Estimation of cost allocation coefficients at the farm level using an entropy approach

Abstract

This paper aims to estimate the farm cost allocation coefficients from whole farm input costs. An entropy approach was developed under a Tobit formulation and was applied to a sample of farms from the 2004 FADN data base for Alentejo region, Southern Portugal. A Generalized Maximum Entropy model and Cross Generalized Entropy model were developed to the sample conditions and were tested. Model results were assessed in terms of their precision and estimation power and were compared with observed data. The entropy approach showed to be a flexible and valid tool to estimate incomplete information, namely regarding farm costs. The costs per output activity can be obtained either from collecting data directly in farms, or through estimated coefficients of input costs from samples of FADN data base. The second approach seems to be the best solution, since the first approach is expensive and too demanding in resources.There are several works that estimate crop-specific inputs (Just et al., 1983;Shumway et al., 1984; and Miller, 1998a e 1998b). Most of them are based on the relationship between input allocations and production coefficients under the assumption of profit maximization. Traditionally the tools used in these approaches are linear regression techniques (LRT), Bayesian estimation techniques (BES) and linear programming (LP), but their use raises some practical concerns.In the problem of farm cost allocation, it is necessary to ensure the accounting balance between total revenue and total costs. In this situation the disturbance terms of the various input-demand equations are not independent from each other and the system 3 of input-demand equations is singular, which invalidates the use of LRT techniques (Bewley, 1986). Another well known result of the LRT technique is the negative inputdemand coefficients that could be estimated. This can be avoided by using BES techniques or inequality least squares methods (Moxey and Tiffin, 1994). However, the application of these alternative methods is heavy and does not allow incorporating the accounting constraints which need to be treated separately in the system. A flexible alternative that has been widely applied to estimate farm input and output coefficients is the entropy approach. This methodology does not require behavioural assumptions and allows the use of non sample information through the introduction of information priors.This paper aims to apply a flexible methodology that allows estimating the coefficients of farm cost allocation per output activity from the whole farm input costs, taking into account general conditions of Mediterranean areas. An entropy approach is used to make the estimation of coefficients at the farm level based on a farms sample of the FADN data base in the Alentejo region, South of Portugal. A Generalized MaximumEntropy (GME) model and a Cross Generalized Entropy (CGE) model are applied and assessed by looking at the precision of the coefficients extracted from the whole farm data and comparing them with the observed input-o...

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