Estimation and Validation of Linear and Non linear Production Functions through Robust Regression

Abstract

As in the presence of High leverage points (HLP) i.e. outliers, the ordinary least square (OLS) method does not provide true estimates of production function. In this study, the impact of HLP have been checked in case of linear and non linear production functions viz Quadratic function (QF),Square root function (SF) and Mitscherlich Baule (MB), Cobb Douglas(CD) respectively. The robust estimation techniques M, MM, S, LTS and OLS after replacing the HLP by robust values had provided the precise estimates of production functions as OLS method led to misleading conclusions. It has been observed that the input variables individually contribute significantly in case of quadratic function whereas the interaction is significant in case of square root production function and QF outperforms SF on the basis of high R2 value, minimum AIC and BIC.In case of large variation, the S estimation technique outperformed than the other as observed in all types of data specifically in apple yield, followed by modified OLS after handling HLP, M and MM estimation techniques. In case of MB function, Marquardt method found best followed by Gauss Newton. The estimates of the production functions have been compared and observed that the influential observations have affected the size, sign and significance of the parameter(s).The marginal value of productivity was found to be positive in SF and MB thereby indicating that an increased used of these inputs could increase the output because these were sub optimally used. In QF and CD Marginal value of productivity was found to be negative hence indicating excess use and should be avoided to check the fall of returns in production. Lastly, Cross validation techniques consisting of validations set approach (data split) and k-folded method having training error not more than the validation error which indicated that the fitted model found to be reliable. newline