On IV estimation of a dynamic linear probability model with fixed effects

Researchers still estimate a dynamic linear probability model (LPM) with fixed effects when analyzing a panel of binary choices. Setting aside the possibility that the average marginal effect may not be point-identified, directly applying IV estimators to this dynamic LPM delivers inconsistent estimators for the true average marginal effect regardless of whether the cross-sectional or time series dimensions diverge. I also show through some examples that these inconsistent estimators are sometimes outside the nonparametric bounds proposed by Chernozhukov et al. (2013). Although there are no analytical results for GMM estimators using Arellano-Bond moment conditions, I show through an empirical example that the resulting GMM estimate of the average treatment effect of fertility on female labor participation is outside the nonparametric bounds under monotonicity.