IDEAS home Printed from https://ideas.repec.org/p/adl/wpaper/2015-01.html
   My bibliography  Save this paper

On Bootstrap Validity for Subset Anderson-Rubin Test in IV Regressions

Author

Listed:
  • Firmin Doko Tchatoka

    () (School of Economics, University of Adelaide)

  • Wenjie Wang

    () (Graduate School of Economics, Kyoto University)

Abstract

This paper sheds new light on subset hypothesis testing in linear structural models in which instrumental variables (IVs) can be arbitrarily weak. For the first time, we investigate the validity of the bootstrap for Anderson-Rubin (AR) type tests of hypotheses specified on a subset of structural parameters, with or without identification. Our investigation focuses on two subset AR type statistics based on the plug-in principle. The first one uses the restricted limited information maximum likelihood (LIML) as the plug-in method, and the second exploits the restricted two-stage least squares (2SLS). We provide an analysis of the limiting distributions of both the standard and proposed bootstrap AR statistics under the subset null hypothesis of interest. Our results provide some new insights and extensions of earlier studies. In all cases, we show that when identification is strong and the number of instruments is fixed, the bootstrap provides a high-order approximation of the null limiting distributions of both plug-in subset statistics. However, the bootstrap is inconsistent when instruments are weak. This contrasts with the bootstrap of the AR statistic of the null hypothesis specified on the full vector of structural parameters, which remains valid even when identification is weak; see Moreira et al. (2009). We present a Monte Carlo experiment that confirms our theoretical findings.

Suggested Citation

  • Firmin Doko Tchatoka & Wenjie Wang, 2015. "On Bootstrap Validity for Subset Anderson-Rubin Test in IV Regressions," School of Economics Working Papers 2015-01, University of Adelaide, School of Economics.
  • Handle: RePEc:adl:wpaper:2015-01
    as

    Download full text from publisher

    File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2015-01.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Berkowitz, Daniel & Caner, Mehmet & Fang, Ying, 2012. "The validity of instruments revisited," Journal of Econometrics, Elsevier, vol. 166(2), pages 255-266.
    2. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(03), pages 669-709, June.
    3. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics,in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
    4. Jean-Marie Dufour, 2003. "Identification, weak instruments, and statistical inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 36(4), pages 767-808, November.
    5. Firmin Doko Tchatoka, 2015. "On bootstrap validity for specification tests with weak instruments," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 137-146, February.
    6. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    7. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    8. Firmin Doko Tchatoka & Jean‐Marie Dufour, 2014. "Identification‐robust inference for endogeneity parameters in linear structural models," Econometrics Journal, Royal Economic Society, vol. 17(1), pages 165-187, February.
    9. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    10. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
    11. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis & Linchun Chen, 2012. "On the Asymptotic Sizes of Subset Anderson–Rubin and Lagrange Multiplier Tests in Linear Instrumental Variables Regression," Econometrica, Econometric Society, vol. 80(6), pages 2649-2666, November.
    12. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1192-1228, December.
    13. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 29(1), pages 117-131.
    15. Mikusheva, Anna, 2010. "Robust confidence sets in the presence of weak instruments," Journal of Econometrics, Elsevier, vol. 157(2), pages 236-247, August.
    16. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    17. Poskitt, D. S. & Skeels, C. L., 2013. "Inference in the Presence of Weak Instruments: A Selected Survey," Foundations and Trends(R) in Econometrics, now publishers, vol. 6(1), pages 1-99, August.
    18. J. Horowitz, 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.
    19. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    20. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    21. Horowitz, Joel L., 2001. "The bootstrap and hypothesis tests in econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 37-40, January.
    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. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-843, August.
    24. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    25. Joel L. Horowitz, 1996. "Bootstrap Critical Values for Tests Based on the Smoothed Maximum Score Estimator," Econometrics 9603003, University Library of Munich, Germany.
    26. Moreira, Marcelo J. & Porter, Jack R. & Suarez, Gustavo A., 2009. "Bootstrap validity for the score test when instruments may be weak," Journal of Econometrics, Elsevier, vol. 149(1), pages 52-64, April.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Subset AR-test; bootstrap validity; bootstrap inconsistency; weak instruments; Edgeworth;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

    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:adl:wpaper:2015-01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Eran Binenbaum). General contact details of provider: http://edirc.repec.org/data/decadau.html .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.