On Omitted Variable Bias and Measurement Error in Returns to Schooling Estimates

Lam and Schoeni (1993) consider an equation where earnings are explained by schooling and ability. They assume that ability data are lacking and that schooling is measured with error. The estimate obtained by regressing earnings on schooling thus contains omitted variable bias (OVB), which is positive, and measurement error bias (MEB), which is negative. Adding a family background variable to proxy for ability is claimed to: i) decrease the OVB towards, but not below, zero and ii) make the MEB even more negative. This note claims that while ii) is true, even in the context of multiple family background variables, i) is in general incorrect. The OVB may increase in magnitude and/or change sign. Conditions are provided under which i) holds. A simulation procedure is suggested that will yield consistent estimates of the total bias and its components, conditional upon values on the true return and the measurement error variance.