Estimating educational production functions: The problem of multicollinearity

Abstract

This article attempts to address the problem of multicollinearity in the estimation of educational production functions. Past studies consistently indicate the seeming lack of importance of school input variables such as teacher salary, class size, and expenditure per student in influencing educational outcomes. Our ordinary least squares results were consistent with these past studies, but collinearity diagnostics revealed the presence of at least four potentially serious sources of collinearity within the data, possibly degrading the coefficients on the school input variables. Ridge regression and principal components regression techniques were employed in an effort to “solve” the collinearity problem. The coefficients of the school input variables continue to have the hypothesized signs, but with smaller standard errors. The results indicate that researchers should be cautioned against reaching the conclusion that school input variables don't matter on the basis of ordinary least squares estimates of these parameters.