1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate $\sqrt{nT}$, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator."> 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate $\sqrt{nT}$, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator.">
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Reconsideration of a simple approach to quantile regression for panel data

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  • Galina Besstremyannaya
  • Sergei Golovan
Abstract
SummaryThis note discusses two errors in the approach proposed in Canay (2011) for constructing a computationally simple two-step estimator in a quantile regression model with quantile-independent fixed effects. Firstly, we show that Canay’s assumption about n/Ts → 0 for some s > 1 is not strong enough and can entail severe bias or even the non-existence of the limiting distribution for the estimator of the vector of coefficients. The condition n/T → 0 appears to be closer to the required set of restrictions. These problems are likely to cause incorrect inference in applied papers with large n/T, but the impact is less in applications with small n/T. In an attempt to improve Canay’s estimator, we propose a simple correction that may reduce the bias. The second error concerns the incorrect asymptotic standard error of the estimator of the constant term. We show that, contrary to Canay’s assumption, the within estimator has an influence function that is not i.i.d. and this affects inference. Moreover, the constant term is unlikely to be estimable at rate $\sqrt{nT}$, so a different estimator may not be available. However, the issue concerning the constant term does not have an effect on slope coefficients. Finally, we give recommendations to practitioners and conduct a meta-review of applied papers that use Canay’s estimator.

Suggested Citation

  • Galina Besstremyannaya & Sergei Golovan, 2019. "Reconsideration of a simple approach to quantile regression for panel data," The Econometrics Journal, Royal Economic Society, vol. 22(3), pages 292-308.
    • Handle: RePEc:oup:emjrnl:v:22:y:2019:i:3:p:292-308.
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    1. Ivan A. Canay, 2011. "A simple approach to quantile regression for panel data," Econometrics Journal, Royal Economic Society, vol. 14(3), pages 368-386, October.
    2. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
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    1. Dimitrios Bakas & Theodore Panagiotidis & Gianluigi Pelloni, 2024. "Labour reallocation and unemployment fluctuations: A tale of two tails," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(3), pages 3444-3468, July.
    2. Boikos, Spyridon & Panagiotidis, Theodore & Voucharas, Georgios, 2022. "Financial development, reforms and growth," Economic Modelling, Elsevier, vol. 108(C).
    3. Tilov, Ivan & Weber, Sylvain, 2023. "Heterogeneity in price elasticity of vehicle kilometers traveled: Evidence from micro-level panel data," Energy Economics, Elsevier, vol. 127(PA).
    4. Galina Besstremyannaya & Sergei Golovan, 2023. "Measuring heterogeneity in hospital productivity: a quantile regression approach," Journal of Productivity Analysis, Springer, vol. 59(1), pages 15-43, February.
    5. Claudiu Tiberiu Albulescu & Matei Tămășilă & Ilie Mihai Tăucean, 2021. "The Nonlinear Relationship Between Firm Size and Growth in the Automotive Industry," Journal of Industry, Competition and Trade, Springer, vol. 21(3), pages 445-463, September.
    6. Ben-Salha Ousama & Zmami Mourad, 2020. "The impact of private capital flows on economic growth in the MENA region," Economics and Business Review, Sciendo, vol. 6(3), pages 45-67, August.
    7. Lang, Jan Hannes & Rusnák, Marek & Greiwe, Moritz, 2023. "Medium-term growth-at-risk in the euro area," Working Paper Series 2808, European Central Bank.
    8. Battagliola, Maria Laura & Sørensen, Helle & Tolver, Anders & Staicu, Ana-Maria, 2022. "A bias-adjusted estimator in quantile regression for clustered data," Econometrics and Statistics, Elsevier, vol. 23(C), pages 165-186.
    9. Liang Chen & Yulong Huo, 2019. "A Simple Estimator for Quantile Panel Data Models Using Smoothed Quantile Regressions," Papers 1911.04729, arXiv.org.
    10. Stelian STANCU & Eugenia GRECU & Mirela Ionela ACELEANU & Daniela Livia TRAŞCĂ & Claudiu Tiberiu ALBULESCU, 2021. "Does Firm Size Matters for Firm Growth? Evidence from the Romanian Health Sector," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 17-31, December.
    11. Yoshihiko Norimasa & Kazuki Ueda & Tomohiro Watanabe, 2021. "Emerging Economies' Vulnerability to Changes in Capital Flows: The Role of Global and Local Factors," Bank of Japan Working Paper Series 21-E-5, Bank of Japan.
    12. Besstremyannaya, Galina & Golovan, Sergei, 2021. "Measuring heterogeneity with fixed effect quantile regression: Long panels and short panels," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 64, pages 70-82.
    13. David Powell, 2022. "Quantile regression with nonadditive fixed effects," Empirical Economics, Springer, vol. 63(5), pages 2675-2691, November.
    14. Fotié, Andrée Kenne & Mbratana, Taoufiki, 2024. "Informality and development: The nonlinear effect," Economics Letters, Elsevier, vol. 234(C).
    15. Yoshibumi Makabe & Yoshihiko Norimasa, 2022. "The Term Structure of Inflation at Risk: A Panel Quantile Regression Approach," Bank of Japan Working Paper Series 22-E-4, Bank of Japan.

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    More about this item

    Keywords

    Quantile regression; panel data; fixed effects; inference;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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