Academic journal article Journal of Agricultural and Resource Economics

Estimating a Profit Function in the Presence of Inefficiency: An Application to Russian Agriculture

Academic journal article Journal of Agricultural and Resource Economics

Estimating a Profit Function in the Presence of Inefficiency: An Application to Russian Agriculture

Article excerpt

The relationships among cost functions, distance functions, and technical inefficiency are utilized to show how technical inefficiency scores can be incorporated into the specification of a profit function and a related system of output supply and input demands. A method also is introduced for incorporating allocative efficiency scores into the same system. The theoretical and empirical approach requires fewer assumptions than those made in many studies. An illustrative example is provided for Russian agriculture for 1994-95, a period when significant technical and allocative inefficiency was known to exist. The results demonstrate inefficiency limits the supply response to prices, thus leading to lower estimates of output response compared to a traditional supply model in which efficiency is assumed.

Key words: distance function, profit function, Russia, supply response, technical efficiency

Introduction

In the past two decades, much of the empirical literature concerning agricultural production has fallen into two major categories. One strand of the literature estimates the price response of agricultural supply and input demands assuming efficiency (e.g., Ball; Shumway, Saez, and Gottret). Another strand calculates various producer inefficiencies, particularly technical inefficiency (e.g., Battese; Seiford), and ignores price responses. However, few studies in the literature have combined these two issues. The objective of this study is to introduce a method for modeling and testing the impact of efficiency measures on output supply and input demand.

One method for dealing with both production inefficiencies and the supply response to prices requires joint estimation of profit function parameters and efficiency scores in a single step (Kumbhakar 1996, 2001). Specific estimates of inefficiency scores for each observation are derived from an estimated parameter in the profit function and a distribution function of model errors. While this technique has many advantages, such as being able to apply statistical testing procedures to estimates of inefficiency, it relies on assumptions about model error structure and can be computationally intensive. Using this technique, it is not always possible to overcome the difficult task of sorting out allocative inefficiency from technical inefficiency.

In this article, a method is developed for representing inefficiency scores as variables when estimating a system of output supply and input demand equations.' Using a novel approach, this study demonstrates theoretically one way technical and allocative inefficiency can be incorporated into a system of output supply and input demand equations. Our theoretical and empirical approach requires fewer assumptions than those made in many studies, but must be implemented in two steps.

In the first step, inefficiency scores are obtained using programming techniques. The second step employs econometric methods to model the impact these scores have on output supply and input demand. To demonstrate the method, technical and allocative inefficiency scores for 73 Russian oblasts (equivalent to states or provinces) are calculated using standard nonparametric methods. Then, the inefficiency scores are specified as an explanatory variable in a profit function for Russian agriculture. A system of output supply and input demand equations is derived from this profit function. Using two years (1994 and 1995) of cross-sectional data, the parameters of the system of output supply and input demands are estimated econometrically, taking into account the effect inefficiency scores may have on parameter estimates.

To test the alternative model specifications in the Russian example, standard econometric tests are used to determine the contribution of inefficiency scores to the performance of the estimated model. Statistical tests of the contribution of technical and allocative inefficiency measures to model performance are mixed. …

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