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A first-stage representation for instrumental variables quantile regression

Javier Alejo, Antonio F. Galvao, Gabriel Montes-Rojas

arXiv 1 Feb 2021 · Econometrics · publishedThe Stata Journal Promoting communications on statistics and Stata (2024) · 3 citations (OpenAlex)

arXiv:2102.01212 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, conditional on the endogeneous and exogenous covariates, and the instruments as well, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first-stage. We then suggest inference procedures to evaluate the adequacy of instruments by evaluating their statistical significance using the first-stage result. The test is developed in an over-identification context, since consistent estimation of the weights for implementation of the first-stage requires at least one valid instrument to be available. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples. An empirical application illustrates that checking for the statistical significance of the instruments at different quantiles is important. The proposed procedures may be specially useful in QR since the instruments may be relevant at some quantiles but not at others.

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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
1Chernozhukov, V. and Hansen, C (2006) Instrumental quantile regression inference for structural and treatment effects models1.00063100%
2Staiger, D. and Stock, J.H (1997) Instrumental variables regression with weak instruments0.84333100%
3Chernozhukov, V. and Hansen, C (2008) Instrumental variable quantile regression: A robust inference approach0.73732100%
4Chernozhukov, V., Hansen, C. and Jansson, M (2009) Finite sample inference for quantile regression models0.73732100%
5Card, D (1995) Using Geographic Variation in College Proximity to Estimate the Return to Schooling0.73732100%
6Amemiya, T (1982) Two stage least absolute deviations estimators0.64422100%
7Andrews, I. and Mikusheva, A (2016) Conditional inference with a functional nuisance parameter0.64422100%
8Chen, L-A. and Portnoy, S Two-stage regression quantiles and two-stage trimmed least squares estimators for structural equation models0.64422100%
9Galvao, A.F. and Montes-Rojas, G (2015) On the equivalence of instrumental variables estimators for linear models self0.64422100%
10Jun, S.J (2008) Weak identification robust tests in an instrumental quantile model0.64422100%

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