IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1809.04016.html
   My bibliography  Save this paper

Bootstrap Methods in Econometrics

Author

Listed:
  • Joel L. Horowitz

Abstract

The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap provides approximations to distributions of statistics, coverage probabilities of confidence intervals, and rejection probabilities of hypothesis tests that are more accurate than the approximations of first-order asymptotic distribution theory. The reductions in the differences between true and nominal coverage or rejection probabilities can be very large. In addition, the bootstrap provides a way to carry out inference in certain settings where obtaining analytic distributional approximations is difficult or impossible. This article explains the usefulness and limitations of the bootstrap in contexts of interest in econometrics. The presentation is informal and expository. It provides an intuitive understanding of how the bootstrap works. Mathematical details are available in references that are cited.

Suggested Citation

  • Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    • Handle: RePEc:arx:papers:1809.04016
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1809.04016
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    3. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589833.
    4. Joel L. Horowitz, 1998. "Bootstrap Methods for Median Regression Models," Econometrica, Econometric Society, vol. 66(6), pages 1327-1352, November.
    5. Orme, Chris, 1990. "The small-sample performance of the information-matrix test," Journal of Econometrics, Elsevier, vol. 46(3), pages 309-331, December.
    6. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    7. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    8. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    9. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
    10. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    11. M. Rajarshi, 1990. "Bootstrap in Markov-sequences based on estimates of transition density," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(2), pages 253-268, June.
    12. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    13. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    14. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    15. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    16. James J. Heckman & Jeffrey Smith & Nancy Clements, 1997. "Making The Most Out Of Programme Evaluations and Social Experiments: Accounting For Heterogeneity in Programme Impacts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(4), pages 487-535.
    17. Horowitz, J., 1996. "Bootstrap Critical Values For Tests Based On The Smoothed Maximum Score Estimator," SFB 373 Discussion Papers 1996,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    18. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    19. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589819.
    20. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    21. Donald W. K. Andrews, 2004. "the Block-Block Bootstrap: Improved Asymptotic Refinements," Econometrica, Econometric Society, vol. 72(3), pages 673-700, May.
    22. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
    23. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    24. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(2), pages 426-468, April.
    25. J.J. Heckman & E.E. Leamer (ed.), 2001. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 5, number 5.
    26. Chatterjee, A. & Lahiri, S. N., 2011. "Bootstrapping Lasso Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 608-625.
    27. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    28. Bowlus, Audra J & Kiefer, Nicholas M & Neumann, George R, 2001. "Equilibrium Search Models and the Transition from School to Work," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(2), pages 317-343, May.
    29. Datta, S. & Mccormick, W. P., 1995. "Some Continuous Edgeworth Expansions for Markov Chains with Applications to Bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 83-106, January.
    30. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    31. Kam‐Hin Chung & Stephen M. S. Lee, 2001. "Optimal Bootstrap Sample Size in Construction of Percentile Confidence Bounds," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 225-239, March.
    32. Federico A. Bugni & Ivan A. Canay & Xiaoxia Shi, 2017. "Inference for subvectors and other functions of partially identified parameters in moment inequality models," Quantitative Economics, Econometric Society, vol. 8(1), pages 1-38, March.
    33. Donald, Stephen G. & Paarsch, Harry J., 1996. "Identification, Estimation, and Testing in Parametric Empirical Models of Auctions within the Independent Private Values Paradigm," Econometric Theory, Cambridge University Press, vol. 12(3), pages 517-567, August.
    34. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, September.
    35. Arup Bose, 1990. "Bootstrap in moving average models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(4), pages 753-768, December.
    36. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    37. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
    38. Edwin Choi & Peter Hall, 2000. "Bootstrap confidence regions computed from autoregressions of arbitrary order," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 461-477.
    39. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    40. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    41. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    42. Bugni, Federico A., 2016. "Comparison Of Inferential Methods In Partially Identified Models In Terms Of Error In Coverage Probability," Econometric Theory, Cambridge University Press, vol. 32(1), pages 187-242, February.
    43. Horowitz, Joel L., 2002. "Bootstrap critical values for tests based on the smoothed maximum score estimator," Journal of Econometrics, Elsevier, vol. 111(2), pages 141-167, December.
    44. Kreps,David M. & Wallis,Kenneth F. (ed.), 1997. "Advances in Economics and Econometrics: Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521589826.
    45. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    46. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    47. Patra, Rohit Kumar & Seijo, Emilio & Sen, Bodhisattva, 2018. "A consistent bootstrap procedure for the maximum score estimator," Journal of Econometrics, Elsevier, vol. 205(2), pages 488-507.
    48. Donald W. K. Andrews & Sukjin Han, 2009. "Invalidity of the bootstrap and the m out of n bootstrap for confidence interval endpoints defined by moment inequalities," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 172-199, January.
    49. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    50. Paparoditis, Efstathios, 1996. "Bootstrapping Autoregressive and Moving Average Parameter Estimates of Infinite Order Vector Autoregressive Processes," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 277-296, May.
    51. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    52. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, May.
    53. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, March.
    54. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
    55. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    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. Cyril Couaillier & Valerio Scalone, 2020. "How does Financial Vulnerability amplify Housing and Credit Shocks?," Working papers 763, Banque de France.
    2. King, Maxwell L. & Zhang, Xibin & Akram, Muhammad, 2020. "Hypothesis testing based on a vector of statistics," Journal of Econometrics, Elsevier, vol. 219(2), pages 425-455.

    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. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    3. Yang, Zhenlin, 2015. "LM tests of spatial dependence based on bootstrap critical values," Journal of Econometrics, Elsevier, vol. 185(1), pages 33-59.
    4. Bergström, Pål, 1999. "Bootstrap Methods and Applications in Econometrics - A Brief Survey," Working Paper Series 1999:2, Uppsala University, Department of Economics.
    5. Zhenlin Yang, 2013. "LM Tests of Spatial Dependence Based on Bootstrap Critical Values," Working Papers 03-2013, Singapore Management University, School of Economics.
    6. Whang, Yoon-Jae, 2006. "Smoothed Empirical Likelihood Methods For Quantile Regression Models," Econometric Theory, Cambridge University Press, vol. 22(2), pages 173-205, April.
    7. Chen, Qihui & Fang, Zheng, 2019. "Inference on functionals under first order degeneracy," Journal of Econometrics, Elsevier, vol. 210(2), pages 459-481.
    8. Kline, Patrick & Santos, Andres, 2012. "Higher order properties of the wild bootstrap under misspecification," Journal of Econometrics, Elsevier, vol. 171(1), pages 54-70.
    9. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    10. Pötscher, Benedikt M. & Preinerstorfer, David, 2023. "How Reliable Are Bootstrap-Based Heteroskedasticity Robust Tests?," Econometric Theory, Cambridge University Press, vol. 39(4), pages 789-847, August.
    11. Tae-Hwan Kim & Halbert White, 2003. "Estimation, Inference, And Specification Testing For Possibly Misspecified Quantile Regression," Advances in Econometrics, in: Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later, pages 107-132, Emerald Group Publishing Limited.
    12. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    13. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    14. Francesca Molinari, 2020. "Microeconometrics with Partial Identi?cation," CeMMAP working papers CWP15/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    16. Jinyong Hahn & Zhipeng Liao, 2021. "Bootstrap Standard Error Estimates and Inference," Econometrica, Econometric Society, vol. 89(4), pages 1963-1977, July.
    17. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    18. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, University Library of Munich, Germany, revised 05 Mar 1996.
    19. Torben Klarl, 2014. "Is Spatial Bootstrapping A Panacea For Valid Inference?," Journal of Regional Science, Wiley Blackwell, vol. 54(2), pages 304-312, March.
    20. Ou Bianling & Long Zhihe & Li Wenqian, 2019. "Bootstrap LM Tests for Spatial Dependence in Panel Data Models with Fixed Effects," Journal of Systems Science and Information, De Gruyter, vol. 7(4), pages 330-343, August.

    More about this item

    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:1809.04016. 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.