A regression model is considered where earnings are explained by schooling and ability. It is assumed that schooling is measured with error and that there are no data on ability. Regressing earnings on observed schooling then yields an estimate of the return to schooling that is subject to positive omitted variable bias (OVB) and negative measurement error bias (MEB). The effects on the OVB and the MEB from using family background variables as proxies for ability are investigated theoretically and empirically. The theoretical analysis demonstrates that the impact on the OVB is uncertain, while the MEB invariably increases in magnitude. The empirical analysis shows that the MEB generally dominates the OVB. As the measurement error increases and/or more family background variables are added, the total bias rapidly becomes negative, driving the estimated return further and further away from the true value.
Missing data proxy variables measurement error consistent estimates of omitted variable bias and measurement error bias