Nonparametric Instrumental Regressions with (Potentially Discrete) Instruments Independent of the Error Term
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We consider a nonparametric instrumental regression model with continuous endogenous regressor where instruments are fully independent of the error term. This assumption allows us to extend the reach of this model to cases where the instrumental variable is discrete, and therefore to substantially enlarge its potential empirical applications. Under our assumptions, the regression function becomes solution to a nonlinear integral equation. We contribute to existing literature by providing an exhaustive analysis of identification and a simple iterative estimation procedure. Details on the implementation and on the asymptotic properties of this estimation algorithm are given. We conclude the paper with a simulation experiment for a binary instrument and an empirical application to the estimation of the Engel curve for food, where we show that our estimator delivers results that are consistent with existing evidence under several discretizations of the instrumental variable.
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