We present a novel approach to nonparametric identification and consistent estimation in economic models using `proxy controls'. Our approach is particularly well-suited to the context of panel data with a fixed time-dimension but also applies in cross-sectional settings. Proxy controls are proxies for unobserved `perfect controls', where perfect controls are variables that are sufficient for the association between potential outcomes and treatments . Our identification strategy requires that the set of available proxy controls be split into two subsets, one subset acting as an instrument for the other. In the panel case, observations from different periods can be used as proxy controls and our key identifying assumptions follow from restrictions on the serial dependence  of the data . Our estimation problem is (under our assumptions) `well-posed' and our estimator is straight-forward to implement. The key step is a penalized sieve minimum distance estimator. We derive simple convergence rates under high-level assumptions .
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 settings that 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 .
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novel approach to nonparametric identification and consistent estimation in economic models using `proxy controls'. Our approach is particularly well-suited to the context of panel data with a fixed time-dimension but also applies in cross-sectional settings. Proxy controls are proxies for unobserved `perfect controls', where perfect controls are variables that are sufficient for the association between potential outcomes and treatments
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
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strategy requires that the set of available proxy controls be split into two subsets, one subset acting as an instrument for the other.
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.
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can be used as proxy controls
serve as proxies for unobserved individual heterogeneity
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structure
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. Our estimation problem is (under our assumptions) `well-posed' and our estimator is straight-forward to implement. The key step is a penalized sieve minimum distance estimator. We derive simple convergence rates under high-level assumptions
and latent variables. We apply our methodology to two separate empirical settings that 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