RANK-BASED ESTIMATION FOR COBB-DOUGLAS MODELLING IN THE PRESENCE OF OUTLIERS

Abstract

Ordinary least square (OLS) has been widely used in estimating the Cobb-Douglas production function when analysing the empirical linkage between inputs and outputs. However, the estimates based on OLS technique may be biased by the presence of outliers. Rank-based regression estimation is resistant to outliers and may result in unbiased estimates. The objective of this study is therefore to investigate by use of Monte Carlo methods, the performance of the Rank-based regression and OLS methods in estimating the Cobb-Douglas regression model using data with and without outliers. Monte Carlo simulation results indicate that the estimates of the coefficients of the Cobb-Douglas regression model derived from the Least Squares and the Rank-based estimation methods are accurate and equivalent or close to their true values for normal data regardless of variability in sample size. For data with outliers, Least Squares method is affected by outliers and yields inaccurate estimates of the coefficients of the Cobb-Douglas model across various sample sizes. Rank-based estimation remains robust to outliers in large samples and provides estimates of the coefficients of the Cobb-Douglas Regression model that are accurate and nearly equivalent to their true values. The evidence from Monte Carlo experimentation suggests that the proposed Rank-based estimation is likely to do no worse than the OLS with normal dataset and promise to do better when the dataset has outliers within the Cobb-Douglas production function modelling context. The presence of outliers can bias the results of the OLS estimation of the Cobb-Douglas model and it is recommended that the use of Rank-based regression can be an appropriate method to avoid such biased estimates.

Keywords

• Monte Carlo simulation
• rank-based regression estimation
• Cobb-Douglas production function
• ordinary least squares estimation
• outlier