Identification of generalized Cobb-Douglass production functions with multiplicative errors in variables

Abstract

The article discusses the identification of a class of generalized Cobb-Douglas production functions with multiplicative errors in all variables. The article proposes a generalization of Cobb-Douglas production functions in the presence of memory for input and output variables. Parametrization of noise in the form of multiplicative noise in all observable variables is proposed. The logarithmic transformation of such production functions leads to the need to solve the problem of estimating the parameters of a linear difference equation in the presence of additive errors in all variables. To identify the parameters of production functions, a modification of the method of total least squares was used. Computational experiments have shown high accuracy of parameter estimation based on the proposed algorithm.