Specification of a stochastic production function model in the extended class of stochastic frontier models
Copulas are being successfully applied for derivation of estimates in the models related to stochastic production functions. They can be used for handling of panel data, for the analysis of models with multiple outputs and for improvement of estimates in classical models. The research proposes an algorithm for specification of extended class of models for stochastic production functions where a possible dependence between the error components is assumed. To describe this dependence we consider two functions: normal copula and Frank copula. Simulated data are used to prove the necessity to take into account potential dependence between the error components and to illustrate the importance of considering several types of copulas for different problems related to estimation of technical efficiency. In addition we analyze an influence of the choice of copula type on estimates of main parameters in the model and propose possible problems where classical models for stochastic production function can be applied.
We propose a method of specification of stochastic production function models for solving problems related to the ranking of objects by the level of technical efficiency at production-regional level. The described method takes into account potential dependence between the random components of the error. Based on actual data on 80 sub-federal units of the Russian Federation grouped according to the basic characteristics of the GRP structure, an empirical analysis of the influence of possible dependence of the error components on the values of regions’ technical efficiency was carried out in accordance with the developed specification scheme. The main types of problems where it is possible to use the premise of the independence of the random error components were described.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.