Combining Regression and Factor Analysis for Use in Agricultural Economics Research

While ordinary least squares regression has become a standard statistical technique, there are problems frequently overlooked or ignored by researchers in applying this statistical method. Two basic assumptions of the OLS regression model—(1) that the explanatory variables are independent of each other and (2) that the explanatory variables are known, fixed numbers—do not hold for most economic data, particularly time series data. This has been a consternation for econometricians, if not for the general researcher, for many years.In the case of nonindependence of explanatory variables (multicollinearity), signs of the regression coefficients often are inconsistent with economic theory and with correlation coefficients calculated from the data. Also, variances of the estimated regression coefficients are inconsistent. In practice for prediction equations, multicollinearity can usually be sufficiently reduced by either dropping one or more multicollinear variables or by indexing them and using the index as a regressor, thus circumventing the assumption regarding independence of the explanatory variables. A chi-square test for multicollinearity is available, and can be used as a guide to alert a researcher to the problem.