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

ABSTRACT

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.

Keywords:

• BLINEX loss
• Cobb–Douglas production function
• LINEX loss
• Multicollinearity
• Preliminary test estimator
• Ridge regression

Mathematics Subject Classification:

• 62J07;62H12;62F10

Acknowledgments

Any opinion, finding and conclusion or recommendation expressed in this material is that of the author(s) and the NRF does not accept any liability in this regard. The authors would also like to thank Prof Burton, the Vice Principal of Research and Postgraduate Education for awarding him the Vice-Chancellor’s Academic Development Grant. The authors acknowledge the useful comments and suggestions by the Associate editor and anonymous reviewers that improved an earlier version of the article.

Funding

This work is based on the research supported in part by the National Research Foundation of South Africa for the grant TTK1206151317.