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We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. Computationally convenient methods for semiparametric models are presented. We also consider semiparametric, discrete-choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. The dynamic bounds provide a partial-identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. Bounds for overall effects in static and dynamic models are given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. It is shown that the usual, linear, fixed-effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. This paper gives identification and estimation results for nonseparable models under time-homogeneity conditions that are like "time is randomly assigned" or "time is an instrument." Partial-identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects.
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