  Average partial effects (APEs) are often not point identified in panel models
with unrestricted unobserved individual heterogeneity, such as a binary
response panel model with fixed effects and logistic errors as a special case.
This lack of point identification occurs despite the identification of these
models' common coefficients. We provide a unified framework to establish the
point identification of various partial effects in a wide class of nonlinear
semiparametric models under an index sufficiency assumption on the unobserved
heterogeneity, even when the error distribution is unspecified and
non-stationary. This assumption does not impose parametric restrictions on the
unobserved heterogeneity and idiosyncratic errors. We also present partial
identification results when the support condition fails. We then propose
three-step semiparametric estimators for APEs, average structural functions,
and average marginal effects, and show their consistency and asymptotic
normality. Finally, we illustrate our approach in a study of determinants of
married women's labor supply.
