Linear regression with an estimated regressor: applications to aggregate indicators of economic development

Abstract

This study examines the consequences of using an estimated aggregate measure as an explanatory variable in linear regression. We show that neglecting the seemingly small sampling error in the estimated regressor could severely contaminate the estimates. We propose a simple statistical framework to account for the error. In particular, we apply our analysis to two aggregate indicators of economic development, the Gini coefficient and sex ratio. Our findings suggest that the impact of the estimated regressor could be substantially underestimated, when the sampling error is not accounted for.