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., & Tsi- boukas, K. (2024). Simulating farm struc- tural change dynamics in Thessaly (Greece) using a recursive program- ming 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 rel- evant 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, Cha- nia Crete, Greece 3 Department of Performance, Innovation and Strategic Analysis for Impact, Bioversity International, Rome, Italy *Corresponding author. E-mail: sta.athens@hotmail.com) Abstract. Although the policy impacts on farms accumulate year by year, most farm decision models focus on short-term decisions, evaluating policies based on snap- shots. 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 pro- gramming model mainly to simulate farm structural change dynamics. The proposed model incorporates new evidence on the strategic decision of arable crop farms regard- ing 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 struc- tural 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- https://creativecommons.org/licenses/by/4.0/legalcode https://creativecommons.org/publicdomain/zero/1.0/legalcode http://www.fupress.com/bae https://doi.org/10.36253/bae-14790 https://doi.org/10.36253/bae-14790 https://doi.org/10.36253/bae-14790 mailto:sta.athens@hotmail.com 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 produc- tive factors required for the development of other sectors of the economy (Balmann and Valentinov, 2016). How- ever, structural change in the agricultural sector is usu- ally 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 farm- ers 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 con- cerning 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 con- sider 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, imple- menting 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 agri- cultural policy decision-making. The European Common Agricultural Policy (CAP) marks essential shifts in the context where farms oper- ate, 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 distri- bution) is highly desirable because it can provide policy- makers and stakeholders with possible alternative sce- narios of structural change adjustments, but it is still not widely used in policy analysis (Ciaian et al., 2013; Espi- nosa 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 sim- ulation models (which aim to analyze farm structural change endogenously) (Espinosa et al., 2016; Zimmer- mann 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 mod- els (e.g., Wiborg, 1998; Guinde et al., 2005; Henningsen et al., 2005; Offermann and Margarian, 2014; Djanibe- kov 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 mod- els can endogenously capture farm structural change, they are considered suited to analyzing policy changes’ allocative and distributive effects on an agricultural pro- duction 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 vari- ous modelers the most comprehensive attempt at ana- lyzing 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., Zim- mermann 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 process- based models1 should not be ignored (Troost and Berg- er, 2020). Therefore, while capturing structural change endogenously and providing meaningful insights into the allocative and distributional effects of various exog- enous 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 simulat- ing the impact of policy experiments on the evolutionary process of farm structural change, the proposed simula- tion model is also secondarily used to simulate the effect 1 Process-based models include models such as simulation models and systems dynamics models. 355Simulating 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/expan- sion. 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 addi- tion to traditional monetary value criteria to determine a surviving/viable farm, we introduce a novel viabil- ity criterion, assuming that farmers may compare their economic performance to societal consumption bench- mark, in the sense that the agent (in our case, real- world individual farm) must achieve a minimum level of profitability, allowing entry into the “rat race” accord- ing 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 neighbor- ing 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 pro- gramming 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-sam- ple 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 sim- ulation model, a representative sample of arable crop farms (in terms of farm structure) of the region of Kar- ditsa (NUTS-3 level), Thessaly, is chosen. The priority of empirical application given to the arable production sys- tem is justified by the fact that Greek arable farming is characterized by a comparatively higher rate of structur- al 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 assess- ments 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 evolution- ary 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 utili- zation 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 exist- ing literature since in similar simulation models; these values are mainly determined either from secondary data sources (e.g., Wiborg, 1998; Hennessy, 2007; Offer- mann 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 produc- tion systems, to our knowledge, farm-level recursive pro- gramming models have not been used to provide a “bot- tom-up” simulation of structural change of Greek arable production system. The rest of the paper is organized as follows. Sec- tion 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 adjust- ments of production capabilities at the farm level, and then with the study of Day and Cingo (1978) regional interdependence and structural elements were incor- porated (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 Marga- rian, 2014; Djanibekov and Finger, 2018; Mittenzwei and Britz, 2018). The main structural elements of a recursive pro- gramming model correspond to a constrained optimi- zation model and a data generator, where the data gen- erator, 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 cur- rent variables to past values of variables and exogenous events (McCarl and Spreen, 1997). Following Chien and Bradford (1976) and McCarl and Spreen (1997), the gen- eral 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 maxi- mized 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; McCa- rl 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 envi- ronmental 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 ele- ments of the model is carried out in subsequent sections. 2.2. ARIMA modeling for economic forecasting in agricul- ture The usefulness of such a simulation model, which is optimized sequentially within a dynamic framework, lies in the ability to provide results outside the refer- ence period (out-of-sample forecasts). Therefore, to con- duct out-of-sample simulations, the forecasted values of the exogenously determined parameters of the farm are required. Various modelers have used ARIMA models to fore- cast exogenously determined parameters such as agri- cultural commodity prices (e.g., Mao et al., 2022), crop yields (e.g., Petsakos et al., 2016), cost of production fac- tors (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 there- fore the independent variables are lagged values of the series. More specifically, the future values of the depend- ent variable can only be described through their prob- ability distribution rendering the series a stochastic pro- cess2 (Pardoe, n.d.). In this vein, several modelers con- sider that the use of ARIMA models is appropriate for economic forecasting in agriculture, especially in cases of lack of well-developed theory or limited informa- tion (Petsakos et al., 2016); as a result, the forecasting of exogenous variables often present problems for econo- metric model users (Oliveira et al., 1979). Within this context, the ARIMA stochastic pro- cess is utilized for estimating the values of exogenously determined parameters of interest (in our case, agricul- tural commodity prices, crop yields, costs, interest rate, total arable land, and total circulating capital) to per- form 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. 357Simulating 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 agri- cultural 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 pro- gramming 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 con- tain: (i) Arable land constraint; (ii) Irrigated land con- straint; 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 reduc- tion program constraints; and (iv) Organic farming pro- gram 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 out- of-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 mod- eling), 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 alter- native 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 mod- el 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 expecta- tions 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 distribu- tion (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 defin- ing 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 via- bility 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 bench- mark 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 satisfac- tion 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 propor- tional to the average level of consumption of the socially close reference group (Barnett et al., 2010) such as neigh- boring farms). The influences for this hypothesis come from evolu- tionary and social psychology, where various research- ers 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 Hei- jdra, 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 great- ly 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 accord- ing to a combination of monetary value and socio-eco- Initial 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 circulating capital) between neighboring surviving farms N ex tg ro w in g se as on (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 indica- tors 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 359Simulating 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 bench- mark of neighboring farms (NBF)6 according to the KUJ preferences and, (ii) the criterion of non-negative opti- mal 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; Mit- tenzwei and Britz, 2018; Seidel and Britz, 2019) we sim- ulate only farm exit according to the farm exit module considering economic and socioeconomic criteria. Con- sequently, 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 expendi- tures of neighboring farms in year t (LENBF,t sim), 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 Mecha- nism (EFM) (whose general structure has been present- ed 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 tra- 7 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; Hen- nessy, 2007; Espinosa et al., 2016). However, given resource constraints, especially land, farm expansion is possible when neighboring farms decide to downsize or abandon agricultural pro- duction (Plogmann et al., 2022). Essentially, the pro- cess 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 profitabil- ity as a criterion/mechanism for the reallocation/alloca- tion 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 adapta- tion, we replace relative farming productivity with rela- tive 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 oper- ating scale, or to enter or exit) is made based on firm profitability rather than firm productivity and conse- quently 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 realloca- tion/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 determi- nation 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: Ωsim rvf,nbf,t = , for t = 1… T, 0 ≤ Ωsim rvf,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 Ωsim rvf,nbf,t is the simulated share of resource r allo- cated/reallocated to viable neighboring farm in year t; FGE*vf,nbf,t is the optimal Farm Growth in Equity of via- ble neighboring farm in year t; FGE*vf,nbf,t is the aggregate optimal Farm Growth in Equity of via- ble neighboring farms in year t. Essentially the simulated share of resource r allo- cated to viable neighboring farm in period t (Ωsim rvf,nbf,t ) expresses the part of EFM which corresponds to optimal decisions (Xjt*) while considering the interdependence of optimal decisions of viable neighboring farms, indicat- ing competitiveness for resources. It is also worth noting that the simulated share (Ωsim rvf,nbf,t ) remains the same for each resource allocated/reallocated. (i) Arable land Therefore, considering the above, the EFM mecha- nism for the resource of arable land will be formulated as follows: ALvf,nbf,t = ALvf,nbf,t-1 + Ωsim ALvf,t-1 [ ALnvf,nbf,t-1 sim + (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; Ωsim ALvf,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-1 sim is the simulated aggregate arable land of non-viable neighboring farms at the end of the year t-1, that is, following the annual optimiza- tion; TALNBF,t is the actual total arable land of neighbor- ing farms in year t; TALNBF,t-1 is the actual total arable land of neighboring farms in year t-1. Essentially, the product Ωsim ALvf,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 real- located among them utilizing the inverse form of the simulated share of arable land (Ωsim ALvf,nbf,t-1 -1), that is, less profitable albeit viable farms will abandon proportion- ately more of their arable land. As can be easily understood by the reader, the above procedure is also applied to the available irrigated land 361Simulating 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 (ILvf,nbf,t), which is expressed as a share of the total arable land and is assumed to be constant at the base year level and equal to 80%. Based on relevant literature (e.g., Bert et al., 2011; Djanibekov and Finger, 2018; Donati et al., 2024), the farm- land is reallocated only on a rental basis through farmland rental arrangements between tenants and landowners, and the land rental price is exogenously determined 10. (ii) Circulating capital Similarly, we apply the EFM in the case of determin- ing the available circulating capital on an annual basis. The noticeable difference lies in the fact that the circulating capital of non-viable neighboring farms is not reallocated to viable neighboring farms as in the case of arable land. CRCvf,nbf,t = CRCvf,nbf,t-1 + Ωsim CRCvf,nbf,t-1 (TCRCNBF,t – CRCvf,nbf,t-1 sim), for t = 2…T (9) CRCvf,nbf,t is the available circulating capital of via- ble neighboring farm in year t; CRCvf,nbf,t-1 is the avail- able circulating capital of viable neighboring farm at the beginning of year t-1; Ωsim CRCvf,nbf,t-1 is the simulated share of circulating capital allocated to viable neighbor- ing farm at the end of the year t-1, that is, following the annual optimization; CRCvf,nbf,t-1 sim is the simulated total circulating capital of viable neighbor- ing farms at the end of the year t-1, that is, following the annual optimization; TCRCNBF,t is the actual total circu- lating capital of neighboring farms in year t. As before (in the case of available arable land), the product Ωsim CRCvf,nbf,t-1 (TCRCNBF,t – CRCvf,nbf,t-1 sim) ref lects the effect of the external eco- nomic factors that can form the availability of financial resources at farm level, such as the financial system, the tax system, macroeconomic conditions (e.g., level of inflation), etc. These factors may create a healthy finan- cial situation or financial stress. Financial stress could therefore lead to an unfavorable situation, i.e., TCRCNBF,t – CRCvf,nbf,t-1 sim < 0 and consequently to a decrease of the available circulating capital for the viable neighboring farms which will be allocated to them uti- lizing the inverse form of the simulated share of circu- lating capital (Ωsim CRCvf,nbf,t-1 -1), that is, less profitable, albeit viable farms, will lose proportionately more of their cir- culating capital11. 10 Detailed information concerning land rental costs/land rental income estimation is provided in Part C: Land rental costs/land rental income estimation in the supplementary material. 11 Detailed information concerning required borrowing circulating 2.3.5. Capital stock evolution at the farm level (Invest- ment module) The intertemporal evolution of capital stock at the farm level is assessed utilizing the Perpetual Inventory Method (PIM) where the capital stock (machinery and equipment) of the farm f in year t is equal to the non- depreciable capital stock of the year t-1 plus gross invest- ment in fixed assets that will be made through the year t (Weyerstrass, 2016). The mathematical formulation of PIM is as follows: Kf,t = (Kf,t-1 – DEPf,t-1) + If,t (10) where Kf,t is the capital stock of farm f in year t; Kf,t-1 is the capital stock of farm f in year t-1; DEPf,t-1 is the depre- ciation of farm f in year t-1, which is obtained from the equation DEPf,t-1 = δKf,t-1, where δ is the fixed deprecia- tion rate equal to 5% (Weyerstrass, 2016; Femenia et al., 2017), and If,t is the gross investment on fixed asset of farm f in year t. Gross investment in fixed assets includes annual cash expenditures for the maintenance of capital stock due to economic depreciation and the acquisition of required investment capital for farm expansion (net investment on fixed assets) (Smale et al., 1986). Following similar modeling approaches (Kay, 1971; Freeman et al., 2009), we assume a Leontief production relationship between capital stock and land. It is there- fore assumed that the capital stock remains constant per hectare of arable land at the base year level ( , so that the amount charged for depreciation in year t-1 (DEPf,t-1) is constantly reinvested in new capital stock (or gross investment on fixed assets) in year t(If,t) (Freeman et al., 2009). Essentially, the constant intertemporal rela- tionship between capital stock and arable land renders the investment process a continuous process of invest- ment or disinvestment (Britz et al., 2016) determined by the arable land acquired or abandoned12. 2.4. Farm data description and specification For the empirical application of the proposed simula- tion model, a representative sample of arable crop farms capital & short-term finance costs estimations is provided in Part D: Borrowed capital & finance costs estimations /D1. Borrowed circulating capital & short-term finance costs estimations in the supplementary material. 12 Detailed information concerning required borrowing investment capital and long-term finance costs estimations is provided in Part D: Borrowed capital & finance costs estimations/D2. Borrowed investment capital & long-term finance costs estimations in the supplementary material. 362 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. in Karditsa (NUTS-3 level) is chosen. The regional unit of Karditsa is one of the five regional units of the region of Thessaly (NUTS-2 level) located southwest of it. This study utilizes farm-level data provided by a research project that thoroughly investigated the per- spective of a sample of farms of the regional unit of Karditsa that specialized in “Other fieldcrops/General field cropping” (according to the TF14 classification of FADN) to cultivate alternative crops such as energy crops. Initially, 70 farms were selected by stratified ran- dom sampling, and detailed data on production, rev- enues, fixed assets, and subsidies for 2005 and 2006 were collected through personal interviews. Two field surveys followed (after 2006) to update mainly data on produc- tion, revenues, fixed assets, and subsidies through per- sonal interviews. Through these two follow-up surveys, we collected additional socio-economic information such as living expenditures and how agricultural subsi- dies were spent (e.g., living expenses, investments, pro- duction costs, loans). The first follow-up field survey was conducted in 2012, where data from 48 remaining farms were updated (from the initial 70), and the second was in 2019, where data from 31 remaining farms (out of 48 in 2012) were updated. For the empirical application of the simula- tion model, the data of the most recent period (2012-19) are utilized to manage the complexity of the model at a computable level. The sample represents at a satisfactory level the farm structure of 6,272 farms specializing in “Other fieldcrops/ General field cropping” in the regional unit of Karditsa for 2012. Specifically, based on a comparison of our sam- ple with the Farm Accountancy Data Network (FADN) data for the base year (2012), we found a significant degree of similarity in terms of farm size distribution, where the Finger–Kreinin (FK) similarity index (Fin- ger and Kreinin, 1979) stands at 90.2% (see also Table 1). Consequently, although the farm sample size can be considered relatively small compared to the population, it sufficiently reflects the heterogeneity in farm structure13. Cotton and durum wheat are the main activi- ties regarding total farmland area shares. All observed activities (i.e., cotton, processing vegetables, tobacco, maize, alfalfa) except durum wheat and set-aside require irrigation. The production of processing vegetables and tobacco is conducted through annual contracts with the industry, while for the activity of alfalfa (seed produc- tion), the farmers conclude a ten-year contract. 13 Using a relatively small sample of farms is not unusual for relevant in-depth analyses in the context of farm-level mathematical programming models (e.g., Iglesias et al., 2003; Viaggi et al., 2010; Viaggi et al., 2011; Djanibekov and Finger, 2018; Lairez et al., 2023). Since field survey through personal interviews is a very costly and slow process (Khanal and Omobitan, 2020), collecting data on an annual basis during the interim years of the period 2012-19 was not possible. This fact created the need to fill in the gaps in the time series of the model parameters. Model parameters were estimated for the period considered utilizing the avail- able national times series setting 2012 as the base year. In addition, the available national times series provid- ed the necessary input data for the ARIMA and linear trend models. The national time series are provided by various exogenous data sources14. However, it should be noted that for the activities cultivated under contract farming, we assume that prices remain constant at the base year levels for all simulation periods since sample farmers stated that they remained almost invariable for the period 2012-19. 2.5. Policy experiments Simulation experiments for two alternative policy scenarios were performed. Additionally, we ran simula- tions for a combined (policy and geopolitical) scenario. Business as usual (BAU) scenario: We assume that the baseline policy implemented from 2015 to 2022 (2013 CAP reform), will continue to be implemented until 2026. Expressly, we assume that decoupled and coupled pay- ments will remain stable at the levels of 2022, as well as the greening obligations related to crop diversification and the ecological focus area (EFA) to receive decoupled payments (Greek Ministry of Rural Development and Food, 2014). 14 For more details see the Part E: Historical dataset and forecasting method of exogenously determined parameters in the supplementary material. Table 1. Farm size distributions comparison of farms specialized in “Other fieldcrops/General field cropping” (according to the TF14 classification of FADN) in the region of Karditsa, 2012 Farm size class (ha) Characterization Sample farms FADN Farms (%) Farms (%) <10 Very Small 37.46 36.28 10-<30 Small 43.75 53.68 30-<50 Medium 12.5 7.94 50-<100 Large 6.25 2.23 ≥100 Very Large - - Notes: 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 and FADN. 363Simulating 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 CAP Post-2020 scenario: According to the Greek Strategic Plan proposal for the CAP 2023-27 (Greek Ministry of Rural Development and Food, 2022), the provisions of the CAP Post-2020 reform scenario apply from the year 2023. In the period 2023-26, internal full convergence will be implemented, i.e., the convergence of the value of payment entitlements at a single unit val- ue (flat rate) at the agronomic region level15(Greek Min- istry of Rural Development and Food, 2022). The value of the payment entitlements in the agronomic region of interest, i.e., arable land, will equal 231.4 EUR/ha in 2026. Farms with available arable land of more than 10 hectares are obligated to apply ecological focus area to 4% of it to receive decoupled payments. It should be mentioned that is maintained the measure of diversifica- tion of crops for farms with available arable land larger than 10 hectares to receive decoupled payments, valid from 2015 in the context of the 2013 CAP reform. The proposed strategic plan also includes implementing the redistributive payment mechanism during the period 2023-27. Specifically, relatively small farms with available arable land between 2 and 11 hectares, will be consid- ered beneficiaries of the redistributive support, equal to 117 ΕUR/ha. In addition, the proposed national strategic plan aims to improve the environmental performance of arable crop farms by adopting voluntary environmental measures referred to as eco-schemes. One of the main measures is considered to be the extension of the appli- cation of the ecological focus areas, where farms with available arable land less than 10 hectares can apply eco- logical focus area to 5% of it, receiving an average eco- scheme payment equal to 200 EUR/ha. Additionally, farms with available arable land more than 10 hectares can apply ecological focus area to 10% of it receiving an average eco-scheme payment equal to 240 EUR/ha (Greek Ministry of Rural Development and Food, 2022). CAP Post-2020 & Long War of Attrition (LWA) sce- nario: This combined scenario is a variant of the previ- ous one, integrating the serious possibility that Russia’s invasion of Ukraine will become a long war of attrition (Modern War Institute, 2022) with severe and prolonged consequences for the global economy. Given the emerging upward trends in grain prices (maize, wheat) due to Russia’s invasion of Ukraine and uncertainty over the future of the Black Sea Grain Initi- ative (European Council, 2022), we assume a high grain price scenario for the period 2022-26 combined with the provisions of CAP Post-2020 reform scenario described 15 Since the 2013 CAP reform, the process of payments convergence has started in the form of partial convergence. above. In particular, we consider the upper bound of the prediction intervals for durum wheat and maize prices provided by ARIMA model forecasts. 3. RESULTS 3.1. Validation of the simulation model The validation results presented in Table 2 confirm the ability of both models to reproduce the evolution of activities allocation to at least a satisfactory level (Per- centage Absolute Deviation (PAD index): 8.05-29.6%; Finger–Kreinin (FK) similarity index (FK index): 85.2- 96%) according to the relevant literature16 (e.g., Gómez- Limón et al., 2016), providing a good representation of reality. However, the NV&QR model is significantly superior in the base year. Validations of the models on their ability to repro- duce the actual farm size distribution and the actual number of farms are carried out for the year 2019 as it is the only year of observations available after the base year. In this context, both models simulate to at least a satisfactory level the evolution of farm size distributions (PAD index = 17.58%; FK index = 91.2%) and the num- ber of viable farms (Absolute Percentage Error (APE) = 6.4%)17 without revealing any difference in terms of forecasting accuracy (see also Table 3). As can be seen, both models slightly overestimate the rate of structural change, that is, the percentage change in the number of surviving farms, in the reference period (Simulated: 39.6% (from 48 to 29 farms) vs. Actual: 35.42% (from 48 to 31 farms)). Although both models are character- ized by satisfactory forecasting accuracy, we will choose the best fitting model, the NV&QR Model, to assess the impact of policy and combined scenarios on structural change and land use change. 3.2. Forecasting models accuracy After estimating the best-fitting ARIMA models for the exogenously determined parameters of interest (i.e., 16 Although there is no commonly accepted threshold in the international literature for these two indicators, Gómez-Limón et al. (2016) consider the values of PAD index = 33.2% and FK index = 83.4% satisfactory. 17 Although there is no commonly accepted threshold for MAPE (Mean Absolute Percentage Error) in the international literature; however, some authors consider that a model is characterized by good forecasting accuracy (or goodness-of-fit) when MAPE (APE, in our case, due to a single year of observations available after the base year) does not exceed 20%, whereas when it does not exceed 10%, the forecasting accuracy is characterized as high or perfect (e.g., Quartey-Papafio 2021). 364 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. costs, prices, crop yields, total arable land, total circulat- ing capital, and interest rate), we measured their fore- casting accuracy by in-sample forecasts according to the MAPE measure. Most ARIMA models are characterized by high forecasting accuracy; the MAPE does not exceed 10%, while the other models are characterized by good forecasting accuracy18 (e.g., Quartey-Papafio et al., 2021). A high forecasting accuracy also characterizes the uti- 18 For more details, see the Part F: ARIMA and linear trend models estimations in the supplementary material. lized linear trend model for the rural households’ living expenditure index (LEI). 3.3. Simulated structural change Figure 2 depicts the evolution of the number of viable/surviving farms and the average farm size over time19. The simulated number of farms decreases by 19 The initial number of farms is normalized to 100. Table 2. Actual and simulated land allocation. Activity Actual 2012 Area (ha) NV&QR Model 2012 Area (ha) QR Model 2012 Area (ha) Actual 2019 Area (ha) NV&QR Model 2019 Area (ha) QR Model 2019 Area (ha) Cotton 467.9 454.36 365.48 305.1 296.52 266.15 Tobacco (Virginia) 58.6 83.74 94.02 82 109.15 105.56 Maize 27 11.82 11.82 27.15 14.83 48.95 Processing Tomato 31 23.11 23.11 52 55.57 55.53 Processing Pepper 30 25.66 37.06 68.8 70.95 71.33 Alfalfa (hay) 66.5 63.75 68.43 96.6 101.7 10 Alfalfa(seed production) - - - 58.5 45.47 45.47 Durum Wheat 139 163.13 217.85 236.75 236.95 236.88 Set-aside 27.2 21.62 29.41 17.9 13.81 14.89 Total area (ha) 847.2 847.2 847.2 944.8 944.8 944.8 PAD index (%) - 11.6 29.6 - 8.05 11.7 FK index (%) - 94.2 85.2 - 96 94.15 Note: NQR model: Naïve and Quasi-Rational expectations Model; QR model: Quasi-Rational expectations Model Source: Authors, based on sample data. Table 3. Actual and simulated farm size distribution and number of farms. Farm size class (ha) Actual 2019 Farms (%) Actual 2019 Farms (%) NV&QR Model 2019 Farms (%) NV&QR Model 2019 Farms (%) QR Model 2019 Farms (%) QR Model 2019 Farms (%) <10 22.57 7 13.79 4 13.79 4 10-<30 45.15 14 48.27 14 48.27 14 30-<50 12.9 4 13.79 4 13.79 4 50-<100 16.12 5 17.24 5 17.24 5 ≥100 3.22 1 6.89 2 6.89 2 Total number of sample farms (N) - 31 - 29 - 29 APE (%) - - - 6.4 - 6.4 PAD index (%) - - 17.58 - 17.58 - FK index (%) - - 91.2 - 91.2 - Note: NV&QR model: Naïve and Quasi-Rational expectations Model; QR model: Quasi-Rational expectations Model. The determination of farm size classes is based on Happe et al. (2008), and Huettel & Margarian (2009). Source: Authors, based on sample data. 365Simulating 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 39.6% for the reference period 2012-19, while the aver- age farm size increases from 17.65 hectares to 32.58 hec- tares. As we can see, the process of structural change continues after 2019, when the simulation model fore- casts a further reduction in the number of viable farms. According to the BAU scenario, for the period 2019- 2026, a decrease in the number of farms by 41.4% and an increase in the average farm size from 32.58 hec- tares to 62.76 hectares are foreseen. For the CAP Post- 2020 reform and CAP Post-2020 & LWA scenarios, the simulation model forecasts a comparatively higher rate of structural change. Specifically, for 2019-26 the num- ber of farms decreases by 48.3%, and the average farm size increases from 32.58 hectares to 70.35 hectares. This simulation result almost coincides with the estimates of some farmers in the sample, who consider that by 2026 the studied farms will be reduced by 50% compared to 2019 (when the most recent survey was conducted). Therefore, regardless of the scenario, the model predicts an increase in the rate of structural change compared to that simulated in the period 2012-19. Examining the dynamics of structural change from the perspective of farm size distribution, we observe a decrease over time in the percentage of very small (farm size class: <10 hectares) and small farms (farm size class: 10-< 30 ha) (see Figure 3). A decline over time is also foreseen for the share of the farmland area of these farms. On the contrary, for the large (farm size class: 50-<100 ha), and very large farms (farm size class ≥100 ha), an increase in the shares of the farms and farmland area is foreseen. Medium-sized farms (farm size class: 30-<50 ha) show a weak upward trend in the share of farms and a weak downward trend in the share of farm- land area. A very high concentration of farmland in very large farms (farm size class ≥100 ha) is foreseen since, accord- ing to all examined scenarios, almost only 10% of farms will concentrate about 50% of the total farmland area. It is worth noting that the CAP Post-2020 and CAP Post- 2020 & LWA scenarios (although they do not show sub- stantial differences in the rate of structural change), com- pared to the BAU scenario, negatively impact the viability of small and very small farms. The above findings are in line with the estimates of the sample farmers who claim that in the region of Karditsa will gradually prevail, arable crop farms with a size of at least 30 hectares since such a farm size can ensure a decent standard of living for the rural household as well as growth prospects. Regarding the evolution of farm profitability, the simulation results depicted in Figure 4 reveal a gradual increase in the average Farm Net Profit after Tax (FNPAT) for all scenarios. This development can be considered rea- sonable since, through the structural change, the compara- tively less profitable farms exit and release resources such Figure 2. Simulated number of farms and average farm size by scenario. Note: The provisions of the CAP Post-2020 scenario apply from the year 2023. Source: Authors, based on sample data. 366 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. as land, which the comparatively more profitable farms acquire. In this framework, surviving and consequently growing farms tend to make more efficient use of available resources, allocating them to comparatively more profit- able productive activities, as we will see below. Although there are no significant differences between the scenarios, in the last two years of the simu- lation (2025-26), a clear distinction is simulated in favor of the CAP Post-2020 and CAP Post-2020 & LWA sce- narios, which is probably due to the higher rate of struc- tural change. Further analyzing the evolution of average profitability by farm size class, the simulation results provided in Table 4 show an increase in profitability for farms with a size of at least 30 hectares, explaining the claim of the sample farmers that shortly the arable crop farms with a size of at least 30 hectares will be able to remain in the production system. Even more, imple- menting the CAP Post-2020 and CAP Post-2020 & LWA Figure 3. Share of farms and farmland area by farm size classes and scenario. Note: The provisions of the CAP Post-2020 scenario apply from the year 2023. Source: Authors, based on sample data. 367Simulating 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 dynam- ics 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 process- ing 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 farm- ers aspire to a significant expansion of their produc- tive 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 effi- cient 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 fur- 20 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 sce- nario 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 incen- tive 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 devel- opments, 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 simu- lating the impact of policy reform on structural change in the arable production system of the region of Kar- ditsa (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 simul- taneously 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 con- tribute to the debate on dynamic assessments of the multidimensional effects in the context of the CAP Post- 2020 reform while considering recent geopolitical devel- opments in the context of the Ukrainian crisis. Validation results demonstrate satisfactory per- formance of the simulation model in reproducing past changes. Therefore, we can use the model to assess the effects of various scenarios on the agricultural produc- tion system. By carrying out policy experiments for two different policy scenarios and a combined scenar- io (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. 369Simulating 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 simulat- ed 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 simula- tion 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, process- ing vegetables), further enhancing average farm profit- ability (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 vegeta- bles 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 profit- able 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 intensi- fying 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 pro- cessing, 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 opera- tional 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 repli- cating varied farm behavior, it does not explicitly capture the interaction between individual farms in the sense of not incorporating an endogenous price formation mech- anism for the market of locally available resource like land (Berger, 2001; Troost and Berger, 2015; Kremmy- das, 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 mod- el 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 sce- narios/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 consider- able importance (Kremmydas, 2019). Second, although the proposed simulation model con- siders the differences in profits among neighboring farms cultivating different farmland areas in the base year, pro- viding a reasonable representation of the farm growth pro- cess, it does not consider economies of scale in an inter- temporal 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 realis- tic framework. Therefore, future developments of the pro- posed 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 pro- gress (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 param- eters 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 asso- ciated with underestimation of variability (e.g., Debrah and Hall, 1989). In particular, aggregated data tends to underestimate the variability of parameters such as pric- es and yields at the farm level (Debrah and Hall, 1989), which may lead to a less adequate representation of real- ity 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 utiliz- ing mean- and effect-based indicators (Lebacq et al., 2013; Donati et al., 2024) but also to incorporate social indicators, allowing us to assess sustainability perfor- mance 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 socio- economic 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. 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Simulated average gross margin for each cropping activ- ity (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 utiliz- ing almost any set of data (Christodoulos et al., 2010). In this framework, other authors consider that ARIMA mod- els have been remarkably successful with an excellent per- formance 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 avail- able (Gottardi & Scarso, 1994; Christodoulos et al., 2010). An important class of stochastic models for describ- ing time series are called stationary models or Autore- gressive-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) param- eters 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 10 hectares: Xf,j,t hf,t ≤ hf,t 0.75 ALf,t for t = 2015,…,T (B6) 26 A farm’s participation in the nitrate pollution reduction programme (Agri-Environmental measure of the Rural Development Programme) is determined through a priori information provided from sample farms. 27 A farm’s participation in the organic farming programme (Agri- Environmental measure of the Rural Development Programme) is determined through a priori information provided from sample farms. 28 Of course, it may be true that bf,t = ßf,t = 0, which indicates the non- mandatory nature of the specific agri-environmental policy measures. 29 where J= {cotton(ct); tobacco(tb); maize(mz); pr. tomato(pt); pr. pepper(pp); alfalfa(aa); alfalfa-seed(aasd); durum wheat(dw); set- aside(st)}, if bf,t = 0 then st ∉ J 30 where WJ = {cotton(ct); tobacco(tb); maize(mz); pr. tomato(pt); pr. pepper(pp); alfalfa(aa); alfalfa-seed (aasd} https://ead.gr/wp-content/uploads/2022/01/cap_sp_proposal_30_12_2021.pdf https://ead.gr/wp-content/uploads/2022/01/cap_sp_proposal_30_12_2021.pdf 378 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. where hf,t denotes the binary variable that corresponds to the farm f in year t, and is equal to 0 when the available arable land (ALf,t) ≤ 10 hectares, while it gets the value 1 when the available arable land (ALf,t) > 10 hectares. Ecologic focus area obligation for farms f with total available arable land (ALf,t) > 15 hectares: 0.7⟦ Xf,lgj,t⟧ + Xf,st,t ≥ gf,t0.05ALf,t for t = 2015,…,T, lgj ∈ LGJ, LGJ ⊆ J (B7) where Xf,lgj,t is the level of legume crops (lgj) in hectares of the farm f in year t; LGJ = {alfalfa-hay (aa); alfalfa- seed (aasd)}; gf,t denotes the binary variable that corre- sponds to the farm f in year t, and is equal to 0 when the available arable land (ALf,t) ≤ 15 hectares, while it gets the value 1 when the available arable land (ALf,t) > 15 hectares. Crop diversification obligation for farm f with total available arable land (ALf,t) > 30 hectares: [Xf,L1 j,t * + Xf,L2 j,t *]uf,t ≤ uf,t 0.95ALf,t) for t = 2015,…,T, L1 j ∈ J, L2 j ∈ J (B8) where Xf,L1 j,t * the optimal level of cropping activity in hec- tares, to which the largest share (L1 j) of the available ara- ble land (ALf,t) of farm f in year t is allocated; Xf,L2 j,t * the optimal level of cropping activity in hectares, to which the second largest share (L2 j) of the available arable land (ALf,t) of farm f in year t is allocated; uf,t denotes the binary variable that corresponds to the farm f in year t, and is equal to 0 when the available arable land (ALf,t) ≤ 30 hectares, while it gets the value 1 when the available arable land (ALf,t) > 30 hectares. CAP Post-2020 reform scenario constraints Crop diversification obligation for farm f with total available arable land (ALf,t) > 10 hectares: Xf,j,t ≤ hf,t 0.75 ALf,t for t = 2023,…,T, j ∈ J (B9) CAP Post-2020 reform scenario constraints- (adoption of eco-schemes) Eco-schemes adoption: Extension of EFA application by farm f with total available arable land (ALf,t) ≤ 10 hec- tares: Xf,st,t = ef,t 0.05 ALf,t for t = 2023,…,T, st ∈ J (B10) Eco-schemes adoption: Extension of EFA application by farm f with total available arable land (ALf,t) > 10 hectares: Xf,st,t = εf,t 0.1 ALf,t for t = 2023,…,T, st ∈ J (B11) CAP Post-2020 reform scenario constraints- (non-adop- tion of eco-schemes) EFA application by farm f with total available arable land (ALf,t) > 10 hectares: Xf,st,t = εf,t 0.04 ALf,t for t = 2023,…,T, st ∈ J (B12) Nitrate pollution reduction program constraints (Agri-Environmental measure of the Rural Development Programme): Xf,nwj,tbf,t ≥ bf,t 0.75 NLf,t, for t = 1,…,T, nwj ∈ NWJ, NWJ ⊆ J (B13) where Xf,nwj,t is the level of irrigated cropping activ- ity included in the nitrate pollution reduction pro- gram (nwj) in hectares of the farm f in year t; NWJ = {cotton(ct); maize(mz); pr. tomato(pt); pr. pepper(pp) } Xf,ndj,t ≥ bf,t 0.2 NLf,t, for t = 1,…,T, ndj ∈ NDJ, NDJ ⊆ J (B14) where Xf,ndj,t is the level of non-irrigated cropping activ- ity included in the nitrate pollution reduction program (ndj) in hectares of the farm f in year t; NDJ = {durum wheat (dw)} Xf,st,t ≥ bf,t 0.05 NLf,t, for t = 1,…,T, st ∈ I (B15) where Xf,st,t is the level of set-aside (st) included in the nitrate pollution reduction program (hectares) of the farm f in year t. We want to point out that from the year 2018 onwards, the vast majority of sample farms implemented the nitrate pollution reduction program as follows: the share of 0.75 of constraint (B13) was set to 0.7; the share of 0.2 of constraint (B14) was set to 0.3, and the share of 0.05 of constraint (B15) was set to 0. Organic farming program constraint (Agri-Environmen- tal measure of the Rural Development Programme): Xf,orj,t ≥ OLorgf,tβf,t, for t = 1,…,T, orj ∈ ORJ, ORJ ⊆ J (B16) 379Simulating 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 where Xf,orj,t is the level of organic cropping activity included in the organic farming program (orj) in hec- tares of the farm f in year t; ORJ = {alfalfa (aa)}. Flexibility constraint of multiannual contract farm- ing 0.85 CLf,t cf,t ≤ Xf,aasd,t cf,t ≤ 1.15 CLf,t cf,t, for t = 2015,…,T, aasd ∈ Ι (B17) where Xf,aasd,t is the level of alfalfa-seed (aasd) in hec- tares of the farm f in year t; CLf,t is the available land of the farm f in year t included in the multiannual con- tract farming program; cf,t denotes the binary variable that corresponds to the farm f in year t, and is equal to 0 when the farm does not participate in the program of multiannual contract farming , while it gets the value 1 when it participates. Part C: Land rental costs/land rental income estimation As mentioned in the main text, land is reallocated only on a rental basis through farmland rental arrange- ments between tenants and landowners. LaPorte et al. (2020) state that “the most popular and frequently used farmland rental arrangement is a fixed cash rent agree- ment, where the landowner receives a predetermined fee to be paid by the tenant regardless of agricultural commodity price or crop yield” (p. 1). This type of land- owners’ rental agreement is also maintained for the case under consideration, where the farmers pay after harvesting and selling the agricultural commodities in the market. The following is an estimate of land rental costs for each year after the initial one, where LRCvf,nbf,t are the land rental costs of viable neighboring farm in year t; LRCvf,nbf,t-1 is the rented land of viable neighbor- ing farm in year t-1; LRIt is the land rental price index in year t; LRPNBF,t=1 is the average land rental price per land unit (EUR/ha) in base year (t=1) applicable to the region where the neighboring farms operate; LRPNBF,t is the average land rental price per land unit (EUR/ha) in year t applicable to the region where the neighboring farms operate; Ωsim ALvf,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-1 is the simulated aggregate ara- ble 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; ALvf,nbf,t is the available arable land of viable neighboring farm in year t. for t = 2…T, RLvf,nbf,t ⊆ ALvf,nbf,t (C1) The average land rental price (applicable to the region where the neighboring farms operate) (LRPNBF,t) was used as a single land rental price for all farms to simplify the modeling process, considering that the observed differences in payable land rental pric- es between farms are negligible. Since the land rental price is exogenously determined in this model version31, updating its variance for each year after the base year is conducted using the land rental price index (LRIt) (ELSTAT, 2019b). Additionally, we must mention that product RLvf,nbf,t-1 LRPNBF,t indicates that land rental pric- es are renegotiated every cropping cycle. To simplify the presentation of the estimation of land rental costs on an annual basis, we did not sepa- rate the land into irrigated and non-irrigated. It is worth mentioning that the average land rental price of non- irrigated land is about 50% lower. To make post-sample forecasts in the medium term, the exogenously identified average land rental price per land unit (LRPNBF,t) is estimated through ARIMA sto- chastic process. Although rare in our analysis, there is the case of viable farms that rent out part of owned land because the estimated reduction of the land attrib- uted to them due to exogenous reasons32 [Ωsim ALvf,nbf,t-1 -1 (TALNBF,t – TALNBF,t-1)] exceeds (i) the previous year rented land (RLvf,nbf,t-1) and (ii) the land that accumulated endoge- nously, i.e., the released land available for rent, derived from 31 Following similar simulation models (Bert et al., 2011; Djanibekov & Finger, 2018; Donati et al., 2024), the land rental price is exogenous in the suggested model. Unfortunately, this version of the model does not fully consider the interaction between farms and the spatial relationships to include a land rental market with the endogenous formation of the rental price through an auction mechanism (Bert et al., 2011) as it is usually applied in agent-based models. However, land rental price endogeneity could be approximated to some extent through shadow values, for example, using the distribution of shadow value for the land of viable farms based on the exogenously determined land rental price, but this aspect requires further investigation. 32 Competitive pressures from other farm types or non-agricultural sectors 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 (Ωsim ALvf,nbf,t-1 ), that is, less profitable albeit viable farms will abandon/ release proportionately more of their arable land. 380 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. non-viable neighboring farms [Ωsim ALvf,nbf,t-1 ( ALnvf,nbf,t-1 sim)]. In this case, land rental costs are negative (LRCvf,nbf,t < 0), equal to land rental income for the viable neighbor- ing farm (LRINCvf,nbf,t > 0). Consequently, the equation FNPAT*f,t = Π*f,t – (DEPf,t + LRCf,t + SFNCf,t + LFNCf,t + SICf,t + FPTXf,t) (5) (in section 2.3.3.Determining farm viability of the main text) is adapted as follows: FNPAT*f,t = (Π*f,t + LRINCf,t) – (DEPf,t + SFNCf,t + LFNCf,t + SICf,t + FPTXf,t) (C2) 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). Part C: References Bert, F. E., Podestá, G. P., Rovere, S. L., Menéndez, Á. N., North, M., Tatara, E., Laciana, C. E., Weber, E., & Toranzo, F. R. (2011). An agent-based model to sim- ulate structural and land use changes in agricultural systems of the argentine pampas. Ecological Model- ling, 222(19), 3486–3499. https://doi.org/10.1016/j. ecolmodel.2011.08.007 Djanibekov, U., & Finger, R. (2018). Agricultural risks and farm land consolidation process in transition countries: The case of cotton production in Uzbeki- stan. Agricultural Systems, 164, 223–235. https://doi. org/10.1016/j.agsy.2018.03.009 Donati, M., Calzolai, S., Baldi, L., & Arfini, F. (2024). Pre- dicting the effect of the Common Agricultural Poli- cy post-2020 using an agent-based model based on PMP methodology. Bio-Based and Applied Econom- ics. Retrieved from https://oaj.fupress.net/index.php/ bae/article/view/14592 ELSTAT (2019b). Costs for the factors of Agricultural and Livestock Production (Costs indices), 2019. Hellenic Statistical Authority. https://www.statistics.gr/en/sta- tistics/-/publication/DKT33/2019 Happe, K., Balmann, A., Kellermann, K., & Sahrbach- er, C. (2008). Does structure matter? The impact of switching the agricultural policy regime on farm structures. Journal of Economic Behavior and Organi- zation, 67(2), 431–444. https://doi.org/10.1016/j. jebo.2006.10.009 LaPorte, J., MacKellar, B., & Pennington, D. (2020). Farmland Rent Considerations - Part 3: Farmland Rental Agreements and Arrangements. Michigan State University.https://www.canr.msu.edu/news/farm_ land_rental_agreements_and_arrangements Part D: Borrowed capital & finance costs estimations D1. Borrowed circulating capital & short-term finance costs estimations Farm growth in equity is the surplus income avail- able to put back into the business by either purchas- ing assets or debt repayment (Hofstrand, 2009; Bert et al., 2011; GRDC, 2015). Therefore, the current level of short-term borrowing will be determined by the opti- mal farm growth in equity of the year t-1 minus the sum of the existing debt and the required circulating capi- tal of the current year. More specifically, if the optimal farm growth in equity of the previous year is enough to serve: 1) the scheduled principal repayment of exist- ing debt of farm f in year t-1 (DPRPf,t-1) which consists of (i) the borrowed circulating capital of farm f (BCRCf,t) to be repaid within the same year received and (ii) the borrowed investment capital of farm f (BINVCf,t) to be repaid within a predetermined duration of years (TL)33 2) and the required circulating capital of farm f of the current year (CRCf,t), then the farm f will not take out a short-term loan, otherwise the farm will be led to short- term borrowing. The mathematical formulation of the condition is as follows: for t = 2,…,T (D1) where BCRCf,t is the borrowed circulating capital of farm f in year t; DPRPf,t-1 is the principal repayment of exist- ing debt of farm f in year t-1. In the case of a short-term loan, the level of bor- rowed circulating capital will be calculated as follows: BCRCf,t = (CRCf,t + DPRMf,t-1) – FGE*f,t-1 (D2) Respectively the short-term finance costs will be estimated as follows: SFNCf,t = BCRCf,t SIRf,t (D3) where SFNCf,t are the short-term finance costs of farm f in year t and SIRf,t is the short-term interest rate in year t. According to the Greek banking system, the short- term interest rate is based on the BFR (Basic Rate for Farmers). 33 We assume an equal annual repayment which corresponds to the ratio https://doi.org/10.1016/j.ecolmodel.2011.08.007 https://doi.org/10.1016/j.ecolmodel.2011.08.007 https://doi.org/10.1016/j.agsy.2018.03.009 https://doi.org/10.1016/j.agsy.2018.03.009 https://oaj.fupress.net/index.php/bae/article/view/14592 https://oaj.fupress.net/index.php/bae/article/view/14592 https://www.statistics.gr/en/statistics/-/publication/DKT33/2019 https://www.statistics.gr/en/statistics/-/publication/DKT33/2019 https://doi.org/10.1016/j.jebo.2006.10.009 https://doi.org/10.1016/j.jebo.2006.10.009 https://www.canr.msu.edu/people/jonathan_laporte https://www.canr.msu.edu/people/bruce_mackellar https://www.canr.msu.edu/people/dennis_pennington https://www.canr.msu.edu/news/farm_land_rental_agreements_and_arrangements https://www.canr.msu.edu/news/farm_land_rental_agreements_and_arrangements 381Simulating 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 D2. Borrowed investment capital & long-term finance costs estimations Farm growth in equity is the surplus income avail- able to put back into the business by either purchasing assets or debt repayment (Hofstrand, 2009; Bert et al., 2011; GRDC, 2015), and hence the current level of long- term borrowing will be partially determined by the opti- mal farm growth in equity. Therefore, the following con- ditions determine the need or not for borrowed invest- ment capital in year t (BINVCf,t): for t = 2,…,T (D4) In case the sum of optimal farm growth in equity of year t-1 (FGE*f,t-1) and depreciation of year t-1 (DEPf,t-1) exceeds the sum of scheduled principal repayment of existing debt in year t-1 (DPRPf,t-1), the required level of circulating capital of year t CRCf,t and the required gross investment on fixed assets in year t (If,t), then the farm will not take out a long-term loan. Alternatively, the farm will have to take out a long-term loan. In the case of a long-term loan, the level of bor- rowed investment capital (BINVCf,t) will be calculated as follows: BINVCf,t = (CRCf,t + DPRPf,t-1 + If,t) – (FGE*f,t-1 + DEPf,t-1) (D5) Respectively the long-term finance costs will be esti- mated as follows: LFNCf,t + LIRt (D6) where LFNCf,t are the long-term finance costs of farm f in year t and LIRt is the long-term interest rate in year t. Based on literature (DAFWA, 2014), we consider that the repayment duration of borrowed investment capital (TL) should be equal to 15 years. The long-term interest rate is based on the BFR (Basic Rate for Farmers) according to the Greek banking system. Part D: References Bert, F. E., Podestá, G. P., Rovere, S. L., Menéndez, Á. N., North, M., Tatara, E., Laciana, C. E., Weber, E., & Toran- zo, F. R. (2011). An agent-based model to simulate struc- tural 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 DAFWA (2014). Generating more profit from you farm business. Department of Agriculture and Food and the State of Western Australia (DAFWA). https:// www.agric.wa.gov.au/sites/gateway/files/Generat- ing%20more%20profit%20from%20your%20farm%20 business_print%20version%2027Aug14.pdf GRDC (2015). How Do I Measure The Financial Perfor- mance Of My Farm Business? Grains Research and Development Corporation (GRDC). https://grdc. com.au/resources-and-publications/all-publications/ publications/2015/01/farming-the-business-manual/ FB_Manual_Document_3rd-edition_Jul19-WEB- 72dpi070-149.pdf Hofstrand, D. (2009). Building Equity in Your Farm Busi- ness. Ag Decision Maker, File C3-60, Iowa State University. https://www.extension.iastate.edu/agdm/ wholefarm/html/c3-60.html https://doi.org/10.1016/j.ecolmodel.2011.08.007 https://www.agric.wa.gov.au/sites/gateway/files/Generating more profit from your farm business_print version 27Aug14.pdf https://www.agric.wa.gov.au/sites/gateway/files/Generating more profit from your farm business_print version 27Aug14.pdf https://www.agric.wa.gov.au/sites/gateway/files/Generating more profit from your farm business_print version 27Aug14.pdf https://www.agric.wa.gov.au/sites/gateway/files/Generating more profit from your farm business_print version 27Aug14.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://grdc.com.au/resources-and-publications/all-publications/publications/2015/01/farming-the-business-manual/FB_Manual_Document_3rd-edition_Jul19-WEB-72dpi070-149.pdf https://www.extension.iastate.edu/agdm/wholefarm/html/c3-60.html https://www.extension.iastate.edu/agdm/wholefarm/html/c3-60.html 382 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. Part E: Historical dataset and forecasting method of exogenously determined parameters Table E1. Data sources of times series and forecasting method of exogenously determined farm model parameters Farm model parameter of interest Range Data source Forecasting method Hired labor costs (hlcf,j,t) [2001-2018 ] ELSTAT (2019b) ARIMA model Input costs (icf,j,t) [2000-2019 ] ELSTAT (2019c) ARIMA model Machinery rental costs (mrcf,j,t) [2000-2019 ] ELSTAT (2019b) ARIMA model Land rental price (LRPNBF,t) [2000-2018 ] ELSTAT (2019b) ARIMA model Interest rate (SIRt; LIRt) [2000-2020 ] ELSTAT (2019b) ARIMA model Cotton yield (yf,ct,t) [1961-2017 ] Greek Ministry of Rural Development and Food; ARIMA model D. wheat yield (yf,dw,t) [1961-2017 ] Greek Ministry of Rural Development and Food; Greek Ministry of Rural Development and Food (2019) ARIMA model Tobacco yield (yf,tb,t) [1979-2017 ] Greek Ministry of Rural Development and Food; Greek Ministry of Rural Development and Food (2019) ARIMA model Pepper yield (yf,pp,t) [1961-2007 ] Greek Ministry of Rural Development and Food ARIMA model Tomato yield (yf,ptm,t) [1961-2007 ] Greek Ministry of Rural Development and Food ARIMA model Legumes crops yield (yf,aasd,t; yf,aa,t) [2000-2017 ] Greek Ministry of Rural Development and Food (2019) ARIMA model Maize yield (yf,mz,t) [1981-2017 ] Greek Ministry of Rural Development and Food; Greek Ministry of Rural Development and Food (2019) ARIMA model Cotton price (pf,ct,t) [2000-2019 ] ELSTAT (2019c) ARIMA model D. wheat price (pf,dw,t) [2000-2019 ] ELSTAT (2019c) ARIMA model Legume crops price (pf,aasd,t; pf,aa,t) [2000-2019 ] ELSTAT (2019c) ARIMA model Maize price (pf,mz,t) [2000-2019 ] ELSTAT (2019c) ARIMA model Total arable land (TALNBF,t) [2004-2019 ] FADN Public Database* ARIMA model Total circulating capital (TCRCNBF,t) [2004-2019 ] FADN Public Database* ARIMA model Living expenditures (LEf,t) [2008-2020 ] ELSTAT (2021) Linear trend model Notes: * The available Farm Accountancy Data Network (FADN) time series were filtered to include Greek farms specialized in “Other fieldcrops” (according to the TF14 classification of FADN), utilizing the parameters of Arable land (SE026) and Other circulating capital (SE480), which were multiplied by the parameter Farms represented (SYS02) to obtain values at an aggregate level. Source: ELSTAT (2019b), ELSTAT (2019c), ELSTAT (2021), FADN Public Database, Greek Ministry of Rural Development and Food, Greek Ministry of Rural Devel- opment and Food (2019). Part E: References ELSTAT (2019b). Costs for the factors of Agricultural and Livestock Production (Costs indices), 2019. Hellenic Statistical Authority. https://www.statistics.gr/en/statis- tics/-/publication/DKT33/2019 ELSTAT (2019c). Input and Output Price Indices in Agri- cultural and Livestock Production, 2019. Hellenic Sta- tistical Authority. https://www.statistics.gr/en/statis- tics/-/publication/DKT30/2019-M12 ELSTAT (2021). Household Budget Survey (after 2008), 2020. Hellenic Statistical Authority. https://www.statis- tics.gr/en/statistics/-/publication/SFA05/2020 FADN Public Database. Farm Accountancy Data Network Public Database. Directorate-General for Agriculture and Rural Development. https://agridata.ec.europa.eu/ extensions/FADNPublicDatabase/FADNPublicData- base.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 prod- ucts (in Greek). http://www.minagric.gr/index.php/el/ the-ministry-2/statistikes-tekmhrioshs/8510-statistika- ekt-parag-fytikonproionton https://www.statistics.gr/en/statistics/-/publication/DKT33/2019 https://www.statistics.gr/en/statistics/-/publication/DKT33/2019 https://www.statistics.gr:443/en/statistics?p_p_id=documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN&p_p_lifecycle=2&p_p_state=normal&p_p_mode=view&p_p_cacheability=cacheLevelPage&p_p_col_id=column-2&p_p_col_count=4&p_p_col_pos=1&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_javax.faces.resource=document&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_ln=downloadResources&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_documentID=405241&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_locale=en https://www.statistics.gr:443/en/statistics?p_p_id=documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN&p_p_lifecycle=2&p_p_state=normal&p_p_mode=view&p_p_cacheability=cacheLevelPage&p_p_col_id=column-2&p_p_col_count=4&p_p_col_pos=1&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_javax.faces.resource=document&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_ln=downloadResources&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_documentID=405241&_documents_WAR_publicationsportlet_INSTANCE_qDQ8fBKKo4lN_locale=en https://www.statistics.gr/en/statistics/-/publication/DKT30/2019-M12 https://www.statistics.gr/en/statistics/-/publication/DKT30/2019-M12 https://www.statistics.gr/en/statistics/-/publication/SFA05/2020 https://www.statistics.gr/en/statistics/-/publication/SFA05/2020 https://agridata.ec.europa.eu/extensions/FADNPublicDatabase/FADNPublicDatabase.html https://agridata.ec.europa.eu/extensions/FADNPublicDatabase/FADNPublicDatabase.html https://agridata.ec.europa.eu/extensions/FADNPublicDatabase/FADNPublicDatabase.html http://wwww.minagric.gr/greek/agro_pol/3.htm http://wwww.minagric.gr/greek/agro_pol/3.htm http://www.minagric.gr/index.php/el/the-ministry-2/statistikes-tekmhrioshs/8510-statistika-ekt-parag-fytikonproionton http://www.minagric.gr/index.php/el/the-ministry-2/statistikes-tekmhrioshs/8510-statistika-ekt-parag-fytikonproionton http://www.minagric.gr/index.php/el/the-ministry-2/statistikes-tekmhrioshs/8510-statistika-ekt-parag-fytikonproionton 383Simulating 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 Pa rt F : A RI M A a nd li ne ar tr en d m od els e sti m at io ns Ta bl e F1 . A RI M A m od el s o f e xo ge no us ly d et er m in ed p ar am et er s o f i nt er es t Εx og en ou sly d et er m in ed pa ra m et er o f f ar m m od el (Y t) Ti m e se rie s d at a po in ts [p er io d] A RI M A M od el (p ,d ,q ) Φ 1 Φ 2 Φ 3 Θ 1 Θ 2 Θ 3 μ M A PE (% ) A IC Au gm en te d D ic ke y- Fu lle r t- St at ist ic Br eu sc h- G od fr ey S er ia l C or re la tio n LM T es t [P ro b. X 2 (p )] H ire d la bo r p ric e in de x 19 [2 00 1- 20 18 ] (2 ,0 ,1 ) 1. 64 ** * (0 .0 5) -0 .8 2** * (0 .0 4) - -0 .9 9** * (0 .0 9) - - 92 .7 9** * (0 .5 9) 0. 95 3. 84 -3 .5 5* Pr ob . X 2 (2 )= 0. 05 9 In pu t p ric e in de x 20 [2 00 0- 20 19 ] (1 ,1 ,1 ) 0. 87 ** * (0 .0 6) - - -0 .9 9** * (0 .1 2) - - - 3. 78 6. 19 -4 .2 9** Pr ob . X 2 (2 )= 0. 44 M ac hi ne ry re nt al p ric e in de x 20 [2 00 0- 20 19 ] (0 ,2 ,1 ) - - - -0 .5 0** (0 .2 1) - - - 1. 29 4. 09 -7 .0 0** * Pr ob . X 2 (2 )= 0. 92 La nd re nt al p ric e in de x 19 [2 00 0- 20 18 ] (1 ,0 ,1 ) 0. 53 ** (0 .2 0) - - 0. 99 ** * (0 .0 6) - - 99 .0 5** * (1 .5 7) 1. 05 3. 76 -4 .0 1** Pr ob . X 2 (2 )= 0. 40 In te re st ra te in de x 21 [2 00 0- 20 20 ] (0 ,2 ,1 ) - - - -0 .9 1** * (0 .0 7) - - - 5. 51 6. 49 -6 .9 2* ** Pr ob . X 2 ( 2) =0 .9 9 C ot to n yi el d (K g/ H a) 57 [1 96 1- 20 17 ] (1 ,0 ,1 ) 0. 92 ** * (0 .0 1) - - -0 .9 7** * (0 .0 3) - - 29 9. 23 ** * (5 .3 6) 7. 55 9. 21 -4 .2 1** * Pr ob .X 2 (2 )= 0. 54 D . w he at y ie ld (K g/ 0 .1 H a) 57 [1 96 1- 20 17 ] (2 ,0 ,1 ) 0. 50 ** * (0 .1 5) 0. 43 ** * (0 .1 4) - -0 .6 2** * (0 .1 4) - - 27 8. 04 ** * (5 1. 51 ) 11 .3 0 9. 83 -3 .4 7** Pr ob .X 2 (2 )= 0. 98 To ba cc o yi el d (V irg in ia ) (K g/ 0. 1 H a) 39 [1 97 9- 20 17 ] (1 ,0 ,3 ) 0. 87 ** * (0 .0 2) - - -1 .0 0** * (0 .1 5) 0. 48 ** (0 .2 1) -0 .4 6** * (0 .1 5) 33 6. 52 ** * (8 .1 7) 6. 73 9. 40 -4 .2 1** * Pr ob .X 2 (2 )= 0. 35 Pe pp er y ie ld (K g/ 0. 1 H a) 47 [1 96 1- 20 07 ] (1 ,0 ,2 ) 0. 98 ** * (0 .0 9) - - -0 .6 6** * (0 .1 4) -0 .2 9** (0 .1 4) - 43 96 .7 2** * (1 07 9. 63 ) 6. 28 13 .2 1 -4 .1 0** * Pr ob .X 2 (2 )= 0. 81 To m at o yi el d (K g/ 0. 1 H a) 47 [1 96 1- 20 07 ] (1 ,1 ,0 ) -0 .4 4** * (0 .1 4) - - - - - 81 .2 7** (3 1. 97 ) 5. 5 14 .3 4 -7 .2 1** * Pr ob .X 2 (2 )= 0. 36 Le gu m es c ro ps y ie ld [A lfa lfa (h ay & se ed )] (K g/ 0. 1 H a) 18 [2 00 0- 20 17 ] (0 ,0 ,2 ) - - - 0. 31 ** * (0 .0 8) 0. 93 ** * (0 .0 2) - 74 0. 24 ** * (2 6. 53 ) 4. 69 10 .8 3 -4 .8 2** * Pr ob .X 2 (2 )= 0. 10 M ai ze y ie ld (K g/ 0. 1 H a) 37 [1 98 1- 20 17 ] (2 ,0 ,0 ) 0. 54 ** * (0 .1 6) 0. 33 ** * (0 .1 6) - - - - 10 86 .8 5** * (1 22 .1 9) 3. 77 10 .6 7 -4 .1 8** Pr ob .X 2 (2 )= 0. 36 C ot to n pr ic e (E U R/ kg ) 20 [2 00 0- 20 19 ] (1 ,0 ,1 ) 0. 85 ** * (0 .0 6) - - -0 .9 6** * (0 .0 4) - - 0. 48 ** * (0 .0 48 ) 15 .1 7 -2 .1 9 -3 .3 9* Pr ob .X 2 (2 )= 0. 16 D . w he at p ric e (E U R/ kg ) 20 [2 00 0- 20 19 ] (3 ,0 ,0 ) 0. 84 ** * (0 .2 3) -0 .6 2** (0 .2 9) 0. 44 * (0 .2 2) - - - 0. 19 ** * (0 .0 2) 10 .8 1 -4 .0 8 -3 .1 9* Pr ob .X 2 (2 )= 0. 32 Le gu m e cr op s p ric e (A lfa lfa -h ay ) (E U R/ kg ) 20 [2 00 0- 20 19 ] (1 ,1 ,0 ) -0 .4 3* (0 .2 2) - - - - - - 6. 00 -6 .3 6 -4 .3 6** Pr ob .X 2 (2 )= 0. 80 M ai ze p ric e (E U R/ kg ) 20 [2 00 0- 20 19 ] (1 ,0 ,1 ) 0. 83 ** * (0 .0 6) - - -0 .9 9** * (0 .1 0) - - 0. 18 ** * (0 .0 0) 8. 48 -4 .7 0 -3 .4 0* Pr ob .X 2 (2 )= 0. 08 (C on tin ue d) 384 Bio-based and Applied Economics 13(4): 353-386, 2024 | e-ISSN 2280-6172 | DOI: 10.36253/bae-14790 Stamatis Mantziaris et al. Εx og en ou sly d et er m in ed pa ra m et er o f f ar m m od el (Y t) Ti m e se rie s d at a po in ts [p er io d] A RI M A M od el (p ,d ,q ) Φ 1 Φ 2 Φ 3 Θ 1 Θ 2 Θ 3 μ M A PE (% ) A IC Au gm en te d D ic ke y- Fu lle r t- St at ist ic Br eu sc h- G od fr ey S er ia l C or re la tio n LM T es t [P ro b. X 2 (p )] To ta l a ra bl e la nd in de x 16 [2 00 4- 20 19 ] (0 ,1 ,3 ) - - - -1 .2 6** * (0 .2 8) 1. 17 ** * (0 .2 2) -0 .8 2** * (0 .1 4) 3. 19 ** * (0 .8 9) 3. 67 6. 98 -7 .7 5** * Pr ob .X 2 (2 )= 0. 64 To ta l c irc ul at in g ca pi ta l i nd ex 16 [2 00 4- 20 19 ] (0 ,1 ,1 ) - - - -0 .9 3** * (0 .0 6) - - 29 . 7 ** * (2 .3 1) 10 .9 1 10 .2 4 -3 .7 5** Pr ob .X 2 (2 )= 0. 19 N ot es : ∇ d Y t = μ + ϕ 1∇ d Y t- 1 + ⋯ ϕ p∇ d Y t-p + ε t − θ 1ε t- 1 − ⋯ − θ qε t- q; Φ 1, . . . , Φ p: au to re gr es siv e (A R) m od el p ar am et er s of o rd er p ; Θ 1, … , Θ q: m ov in g av er ag e (M A ) m od el p ar am et er s of o rd er q (M ar tín ez -A co st a et a l., 2 02 0) ; ε t is w hi te n oi se ; μ= a co ns ta nt e qu al to th e m ea n of th e se rie s if d = 0 (N ar ay an a & P ar ik h, 1 98 1) ; * in di ca te s sig ni fic an ce a t 0 .1 le ve l, ** in di ca te s sig ni fic an ce a t 0 .0 5 le ve l, ** * in di ca te s sig ni fic an ce a t 0 .0 1 le ve l; Th e nu ll hy po th es is H 0 of th e B re us ch -G od fr ey S er ia l C or re la tio n LM T es t i s th at th er e is no a ut oc or re la tio n in th e re sid ua ls se rie s up to p re -d et er m in ed la g or de r (p =2 in o ur an al ys is) a t t he 0 .0 5 le ve l o f s ig ni fic an ce (W ey er st ra ss , 2 01 6) . So ur ce : A ut ho rs , b as ed o n EL ST AT ( 20 19 b) , E LS TA T (2 01 9c ), FA D N P ub lic D at ab as e, G re ek M in ist ry o f R ur al D ev el op m en t a nd F oo d, G re ek M in ist ry o f R ur al D ev el op m en t a nd Fo od (2 01 9) . Ta bl e F2 . L in ea r t re nd m od el re gr es sio n st at ist ic s o f r ur al h ou se ho ld s’ liv in g ex pe nd itu re in de x (L EI ) Va ria bl e C oe ffi ci en t St d. E rr or t- St at ist ic Pr ob .   C 0. 95 47 77 0. 01 96 44 48 .6 03 63 0. 00 00 @ TR EN D -0 .0 23 92 5 0. 00 27 78 -8 .6 12 05 7 0. 00 00 R- sq ua re d 0. 87 08 43 M ea n de pe nd en t v ar 0. 81 12 26 A dj us te d R- sq ua re d 0. 85 91 01 S. D . d ep en de nt v ar 0. 09 98 46 S. E. o f r eg re ss io n 0. 03 74 79 A ka ik e in fo c rit er io n -3 .5 89 45 3 Su m sq ua re d re sid 0. 01 54 51 Sc hw ar z cr ite rio n -3 .5 02 53 8 Lo g lik el ih oo d 25 .3 31 45 H an na n- Q ui nn c rit er . -3 .6 07 31 8 F- st at ist ic 74 .1 67 53 D ur bi n- W at so n st at 0. 64 28 14 Pr ob (F -s ta tis tic ) 0. 00 00 03 So ur ce : A ut ho rs , b as ed o n EL ST AT (2 02 1) d at a. Ta bl e F1 . ( C on tin ue d) . 385Predicting 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) Tobac- co 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). 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Wien: LIT-Verlag. 224 p. _Ref114578152 _Ref114489287 _Ref114578337 _Ref115429676 _Hlk124753738 _Hlk124753769 _Ref114578159 _Hlk125619779 _Hlk125620100 _Hlk125620116 _Hlk168057609 _Hlk125617961 _Hlk125617978 _heading=h.1fob9te _heading=h.1y810tw _heading=h.3whwml4 _Hlk105387355 _Hlk162970176 _Hlk120503612 _Hlk94825625 _Hlk101307043 _Hlk112165281 _Hlk110795819 _Hlk163789378 _Hlk101572865 _Hlk101574469 _Hlk162424605 _Hlk163657897 _Hlk163658986 _Hlk163657719 _Hlk163657691 _Hlk163658456 _Hlk163658513 _Hlk163658646 _Hlk162446713 _Hlk125919866 _Hlk107164817 _Hlk162973538 _Hlk162447045 _Hlk107174352 _Hlk162447083 _Hlk124882770 _Hlk142394334 _Hlk142395728 _Hlk142430461 _Hlk142337917 _Hlk142342729 _Hlk142337969 _Hlk142337867 _Hlk142342461 _Hlk142342928 _Hlk142338077 _Hlk142348528 _Hlk164779807 _Hlk125467744 _Hlk141790649 Assessing the bioeconomy’s contribution to evidence-based policy: A comparative analysis of value added measurements Tévécia Ronzon1,2,*, Patricia Gurria2, Michael Carus3, Kutay Cingiz2, Andrea El-Meligi1, Nicolas Hark3, Susanne Iost4, Robert M’Barek1, George Philippidis5, Myrna van Leeuwen6, Justus Wesseler2 Predicting the effect of the Common Agricultural Policy post-2020 using an agent-based model based on PMP methodology Lisa Baldi1, Sara Calzolai2, Filippo Arfini2,*, Michele Donati1 Simulating farm structural change dynamics in Thessaly (Greece) using a recursive programming model Stamatis Mantziaris1,*, Stelios Rozakis2, Pavlos Karanikolas1, Athanasios Petsakos3, Konstantinos Tsiboukas1 Analyzing the impact of government subsidies on household welfare during economic shocks: A case study of Iran Mohammad Dehghan1,*, Seyyed Nematollah Moosavi2*, Ebrahim Zare3 Crop production, the pollinator deficit and land use management: UK farm level survey results Iain Fraser1,*, Michelle T. 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