Correcting for Omitted-Variables and Measurement-Error Bias in Regression with an Application to the Effect of Lead on IQ

Abstract

Ordinary least squares (OLS) regression estimates are biased, in general, when relevant variables are omitted from the regression equation or when included variables are measured with error. The errors-in-variables bias can be corrected using auxiliary information about unobservable measurement errors. In this article we demonstrate how auxiliary information can also be used to correct for omitted-variables bias. We illustrate our methods with an application to four published studies of the effect on IQ of childhood exposure to lead. Each of the published studies used OLS methods (or equivalent). None of the studies includes a father IQ variable, and none accounts for the biasing effect of measurement error in the right-side variables. For each of the studies we demonstrate that bias-corrected estimates of the effect of lead on IQ are much reduced in size and are not significantly different from 0. Our methods can be used in other applications involving omitted variables or errors of measurement in the included variables.