IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2208.02028.html
   My bibliography  Save this paper

Bootstrap inference in the presence of bias

Author

Listed:
  • Giuseppe Cavaliere
  • S'ilvia Gonc{c}alves
  • Morten {O}rregaard Nielsen
  • Edoardo Zanelli

Abstract

We consider bootstrap inference for estimators which are (asymptotically) biased. We show that, even when the bias term cannot be consistently estimated, valid inference can be obtained by proper implementations of the bootstrap. Specifically, we show that the prepivoting approach of Beran (1987, 1988), originally proposed to deliver higher-order refinements, restores bootstrap validity by transforming the original bootstrap p-value into an asymptotically uniform random variable. We propose two different implementations of prepivoting (plug-in and double bootstrap), and provide general high-level conditions that imply validity of bootstrap inference. To illustrate the practical relevance and implementation of our results, we discuss five examples: (i) inference on a target parameter based on model averaging; (ii) ridge-type regularized estimators; (iii) nonparametric regression; (iv) a location model for infinite variance data; and (v) dynamic panel data models.

Suggested Citation

  • Giuseppe Cavaliere & S'ilvia Gonc{c}alves & Morten {O}rregaard Nielsen & Edoardo Zanelli, 2022. "Bootstrap inference in the presence of bias," Papers 2208.02028, arXiv.org, revised Nov 2023.
  • Handle: RePEc:arx:papers:2208.02028
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2208.02028
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sebastian Calonico & Matias D. Cattaneo & Max H. Farrell, 2018. "On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 767-779, April.
    2. Cornea-Madeira, Adriana & Davidson, Russell, 2015. "A Parametric Bootstrap For Heavy-Tailed Distributions," Econometric Theory, Cambridge University Press, vol. 31(3), pages 449-470, June.
    3. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    4. Hounyo, Ulrich & Lahiri, Kajal, 2023. "Estimating the variance of a combined forecast: Bootstrap-based approach," Journal of Econometrics, Elsevier, vol. 232(2), pages 445-468.
    5. Sebastian Calonico & Matias D. Cattaneo & Rocio Titiunik, 2014. "Robust Nonparametric Confidence Intervals for Regression‐Discontinuity Designs," Econometrica, Econometric Society, vol. 82, pages 2295-2326, November.
    6. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    7. Matias D. Cattaneo & Michael Jansson, 2018. "Kernel†Based Semiparametric Estimators: Small Bandwidth Asymptotics and Bootstrap Consistency," Econometrica, Econometric Society, vol. 86(3), pages 955-995, May.
    8. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    9. Stefano Giglio & Dacheng Xiu, 2021. "Asset Pricing with Omitted Factors," Journal of Political Economy, University of Chicago Press, vol. 129(7), pages 1947-1990.
    10. Jinyuan Chang & Peter Hall, 2015. "Double-bootstrap methods that use a single double-bootstrap simulation," Biometrika, Biometrika Trust, vol. 102(1), pages 203-214.
    11. Liu, Chu-An, 2015. "Distribution theory of the least squares averaging estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 142-159.
    12. Chenchuan (Mark) Li & Ulrich K. Müller, 2021. "Linear regression with many controls of limited explanatory power," Quantitative Economics, Econometric Society, vol. 12(2), pages 405-442, May.
    13. Emily Oster, 2019. "Unobservable Selection and Coefficient Stability: Theory and Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 187-204, April.
    14. Jochmans, Koen & Higgins, Ayden, 2022. "Bootstrap inference for fixed-effect models," TSE Working Papers 22-1328, Toulouse School of Economics (TSE), revised Dec 2023.
    15. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    16. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    17. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    18. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
    19. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    20. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, July.
    21. Gonçalves, Sílvia & Kaffo, Maximilien, 2015. "Bootstrap inference for linear dynamic panel data models with individual fixed effects," Journal of Econometrics, Elsevier, vol. 186(2), pages 407-426.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.
    2. De Vos, Ignace & Stauskas, Ovidijus, 2024. "Cross-section bootstrap for CCE regressions," Journal of Econometrics, Elsevier, vol. 240(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jochmans, Koen & Higgins, Ayden, 2022. "Bootstrap inference for fixed-effect models," TSE Working Papers 22-1328, Toulouse School of Economics (TSE), revised Dec 2023.
    2. Xuan Leng & Jiaming Mao & Yutao Sun, 2023. "Debiased inference for dynamic nonlinear models with two-way fixed effects," Papers 2305.03134, arXiv.org, revised Oct 2023.
    3. Carneiro, Anabela & Portugal, Pedro & Raposo, Pedro & Rodrigues, Paulo M.M., 2023. "The persistence of wages," Journal of Econometrics, Elsevier, vol. 233(2), pages 596-611.
    4. Chen, Weihao & Cizek, Pavel, 2023. "Bias-Corrected Instrumental Variable Estimation in Linear Dynamic Panel Data Models," Discussion Paper 2023-028, Tilburg University, Center for Economic Research.
    5. Lu, Xun & Su, Liangjun, 2023. "Uniform inference in linear panel data models with two-dimensional heterogeneity," Journal of Econometrics, Elsevier, vol. 235(2), pages 694-719.
    6. Antonio F. Galvao & Thomas Parker & Zhijie Xiao, 2024. "Bootstrap Inference for Panel Data Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 628-639, April.
    7. Smith, Simon C. & Timmermann, Allan & Zhu, Yinchu, 2019. "Variable selection in panel models with breaks," Journal of Econometrics, Elsevier, vol. 212(1), pages 323-344.
    8. Dhaene, Geert & Jochmans, Koen, 2016. "Likelihood Inference In An Autoregression With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1178-1215, October.
    9. Schumann, Martin & Severini, Thomas A. & Tripathi, Gautam, 2021. "Integrated likelihood based inference for nonlinear panel data models with unobserved effects," Journal of Econometrics, Elsevier, vol. 223(1), pages 73-95.
    10. Pakel, Cavit, 2019. "Bias reduction in nonlinear and dynamic panels in the presence of cross-section dependence," Journal of Econometrics, Elsevier, vol. 213(2), pages 459-492.
    11. Jiaqi Xiao & Artūras Juodis & Yiannis Karavias & Vasilis Sarafidis & Jan Ditzen, 2023. "Improved tests for Granger noncausality in panel data," Stata Journal, StataCorp LP, vol. 23(1), pages 230-242, March.
    12. Alexander Chudik & M. Hashem Pesaran & Jui‐Chung Yang, 2018. "Half‐panel jackknife fixed‐effects estimation of linear panels with weakly exogenous regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 816-836, September.
    13. Chudik, Alexander & Pesaran, M. Hashem, 2015. "Common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors," Journal of Econometrics, Elsevier, vol. 188(2), pages 393-420.
    14. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    15. Jochmans, Koen & Weidner, Martin, 2024. "Inference On A Distribution From Noisy Draws," Econometric Theory, Cambridge University Press, vol. 40(1), pages 60-97, February.
    16. Ivan Fernandez-Val & Martin Weidner, 2015. "Individual and time effects in nonlinear panel models with large N , T," CeMMAP working papers 17/15, Institute for Fiscal Studies.
    17. Chengwang Liao & Ziwei Mei & Zhentao Shi, 2024. "Nickell Meets Stambaugh: A Tale of Two Biases in Panel Predictive Regressions," Papers 2410.09825, arXiv.org.
    18. Francesco Bartolucci & Claudia Pigini & Francesco Valentini, 2023. "Conditional inference and bias reduction for partial effects estimation of fixed-effects logit models," Empirical Economics, Springer, vol. 64(5), pages 2257-2290, May.
    19. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    20. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2208.02028. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.