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 from the 2004 German Socio-Economic Panel and Bayesian analysis to analyze to what degree violations of the strict 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's exclusion restriction). In many cases, the size of the bias is smaller than the width of the 95% posterior interval for the effect of education on income. Thus, a violation of the strict validity assumption does not necessarily lead to results which are strongly different from those of the strict validity case. This finding provides confidence in the use of family background variables as instruments in income regressions.