We present a flexible approach to the identification and estimation of causal objects in nonparametric, non-separable models with confounding. Key to our analysis is the use of `proxy controls': covariates that do not satisfy a standard `unconfoundedness' assumption but which are informative proxies for variables that do. Our methods are presented in sufficient generality that they apply to both cross-sectional and panel models. Our identification results motivate an easy-to-implement nonparametric estimation method. Under our identifying assumptions the estimation problem is `well-posed' . We describe the estimator and derive convergence rates. When applied in panel settings our methods provide a novel approach to  identification with non-separable general heterogeneity and a fixed time dimension. In the panel case , observations from different periods serve as proxies for unobserved individual heterogeneity and our key identifying assumptions follow from restrictions on the serial dependence structure of the data and latent variables . We apply our methodology to two separate empirical settingsthat respectively showcase the cross-sectional and the panel implementations of our approach . We estimate causal effects of grade retention on performance in a range of cognitive tests using cross-sectional variation in the data and we estimate a structural Engel curve for food using panel data.
We present a flexible approach to the identification and estimation of causal objects in nonparametric, non-separable models with confounding. Key to our analysis is the use of `proxy controls': covariates that do not satisfy a standard `unconfoundedness' assumption but are informative proxies for variables that do. Our analysis applies to both cross-sectional and panel models. Our identification results motivate a simple and `well-posed' nonparametric estimator and we analyze its asymptotic properties. 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 methodology to two empirical settings . We estimate causal effects of grade retention on cognitive performance using cross-sectional variation and we estimate a structural Engel curve for food using panel data.
D
which
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methods are presented in sufficient generality that they apply
analysis applies
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an easy-to-implement nonparametric estimation method. Under our identifying assumptions the estimation problem is
a simple and
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. We describe the estimator and derive convergence rates. When applied in panel settings
nonparametric estimator and we analyze its asymptotic properties. In panel settings,
A
the difficult problem of
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a fixed time dimension. In the panel case
fixed T. In panels
D
individual
D
of the data and latent variables
R
separate empirical settingsthat respectively showcase the cross-sectional and the panel implementations of our approach
empirical settings
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performance in a range of cognitive tests
cognitive performance
D
in the data