Bootstrap inference for misspecified moment condition models

  • Mihai Giurcanu
  • Brett Presnell


We study the standard-bootstrap, the centered-bootstrap, and the empirical-likelihood bootstrap tests of hypotheses used in conjunction with generalized method of moments inference in correctly specified and misspecified moment condition models. We show that, under correct specification, the standard-bootstrap estimator of the null distribution of the J-test converges in distribution to a random distribution, verifying its inconsistency, while the centered and the empirical-likelihood bootstrap estimators are consistent. We provide higher-order expansions of the size distortions of the analytic and the bootstrap tests. We show that the standard-bootstrap parameter-tests are consistent under misspecification, while the centered-bootstrap parameter-tests are inconsistent. We propose a general bootstrap methodology which is highly accurate under correct specification and consistent under misspecification. In a simulation study, we explore the finite sample behavior of the analytic and the bootstrap tests for a panel data model and we apply our methodology on a real-world data set.


GMM inference Standard-bootstrap Centered-bootstrap Empirical-likelihood bootstrap Edgeworth expansions Misspecified models 

Supplementary material

10463_2017_604_MOESM1_ESM.pdf (152 kb)
Supplementary material 1 (pdf 152 KB)


  1. Andrews, D. W. K. (2002). Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators. Econometrica, 70, 119–162.MathSciNetCrossRefzbMATHGoogle Scholar
  2. Arellano, M., Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. The Review of Economic Studies, 58, 277–297.Google Scholar
  3. Bhattacharya, R. N., Ghosh, J. K. (1978). On the validity of the formal Edgeworth expansion. The Annals of Statistics, 6, 434–451.Google Scholar
  4. Blundell, R., Bond, S. (1998). Initial conditions and moment conditions in dynamic panel data models. Journal of Econometrics, 87, 115–143.Google Scholar
  5. Brown, B. W., Newey, W. K. (2002). Generalized method of moments, efficient bootstrapping, and improved inference. Journal of Business & Economic Statistics, 20, 507–517.Google Scholar
  6. Croissant, Y., Millo, G. (2008). Panel data econometrics in R: The plm package. Journal of Statistical Software, 27(2), 21–24.Google Scholar
  7. Dudley, R. M. (2002). Real analysis and probability. Cambridge: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  8. Efron, B. (1979). Bootstrap methods: Another look at jackknife. The Annals of Statistics, 7, 1–26.MathSciNetCrossRefzbMATHGoogle Scholar
  9. Hahn, J. (1996). A note on bootstrapping generalized method of moments estimators. Econometric Theory, 12, 187–197.MathSciNetCrossRefGoogle Scholar
  10. Hall, P. (1992). The bootstrap and Edgeworth expansion. New York: Springer-Verlag.CrossRefzbMATHGoogle Scholar
  11. Hall, P., Horowitz, J. L. (1996). Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica, 64, 891–916.Google Scholar
  12. Hall, A. R., Inoue, A. (2003). The large sample behaviour of the generalized method of moments estimator in misspecified models. Journal of Econometrics, 114, 361–394.Google Scholar
  13. Hall, P., Presnell, B. (1999). Intentionally biased bootstrap methods. Journal of the Royal Statistical Society. Series B (Statistical Methodology), 61, 143–158.Google Scholar
  14. Hall, P., Wilson, S. R. (1991). Two guidelines for bootstrap hypothesis testing. Biometrics, 47, 757–762.Google Scholar
  15. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50, 1029–1054.MathSciNetCrossRefzbMATHGoogle Scholar
  16. Hansen, L. P., Heaton, J., Yaron, A. (1996). Finite-sample properties of some alternative GMM estimators. Journal of Business & Economic Statistics, 14, 262–280.Google Scholar
  17. Hsiao, C. (2003). Analysis of panel data. New York: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  18. Imbens, G. W., Lancaster, T. (1994). Combining micro and macro data in microeconomic models. The Review of Economic Studies, 61, 655–680.Google Scholar
  19. Inglot, T., Ledwina, T. (2006). Asymptotic optimality of new adaptive test in regression model. Annales de l’Institute Henri Poincaré, 42, 579–590.Google Scholar
  20. Lee, S. (2014). Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators. Journal of Econometrics, 178, 398–413.MathSciNetCrossRefzbMATHGoogle Scholar
  21. Lindsay, B. G., Qu, A. (2003). Inference functions and quadratic score tests. Statistical Science, 18, 394–410.Google Scholar
  22. Owen, A. (1990). Empirical likelihood ratio confidence regions. The Annals of Statistics, 18, 90–120.MathSciNetCrossRefzbMATHGoogle Scholar
  23. Qin, J., Lawless, J. (1994). Empirical likelihood and general estimating equations. The Annals of Statistics, 22, 300–325.Google Scholar
  24. R Core Team. (2016). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.Google Scholar
  25. Van der Vaart, A. W. (1998). Asymptotic statistics. New York: Springer.CrossRefzbMATHGoogle Scholar
  26. Zhang, B. (1999). Bootstrapping with auxiliary information. The Canadian Journal of Statistics, 27, 237–249.MathSciNetCrossRefzbMATHGoogle Scholar
  27. Zhou, M. (2015). Emplik: Empirical likelihood ratio for censored/truncated data. R package version 1.0-2.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 2017

Authors and Affiliations

  1. 1.Department of Public Health SciencesUniversity of ChicagoChicagoUSA
  2. 2.Department of StatisticsUniversity of FloridaGainesvilleUSA

Personalised recommendations