Abstract
Despite constituting a major theoretical breakthrough, the quantile selection model of Arellano and Bonhomme (2017, Econometrica 85: 1–28) based on copulas has not found its way into many empirical applications. We introduce the command arhomme, which implements different variants of the estimator along with standard errors based on bootstrapping and subsampling. We illustrate the command by replicating parts of the empirical application in the original article and a related application in Arellano and Bonhomme (2018, Handbook of Quantile Regression, chap. 13).
Highlights
Ever since the contributions by Gronau (1974) and Heckman (1974), economists and researchers from other disciplines have been aware of the possibility that measured relationships may suffer from selection bias
Buchinsky (1998, 2001) proposed a control function approach to correcting quantile regressions for selection bias. It was later shown by Huber and Melly (2015) that the proposed correction was based on restrictive assumptions that are unlikely to hold in general
The rotated versions (7) and (8) cannot be handled with standard implementations of quantile regression such as qreg, because these do not allow for individual specific ranks Gτ,i
Summary
Ever since the contributions by Gronau (1974) and Heckman (1974), economists and researchers from other disciplines have been aware of the possibility that measured relationships may suffer from selection bias. Arellano and Bonhomme’s (2017) contribution is part of an active recent literature that addresses the problem of correcting entire distributions for selection with potential applications in many fields (for example, Albrecht, van Vuuren, and Vroman [2009]; Picchio and Mussida [2011]; Fernández-Val, van Vuuren, and Vella [2018]; D’Haultfoeuille et al [2020]; and Biewen, Fitzenberger, and Seckler [2020]). Because the left-hand side of (4) describes outcome quantiles in the selected population, this means that the coefficients β(τ ) belonging to the τ th quantile in the overall population can be recovered by looking at the Gx{τ, p(z)}-quantile observations of the selected population This establishes the validity of the following “rotated” quantile regression, which uses the observed outcomes Y but applies to them individual specific ranks Gx{τ, p(z)} (instead of the target rank τ )
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