A cautionary tale about control variables in IV estimation

Many instrumental variable (IV) regressions include control variables to justify (conditional) independence of the instrument and the potential outcomes. The plausibility of conditional IV independence crucially depends on the timing when the control variables are determined. This paper systemically works through different IV models and discusses the (conditions for the) satisfaction of conditional IV independence when controlling for covariates measured (a) prior to the instrument, (b) after the treatment, or (c) both. To illustrate these identification issues, we consider an empirical application using the Vietnam War draft risk as instrument either for veteran status or education to estimate the effects of these variables on labor market and health outcomes.