Effects of Multicollinearity and Autocorrelation on Some Estimators in a System of Regression Equation (Published)
When dealing with time series data, some of these assumptions especially that of independence of regressors and error terms leading to multicolinearity and autocorrelation respectively, are not often satisfied in Economics, Social Sciences, Agricultural Economics and some other fields. This study therefore examined the effect of correlation between the error terms, multicollinearity and autocorrelation on some methods of parameter estimation in SUR model using Monte Carlo approach. A two equation model in which the first equation was having multicollinearity and autocorrelation problems while the second has no correlational problem was considered. The error terms of the two equations were also correlated. The levels of correlation between the error terms, multicolinearity and autocorrelation were specified between at interval of 0.2 except when the correlation tends to unity. A Monte Carlo experiment of 1000 trials was carried out at five levels of sample sizes 20, 30, 50, 100 and 250 at two runs. The performances of seven estimation methods; Ordinary Least Squares (OLS), Cochran – Orcut (COCR), Maximum Likelihood Estimator (MLE), Multivariate Regression, Full Information Maximum Likelihood (FIML), Seemingly Unrelated Regression (SUR) Model and Three Stage Least Squares (3SLS) were examined by subjecting the results obtained from each finite properties of the estimators into a multi factor analysis of variance model. The significant factors were further examined using their estimated marginal means and the Least Significant Difference (LSD) methodology to determine the best estimator. The results generally show that the estimators’ performances are equivalent asymptotically but at low sample sizes, the performances differ. Moreover, when there is presence of multicollinearity and autocorrelation in the seemingly unrelated regression model, the estimators of MLE, SUR, FIML and 3SLS are preferred but the most preferred among them is MLE.
In the literature, apart from Gross Domestic Product (GDP) per Capita, a number of factors have been identified as non-income determinants of health care expenditure. Most studies linking health care expenditure to income and other important variables have originated in advanced countries. This study considers a linear regression model via shrinkage methods to identify key predictors of health care expenditure in Africa. Shrinkage is a process of estimation where a subset of redundant predictor variables is discarded, leaving only important ones in the linear regression model. The study was based on 42 African countries for the year 2012 and GDP per Capita, Consumer Price Index (CPI), Exchange Rate (EXC), Corruption Perception Index (COP), and Population Density (POP) were identified as key predictors of Health Expenditure per Capita (HEC). A major finding identified the Elastic net model as critical in accurately estimating HEC in Africa.