Estimation of logarithmic derivative of Cobb-Douglas production function by time series with accidental errors

Abstract

The production time series for the classical Cobb-Douglas function on capital and labor costs is considered. Discrepancies between theoretical values of output (Cobb-Douglas function) and real indicator values are interpreted as random deviations. Instead of the classical problem of Cobb-Douglas function estimation, the problem of its logarithmic derivative estimation is considered for the first time. The estimating problem for a production function logarithmic derivative with use of differential equations technique is reduced to the problem of estimating one of the parameters of the drift coefficient in the signal-to-noise model. To construct estimates, the least squares method applied to the time series of production real values is used. It uses the linear dependence of the logarithmic derivative of the volume of production on the logarithmic derived costs of capital and labor with the corresponding coefficients of elasticity and volumes of production. For the case of constant logarithmic derivative costs of capital and labor the estimate expression for the production volume logarithmic derivative is obtained. For the case of variable logarithmic derivatives of capital and labor expenditures, we obtained the equality for estimating the logarithmic derivative of the production function.