Using Non-parametric Methods in Econometric Production Analysis: An Application to Polish Family Farms

Econometric estimation of production functions is one of the most common methods in appliedeconomic production analysis. These studies usually apply parametric estimation techniques,which obligate the researcher to specify the functional form of the production function. Mostoften, the Cobb-Douglas or the Translog production function is used.However, the specification of a functional form for the production function involves the risk ofspecifying a functional form that is not similar to the “true” relationship between the inputs andthe output. This misspecification might result in biased estimation results—including measuresthat are of interest of applied economists, such as elasticities. Therefore, we propose to use nonparametriceconometric methods. First, they can be applied to verify the functional form used inparametric estimations of production functions. Second, they can be directly used for estimatingproduction functions without specifying a functional form and thus, avoiding possible misspecificationerrors.We use a balanced panel data set of farms specialized in crop production that is constructed fromPolish FADN data for the years 2004-2007. Our analysis shows that neither the Cobb-Douglasfunction nor the Translog function are consistent with the “true” relationship between the inputsand the output in our data set. We solve this problem by using non-parametric regression. Thisapproach delivers reasonable results, which are on average not too different from the results of theparametric estimations but many individual results are rather different.