A Method for Estimating Output Elasticity of Input Factors in Cobb-Douglas Production Function and Measuring Agricultural Technological Progress

Abstract

When using the Cobb-Douglas (C-D) production function to measure the contribution rate of agricultural technological progress (ATP), it is necessary to estimate the output elasticity coefficient (OEC) of each input factor in C-D production function. For this purpose, it is usually necessary to take logarithm at both sides of C-D production function and convert it into a linear function, and then use regression analysis method to estimate the OECs of input factors. However, there are some problems in this method remains unsolved: first, the OECs estimated by taking logarithm of C-D production function are not the optimal estimation of the original C-D production function; second, the regression results sometimes fail to pass statistical test; third, some OECs cannot be guaranteed to be non-negative. Aiming at resolving these problems, a method for estimating OECs in C-D production function based on the Hybrid Improved Bat Optimization Algorithm (HIBA) was proposed. This method solves the problems existing in the OEC estimation methods in the existing literatures. To verify the effectiveness of the proposed method in this study, the OECs of input factors in China' Sichuan Province from 1996 to 2018 was estimated. The estimation results show that, compared with other estimation methods in the existing literatures, the proposed method can not only guarantee that it is the optimal estimation of the OECs in the original C-D production function, but also ensure that the OECs are non-negative and with high precision and good fitting effect. Finally, based on the estimation results, this study measured and analyzed the contribution rate of agricultural input factors and ATP of Sichuan Province and puts forward corresponding suggestions for the agricultural development in this region.