Testing Partial Instrument Monotonicity

When multi-dimensional instruments are used to identify and estimate causal effects, the monotonicity condition may not hold due to heterogeneity in the population. Under a partial monotonicity condition, which only requires the monotonicity to hold for each instrument separately holding all the other instruments fixed, the 2SLS estimand can still be a positively weighted average of LATEs. In this paper, we provide a simple nonparametric test for partial instrument monotonicity. We demonstrate the good finite sample properties of the test through Monte Carlo simulations. We then apply the test to monetary incentives and distance from results centers as instruments for the knowledge of HIV status.