Abstract
This paper aims to understand the state of adjustment processes and dynamic structure in Polish agriculture. A dynamic cost frontier model using the shadow cost approach is formulated to decompose cost efficiency into allocative and technical efficiencies. The dynamic cost efficiency model is developed into a more general context with a multiple quasi-fixed factor case. The model is empirically implemented using a panel data set of 1,380 Polish farms over the period 2004–2007. Due to regional differences and a wide variety of farm specializations, farms are categorized into two regions and five types of farm production specializations. The estimation results confirm our observation that adjustment was rather sluggish, implying that adjustment costs were considerably high. According to this study, it will take up to 30 years for Polish farmers to reach their optimal level of capital and land input. Allocative and technical efficiency widely differ across regions. Moreover, efficiencies prove rather stable over time and among farm specializations, although the results indicate that the regions with larger farms performed slightly better.
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Notes
Totally differentiating \( y = F({\mathbf{x}},{\mathbf{q}},{\dot{\mathbf{q}}},t) \) leads to \( \nabla_{{\mathbf{x}}} Fd{\mathbf{x}} + \nabla_{{\mathbf{q}}} Fd{\mathbf{q}} + \nabla_{{{\dot{\mathbf{q}}}}} Fd{\dot{\mathbf{q}}} + \nabla_{t} Fdt = 0 \). Given \( d{\mathbf{q}} = 0 \) and \( dt = 0 \), the slope of the isoquant yields \( - \nabla_{x} F/\nabla_{{{\dot{\mathbf{q}}}}} F = \nabla_{{\mathbf{x}}} {\dot{\mathbf{q}}} \). Differentiating the slope of the isoquant with respect to \( {\mathbf{x}} \) provides \( \nabla_{{{\mathbf{xx}}}} {\dot{\mathbf{q}}} = - \left[ {{{\left( {\nabla_{{{\dot{\mathbf{q}}}}} F\nabla_{{{\mathbf{xx}}}} F - \nabla_{{\mathbf{x}}} F\nabla_{{{\mathbf{\dot{q}\dot{q}}}}} F} \right)} \mathord{\left/ {\vphantom {{\left( {\nabla_{{{\dot{\mathbf{q}}}}} F\nabla_{{{\mathbf{xx}}}} F - \nabla_{{\mathbf{x}}} F\nabla_{{{\mathbf{\dot{q}\dot{q}}}}} F} \right)} {\left( {\nabla_{{{\dot{\mathbf{q}}}}} F} \right)^{2} }}} \right. \kern-0pt} {\left( {\nabla_{{{\dot{\mathbf{q}}}}} F} \right)^{2} }}} \right] < 0 \).
This model assumes that economic agents are risk neutral and that their price expectations are static. However, if these restrictive assumptions are relaxed investments under uncertainty can be derived within the dynamic duality model of intertemporal decision making. In the intertemporal model setting, risks and uncertainties can be defined as stochastic variables about which firms are assumed to have rational expectations regarding the future evolution of these variables. For more details about non-static price expectations and risk in the dynamic dual model of investment, see Luh and Stefanou (1996) and Pietola and Myers (2000).
The Farm Accountancy Data Network (FADN), Source: http://ec.europa.eu/agriculture/rica/.
We follow the conventional dynamic analysis of production structures and consider capital as one of the quasi-fixed factors to capture possibly resulting adjustment costs to which the producer can appropriately respond and minimize entailed losses by dividing their investment requirement into several steps. Land was also considered as a quasi-fixed factor, given that farm structures are rather stable, which implies that changing the amount of cultivated acreage will entail considerable costs so that the adjustment of farm structures is only of minor importance/relevance. It is often argued that labor also belongs to the group of quasi-fixed inputs. In Poland, however, labor input reacts rather flexible and thus might considerably change following the overall economic situation. Correspondingly, part-time farming is a widespread phenomenon in Poland, thus implying that labor is more a flexible than a quasi-fixed input (Csaki and Lerman 2001).
The depreciation rate was obtained by relating depreciation to fixed assets. The interest rate was obtained by the relation between interest paid and the amount of proportion of interest paid on long and medium-term loans.
All price indices were taken from national statistics and the EUROSTAT website.
These include dummy variables on specialization, farm size in European Size Units, location by Wojwodship (e.g. region), altitude of the farm, the existence of environmental limitations, the availability of structural funds and the education level of the farmer.
Partial productivity and value shares were computed using the information given in Table 1.
In the context of this study, when firms decide to increase farm land, net investment will not be simultaneously affected; rather, it might take several periods for net investment to adjust. Therefore, the decision to increase farm land is not fully dependent on the decision to increase a firm’s net investment. Over the study period, average land input increased by 4.5 % per year, while farm capital input increased by more than 7.5 %. These differences in the growth rates provide some support for our conjecture.
The behavioral value function in Eq. (25) must satisfy the following regularity conditions: J b(∙) is non-increasing in (k, l); non-decreasing in (w b, p k , p l , y); convex in (k, l); concave in (w b, p k , p l ); and linearly homogenous in (w b, p k , p l ).
In the estimation, dummy variables are incorporated to account for firm’s allocative and technical inefficiency parameters dynamic and variable factors demands. The inclusion of these dummy variables requires the implementation of a restricted version of the fixed effects panel data technique. The full sets of estimated coefficients including these dummy variables are not reported.
As explained in Sect. 2 (Fig. 1), this dissimilarity mainly results from both the different conceptual approaches in the conventional and shadow cost approach as well as the different assumption made in SFA and DEA analysis. Usually DEA efficiency scores are much lower than SFA scores since in DEA there is no two-sided error term to buffer some of the structural differences among farms.
The letter p is used to denote the shadow cost of the quasi-fixed factors \( \left( {\nabla_{{\mathbf{q}}} J} \right) \).
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Acknowledgments
The authors gratefully acknowledge financial support from the Thailand Research Fund (TRF), the Commission on Higher Education (CHE), Ministry of Education (Thailand) [TRF-CHE Research Grant for Mid-Career University Faculty], the German Academic Exchange Service (DAAD) and the Leibniz Institute of Agricultural Development in Central and Eastern Europe (IAMO). Usual disclaimer applies.
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Rungsuriyawiboon, S., Hockmann, H. Adjustment costs and efficiency in Polish agriculture: a dynamic efficiency approach. J Prod Anal 44, 51–68 (2015). https://doi.org/10.1007/s11123-015-0430-6
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DOI: https://doi.org/10.1007/s11123-015-0430-6