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IV Quantile Regression for Group-level Treatments, with an Application to the Distributional Effects of Trade -- by Denis Chetverikov, Bradley Larsen, Christopher PalmerWe 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. An empirical application indicates that low-wage earners in the US from 1990--2007 were significantly more affected by increased Chinese import competition than high-wage earners. Our approach applies to a broad range of settings in labor, industrial organization, trade, public finance, and other applied fields.
http://papers.nber.org/papers/w21033#fromrss
http://papers.nber.org/papers/w21033#fromrssQuantile Regression with Panel Data -- by Bryan S. Graham, Jinyong Hahn, Alexandre Poirier, James L. PowellWe propose a generalization of the linear quantile regression model to accommodate possibilities afforded by panel data. Specifically, we extend the correlated random coefficients representation of linear quantile regression (e.g., Koenker, 2005; Section 2.6). We show that panel data allows the econometrician to (i) introduce dependence between the regressors and the random coefficients and (ii) weaken the assumption of comonotonicity across them (i.e., to enrich the structure of allowable dependence between different coefficients). We adopt a "fixed effects" approach, leaving any dependence between the regressors and the random coefficients unmodelled. We motivate different notions of quantile partial effects in our model and study their identification.
For the case of discretely-valued covariates we present analog estimators and characterize their large sample properties. When the number of time periods (T) exceeds the number of random coefficients (P), identification is regular, and our estimates are root-N-consistent. When T=P, our identification results make special use of the subpopulation of stayers - units whose regressor values change little over time - in a way which builds on the approach of Graham and Powell (2012). In this just-identified case we study asymptotic sequences which allow the frequency of stayers in the population to shrink with the sample size. One purpose of these "discrete bandwidth asymptotics" is to approximate settings where covariates are continuously-valued and, as such, there is only an infinitesimal fraction of exact stayers, while keeping the convenience of an analysis based on discrete covariates. When the mass of stayers shrinks with N, identification is irregular and our estimates converge at a slower than root-N rate, but continue to have limiting normal distributions.
We apply our methods to study the effects of collective bargaining coverage on earnings using the National Longitudinal Survey of Youth 1979 (NLSY79). Consistent with prior work (e.g., Chamberlain, 1982; Vella and Verbeek, 1998), we find that using panel data to control for unobserved worker heterogeneity results in sharply lower estimates of union wage premia. We estimate a median union wage premium of about 9 percent, but with, in a more novel finding, substantial heterogeneity across workers. The 0.1 quantile of union effects is insignificantly different from zero, whereas the 0.9 quantile effect is of over 30 percent. Our empirical analysis further suggests that, on net, unions have an equalizing effect on the distribution of wages.
http://papers.nber.org/papers/w21034#fromrss
http://papers.nber.org/papers/w21034#fromrss