Preliminary testing of the Cobb–Douglas production function and related inferential issues

In this article, we consider the multiple regression model in the presence of multicollinearity and study the performance of the preliminary test estimator (PTE) both analytically and computationally, when it is a priori suspected that some constraints may hold on the vector parameter space. The performance of the PTE is further analyzed by comparing the risk of some well-known estimators of the ridge parameter through an extensive Monte Carlo simulation study under some bounded and or asymmetric loss functions. An application of the Cobb–Douglas production function is included and from these results as well as the simulation studies, it is clear that the bounded linear exponential loss function outperforms the other loss functions across all the proposed ridge parameters by comparing the risk values.