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I derive conditions under which a class of fixed-effects estimators consistently estimates the population-averaged slope coefficients in panel data models with individual-specific slopes, where the slopes are allowed to be correlated with the covariates. In addition to including the usual fixed-effects estimator, the results apply to estimators that eliminate individual-specific trends. I apply the results, and propose alternative estimators, to estimation of average treatment in a class of nonlinear unobserved-effects models.
Jeffrey M. Wooldridge (Sun,) studied this question.