ABSTRACT
In this paper, we propose a robust test of exogeneity. The test statistics is constructed from quantile regression estimators, which are robust to heavy tails of errors. We derive the asymptotic distribution of the test statistic under the null hypothesis of exogeneity at a given quantile. The finite sample properties of the test are investigated through Monte Carlo simulations that exhibit not only good size and power properties, but also good robustness to outliers.
Acknowledgements
We are grateful for comments by participants in the 2013 French Econometrics Conference and the 2014 EEA conference in Toulouse.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
2. To name just a few, see Amemiya [Citation7], Powell [Citation14], Chen and Portnoy [Citation15], Kemp [Citation16], Sakata [Citation17], Arias et al. [Citation18], Garcia et al. [Citation19], Chen et al. [Citation20], Hong and Tamer [Citation21], Kim and Muller [Citation5,Citation22], Chernozhukov and Hansen [Citation6,Citation23,Citation24], Ma and Koenker [Citation25], Horowitz and Lee [Citation26], and Lee [Citation27].
4. However, they may be efficient is some particular cases. For example, LAD regressions are efficient under errors following a Laplace distribution law.
5. Readers are referred to Kim and White [Citation29] for how the value of m is determined.
6. In the Hausman test specification, one would have instead: σ11 = var(ut), σ22 = var(vt), and σ12 = cov(ut, vt).
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Funding
The first author acknowledges financial support from the National Research Foundation of Korea – a grant funded by the Korean Government [NRF-2009-327-B00088] and from the Aix-Marseille School of Economics. The second author acknowledges financial support from the A*MIDEX project [no. ANR-11-IDEX-0001-02] funded by the Investissements d'Avenir French Government program, managed by the French National Research Agency (ANR).