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PreprintarXiv licencearXiv

Bias Correction and Inference for Panel Quantile Regression

  • Harold D Chiang
  • Wei Biao Wu
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Abstract

We develop a large-n, large-T theory for the unsmoothed fixed-effects quantile regression estimator, paralleling Hahn and Newey (2004) for smooth nonlinear panel models. An exact rank-score identity for the profiled criterion, with a convexity argument, delivers the leading incidental parameter bias of the slope estimator, of order T−1, in closed form. When n and T grow at the same rate, the estimator is asymptotically normal but in general not centred, and conventional intervals are invalid. Admissible growth of n relative to T, up to n=o(T3), depends on the regularity of the conditional error densities. A split-panel jackknife removes the leading bias throughout this range and yields valid inference. In serially dependent panels whose dependence decays geometrically or polynomially, the bias acquires a term from the dependence between regressors and errors of different periods, the jackknife remains valid with contiguous but not with interleaved half-panels, and clustered standard errors are valid.

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Cite

BibTeXRIS
BibTeX
@misc{chiang2026bias,
  title = {{Bias Correction and Inference for Panel Quantile Regression}},
  author = {Harold D Chiang and Wei Biao Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36443},
  eprint = {2610.36443},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36443},
}
RIS
TY  - UNPB
TI  - Bias Correction and Inference for Panel Quantile Regression
AU  - Harold D Chiang
AU  - Wei Biao Wu
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36443
UR  - https://arxiv.org/abs/2610.36443
AB  - We develop a large-n, large-T theory for the unsmoothed fixed-effects quantile regression estimator, paralleling Hahn and Newey (2004) for smooth nonlinear panel models. An exact rank-score identity for the profiled criterion, with a convexity argument, delivers the leading incidental parameter bias of the slope estimator, of order T^−1, in closed form. When n and T grow at the same rate, the estimator is asymptotically normal but in general not centred, and conventional intervals are invalid. Admissible growth of n relative to T, up to n=o(T^3), depends on the regularity of the conditional error densities. A split-panel jackknife removes the leading bias throughout this range and yields valid inference. In serially dependent panels whose dependence decays geometrically or polynomially, the bias acquires a term from the dependence between regressors and errors of different periods, the jackknife remains valid with contiguous but not with interleaved half-panels, and clustered standard errors are valid.
ER  -