., 2009), and they are very demanding in terms of parameterisation (e.g., Zimmermann et al., 2009; Rowan et al., 2011; Kremmydas et al., 2023) and calibration (e.g., Zimmermann et al., 2009). In addition, the preference for simpler processbased models1 should not be ignored (Troost and Berger, 2020). Therefore, while capturing structural change endogenously and providing meaningful insights into the allocative and distributional effects of various exogenous factors, the farm-level recursive programming models can also be manageable regarding the degree of complexity and data requirements compared to other simulation models such as agent-based models. Based on the above discussion, the main objective of this research is to investigate the impacts of policy experiments on farm structural change dynamics in Greece through an endogenous modeling approach based on a newly developed farm-level recursive linear programming model. While primarily aimed at simulating the impact of policy experiments on the evolutionary process of farm structural change, the proposed simulation model is also secondarily used to simulate the effect 1 Process-based models include models such as simulation models and systems dynamics models. 355 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 on land use change while analyzing its relationship with structural change adjustment. In the context of structural changes, the strategic decision of farms is summarized through the phrase “grow or go” (Plogmann et al., 2022), implying the aspects of (i) farm viability and (ii) farm growth/expansion. Through the proposed modeling approach, we integrate the farm’s economic performance as the main driver of this decision (e.g., Wiborg, 1998; Paroissien et al., 2021; Plogmann et al., 2022). In more detail, in addition to traditional monetary value criteria to determine a surviving/viable farm, we introduce a novel viability criterion, assuming that farmers may compare their economic performance to societal consumption benchmark, in the sense that the agent (in our case, realworld individual farm) must achieve a minimum level of profitability, allowing entry into the “rat race” according to “Keeping up with the Joneses” (KUJ) preferences (e.g., Barnett et al., 2010; Lombardo, 2021; Paroissien et al., 2021). Regarding farm expansion, the proposed modeling approach introduces a further novel element through the concept of relative optimal farm growth in equity to reallocate/allocate resources between neighboring surviving farms. The proposed model can also be characterized as a One-Way Communication Model where the information flows from the econometric model to the recursive programming farm model (Huang et al., 1980). In particular, the Autoregressive Integrated Moving Average (ARIMA) models are used to forecast the values of the exogenously determined parameters of interest to conduct out-of-sample simulations. Additionally, ARIMA stochastic process estimates express the agents’ quasi-rational expectations regarding agricultural commodity prices and crop yields (Nerlove and Bessler, 2001; Siegle et al., 2024). For the empirical application of the proposed simulation model, a representative sample of arable crop farms (in terms of farm structure) of the region of Karditsa (NUTS-3 level), Thessaly, is chosen. The priority of empirical application given to the arable production system is justified by the fact that Greek arable farming is characterized by a comparatively higher rate of structural change concerning the other main types of farming (other permanent crops, other grazing livestock) (FADN Public Database). From a general perspective, with this analysis, we attempt to contribute to the debate on dynamic assessments of the multidimensional effects in the context of policy reforms. Additionally, more specific contributions to literature are expressed through at least four ways: First, we add knowledge by integrating evolutionary and social psychology elements to define a farm as viable based on KUJ preferences. Second, we simulate resource reallocation based on the criterion of relative optimal farm growth in equity as an alternative farm expansion/growth criterion to traditional criteria such as the shadow values of resources (e.g., Guinde et al., 2005; Hennessy, 2007; Espinosa et al., 2016). Third, the utilization of the ARIMA stochastic process for time series forecasting of the values of the exogenously determined parameters (such as agricultural commodities prices, input prices, and crop yields) is an addition to the existing literature since in similar simulation models; these values are mainly determined either from secondary data sources (e.g., Wiborg, 1998; Hennessy, 2007; Offermann and Margarian, 2014) or through assumptions/ scenarios (e.g., Guinde et al., 2005; Henningsen et al., 2005; Troost and Berger, 2016; Mittenzwei and Britz, 2018) or simplified trend models (e.g., Happe et al., 2008; Bert et al., 2011; Beckers et al., 2018). Fourth, despite the great importance of the arable production system for the Greek agricultural sector and the comparatively higher rate of structural change than the other main production systems, to our knowledge, farm-level recursive programming models have not been used to provide a “bottom-up” simulation of structural change of Greek arable production system. The rest of the paper is organized as follows. Section 2 describes the applied methodology, the data used to apply the methodology, and the policy experiments. The empirical results are presented in Section 3, Section 4 discusses them, and concludes. 2. METHODOLOGY AND DATA 2.1. Recursive programming models for impact assessment in agriculture Recursive programming models have already been introduced in the 1960s to represent dynamic adjustments of production capabilities at the farm level, and then with the study of Day and Cingo (1978) regional interdependence and structural elements were incorporated (Espinosa et al., 2016). Indicatively, recursive programming farm models have been utilized for the development of farm firm growth models (e.g., Chien and Bradford, 1976; Cittadini et al., 2008; Dowson et al., 2019) to investigate the economic consequences due to farmers’ adaptability to different water availability scenarios (e.g., Iglesias et al., 2003; Rowan et al., 2011; Robert et al., 2018; Dowson et al., 2019), to assess the impacts of various policy reform and price scenarios on farm income and investment behavior (e.g., Viaggi et al., 2010; Viaggi et al., 2011; Davis et al., 2013; Britz et 356 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. al., 2016) and to analyze the impact of policies on farm structural change (e.g., Wiborg, 1998; Guinde et al., 2005; Henningsen et al., 2005; Offermann and Margarian, 2014; Djanibekov and Finger, 2018; Mittenzwei and Britz, 2018). The main structural elements of a recursive programming model correspond to a constrained optimization model and a data generator, where the data generator, given the optimal value or solution in period t, reinitializes the parameters of period t+1, including a set of constraints that relates the feasible values of current variables to past values of variables and exogenous events (McCarl and Spreen, 1997). Following Chien and Bradford (1976) and McCarl and Spreen (1997), the general formulation of the recursive programming farm model is as follows: Max E{Πt} = ∑ j E{Cj,t}T Xj,t (1) Subject to: ∑ j Ai,j,t Xj,t ≤ bi,t ∀i (2) Xj,t ≥ 0 ∀j (3) where E{ } denotes the expectation operator; E{Πt} is farm’s expected gross profit in EUR which is maximized in year t ; E{Cj,t} is the vector of expected gross profit in EUR/hectare (ha) of the j cropping activity in period t ; Xj,t is the vector of the decisions variables that denotes the level of the j cropping activity (hectares for crops) in period t; Ai,j,t are the resource I usages by the j cropping activity per ha in period t; bi,t is the vector of available resources i in period t, functionally dependent upon lagged phenomena (Kay, 1971; McCarl and Spreen, 1997). The reinitialization of the vector of available resources (bi,t) is conducted through farm firm growth rules such as the Endogenous Feedback Mechanism (EFM) (e.g., Kay, 1971; Chien and Bradford, 1976; McCarl and Spreen, 1997; Cittadini et al., 2008; Davis et al., 2013; Robert et al., 2016). Although EFM has been applied with some variations, the general mathematical formulation is as follows: bi,t = f(bi,t-1, Xi,t-1*, Vi,t)) (4) where the vector of available resources (bi,t) in period t is determined by the vector of available resources in the previous period (bi,t-1), the optimal decisions in the previous period (Xi,t-1) and by the vector Vi,t that allows for external changes in the resource restrictions due to exogenous events that will occur in the period t which are rather determined by external economic and environmental factors (Kay, 1971; McCarl and Spreen, 1997; Davis et al., 2013; Robert et al., 2016). Since the proposed model is used for structural change analysis, three more basic structural elements are included to determine (i) farm viability, (ii) farm growth/expansion, and (iii) capital stock evolution at the farm level. A detailed description of these structural elements of the model is carried out in subsequent sections. 2.2. ARIMA modeling for economic forecasting in agriculture The usefulness of such a simulation model, which is optimized sequentially within a dynamic framework, lies in the ability to provide results outside the reference period (out-of-sample forecasts). Therefore, to conduct out-of-sample simulations, the forecasted values of the exogenously determined parameters of the farm are required. Various modelers have used ARIMA models to forecast exogenously determined parameters such as agricultural commodity prices (e.g., Mao et al., 2022), crop yields (e.g., Petsakos et al., 2016), cost of production factors (e.g., Hloušková et al., 2018) and supply of various resources (e.g., the total amount of agricultural land, total amount of pesticides) (Costache et al., 2021). ARIMA models are fitted utilizing the information in the series itself to predict future points in the series (Christodoulos et al., 2010; Garnier, n.d.), and therefore the independent variables are lagged values of the series. More specifically, the future values of the dependent variable can only be described through their probability distribution rendering the series a stochastic process2 (Pardoe, n.d.). In this vein, several modelers consider that the use of ARIMA models is appropriate for economic forecasting in agriculture, especially in cases of lack of well-developed theory or limited information (Petsakos et al., 2016); as a result, the forecasting of exogenous variables often present problems for econometric model users (Oliveira et al., 1979). Within this context, the ARIMA stochastic process is utilized for estimating the values of exogenously determined parameters of interest (in our case, agricultural commodity prices, crop yields, costs, interest rate, total arable land, and total circulating capital) to perform out-of-sample forecasts in the medium term. In 2 Details on ARIMA modeling framework are provided in Part A: Conceptual framework of ARIMA modeling in the supplementary material. 357 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 addition, ARIMA models are utilized to estimate the values for random/stochastic parameters, such as agricultural commodity prices and crop yields, to express agents’ quasi-rational expectations mechanism (Nerlove and Bessler, 2001; Siegle et al., 2024). 2.3. Simulation model specification and assumptions 2.3.1. Model’s basic structure The initial endowments with production factors are specified before the sequential simulation starts (in our case, arable land, irrigated land, circulating capital, capital stock, and borrowed capital) (Happe et al., 2008) (see Figure 1). To simulate farms’ productive decisions through the proposed farm-level recursive linear programming model, we assume that farms optimize the expected gross profit (e.g., Rowan et al., 2011) for each year t given the farm’s resource, policy, and flexibility constraints. To elaborate more, resource constraints contain: (i) Arable land constraint; (ii) Irrigated land constraint; and (iii) Circulating capital constraint. Policy constraints contain: (i) 2013 CAP reform constraints (greening obligations); (ii) CAP Post-2020 reform scenario constraints; (iii) Nitrate pollution reduction program constraints; and (iv) Organic farming program constraint. Flexibility constraint corresponds to the constraint of multiannual contract farming3. Each sub-model (based on representative individual real-world farm) optimized recursively4 for a sequence of 15 years (from 2012 to 2026). Time progresses in discrete time intervals, symbolizing the commencement of a growing season at time t (see Figure 1). To perform outof-sample simulations (i.e., outside the reference period, specifically after 2019), mainly ARIMA models are used to forecast the values of the exogenously determined parameters of interest (see Figure 1). 2.3.2. Farm agents’ expectations specification and model validation Various authors (e.g., Femenia et al., 2017) consider naïve and quasi-rational expectations (ARIMA modeling), both based on past observations, to be the most frequent expectation mechanisms5 in some types of 3 A detailed description of the objective function and constraints is provided in Part B: Structure of the model’s objective function and constraints in the supplementary material. 4 The model is written in GAMS language. 5 A detailed description of farm agents’ expectations mechanisms is provided in Nerlove and Bessler (2001), Haile et al. (2016), Femenia et al. (2017), and Siegle et al. (2024). farming. Influenced by this finding, we emphasize these two mechanisms of expectations regarding agricultural commodity prices and crop yields in the present study, considering that they will be representative of sample farms and the information available to them (mainly based on past observations). More specifically, we have formulated two alternative models; one referred to as the Quasi-Rational expectations (QR) model and the other as the Naïve and Quasi-Rational expectations (NV&QR) model. In more detail, in the QR model case, the agent’’ expectations are expressed through quasi-rational expectations (ARIMA modeling) for agricultural commodity prices and crop yields (e.g., Narayana and Parikh, 1981; Nerlove and Bessler, 2001; Siegle et al., 2024). In the NV&QR model case, the agent’’ expectations are expressed through naïve price expectations for agricultural commodity prices (e.g., Nerlove and Bessler, 2001; Robert et al., 2018; Siegle et al., 2024) and through quasi-rational expectations for crop yields. Then the two proposed models are validated for their capability to reproduce activities allocation (Gómez-Limón et al., 2016), the number of surviving farms (Beckers et al., 2018), and the farm size distribution (Freeman et al., 2009; Beckers et al., 2018). 2.3.3. Determining farm viability Usual approaches to defining farm viability are based on the opportunity cost of farming (e.g., Loughrey et al., 2022) and the poverty line (e.g., Miller et al., 1981; Loughrey et al., 2022). Other approaches to defining farm viability focus on monetary returns, where the farm income should ensure long-term farm growth in equity, or at least the equity should remain stable into the future (e.g., Bright et al., 2007; Barnes et al., 2015). Another interesting approach to defining farm viability from a socio-economic perspective is based on the “Keeping up with the Joneses” (KUJ) preferences (Miller et al., 1981; Paroissien et al., 2021). Farmers may compare their profits to the overall standard of living (average living expenditures/average consumption level) of socially close reference group (neighboring farms), which is considered the societal consumption benchmark or social reference point of consumption level (Paroissien et al., 2021). From this perspective, agents that stand below their societal reference point (in the sense of not being able to finance this level of consumption) are forced to stay out of the “rat race of keeping up with the Joneses” (Barnett et al., 2010), may experience lower life satisfaction and professional well-being, a situation which may 358 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. create incentives to exit the system (Paroissien et al., 2021; Nguyen and Herron, 2021). Therefore, a farm must achieve a minimum level of profitability, allowing entry into the “rat race” (Lombardo, 2021) according to KUJ preferences (i.e., keeping up with a benchmark proportional to the average level of consumption of the socially close reference group (Barnett et al., 2010) such as neighboring farms). The influences for this hypothesis come from evolutionary and social psychology, where various researchers assume that the quest for status – frequently referred to in this context as “Keeping-up-with-the Joneses”– depends on the social norms related to a benchmark consumption level such as the average consumption level of the socially close reference group (Fisher and Heijdra, 2009; Lombardo, 2021; Mageli et al., 2022). Based on the above reasoning, various researchers assume that the quest for social status can be linked to the striving to survive (Mageli et al., 2022). Notably, since social groups can distribute resources among their members, an agent’s chances to survive and reproduce are greatly enhanced if she/he belongs to a group and if she/he holds a relatively high social rank within the group, in the sense that an agent’s relative position may give her/ him a survival advantage through access to material and reproductive resources (Mageli et al., 2022). Alternatively, farm viability can be defined according to a combination of monetary value and socio-ecoInitial conditions : Number of neighboring surviving farms, farm size distribution,available arable land at farm level, available circulating capital at farm level, capital stock at farm level, borrowed capital at farm level Farm-level data (Field survey) Farm-level optimization model : Expected Farm Gross Profit maximization under resource, policy and flexibility constraints Farm agents' expecations Quasi-rational agents’ expectations for prices and crop yields OR Naive agents’expecations for prices and quasi-rational agents’ expectations for crop yields Out-of-sample simulations ARIMA models: Forecasting values of costs, prices, crop yields,interest rate, total arable land, and total circulating capital Linear trend model:Forecasting value of living expenditures index Farm viability algorithm: i) Optimal Farm Net Profit After Tax ≥ Simulated Societal Consumption Benchmark of neighboring farms AND ii) Optimal Farm Growth in Equity ≥ 0 Number of neighboring surviving farms Farm size distribution Share of farmland by farm size classes Regional land use change dynamics Economic performance by farm size classes Environmental impact assessement Re-initialization of resources & farm firm growth rules of surviving farms: -Endogenous Feedback Mechanism (EFM) for resources (land, circulating capital) Coupled with: Relative optimal Farm Growth in Equity to reallocate/allocate resources (abandoned/relesased land available for rent, regional availability of circulatingcapital)between neighboring surviving farms Next growing season (t=t+1) Post-solution module of Economic indicators : i) Optimal Farm Net Profit After Tax ii) Optimal Farm Growth in Equity Post-solution module of Means-based environmental indicators: i) Fertilizer use ii) Pesticide use iii) Water use Capital stock evolution (Investement module): -Perpetual Inventory Method (PIM) coupled with: -Leontief production relationship between capital stock and land Actual prices; Actual crop yields Determining required borrowing capital: i) Required borrowing circulating capital ii) Required borrowing investment capital Updated information on initial conditions Optimal cropping activities allocation Regional crop supply Number of neighboring surviving farms Farm size distribution Times series data (Statistical authority, Rural institutions, FADN) Policy scenarios Figure 1. Conceptual diagram of the proposed modeling framework. Notes: A post-solution module of means-based environmental indicators enables the model to estimate the environmental performance of farms. However, to limit the size of this paper, the environmental impact assessment will not be presented here. Source: Authors 359 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 nomic criteria (Bert et al., 2011; Mittenzwei and Britz, 2018; Seidel and Britz, 2019). In the present modeling approach, a sample farm is considered viable/surviving by satisfying two viability criteria: (i) the criterion of societal consumption benchmark of neighboring farms (NBF)6 according to the KUJ preferences and, (ii) the criterion of non-negative optimal farm growth in equity. At this point, we would like to mention that, following similar simulation models (Bert et al., 2011; Offermann and Margarian, 2014; Mittenzwei and Britz, 2018; Seidel and Britz, 2019) we simulate only farm exit according to the farm exit module considering economic and socioeconomic criteria. Consequently, we do not model the life cycle of agents who enter farming, get old, and retire (Bert et al., 2011). Therefore, following each discrete optimization time-step (annual), every neighboring farm nbf decides whether to remain in the system or exit (see also Figure 1). Specifically, a neighboring farm is considered viable and remains in the production system when at the end of the year t meets both viability criteria, i.e., (i) the optimal Farm Net Profit after Tax (FNPAT*nbf,t) should be at least equal to the simulated average living expenditures of neighboring farms in year t (LENBF,tsim), and (ii) optimal farm growth in equity (FGE*nbf,t) should be at least equal to zero. 6 The literature on whom agents compete with for social status, i.e., who the Joneses are, is relatively limited (Mageli et al., 2022). Nevertheless, it is conceivable that agents compare more intensely with agents who are socially proximate to them (Mageli et al., 2022). For example, society serves as a socially distant reference group, whereas colleagues are socially close reference groups (Mageli et al., 2022). In this framework, we could consider a socially close reference group to each agent (individual real-world farm), farms with the same productive specialization located in the same region, i.e., neighboring farms (NBF) correspond to arable crop farms of the regional unit of Karditsa (NUTS-3 level). In particular, farmers of this reference group could be considered colleagues due to their similar professional goals and intense professional interactions, which are expressed through their professional collective bodies, such as trade union bodies, groups of producers, and cooperatives, which are mainly made up of farmers of common productive specialization. From this perspective, the intense professional and, consequently, social interactions may provide each agent of the reference group (neighboring farm) with a comparatively better level of information about the economic performance of its neighbors and the livelihood level (consumption level, particularly for visual commodities that are connected to income or wealth, e.g., cars and houses) (Mageli et al., 2022) than for socially distant reference groups (i.e., farms with different productive specializations compared to the agent). Consequently, this comprehensive information signals the process of forming social norms based on which a social group’s social status or position is determined. In our case, the quest for social status is reflected in KUJ preferences (Fisher and Heijdra, 2009; Lombardo, 2021; Mageli et al., 2022). Finally, we also relied on a strict definition of neighboring farms for this selection based on the relevant literature (Paroissien et al., 2021), where only farms with the same specialization located in the same region are included in the socially close reference group (neighboring farms). As regards the mathematical formulations of the specific profitability measures are as follows considering the relevant literature (GRDC, 2015): FNPAT*f,t = Π*f,t – (DEPf,t + LRCf,t + SFNCf,t + LFNCf,t + SICf,t + FPTXf,t) (5) FGE*f,t = FNPAT*f,t – LEf,t (6) where FNPAT*f,t is the optimal Farm Net Profit after Tax f in year t; Π*f,t is the optimal gross profit of farm f in year t; DEPf,t is the depreciation of machinery of farm f in year t; LRCf,t are the land rental costs7 of farm f in year t; SFNCf,t are the short-term finance costs which correspond to the interest paid for short-term loans of farm f in year t; LFNCf,t are the long-term finance costs which correspond to the interest paid for long-term loans of farm f in year t; SICf,t are the social insurance contributions paid by farm f in year t; FPTXf,t is the farm profit tax paid by farm f in year t; FGE*f,t is the optimal Farm Growth in Equity of farm f in year t; LEf,t are the living expenditures8 of farm f in year t. 2.3.4. Re-initialization of resources and farm firm growth rules The annual re-initialization of resources required for the farms’ operation and growth/expansion process is conducted through the Εndogenous Feedback Mechanism (EFM) (whose general structure has been presented in the 2.1 section). An essential part of the literature indicates that growth in equity determines the prospects for growth/expansion of the farm (e.g., Painter, 2005; Cittadini et al., 2008; Bert et al., 2011; GRDC, 2015), that is, that the acquisition of resources will be determined through this profitability measure. Hence, we consider that optimal farm growth in equity could be used as an alternative criterion of farm expansion/growth to tra7 In case that farm rents out part of owned farmland, then receives land rental income LRINCf,t. Consequently the equation (5) is adapted as follows: FNPAT*f,t = (Π*f,t + LRINCf,t) – (DEPf,t + SFNCf,t + LFNCf,t + SICf,t + FPTXf,t), indicating that a farm cannot simultaneously rent in and rent out farmland, a condition we also find in similar simulation models (e.g., Donati et al., 2024). 8 The estimation of living expenditures following the base year (2012) is carried out by utilizing the living expenditures index (LEI) of households in rural areas (ELSTAT, 2021). That is, heterogeneity between farms in the living expenditures in the base year (2012) is captured, but its evolution over time is based on the exogenously determined living expenditures index (LEI). Since the available time series of the living expenditures index (LEI) does not meet the minimum required time horizon of 16 data points of the ARIMA model (Christodoulos et al., 2010), we use a linear trend model instead of the ARIMA model to make post-sample forecasts. 360 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. ditional criteria such as the shadow values of resources (e.g., land, circulating capital) (Guinde et al., 2005; Hennessy, 2007; Espinosa et al., 2016). However, given resource constraints, especially land, farm expansion is possible when neighboring farms decide to downsize or abandon agricultural production (Plogmann et al., 2022). Essentially, the process of structural change drives the reallocation of the resources required for expansion, where the resources of non-viable neighboring farms (e.g., land) are reallocated to viable ones (see also Figure 1). Various modelers (e.g., Bert et al., 2011; Sheng et al., 2015; Herrera et al., 2022; Sun et al., 2022) highlight the role of relative profitability as a criterion/mechanism for the reallocation/allocation of resources between surviving farms. Within this context, our concern was how optimal farm growth in equity could be expressed as a criterion/mechanism for resource reallocation among viable farms and integrated into the EFM. To model this mechanism, we adapted the concept of efficient allocation (Ayerst et al., 2020; Chen et al., 2022). According to the proposed adaptation, we replace relative farming productivity with relative farm growth in equity. We consider this adjustment to be reasonable since Foster et al. (2008) found that “firms’ self-selection behavior (in choosing an operating scale, or to enter or exit) is made based on firm profitability rather than firm productivity and consequently resource reallocation may not always align with firm productivity growth, particularly in the short run” (Sheng et al., 2015: 75). By incorporating the proposed resource reallocation/allocation mechanism into the EFM, each farm’s annual level of resource is determined by the available level of the resource at the beginning of the previous growing season, the relative optimal growth in equity at the end of the previous growing season (indicating the optimal decisions), and by exogenous events9 that will occur in the current growing season. Since we have ensured (from the viability determination assumptions) that a viable farm will not reveal negative optimal growth in equity, the mathematical formulation of the share of any resource r ∈ {AL,CRC} allocated or reallocated is as follows: Ωsimrvf,nbf,t = , for t = 1… T, 0 ≤ Ωsimrvf,nbf,t (7) 9 We assume that exogenous events are expressed through successive differences in the aggregate level of resources where the relative optimal growth in equity of the previous growing season allocates these positive or negative differences across farms. where Ωsimrvf,nbf,t is the simulated share of resource r allocated/reallocated to viable neighboring farm in year t; FGE*vf,nbf,t is the optimal Farm Growth in Equity of viable neighboring farm in year t; FGE*vf,nbf,t is the aggregate optimal Farm Growth in Equity of viable neighboring farms in year t. Essentially the simulated share of resource r allocated to viable neighboring farm in period t (Ωsimrvf,nbf,t) expresses the part of EFM which corresponds to optimal decisions (Xjt*) while considering the interdependence of optimal decisions of viable neighboring farms, indicating competitiveness for resources. It is also worth noting that the simulated share (Ωsimrvf,nbf,t) remains the same for each resource allocated/reallocated. (i) Arable land Therefore, considering the above, the EFM mechanism for the resource of arable land will be formulated as follows: ALvf,nbf,t = ALvf,nbf,t-1 + ΩsimALvf,t-1 [ ALnvf,nbf,t-1sim + (TALNBF,t – TALNBF,t-1)], for t=2…T (8) where ALvf,nbf,t is the available arable land of viable neighboring farm in year t; ALnvf,nbf,t-1 is the available arable land of viable neighboring farm at the beginning of year t-1; ΩsimALvf,nbf,t-1 is the simulated share of arable land reallocated to viable neighboring farm at the end of the year t-1, that is, following the annual optimization; ALnvf,nbf,t-1sim is the simulated aggregate arable land of non-viable neighboring farms at the end of the year t-1, that is, following the annual optimization; TALNBF,t is the actual total arable land of neighboring farms in year t; TALNBF,t-1 is the actual total arable land of neighboring farms in year t-1. Essentially, the product ΩsimALvf,nbf,t-1(TALNBF,t – TALNBF,t-1) corresponds to the vector Vit of EFM that allows for external changes in the resource restrictions due to exogenous events, and probably reflects the competition for resources with other types of farms or non-agricultural sectors which operate within the same region. However, competitive pressures are likely to lead to an unfavorable situation, i.e., TALNBF,t – TALNBF,t-1 < 0 and consequently to a decrease of available arable land for the viable neighboring farms, which will be reallocated among them utilizing the inverse form of the simulated share of arable land (ΩsimALvf,nbf,t-1 -1), that is, less profitable albeit viable farms will abandon proportionately more of their arable land. As can be easily understood by the reader, the above procedure is also applied to the available irrigated land 367 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 scenarios is projected to enhance the profitability of these farms further. It is also worth noting that between these two scenarios, no substantial differences can be found in the evolution of profitability. 3.4. Simulated land use change As regards the simulated land use change dynamics illustrated in Figure 5, the main change can be seen in the progressive expansion of the processing vegetable area and especially for processing pepper. This finding thoroughly verifies farmers’ expectations for the further expansion of these crops. In particular, the processing pepper farmers of the sample state that their export activity will increase significantly in the coming years since they receive more than double commodity prices compared to domestic prices. Processing tomato farmers aspire to a significant expansion of their productive activity due to the positive growth prospects of the local tomato processing industry, as they also consider the role of the local group of processing tomato farmers to be particularly beneficial. An increasing trend in the processing vegetable area is simulated for both scenarios. Still, a more significant upward trend is simulated for the CAP Post-2020 reform scenario, possibly due to the increased rate of structural change leading to more efficient use of resources, in the sense that surviving farms tend to allocate farmland area to comparatively more profitable activities20. Conversely, we simulated a significant gradual decrease in the cotton and tobacco areas. In fact, for the CAP Post-2020 reform scenario, we observe a fur20 Details are provided in Table A1 in the Appendix. Figure 4. Evolution of simulated average Farm Net Profit after Tax (FNPAT) by scenario. Note: The provisions of the CAP Post-2020 scenario apply from the year 2023. Source: Authors, based on sample data. Table 4. Simulated mean Farm Net Profit after Tax (FNPAT) in EUR by farm size classes (2012-2026). Farm size class in ha (Characterization) 2012 2019 2026 (BAU scenario) 2026 (CAP Post-2020 scenario) 2026 (CAP Post-2020 & LWA scenario) <10 (Very Small) 18,156 13,706 12,196 - - 10-<30 (Small) 41,931 26,707 25,989 24,987 25,010 30-<50 (Medium) 59,829 68,250 98,608 104,309 107,964 50-<100 (Large) 110,370 69,918 115,803 122,013 126,539 ≥100 (Very Large) - 695,181 1.738,668 1.855,216 1.865,563 Aggregate 39,526 84,644 271,183 323,692 327,622 Note: The determination and characterization of farm size classes is based on Happe et al. (2008), and Huettel & Margarian (2009). Source: Authors, based on sample data. 368 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. ther reduction of the cotton and tobacco areas. Durum wheat area increases significantly over time for the BAU scenario, while for the CAP Post-2020 reform scenario, a decrease after 2022 is foreseen due to the set-aside applied by the vast majority of sample farms (more than 90%) in the context of eco-scheme payments. Based on this finding, we conclude that farms have a strong incentive to adopt eco-schemes since the majority exceed 10 hectares and, therefore, would be required to implement set-aside on 4% of arable land without extra payment. In the CAP Post-2020 & LWA scenario, an expected increase is simulated for the area of the grain (durum wheat, maize), especially maize, due to the possible increase and maintenance of farm gate prices at high levels due to the Ukrainian crisis. Accordingly, a further reduction in cotton and tobacco areas is simulated. 4. DISCUSSION AND CONCLUSIONS Dynamic modeling methodologies are deemed crucial for comprehending the evolution of economic agents’ behaviors in response to shifts in the economic environment or policies (Gardebroek and Oude Lansink, 2008). Considering the volatile economic environment in which farms operate due to recent international developments, such assessments gain significant weight when using simulation models like the one we propose herein since they can support policy analysts in formulating and specifying the appropriate policy measures. In this context, this study described the conceptual framework of a newly developed farm-level recursive linear programming model primarily aiming at simulating the impact of policy reform on structural change in the arable production system of the region of Karditsa (NUTS-3 level), one of the central growing regions of arable crops in Greece. While managing to capture mainly endogenously the dynamics of structural change adaptation, the proposed simulation model can simultaneously be characterized by a comparatively low level of modeling complexity compared to other simulation models, such as agent-based models. From a general perspective, this paper seeks to contribute to the debate on dynamic assessments of the multidimensional effects in the context of the CAP Post2020 reform while considering recent geopolitical developments in the context of the Ukrainian crisis. Validation results demonstrate satisfactory performance of the simulation model in reproducing past changes. Therefore, we can use the model to assess the effects of various scenarios on the agricultural production system. By carrying out policy experiments for two different policy scenarios and a combined scenario (policy and geopolitical) we estimated an increased rate of structural change compared to the reference period (2012-19), and especially for the CAP Post-2020 and CAP Post-2020 & Long War of Attrition (LWA) scenarios. The proposed model simulated an evident gradual concentration of farmland in relatively large farms (farm size ≥50 ha), accompanied by a decrease in the number of relatively small farms (farm size < 30 ha), making these findings consistent with the results obtained from simulation models (e.g., Happe et al., 2008; Bert et al., 2011; Donati et al., 2024) and other dynamic modeling approaches (Herrera et al., 2022; Schuh et al., 2022). (a) BAU scenario (b) CAP Post-2020 scenario (c) CAP Post-2020 & LWA scenario Figure 5. Simulated arable land allocation by scenario. Note: The provisions of the CAP Post-2020 reform scenario apply from the year 2023. Source: Authors, based on sample data. 369 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Regardless of the examined scenario, the simulated average farm profitability shows a gradual increase, which is partly explained by the fact that relatively more profitable farms remain in the production system confirming previous findings obtained from simulation models (Happe et al., 2008; Bert et al., 2011) and other dynamic modeling approaches (Herrera et al., 2022; Schuh et al., 2022). Obviously, the surviving farms which achieve growth in equity tend to allocate their growing resources (such as farmland, circulating capital and fixed assets) more efficiently, i.e., to relatively more profitable productive activities (in our case, processing vegetables), further enhancing average farm profitability (Bert et al., 2011). However, a downward trend is simulated for the average profitability of relatively small farms (farm size < 30 ha). In terms of land use change dynamics, regardless of the scenario, our model simulated an increasing trend of the land allocated to food crops such as processing vegetables and a simultaneous decreasing trend of the farmland allocated to industrial crops such as cotton and tobacco. The rationale explains this result discussed earlier, namely that surviving farms tend to expand productive activities with comparatively higher profitability, a finding that is also consistent with findings obtained from a simulation model applied to the agricultural system of the Argentine Pampas (Bert et al., 2011). Additionally, Bert et al. (2011) consider that this behavior of the farms is interpreted by their survival strategy. Considering the above, it could be said that a correlation of land use change with structural change emerges, in the sense that the viability of farms is strongly dependent on the land use chosen (Bert et al., 2011) and is expressed through their survival strategy to allocate their farmland area and capital to the most profitable cropping activity gradually. Focusing on the paper’s main finding – namely, the agricultural production concentration in relatively large farms (farm size ≥ 50 ha) – it is found that this has some significant policy implications. In particular, an intensifying continuation of pressures towards fewer but larger farms (i.e., an increasing rate of structural change) could lead to a breakdown of social cohesion, a prerequisite for addressing rural communities’ challenges (Knutson et al., 1986). From this perspective, appropriate policy measures could focus, for example, on the enhancement of farmers’ market access since small and medium-sized farms have issues accessing markets, achieving a proper share in the EU food chain, including value-added processing, and maintaining bargaining power (Schuh et al., 2022). In this vein, cooperatives are one way to improve farmers’ access to markets and strengthen bargaining power, primarily through vertical integration, which can often play a significant role in increasing the economic benefits of farmers (Schuh et al., 2022). Therefore, it is essential to prioritize examining exemplary cooperative practices and supporting the adoption of similar operational models through policy actions (Schuh et al., 2022). Even if essential insights were gained, this modeling exercise is characterized by several caveats, where we will focus on the main ones. First, although the proposed recursive linear programming model utilizes input data of representative individual real-world farms, effectively capturing the heterogeneity in farm structure and replicating varied farm behavior, it does not explicitly capture the interaction between individual farms in the sense of not incorporating an endogenous price formation mechanism for the market of locally available resource like land (Berger, 2001; Troost and Berger, 2015; Kremmydas, 2019). Additionally, it does not fully consider spatial relationships, overlooking the imperfect land allocation among farms by disregarding internal transport costs and the physical immobility of land (Berger, 2001; Troost and Berger, 2015; Kremmydas, 2019). In this context, the determination of the regional level at which farms can be regarded as competitors for the farmland offered is left to the subjectivity of the modeler. Although administrative units are often used as a realistic approach (in our case, the regional unit of Karditsa (NUTS-3 level)), ideally, the regional level could be defined by the viewpoint of active farmers who operate the land (Plogmann et al., 2022). Consequently, these weaknesses of the proposed model limit its ability to fully capture interactions between farms and spatial dynamics, limiting its explanatory power in policy analysis. Especially, the model cannot provide detailed insights into the impacts of policy scenarios/options on farm structure due to their effects on local resource markets (Kremmydas, 2019). Furthermore, the incomplete incorporation of spatial dynamics curtails the model’s explanatory capacity regarding policy effects on the environment, where spatial aspects hold considerable importance (Kremmydas, 2019). Second, although the proposed simulation model considers the differences in profits among neighboring farms cultivating different farmland areas in the base year, providing a reasonable representation of the farm growth process, it does not consider economies of scale in an intertemporal context. The capture of economies of scale at a longitudinal level by the proposed model was not carried out to maintain its computational complexity. However, a more detailed model that considers this dimension could enhance the representation of farm heterogeneity and, consequently, policy representation towards a more realistic framework. Therefore, future developments of the proposed simulation model could incorporate cost reductions 370 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. as a function of farm expansion and/or technological progress (Happe et al., 2008; Bert et al., 2011). Third, due to the lack of farm-level data for the interim years of the reference period, we were forced to use the available national-level time series for parameters of interest to bridge the time series data gap at the farm level. However, various authors have highlighted and documented the statistical differences between regional/national and farm-level time series data associated with underestimation of variability (e.g., Debrah and Hall, 1989). In particular, aggregated data tends to underestimate the variability of parameters such as prices and yields at the farm level (Debrah and Hall, 1989), which may lead to a less adequate representation of reality regarding farms’ behavior and adaptation. This modeling exercise has identified many avenues for further research, highlighting only a few. First, the geographical and sectoral coverage should be expanded. Second, it is of particular importance to run simulations using alternative allocation/reallocation mechanisms of resources, such as relative shadow values of resources. Third, an interesting avenue for further research is to conduct an environmental impact assessment by utilizing meanand effect-based indicators (Lebacq et al., 2013; Donati et al., 2024) but also to incorporate social indicators, allowing us to assess sustainability performance at the farm level (e.g., Lairez et al., 2023). Finally, further research could be conducted on the investigation of farm viability using alternative monetary and socioeconomic viability criteria. To conclude, although our modeling results may not represent all Greek regions, they may be particularly informative for trends that may emerge due to structural and land-use changes in rural areas with similar arable production systems, not only in the country but also in the wider Mediterranean area. ACKNOWLEDGEMENTS This research is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Strengthening Human Resources Research Potential via Doctorate Research” (MIS-5000432), implemented by the State Scholarships Foundation (ΙΚΥ). REFERENCES Ayerst, S., Brandt, L., and Restuccia, D. (2020). Market constraints, misallocation, and productivity in Vietnam agriculture, Food Policy, 94. https://doi. org/10.1016/j.foodpol.2020.101840 Baldi, L., Calzolai, S., Arfini, F., & Donati, M. (2024). Predicting the effect of the Common Agricultural Policy post-2020 using an agent-based model based on PMP methodology. Bio-Based and Applied Economics. https://doi.org/10.36253/bae-14592 Balmann, A. (1997). Farm-based modelling of regional structural change: A cellular automata approach. European Review of Agricultural Economics, 24(1): 85–108. https://doi.org/10.1093/ erae/24.1.85 Balmann, Al., and Valentinov, V. (2016). Towards a theory of structural change in agriculture: Just economics? 149 Th EAAE Seminar: Structural Change in Agri-Food Chain, New Relations between Farm Sector, Food Industry and Retail Sector, 3. https://doi. org/10.22004/ag.econ.246420 Barnes, A. P., Hansson, H., Manevska-Tasevska, G., Shrestha, S. S., and Thomson, S. G. (2015). The influence of diversification on long-term viability of the agricultural sector. Land Use Policy, 49, 404–412. https://doi.org/10.1016/j.landusepol.2015.08.023 Barnett, R. C., Bhattacharya, J., and Bunzel, H. (2010). Choosing to keep up with the Joneses and income inequality. Economic Theory, 45(3): 469–496. https:// doi.org/10.1007/s00199-009-0494-5 Beckers, V., Beckers, J., Vanmaercke, M., van Hecke, E., van Rompaey, A., and Dendoncker, N. (2018). Modelling farm growth and its impact on agricultural land use: A country scale application of an agent-based model. Land, 7(3). https://doi.org/10.3390/land7030109 Berger, T. (2001). Agent-based spatial models applied to agriculture: a simulation tool for technology diffusion, resource use changes and policy analysis. Agricultural Economics, 25(2-3): 245-260. https://doi. org/10.1111/j.1574-0862.2001.tb00205.x Bert, F. E., Podestá, G. P., Rovere, S. L., Menéndez, Á. N., North, M., Tatara, E., Laciana, C. E., Weber, E., and Toranzo, F. R. (2011). An agent-based model to simulate structural and land use changes in agricultural systems of the Argentine pampas. Ecological Modelling, 222(19): 3486–3499. https://doi.org/10.1016/j. ecolmodel.2011.08.007 Bright, G., Florey, B., and Adams, J. (2007). Indicators and determinants of farm financial success. Journal of Farm Management 13(2): 75-93. https://www. iagrm.com/files.php?file=large/journals/jofm/volume_13/jofm-vol13-no2-pages-75-93.pdf Britz, W., Lengers, B., Kuhn, T., and Schäfer, D. (2016). A highly detailed template model for dynamic optimization of farms-FARMDYN. Model documentation. 371 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Institute for Food and Resource Economics, University Bonn. https://www.ilr1.uni-bonn.de/en/research/ research-groups/economic-modeling-of-agriculturalsystems/farmdyn Chen, C., Restuccia, D., and Santaeulàlia-Llopis, R. (2022). The effects of land markets on resource allocation and agricultural productivity. Review of Economic Dynamics, 45, 41–54. https://doi. org/10.1016/j.red.2021.04.006 Chien, Y. I., and Bradford, G. L. (1976). A Sequential Model of the Farm Firm Growth Process. American Journal of Agricultural Economics, 58(3): 456-465. https://doi.org/10.2307/2290724 Christodoulos, C., Michalakelis, C., and Varoutas, D. (2010). Forecasting with limited data: Combining ARIMA and diffusion models. Technological Forecasting and Social Change, 77(4), 558–565. https:// doi.org/10.1016/j.techfore.2010.01.009 Ciaian, P., Espinosa, M., Paloma, G.Y., Heckelei, T., Sckokai, P., Langrell, S., Louhichi, K., Thomas, A., and Vard, T. (2013). Farm level modelling of the CAP: a methodological overview. EUR 25873. Luxembourg (Luxembourg): Publications Office of the European Union; 2013. JRC79969. https://publications.jrc.ec.europa.eu/repository/bitstream/ JRC79969/jrc79969onlinefinal.pdf Cittadini, E. D., Lubbers, M. T. M. H., de Ridder, N., van Keulen, H., and Claassen, G. D. H. (2008). Exploring options for farm-level strategic and tactical decisionmaking in fruit production systems of South Patagonia, Argentina. Agricultural Systems, 98(3): 189–198. https://doi.org/10.1016/j.agsy.2008.07.001 Cochrane, W. (1958). Farm Prices: Myth and Reality. Minneapolis: University of Minnesota Press, 1958. https://searchworks.stanford.edu/view/9972413 Costache, M., Sebastian Cristea, D., Petrea, S. M., Neculita, M., Rahoveanu, M. M. T., Simionov, I. A., Mogodan, A., Sarpe, D., and Rahoveanu, A. T. (2021). Integrating aquaponics production systems into the Romanian green procurement network. Land Use Policy, 108. https://doi.org/10.1016/j.landusepol.2021.105531 Davis, J., Caskie, P., and Wallace, M. (2013). Promoting structural adjustment in agriculture: The economics of New Entrant Schemes for farmers. Food Policy, 40, 90–96. https://doi.org/10.1016/j.foodpol.2013.02.006 Day, R. H., and Cigno, A. (1978). Modelling economic change: The recursive programming approach. Day, R H, Cigno, A (eds). Modelling Economic Change. Elsevier North-Holland, Inc. Debrah, S., and Hall, H. H. (1989). Data Aggregation and Farm Risk Analysis. In Agricultural Systems (Vol. 31). Djanibekov, U., and Finger, R. (2018). Agricultural risks and farm land consolidation process in transition countries: The case of cotton production in Uzbekistan. Agricultural Systems, 164, 223–235. https://doi. org/10.1016/j.agsy.2018.03.009 Dowson, O., Philpott, A., Mason, A. and Downward, A. (2019). A multi-stage stochastic optimization model of a pastoral dairy farm. European Journal of Operational Research 274: 1077–1089. ELSTAT (2021). Household Budget Survey (after 2008), 2020. Hellenic Statistical Authority. https://www.statistics.gr/en/statistics/-/publication/SFA05/2020 Espinosa, M., Gocht, A., Heckelei, T., and Paloma, S. G. y. (2016). Incorporating farm structural change in models assessing the Common Agricultural Policy: An application in the CAPRI farm type model. Journal of Policy Modeling, 38(6): 1040–1059. https://doi. org/10.1016/j.jpolmod.2016.03.005 European Council (2022). Infographic - Ukrainian grain exports explained. https://www.consilium.europa.eu/ en/infographics/ukrainian-grain-exports-explained/ FADN Public Database. Farm Accountancy Data Network Public Database. Directorate-General for Agriculture and Rural Development. https://agridata. ec.europa.eu/extensions/FADNPublicDatabase/FADNPublicDatabase.html Femenia, F., Latruffe, L., and Chavas, J. P. (2017). Responsiveness of farm investment to price changes: An empirical study of the French crop sector. Journées de Microéconomie Appliquées (JMA), Groupe d’Analyse des Itinéraires et Niveaux Salariaux (GAINS). FRA. Université du Maine, FRA., Jun 2017, Le Mans, France. https://hal.science/hal-01571567 Finger, R., and el Benni, N. (2021). Farm income in European agriculture: New perspectives on measurement and implications for policy evaluation. European Review of Agricultural Economics, 48(2): 253-265. https://doi.org/10.1093/erae/jbab011 Finger, J. M., and Kreinin, M. E. (1979). A Measure of ‘Export Similarity’ and Its Possible Uses. The Economic Journal, 89(356). https://doi. org/10.2307/2231506 Fisher, W. H., and Heijdra, B. J. (2009). Keeping up with the ageing Joneses. Journal of Economic Dynamics and Control, 33(1): 53–64. https://doi.org/10.1016/j. jedc.2008.04.010 Foster, L., Haltiwanger, J., and Syverson, C. (2008). Reallocation, firm turnover, and efficiency: Selection on productivity or profitability? American Economic Review, 98(1): 394-425. https://doi.org/10.1257/aer.98.1.394 Freeman, T., Nolan, J., and Schoney, R. (2009). An agentbased simulation model of structural change in 372 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. Canadian prairie agriculture, 1960-2000. Canadian Journal of Agricultural Economics, 57(4): 537–554. https://doi.org/10.1111/j.1744-7976.2009.01169.x Gardebroek, C., and Oude Lansink, A., 2008. Dynamic microeconometric approaches to analysing agricultural policy. Paper presented at the 107th EAAE Seminar “Modelling of Agricultural and Rural Development Policies”, January 29–February 1, 2008, Seville, Spain. Garnier, H. (n.d.). Introduction to time series analysis and forecasting. University of Lorraine. http://w3.cran. univ-lorraine.fr/perso/hugues.garnier/Enseignement/ TSAF/C-TSAF-Box-Jenkins_method.pdf Goddard, E., Weersink, A., Chen, K., and Turvey, C. G. (1993). Economics of Structural Change in Agriculture. Canadian Journal of Agricultural Economics/ Revue Canadienne d’agroeconomie, 41(4): 475-489. https://doi.org/10.1111/j.1744-7976.1993.tb03772.x Gómez-Limón, J. A., Gutiérrez-Martín, C., and Riesgo, L. (2016). Modeling at farm level: Positive Multi-Attribute Utility Programming. Omega (United Kingdom), 65: 17-27. https://doi.org/10.1016/j.omega.2015.12.004 Greek Ministry of Rural Development and Food (2014). The context of Common Agricultural Policy after 2015-First Pillar: Direct Payments (in Greek). http:// minagric.gr/images/stories/agropol/Greek/Agro_pol/ KAP/ParousiasiFINAL2015_290715.pdf Greek Ministry of Rural Development and Food (2022). Greek Strategic Plan proposal for the CAP 2023-2027 (in Greek). https://ead.gr/wp-content/ uploads/2022/01/cap_sp_proposal_30_12_2021.pdf GRDC (2015). How Do I Measure The Financial Performance Of My Farm Business? Grains Research and Development Corporation (GRDC). Guinde, L., Millet, G., Rozakis, S., Sourie, J.-C., and Tréguer, D. (2005). The CAP Mid-Term Reform Impacts to French Cereal-Oriented Farms. Proceedings of the 89th EAAE Seminar.10.22004/ ag.econ.232607 Haile, M. G., Kalkuhl, M., and von Braun, J. (2016). Worldwide acreage and yield response to international price change and volatility: A dynamic panel data analysis for wheat, rice, corn, and soybeans. In Food Price Volatility and Its Implications for Food Security and Policy. https://doi.org/10.1007/978-3-319-28201-5_7 Happe, K., Balmann, A., Kellermann, K., and Sahrbacher, C. (2008). Does structure matter? The impact of switching the agricultural policy regime on farm structures. Journal of Economic Behavior and Organization, 67(2): 431–444. https://doi.org/10.1016/j. jebo.2006.10.009 Hennessy, T. C. (2007). Modelling the Effect of Policy Reform on Structural Change in Irish Farming. Irish Agriculture and Food Development Authority, Rural Economy Research Centre, Ionad Taighde Eacnamaíochta Tuatha. Henningsen, A., Henning, C., Struve, C., and MüllerScheessel, J. (2005). Economic impact of the Mid-Term Review on agricultural production, farm income and farm survival: A quantitative analysis for local subregions of Schleswig-Holstein in Germany, 11th EAAE Congress, August 24-27, 2005. Copenhagen, Denmark. Herrera, H., Schütz, L., Paas, W., Reidsma, P., and Kopainsky, B. (2022). Understanding resilience of farming systems: Insights from system dynamics modelling for an arable farming system in the Netherlands. Ecological Modelling, 464: 109848. https:// doi.org/10.1016/j.ecolmodel.2021.109848 Hloušková, Z., Ženíšková, P., and Prášilová, M. (2018). Comparison of agricultural costs prediction approaches. Agris On-Line Papers in Economics and Informatics, 10(1). https://doi.org/10.7160/aol.2018.100101 Huang, W.-Y., Weisz, R. N., & Heady, E. O. (1980). An econometric-programming model for agricultural policy analysis. CARD Reports. 89, Center for Agricultural and Rural Development, Iowa State University. http://lib.dr.iastate.edu/card_reports/89 Huettel, S., and Margarian, A. (2009). Structural change in the West German agricultural sector. Agricultural Economics, 40: 759–772. https://doi.org/10.1111/ j.1574-0862.2009.00413.x Iglesias, E., Garrido, A., and Gómez-Ramos, A. (2003). Evaluation of drought management in irrigated areas. Agricultural Economics, 29(2): 211–229. https://doi. org/10.1016/S0169-5150(03)00084-7 Kay, R. D. (1971). A dynamic linear programming model of farm firm growth in North Central Iowa. Retrospective Theses and Dissertations. 4470, Iowa State University. https://lib.dr.iastate.edu/rtd Khanal, A. R., and Omobitan, O. (2020). Rural Finance, Capital Constrained Small Farms, and Financial Performance: Findings from a Primary Survey. Journal of Agricultural and Applied Economics, 52(2). https://doi.org/10.1017/aae.2019.45 Knutson, R., Richardson, J., and Smith, E. (1986). Impact of Farm Policies on Agriculture, Farm Structure, and Rural Communities. Journal of Rural Social Sciences, 4(1). Kremmydas, D. (2019). Integrated mathematical programming and agent based model for policy analysis of Greek agriculture. PhD Thesis, Agricultural University of Athens. Kremmydas, D., Ciaian, P., and Baldoni, E. (2023). Modeling conversion to organic agriculture with an EUwide farm model. Bio-Based and Applied Economics, 12(4), 261–304. https://doi.org/10.36253/bae-13925 373 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Lairez, J., Jourdain, D., Lopez-Ridaura, S., Syfongxay, C., and Affholder, F. (2023). Multicriteria assessment of alternative cropping systems at farm level. A case with maize on family farms of South East Asia. Agricultural Systems, 212. https://doi.org/10.1016/j. agsy.2023.103777 Lebacq, T., Baret, P. v., and Stilmant, D. (2013). Sustainability indicators for livestock farming. A review. In Agronomy for Sustainable Development (Vol. 33, Issue 2, pp. 311–327). https://doi.org/10.1007/s13593012-0121-x Lombardo, V. (2021). Social inclusion through social status and the emergence of development traps. Metroeconomica, 72(4), 798–825. https://doi.org/10.1111/ meca.12348 Loughrey, J., O’Donoghue, C., and Conneely, R. (2022). Alternative measures of Family Farm Viability – Incorporating gap measures. Journal of Rural Studies, 89: 257–274. https://doi.org/10.1016/j. jrurstud.2021.11.022 Mageli, I., Mannberg, A., and Heen, E. E. (2022). With whom, and about what, do we compete for social status? Effects of social closeness and relevance of reference groups for positional concerns. Journal of Behavioral and Experimental Economics, 98. https:// doi.org/10.1016/j.socec.2022.101867 Mao, L., Huang, Y., Zhang, X., Li, S., and Huang, X. (2022). ARIMA model forecasting analysis of the prices of multiple vegetables under the impact of the COVID-19. PLoS ONE 17(7): e0271594. https:// doi. org/10.1371/journal.pone.0271594 McCarl, B.A., and Spreen, T.H. (1997). Applied Mathematical Programming Using Algebraic Systems. Texas A&M University, College Station, Texas. https://agecon2.tamu.edu/people/faculty/mccarl-bruce/ mccspr/thebook.pdf Miller, T. A., Rodewald, G. E., and Mcelroy, R. G. (1981). Economies of Size in U.S. Field Crop Farming. Agricultural Economic Report No. 472, National Economics Division, Economics and Statistics Service, U.S. Department of Agriculture. https://doi. org/10.22004/ag.econ.307907 Mittenzwei, K., and Britz, W. (2018). Analysing Farmspecific Payments for Norway using the Agrispace Model. Journal of Agricultural Economics, 69(3): 777-793. https://doi.org/10.1111/1477-9552.12268 Modern War Institute (2022). What Comes Next in Ukraine: Three Scenarios. Modern War Institute – West Point. https://mwi.usma.edu/what-comes-nextin-ukraine-three-scenarios/ Narayana, N. S. S., and Parikh, K. S. (1981). Estimation of farm supply response and acreage allocation: a case study of Indian agriculture. Research Report, International Institute for Applied Systems Analysis, 81–1. Nerlove, M. and D.A. Bessler (2001), “Expectations, Information and Dynamics” in B. Gardner and G. Rausser (Eds.) (2001), Handbook of Agricultural Economics, Vol.1 (Elsevier Science BV), pp. 155-206. Neuenfeldt, S., Gocht, A., Heckelei, T. and Ciaian, P. (2019). Explaining farm structural change in the European agriculture: A novel analytical framework. European Review of Agricultural Economics 46: 713–768. Nguyen, D. J., and Herron, A. (2021). Keeping Up With the Joneses or Feeling Priced Out?: Exploring How LowIncome Students’ Financial Position Shapes Sense of Belonging. Journal of Diversity in Higher Education, 14(3): 429-440. https://doi.org/10.1037/dhe0000191 Offermann, F., and Margarian, A. (2014). Modelling Structural Change in Ex-Ante Policy Impact Analysis. In: Zopounidis, C., Kalogeras, N., Mattas, K., van Dijk, G., Baourakis, G. (eds) Agricultural Cooperative Management and Policy. Cooperative Management. Springer, Cham. https://doi.org/10.1007/978-3-319-06635-6_8 Oliveira, R. A., O ’connor, C. W., and Smith, G. W. (1979). Short-Run Forecasting Models of Beef Prices. Western Journal of Agricultural Economics, 4(1). Painter, M. J. (2005). Returns to Farmland and Farm Labour and Management in Western Canada. Journal of Farm Management, 12(3): 123-141. https:// ageconsearch.umn.edu/nanna/record/122234/files/ Painter%201.pdf?withWatermark=0&withMetadata= 0&version=1®isterDownload=1 Pardoe, I. (n.d.). Course notes for STAT 501: Regression Methods: T.2.5.1 - ARIMA Models. Department of Statistics, Pennsylvania State University. https:// online.stat.psu.edu/stat501/lesson/t/t.2/t.2.5/t.2.5.1arima-models Paroissien, E., Latruffe, L., and Piet, L. (2021). Early exit from business, performance and neighbours’ influence: a study of farmers in France. European Review of Agricultural Economics, 48(5): 1132–1161. https:// doi.org/10.1093/erae/jbab008 Petsakos, A., Hareau, G., Pradel, W., and Suarez, V. (2016). Forecasting Potato and Sweetpotato Yields for 2050. International Potato Center (CIP) Lima, Peru. Working Paper 2016-1. 26 p. Plogmann, J., Mußhoff, O., Odening, M., and Ritter, M. (2022). Farm growth and land concentration. Land Use Policy, 115: 106036. https://doi.org/10.1016/j.landusepol.2022.106036 Quartey-Papafio, T. K., Javed, S. A., and Liu, S. (2021). Forecasting cocoa production of six major producers through ARIMA and grey models. Grey Systems, 11(3): 434-462. https://doi.org/10.1108/GS-04-2020-0050 374 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. RIRDC (2007). Drivers of Structural Change in Australian Agriculture. Rural Industries Research and Development Corporation (RIRDC). Publication No. 07/057. Robert, M., Bergez, J. E., and Thomas, A. (2018). A stochastic dynamic programming approach to analyze adaptation to climate change – Application to groundwater irrigation in India. European Journal of Operational Research, 265(3): 1033–1045. https://doi. org/10.1016/j.ejor.2017.08.029 Robert, M., Thomas, A., and Bergez, J. E. (2016). Processes of adaptation in farm decision-making models. A review. Agronomy for Sustainable Development, 36(4): 64. https://doi.org/10.1007/s13593-016-0402-x Rowan, T. S. C., Maier, H. R., Connor, J., and Dandy, G. C. (2011). An integrated dynamic modeling framework for investigating the impact of climate change and variability on irrigated agriculture. Water Resources Research, 47(7): W0752. https://doi. org/10.1029/2010WR010195 Saint-Cyr, L. D. F., Storm, H., Heckelei, T., and Piet, L. (2019). Heterogeneous impacts of neighbouring farm size on the decision to exit: Evidence from Brittany. European Review of Agricultural Economics, 46(2): 237–266. https://doi.org/10.1093/erae/jby029 Schuh, B. et al. (2022) Research for AGRI Committee – The Future of the European Farming Model: Socioeconomic and territorial implications of the decline in the number of farms and farmers in the EU, European Parliament, Policy Department for Structural and Cohesion Policies, Brussels. https://www.europarl.europa.eu/RegData/etudes/STUD/2022/699620/ IPOL_STU(2022)699620(SUM01)_EN.pdf Seidel, C., and Britz, W. (2019). Estimating a dual value function as a meta-model of a detailed dynamic mathematical programming model. Bio-Based and Applied Economics, 8(1): 75-99. https://doi. org/10.13128/bae-8147 Sheng, Y., Jackson, T., and Gooday, P. (2015). Resource reallocation and its contribution to productivity growth in Australian broadacre agriculture. Australian Journal of Agricultural and Resource Economics, 61(1): 56-75. https://doi.org/10.1111/1467-8489.12137 Siegle, J., Astill, G., Plakias, Z., and Tregeagle, D. (2024). Estimating perennial crop supply response: A methodology literature review. Agricultural Economics (United Kingdom). https://doi.org/10.1111/ agec.12812 Smale M., Saupe W.E., Salant P. (1986). Farm family characteristics and the viability of farm households in Wisconsin, Mississippi, and Tennessee. Agricultural Economics Research, 38: 11–27. Sun, R., Nolan, J., and Kulshreshtha, S. (2022). Agentbased modeling of policy induced agri-environmental technology adoption. SN Business & Economics, 2(8). https://doi.org/10.1007/s43546-022-00275-6 Troost, C., and Berger, T. (2015). Dealing with uncertainty in agent-based simulation: Farm-level modeling of adaptation to climate change in southwest Germany. American Journal of Agricultural Economics, 97(3), 833–854. https://doi.org/10.1093/ajae/aau076 Troost, C., and Berger, T. (2016). Simulating structural change in agriculture: Modelling farming households and farm succession. In: Sauvage, S., Sánchez-Pérez, J.M., Rizzoli, A.E. (Eds.), 2016. Proceedings of the 8th International Congress on Environmental Modelling and Software, July 10-14, Toulouse, France. ISBN: 978-88-9035-745-9. Troost, C., and Berger, T. (2020). Formalising validation? Towards criteria for valid conclusions from agentbased simulation. 10th International Congress on Environmental Modelling and Software Brussels, Belgium. https://scholarsarchive.byu.edu/iemssconference/2020/ Viaggi, D., Raggi, M., and Gomez Y Paloma, S. (2010). An integer programming dynamic farm-household model to evaluate the impact of agricultural policy reforms on farm investment behaviour. European Journal of Operational Research, 207(2): 1130–1139. https://doi.org/10.1016/j.ejor.2010.05.012 Viaggi, D., Bartolini, F., Raggi, M., Sardonini, L., Sammeth, F., Gomez, Y., Paloma, S. (2011). Farm investment behaviour under the CAP reform Process. JRC European Comission: Luxembourg. Weyerstrass, K. (2016). A tool for supporting economic policy-making in the former Yugoslavia. Documentation and applications of a macroeconomic multi-country model. Osteuropa: Geschichte, Wirtschaft, Politik, 49. Wien: LIT-Verlag. 224 p. Wiborg, T. (1998). KRAM - A Sector Model of Danish Agriculture: Background and Framework Development. http://lib.dr.iastate.edu/card_workingpapers/221 Zimmermann, A., and Heckelei, T. (2012). Structural Change of European Dairy Farms - A CrossRegional Analysis. Journal of Agricultural Economics, 63(3): 576-603. https://doi.org/10.1111/j.14779552.2012.00355.x Zimmermann, A., Heckelei, T., and Domínguez, I. P. (2009). Modelling farm structural change for integrated ex-ante assessment: review of methods and determinants. Environmental Science and Policy, 12(5): 601-618. https://doi.org/10.1016/j.envsci.2009.01.014 375 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 APPENDIX Table A1. Simulated average gross margin for each cropping activity (EUR/ha). 2012 2019 Cotton 1,176 1,549 Tobacco (Virginia) 4,750 4,757 Maize 2,300 1,409 Processing Tomato 6,370 4,863 Processing Pepper 17,331 27,800 Alfalfa (hay) 807.3 817.6 Alfalfa (seed production) - 509.5 Durum Wheat 258.2 207.3 Source: Authors, based on sample data. SUPPLEMENTARY MATERIAL TO “SIMULATING FARM STRUCTURAL CHANGE DYNAMICS IN THESSALY (GREECE) USING A RECURSIVE PROGRAMMING MODEL” Part A: Conceptual framework of ARIMA modeling The Box-Jenkins method for Autoregressive Integrated Moving Average (ARIMA) models is considered one of the most efficient time series forecasting methods utilizing almost any set of data (Christodoulos et al., 2010). In this framework, other authors consider that ARIMA models have been remarkably successful with an excellent performance on small data sets (Garnier, n.d.). According to various modelers, ARIMA models can provide acceptable results when at least 16-time series data points are available (Gottardi & Scarso, 1994; Christodoulos et al., 2010). An important class of stochastic models for describing time series are called stationary models or Autoregressive-Moving Average (ARMA) models varying about a fixed constant mean level and with constant variance (Box et al., 2016). An ARMA (p,q) model is formulated as follows: Yt = φiYt-i + εt – θjεt-j, (A1) where φ1 .…, φp are the autoregressive (AR) parameters to be estimated, θ1 ,…,θq are the moving average (MA) parameters to be estimated, and ε1…εt are a series of unknown random “shocks” (or residuals) that are assumed to follow a normal distribution (Pardoe, n.d.). The model can be simplified by introducing the Box-Jenkins backward shift operator21 where BiYt = Yt-i 21 The Backward shift operator is a useful notational device expressing and Bjεt = εt-j; Y1,…,Yt is any time series ; p<t and q<t (Pardoe, n.d.). Substituting backward shift operators in equation (A1), we obtain the following form: (1 – φiBi)Yt = (1 – θjBj)εt (A2) Which is often reduced further to (Pardoe, n.d.): φp(B)Yt = θq(B)εt (A3) Many series encountered in industry or business reveal nonstationary behavior 22and do not vary about a fixed mean, showing a stochastic trend (Box et al., 2016). We should therefore convert a non-stationary time series to a stationary one by differencing the ARMA (p,q) model. Then the ARMA (p,q) model can be extended and written using differences ΔYt = (1 – Β)dYt = ∇dYt as follows: φp(B)(1 – Β)dYt = θq(B)εt (A4) where d is the order of differencing. Replacing in the ARMA model with the differences above, we obtain the formal ARIMA p,d,q) model (Pardoe, n.d.). To detect non-stationarities, we utilize one of the most well-known tests, which corresponds to the augmented Dickey-Fuller (ADF) test (Asteriou & Hall, 2007; Mahan et al., 2015; Box et al., 2016). The identification of possible model orders (p,q) is approached through the utilization of Autocorrelation function (ACF) and Partial Autocorrelation function (PACF) plots (Mahan et al., 2015; Box et al., 2016; Garnier, n.d.) while trying to keep the model orders at low levels (≤ 2) for most of the estimated models (Gottardi & Scarso, 1994). After estimating several models, we test whether the condition of invertibility (Asteriou & Hall, 2007; Garnier, n.d.) and statistical significance of the AR and MA parts of the model are satisfied (Mossad & Alazba, 2015). The estimated models are then compared according to the Akaike information criterion (AIC) by selecting the model with the lowest value (Mahan et al., 2015; Box et al., 2016; Garnier, n.d.). The diagnostic check of the model is then performed, which is applied to residuals to detect whether they exhibit the length of previous data the model uses to provide forecasts (Christodoulos et al., 2010). 22 ARIMA modeling requires that the time series be stationary (Schaffer et al., 2021). A stationary series is characterized by three properties: a constant mean, constant variance, and constant covariance that depends only on the time intervals (Schaffer et al., 2021). Time series with trends or changing variance is non-stationary. 376 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. autocorrelation, utilizing the Breusch-Godfrey Lagrange Multiplier (LM) test (Mahan et al., 2015; Weyerstrass, 2016; Ayele et al., 2017). The null hypothesis of the LM test is that there is no autocorrelation in the residuals series up to the pre-determined lag order (p=2 in our analysis) at the 5% level of significance (Weyerstrass, 2016; Ayele et al., 2017). Regarding the measurement of the forecasting accuracy of ARIMA models, there is no universally preferred measure; however, according to various modelers (Gottardi and Scarso, 1994; Christodoulos et al., 2010), particular emphasis is given to the measure of Mean Absolute Percentage Error (MAPE). At this point, we would like to point out that there is no commonly accepted threshold for MAPE in the international literature; however, some authors consider that a forecasting model is characterized by good forecasting accuracy (or goodness-of-fit) when MAPE does not exceed 20%, whereas when it does not exceed 10%, the forecasting accuracy is characterized as high or perfect (e.g., Quartey-Papafio et al., 2021). Estimates and statistical tests of ARIMA models were performed using EViews statistical package. Part A: References Asteriou, D., & Hall, S. (2007). Applied Econometrics: A Modern Approach. Palgrave Macmillan, New York. Ayele, A. W., Gabreyohannes, E., & Tesfay, Y. Y. (2017). Macroeconomic Determinants of Volatility for the Gold Price in Ethiopia: The Application of GARCH and EWMA Volatility Models. Global Business Review, 18(2), 308–326. https://doi. org/10.1177/0972150916668601 Box, G., Jenkins, G., Reinsel, G., & Ljung G. (2016). Time Series Analysis: Forecasting and Control, 5th Edition, by George E. P. Box, Gwilym M. Jenkins, Gregory C.Reinsel and Greta M. Ljung, 2015. Published by John Wiley and Sons Inc. Christodoulos, C., Michalakelis, C., & Varoutas, D. (2010). Forecasting with limited data: Combining ARIMA and diffusion models. Technological Forecasting and Social Change, 77(4), 558–565. https://doi. org/10.1016/j.techfore.2010.01.009 Garnier, H. (n.d.). Introduction to time series analysis and forecasting. University of Lorraine. https://w3.cran. univ-lorraine.fr/perso/hugues.garnier/Enseignement/ TSAF/C-TSAF-Box-Jenkins_method.pdf Gottardi, G., & Scarso, E. (1994). Diffusion models in forecasting: A comparison with the Box-Jenkins approach. European Journal of Operational Research, 75(3). https://doi.org/10.1016/0377-2217(94)90300-X Mahan, M., Chorn, C., & Georgopoulos, A. (2015). White Noise Test: detecting autocorrelation and nonstationarities in long time series after ARIMA modeling. Proceedings of the 14th Python in Science Conference, 97–104. https://doi.org/10.25080/majora-7b98e3ed-00f Mossad, A., & Alazba, A. A. (2015). Drought forecasting using stochastic models in a hyper-arid climate. Atmosphere, 6(4), 410–430. https://doi.org/10.3390/ atmos6040410 Pardoe, I. (n.d.). Course notes for STAT 501: Regression Methods: T.2.5.1 - ARIMA Models. Department of Statistics, Pennsylvania State University. https:// online.stat.psu.edu/stat501/lesson/t/t.2/t.2.5/t.2.5.1arima-models Quartey-Papafio, T. K., Javed, S. A., & Liu, S. (2021). Forecasting cocoa production of six major producers through ARIMA and grey models. Grey Systems, 11(3), 434-462. https://doi.org/10.1108/GS-04-20200050 Schaffer, A.L., Dobbins, T.A. & Pearson, SA. (2021). Interrupted time series analysis using autoregressive integrated moving average (ARIMA) models: a guide for evaluating large-scale health interventions. BMC Medical Research Methodology, 58(21), https://doi. org/10.1186/s12874-021-01235-8 Weyerstrass, K. (2016). A tool for supporting economic policy-making in the former Yugoslavia. Documentation and applications of a macroeconomic multi-country model. Osteuropa: Geschichte, Wirtschaft, Politik, 49. Wien: LIT-Verlag. 224 p. Part B: Structure of the model’s objective function and constraints The following describes the objective function’s structure and the constraints typical to each sub-model. The objective function of the expected gross profit of the farm f in year t is defined as follows: Max E{Πf,t} = XTf,j,t [E{pf,j,t} E{yf,j,t} – vcf,j,t + lsj,t + ef,tecop1f,j,t + εf,tecop2f,j,t] + DPf,tDLf,t + bf,tNPf,tNLf,t + βf,t OPf,tOLf,t + rf,tRPf,tALf,t (B1) Subject to: Arable land constraint Xf,j,t = ALf,t ,for t = 1,…,T, j ∈ J (B2) Irrigated land constraint Xf,wj,t ≤ ILf,t ,for t = 1,…,T, wj ∈ WJ, WJ ⊆ J (B3) Circulating capital constraint Xf,j,tvcf,j,t ≤ CRCf,t ,for t = 1,…,T, j ∈ J (B4) Xf,j,t ≥ 0 ,for t = 1,…,T (B5) 383 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Part F: ARIMA and linear trend models estimations Table F1. ARIMA models of exogenously determined parameters of interest Εxogenously determined parameter of farm model (Yt) Time series data points [period] ARIMA Model (p,d,q) Φ1Φ2Φ3Θ1Θ2Θ3μMAPE (%) AIC Augmented Dickey-Fuller t-Statistic Breusch-Godfrey Serial Correlation LM Test [Prob. X2 (p)] Hired labor price index 19 [2001-2018 ] (2,0,1) 1.64*** (0.05) -0.82*** (0.04) --0.99*** (0.09) - - 92.79*** (0.59) 0.95 3.84 -3.55*Prob. X2 (2)=0.059 Input price index 20 [2000-2019 ] (1,1,1) 0.87*** (0.06) - - -0.99*** (0.12) - - - 3.78 6.19 -4.29** Prob. X2 (2)=0.44 Machinery rental price index 20 [2000-2019 ] (0,2,1) - - - -0.50** (0.21) - - - 1.29 4.09 -7.00*** Prob. X2 (2)=0.92 Land rental price index 19 [2000-2018 ] (1,0,1) 0.53** (0.20) - - 0.99*** (0.06) - - 99.05*** (1.57) 1.05 3.76 -4.01** Prob. X2 (2)=0.40 Interest rate index 21 [2000-2020 ] (0,2,1) - - - -0.91*** (0.07) - - -5.51 6.49 -6.92*** Prob. X2 (2)=0.99 Cotton yield (Kg/Ha) 57 [1961-2017 ] (1,0,1) 0.92*** (0.01) - - -0.97*** (0.03) - - 299.23*** (5.36) 7.55 9.21 -4.21*** Prob.X2 (2)=0.54 D. wheat yield (Kg/ 0.1 Ha) 57 [1961-2017 ] (2,0,1) 0.50*** (0.15) 0.43*** (0.14) --0.62*** (0.14) - - 278.04*** (51.51) 11.30 9.83 -3.47** Prob.X2 (2)=0.98 Tobacco yield (Virginia) (Kg/0.1 Ha) 39 [1979-2017 ] (1,0,3) 0.87*** (0.02) - - -1.00*** (0.15) 0.48** (0.21) -0.46*** (0.15) 336.52*** (8.17) 6.73 9.40 -4.21*** Prob.X2 (2)=0.35 Pepper yield (Kg/0.1 Ha) 47 [1961-2007 ] (1,0,2) 0.98*** (0.09) - - -0.66*** (0.14) -0.29** (0.14) -4396.72*** (1079.63) 6.28 13.21 -4.10*** Prob.X2 (2)=0.81 Tomato yield (Kg/0.1 Ha) 47 [1961-2007 ] (1,1,0) -0.44*** (0.14) -----81.27** (31.97) 5.5 14.34 -7.21*** Prob.X2 (2)=0.36 Legumes crops yield [Alfalfa (hay & seed)] (Kg/0.1 Ha) 18 [2000-2017 ] (0,0,2) - - - 0.31*** (0.08) 0.93*** (0.02) -740.24*** (26.53) 4.69 10.83 -4.82*** Prob.X2 (2)=0.10 Maize yield (Kg/0.1 Ha) 37 [1981-2017 ] (2,0,0) 0.54*** (0.16) 0.33*** (0.16) ----1086.85*** (122.19) 3.77 10.67 -4.18** Prob.X2 (2)=0.36 Cotton price (EUR/kg) 20 [2000-2019 ] (1,0,1) 0.85*** (0.06) - - -0.96*** (0.04) - - 0.48*** (0.048) 15.17 -2.19 -3.39*Prob.X2 (2)=0.16 D. wheat price (EUR/kg) 20 [2000-2019 ] (3,0,0) 0.84*** (0.23) -0.62** (0.29) 0.44* (0.22) ---0.19*** (0.02) 10.81 -4.08 -3.19*Prob.X2 (2)=0.32 Legume crops price (Alfalfa-hay) (EUR/kg) 20 [2000-2019 ] (1,1,0) -0.43* (0.22) ---- - - 6.00 -6.36 -4.36** Prob.X2 (2)=0.80 Maize price (EUR/kg) 20 [2000-2019 ] (1,0,1) 0.83*** (0.06) - - -0.99*** (0.10) - - 0.18*** (0.00) 8.48 -4.70 -3.40* Prob.X2 (2)=0.08 (Continued) 384 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. Εxogenously determined parameter of farm model (Yt) Time series data points [period] ARIMA Model (p,d,q) Φ1Φ2Φ3Θ1Θ2Θ3μMAPE (%) AIC Augmented Dickey-Fuller t-Statistic Breusch-Godfrey Serial Correlation LM Test [Prob. X2 (p)] Total arable land index 16 [2004-2019 ] (0,1,3) - - - -1.26*** (0.28) 1.17*** (0.22) -0.82*** (0.14) 3.19*** (0.89) 3.67 6.98 -7.75*** Prob.X2 (2)=0.64 Total circulating capital index 16 [2004-2019 ] (0,1,1) - - - -0.93*** (0.06) - - 29. 7*** (2.31) 10.91 10.24 -3.75** Prob.X2 (2)=0.19 Notes: ∇dYt = μ + ϕ1∇dYt-1 + ⋯ ϕp∇dYt-p + εt − θ1εt-1 − ⋯ − θqεt-q; Φ1, . . . , Φp: autoregressive (AR) model parameters of order p; Θ1, … , Θq: moving average (MA) model parameters of order q (Martínez-Acosta et al., 2020) ; εt is white noise; μ= a constant equal to the mean of the series if d = 0 (Narayana & Parikh, 1981); * indicates significance at 0.1 level, ** indicates significance at 0.05 level, *** indicates significance at 0.01 level; The null hypothesis H0 of the Breusch-Godfrey Serial Correlation LM Test is that there is no autocorrelation in the residuals series up to pre-determined lag order (p=2 in our analysis) at the 0.05 level of significance (Weyerstrass, 2016). Source: Authors, based on ELSTAT (2019b), ELSTAT (2019c), FADN Public Database, Greek Ministry of Rural Development and Food, Greek Ministry of Rural Development and Food (2019). Table F2. Linear trend model regression statistics of rural households’ living expenditure index (LEI) Variable Coefficient Std. Error t-Statistic Prob. C 0.954777 0.019644 48.60363 0.0000 @TREND -0.023925 0.002778 -8.612057 0.0000 R-squared 0.870843 Mean dependent var 0.811226 Adjusted R-squared 0.859101 S.D. dependent var 0.099846 S.E. of regression 0.037479 Akaike info criterion -3.589453 Sum squared resid 0.015451 Schwarz criterion -3.502538 Log likelihood 25.33145 Hannan-Quinn criter. -3.607318 F-statistic 74.16753 Durbin-Watson stat 0.642814 Prob(F-statistic) 0.000003 Source: Authors, based on ELSTAT (2021) data. Table F1. (Continued). 385 Predicting the effect of the Common Agricultural Policy post-2020 using an agent-based model based on PMP methodology Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) Figure F1. ARIMA and linear trend models of the exogenously determined parameters of interest. Notes: the horizontal axis indicates the year; 0.1 Ha (hectare) =1 stremma is the Greek unit of land area. (a) Hired labor price index; (b) Input price index; (c) Machinery rental price index; (d) Land rental price index; (e) Interest rate index; (f) Cotton yield (kg/0.1 Ha); (g) Durum wheat yield (kg/0.1 Ha); (h) Tobacco yield (kg/0.1 Ha); (i) Pepper yield (kg/0.1 Ha); (j) Tomato yield (kg/0.1 Ha); (k) Legume crops yield (kg/0.1 Ha) including Alfalfa (hay & seed); (l) Maize yield (kg/0.1 Ha); (m) Cotton price (EUR/kg); (n) Durum wheat price (EUR/kg); (o) Alfalfa (hay) price (EUR/kg); (p) Maize price (EUR/kg); (q) Total arable land index; (r) Total circulating capital index; (s) Living expenditures index. Source: Authors, based on ELSTAT (2019b), ELSTAT (2019c), ELSTAT (2021), FADN Public Database, Greek Ministry of Rural Development and Food, Greek Ministry of Rural Development and Food (2019). 386 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. Part F: References ELSTAT (2019b). Costs for the factors of Agricultural and Livestock Production (Costs indices), 2019. Hellenic Statistical Authority. https://www.statistics.gr/en/statistics/-/publication/DKT33/2019 ELSTAT (2019c). Input and Output Price Indices in Agricultural and Livestock Production, 2019. Hellenic Statistical Authority. https://www.statistics.gr/en/statistics/-/publication/DKT30/2019-M12 ELSTAT (2021). Household Budget Survey (after 2008), 2020. Hellenic Statistical Authority.https://www.statistics.gr/en/statistics/-/publication/SFA05/2020 Martínez-Acosta, L., Medrano-Barboza, J. P., LópezRamos, Á., López, J. F. R., & López-Lambraño, Á. A. (2020). SARIMA approach to generating synthetic monthly rainfall in the Sinú river watershed in Colombia. Atmosphere, 11(6). https://doi. org/10.3390/atmos11060602 FADN Public Database. Farm Accountancy Data Network Public Database. Directorate-General for Agriculture and Rural Development. https://agridata. ec.europa.eu/extensions/FADNPublicDatabase/FADNPublicDatabase.html Greek Ministry of Rural Development and Food. Statistical Data-time series (in Greek). http://wwww.minagric.gr/greek/agro_pol/3.htm Greek Ministry of Rural Development and Food (2019). Statistics Data of areas and production of plant products (in Greek). http://www.minagric.gr/index.php/el/ the-ministry-2/statistikes-tekmhrioshs/8510-statistika-ekt-parag-fytikonproionton Narayana, N. S. S., & Parikh, K. S. (1981). Estimation of farm supply response and acreage allocation: a case study of Indian agriculture. Research Report, International Institute for Applied Systems Analysis, 81–1. Weyerstrass, K. (2016). A tool for supporting economic policy-making in the former Yugoslavia. Documentation and applications of a macroeconomic multi-country model. Osteuropa: Geschichte, Wirtschaft, Politik, 49. Wien: LIT-Verlag. 224 p.