Family Background Variables as Instruments for Education in Income Regressions: A Bayesian Analysis

The validity of family background variables instrumenting education in income regressions has been much criticized. In this paper, we use data of the 2004 German Socio-Economic Panel and Bayesian analysis in order to analyze to what degree violations of the strong validity assumption affect the estimation results. We show that, in case of moderate direct effects of the instrument on the dependent variable, the results do not deviate much from the benchmark case of no such effect (perfect validity of the instrument). The size of the bias is in many cases smaller than the standard error of education’s estimated coefficient. Thus, the violation of the strict validity assumption does not necessarily lead to strongly different results when compared to the strict validity case. This provides confidence in the use of family background variables as instruments in income regressions.