The Estimation of Cobb-Douglas Production Function Parameter through A Robust Partial Least Squares

Abstract

The Cobb-Douglas production function (Cobb and Douglas, 1928) is still today the most ubiquitous form in theoretical and empirical analyses of growth and productivity. The estimation of the parameters of aggregate production functions is central to much of today’s work on growth, technological change, productivity, and labour. Empirical estimates of aggregate production functions are a tool of analysis essential in macroeconomics, and important theoretical constructs, such as potential output, technical change, or the demand for labour, are based on them. It is usually fitted by first linearizing the models through logarithmic transformation and then applying method of least squares (Prajneshu, 2008), but the ordinary least squares (OLS) is erom dna erom ,scirtemonoce dna scitsitats nI .)1002 ,‏enahaK( dohtem noitamitse tseb eht ton attention is paid to techniques that can deal with data containing atypical observations, which can arise from outliers, miscoding, or heterogeneity and not captured or presumed in a model. This is of very high importance especially in (non) linear regression models and time series as the least squares (LS) and maximum likelihood estimators (MLE) are heavily influenced by data contamination (Pavel, 2007). In addition, multicollinearity often exists between the economic factors and could greatly affect parameter estimation. The seriousness of multicollinearity will affect the results mostly negatively. Partial least squares (PLS) are especially good in dealing with small sample data, plenty of variables and multicollinearity. It can greatly improve reliability and precision of model (Zhang & Shang, 2009). While Robust Partial Least Squares (RPLS) is used to solve the problems of multicollinearity and outliers. This can be done through Minimum Covariance Determinant (MCD) and the reweighted MCD (RMCD) estimator. This method is called RSIMPLS (Branden & Hubert, 2003). The purpose of this article is to suggest the best method in overcoming the outliers and multicollinearity problems of Cobb-Douglas production function. This is done by using the robust partial least squares (RPLS) method. This developed methodology will be illustrated in the contacts of its theoretical background.