  We provide new results for nonparametric identification, estimation, and
inference of causal effects using `proxy controls': observables that are noisy
but informative proxies for unobserved confounding factors. Our analysis
applies to cross-sectional settings but is particularly well-suited to panel
models. Our identification results motivate a simple and `well-posed'
nonparametric estimator. We derive convergence rates for the estimator and
construct uniform confidence bands with asymptotically correct size. In panel
settings, our methods provide a novel approach to the difficult problem of
identification with non-separable, general heterogeneity and fixed $T$. In
panels, observations from different periods serve as proxies for unobserved
heterogeneity and our key identifying assumptions follow from restrictions on
the serial dependence structure. We apply our methods to two empirical
settings. We estimate consumer demand counterfactuals using panel data and we
estimate causal effects of grade retention on cognitive performance.
