Econometric estimation of production functions is one of the most common methods in applied economic production analysis. These studies usually apply parametric estimation techniques, which obligate the researcher to specify a functional form of the production function of which the Cobb-Douglas and the Translog functional forms are most widely used. However, the specification of a functional form for the production function involves the risk of specifying a functional form that is not similar to the ``true'' relationship between the inputs and the output. This misspecification can result in biased parameter estimates, but also in biased measures which are derived from the parameters, such as elasticities. Therefore, we propose to use non-parametric econometric methods. First, these can be applied to verify the functional form used in parametric production analysis. Second, they can be directly used to estimate production functions without the specification of a functional form. Therefore, they avoid possible misspecification errors due to the use of an unsuitable functional form.

In this paper, we use parametric and non-parametric methods to identify the optimal size of Polish crop farms by investigating the relationship between the elasticity of scale and the farm size. We use a balanced panel data set of 371~specialised crop farms for the years 2004-2007. A non-parametric specification test shows that neither the Cobb-Douglas function nor the Translog function are consistent with the "true" relationship between the inputs and the output in our data set. We solve this problem by using non-parametric regression. This approach delivers reasonable results, which are on average not too dissimilar from the results of the parametric estimations. However, many individual results are considerably different so that general conclusions based on the non-parametric estimation deviate from the conclusions based on the Translog model.