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Abstract
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 the functional form of the production function. Most
often, the Cobb-Douglas or the Translog production function is 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 might result in biased estimation results—including measures
that are of interest of applied economists, such as elasticities. Therefore, we propose to use nonparametric
econometric methods. First, they can be applied to verify the functional form used in
parametric estimations of production functions. Second, they can be directly used for estimating
production functions without specifying a functional form and thus, avoiding possible misspecification
errors.
We use a balanced panel data set of farms specialized in crop production that is constructed from
Polish FADN data for the years 2004-2007. Our analysis 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 different from the results of the
parametric estimations but many individual results are rather different.