Estimated coefficient as a variable with measurement errors

Abstract

This paper examines the econometric issues arising from using estimated coefficients as a dependent or an independent variable in a second-stage regression. While this practice is common in finance and applied econometrics, it introduces measurement errors that affect efficiency, bias test statistics, and create regressor/residual correlation. This paper rigorously analyzes these issues and discusses statistical tests, such as White’s and Hausman’s tests, to diagnose heteroscedasticity and inconsistency. The findings have broader implications for econometric modeling and estimation techniques.