Bias correction for the use of educational and psychological assessments as covariates in linear regression

The use of aggregate scores on item response assessments as a proxy for an underlying trait in an econometric model generally produces biased estimators. I show that if the number of items on the assessment is proportional to the square root of the sample size then standard inferential procedures for the linear regression model are incorrect. I propose a bias-corrected estimator based on nonparametric estimation of the bias term which produces valid inference under relatively weak conditions. I also demonstrate the finite sample performance in a Monte Carlo study and implement the procedure for a wage regression using data from the NLSY 1979. JEL codes: C14, C38, C39, C55