Identification and Estimation of Average Marginal Effects in Fixed Effects Logit Models

This article considers average marginal effects (AME) in a panel data fixed effects logit model. Relating the identified set of the AME to an extremal moment problem, we first show how to obtain sharp bounds on the AME straightforwardly, without any optimization. Then, we consider two strategies to build confidence intervals on the AME. In the first, we estimate the sharp bounds with a semiparametric two-step estimator. The second, very simple strategy estimates instead a quantity known to be at a bounded distance from the AME. It does not require any nonparametric estimation but may result in larger confidence intervals. Monte Carlo simulations suggest that both approaches work well in practice, the second being often very competitive. Finally, we show that our results also apply to average treatment effects, the average structural functions and ordered, fixed effects logit models.