Technological differences, theoretically consistent frontiers and technical efficiency : a random parameter application in the Hungarian crop producing farms

Existing studies of agricultural production largely neglect technology heterogeneity. However, the assumption of homogeneous production may result in inadequate policy implications. There is a growing literature on this issue. In this paper we contribute to this literature by modelling the effect of heterogeneous technologies and its impact on technological parameters and technical efficiency using a reformulated Random parameter Model. Our approach is based on the model developed by Alvarez et al. (2004). However, the original version of this model faces one crucial econometric problem: the assumption of independence of technical inefficiency and input variables does not, hence the estimated results are not necessarily consistent. Therefore we reformulate the model to allow for a more consistent estimation. Additionally, we examine the importance of the fulfilment of theoretical consistency: monotonicity and quasi-concavity. In order to fulfil these criteria we apply constrained maximum likelihood estimation, more specifically we build linear and non-linear constraints into the model and force it to yield theoretically consistent results, not only in the mean but also in different approximation points. For the empirical analysis we use farm level data from the Hungarian FADN Database. The results showed that considering technological differences is important. According to model selection criteria the modified Alvarez model with constraints was the preferred specification. Additionally, the results imply that the consideration of the effect of heterogeneous technologies on production potential and efficiency crucial in order to get adequate policy implication.