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Nonparametric identification and estimation with discrete instruments and regressors

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  • Loh, Isaac

Abstract

In a nonparametric instrumental regression model in which the regressor and instrument are discretely distributed, we strengthen the conventional moment independence assumption between instrument and residual to include higher order moments. We give conditions under which a function of interest is partially identified when the regressor has more mass points than the instrument. We also show that the function is point identified as long as certain latent parameters corresponding to conditional moments of the residual lie outside of a set of measure zero. We give an asymptotically normal estimator for the structural function when it is point identified. We also provide a straightforward method for inference under partial identification. These perform well in Monte-Carlo simulations and in two empirical applications.

Suggested Citation

  • Loh, Isaac, 2023. "Nonparametric identification and estimation with discrete instruments and regressors," Journal of Econometrics, Elsevier, vol. 235(2), pages 1257-1279.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1257-1279
    DOI: 10.1016/j.jeconom.2022.10.006
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