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Nonparametric Identification and Estimation with Independent, Discrete Instruments

Isaac Loh

arXiv 12 Jun 2019 · Econometrics · 1 citations (OpenAlex)

arXiv:1906.05231 · PDF · DOI · OpenAlex · Extracted main text

Abstract

In a nonparametric instrumental regression model, we strengthen the conventional moment independence assumption towards full statistical independence between instrument and error term. This allows us to prove identification results and develop estimators for a structural function of interest when the instrument is discrete, and in particular binary. When the regressor of interest is also discrete with more mass points than the instrument, we state straightforward conditions under which the structural function is partially identified, and give modified assumptions which imply point identification. These stronger assumptions are shown to hold outside of a small set of conditional moments of the error term. Estimators for the identified set are given when the structural function is either partially or point identified. When the regressor is continuously distributed, we prove that if the instrument induces a sufficiently rich variation in the joint distribution of the regressor and error term then point identification of the structural function is still possible. This approach is relatively tractable, and under some standard conditions we demonstrate that our point identifying assumption holds on a topologically generic set of density functions for the joint distribution of regressor, error, and instrument. Our method also applies to a well-known nonparametric quantile regression framework, and we are able to state analogous point identification results in that context.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Victor Chernozhukov and Christian Hansen (2005) An IV model of quantile treatment effects0.87462100%
2D.A. Cox, J. Little, and D. O'Shea (2005) Using Algebraic Geometry0.8435360%
3Samuele Centorrino, Frédérique Fève, and Jean-Pierre Florens (2019) Nonparametric instrumental regressions with (potentially discrete) instruments independent of the error term, 20190.73732100%
4Fabian Dunker, Jean-Pierre Florens, Thorsten Hohage, Jan Johannes, a… (2014) Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression0.73732100%
5Alexandre Poirier (2017) Efficient estimation in models with independence restrictions0.73732100%
6Xavier D'Haultfoeuille (2011) On the completeness condition in nonparametric instrumental problems0.58531100%
7Joel L. Horowitz and Sokbae Lee (2007) Nonparametric instrumental variables estimation of a quantile regression model0.58531100%
8A.W. Van der Vaart and Jon Wellner (1996) Weak Convergence and Empirical Processes0.56711318%
9Joachim Freyberger and Joel Horowitz (2015) Identification and shape restrictions in nonparametric instrumental variables estimation0.51121100%
10Donald W.K. Andrews Examples of l2 complete and boundedly-complete distributions0.40511100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Adaptive estimation for some nonparametric instrumental variable models0.40511