The estimation of the technical efficiency comprises a vast literature in the field of applied production economics. There are two predominant approaches: the non-parametric and non-stochastic Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). The DEA is criticised, because it cannot account for statistical noise such as random production shocks and measurement errors, which are inherent in more or less all production data sets. In contrast, the SFA is criticised, because it requires the specification of a functional form, which involves the risk of specifying an unsuitable functional form and thus, model misspecification and biased parameter estimates. Given these problems of the DEA and the SFA, Fan, Li and Weersink (1996) proposed a semi-parametric stochastic frontier model that estimates the production function (frontier) by non-parametric regression based on kernel estimators. This approach combines the virtues of the DEA and the SFA, while avoiding their drawbacks: it avoids the specification of a functional form and at the same time accounts for statistical noise. More recently, this approach was used by Henderson and Simar (2005), Kumbhakar et al. (2007), and Henningsen and Kumbhakar (2009). The aim of this paper and its main contribution to the existing literature is the estimation semi-parametric stochastic frontier models using a different non-parametric estimation technique: spline regression (Ma et al. 2011). We apply this approach to the Polish dairy sector and use a panel data set of Polish dairy farms from the years 2004-2010. The Polish dairy sector has changed considerably since the integration of Poland in the European Union: the number of dairy producers decreased by one third and the average herd size increased from 3.8 to 5.7 cows per farm within the period 2004-2010. It is expected that farms with small herds (less than 30 dairy cows) will quit and that the number of large farms (with more than 100 dairy cows) will increase. Therefore, a thorough empirical study of the technical efficiency and scale efficiency of Polish dairy farms contributes to the insight into this dynamic process. Furthermore, we compare and evaluate the results of this spline-based semi-parametric stochastic frontier model with results of other semi-parametric stochastic frontier models and of traditional parametric stochastic frontier models.

References:

Fan, Y.; Li, Q. , Weersink, A. (1996), Semiparametric Estimation of Stochastic Production
Frontier Models, Journal of Business and Economic Statistics.

Henderson, D. J., Simar, L. (2005), A Fully Nonparametric Stochastic Frontier Model for Panel Data, University of New York

Henningsen, A. , Kumbhakar, S. C. (2009), Semiparametric Stochastic Frontier Analysis: An Application to Polish Farms During Transition, Paper presented at the (EWEPA) in Pisa, Italy.

Kumbhakar S. C., Park, B. U., Simar, L. Tsionas E. G. (2007), Nonparametric Stochastic Frontiers: A Local Maximum Likelihood Approach, Journal of Econometrics.

Ma, S., Racine, J. S. & Yang, L. (2011), Spline regression in the presence of categorical predictors, Working Paper