Working Paper: NBER ID: w21033
Authors: Denis Chetverikov; Bradley Larsen; Christopher Palmer
Abstract: 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. 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.
Keywords: Quantile Regression; Endogenous Treatment; Trade Effects; Wage Distribution
JEL Codes: C21; C31; C33; C36; F16; J30
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| traditional quantile regression methods (C21) | inconsistency due to group-level unobservables (C92) |
| two-stage least squares (2SLS) (C36) | address potential endogeneity issues (C51) |
| endogenous group-level treatment (C92) | micro-level outcomes (D29) |
| quantile regression methodology (C21) | distributional effects of an endogenous treatment (C21) |
| group-level treatment (C92) | wage distribution (J31) |
| micro-level covariates (D79) | endogenous group-level treatment (C92) |