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.”