Econometrica: Mar 2016, Volume 84, Issue 2

IV Quantile Regression for Group-Level Treatments, with an Application to the Distributional Effects of Trade

https://doi.org/10.3982/ECTA12121
p. 809-833

Denis Chetverikov, Bradley Larsen, Christopher Palmer

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group‐level unobservables, a quantile extension of Hausman and Taylor, 1981. Because of the presence of group‐level unobservables, standard quantile regression techniques are inconsistent in our setting even if the treatment is independent of unobservables. In contrast, our estimation technique is consistent as well as computationally simple, consisting of group‐by‐group quantile regression followed by two‐stage least squares. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic zero‐mean normality of our estimator. As in Hausman and Taylor, 1981, micro‐level covariates can be used as internal instruments for the endogenous group‐level treatment if they satisfy relevance and exogeneity conditions. Our approach applies to a broad range of settings including labor, public finance, industrial organization, urban economics, and development; we illustrate its usefulness with several such examples. Finally, an empirical application of our estimator finds that low‐wage earners in the United States from 1990 to 2007 were significantly more affected by increased Chinese import competition than high‐wage earners.

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Supplement to "IV Quantile Regression For Group-Level Treatments, with an Application to the Distributional Effects of Trade"

This appendix contains Monte Carlo simulations; inference extensions including uniform confidence bands, joint inference for group-specific effects, and clustered standard errors; all proofs; and a description of the theoretical tools employed in the paper.

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Supplement to "IV Quantile Regression For Group-Level Treatments, with an Application to the Distributional Effects of Trade"

This zip file contains the replication files for the estimation results in the manuscript and simulations in the appendix as well as a generic example of Stata code implementing the estimator.

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