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Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments

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  • Chao, John C.
  • Swanson, Norman R.
  • Hausman, Jerry A.
  • Newey, Whitney K.
  • Woutersen, Tiemen

Abstract

This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that null as n →∞, where K and r denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless K n / r n →0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of r and K .

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  • Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(01), pages 42-86, February.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:01:p:42-86_00
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    References listed on IDEAS

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    Cited by:

    1. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(02), pages 277-301, April.
    2. Cheng Hsiao & Qiankun Zhou, 2017. "JIVE for Panel Dynamic Simultaneous Equations Models," Departmental Working Papers 2017-10, Department of Economics, Louisiana State University.
    3. repec:taf:jnlbes:v:34:y:2016:i:4:p:590-605 is not listed on IDEAS
    4. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    5. Brian P. Poi, 2006. "Jackknife instrumental variables estimation in Stata," Stata Journal, StataCorp LP, vol. 6(3), pages 364-376, September.
    6. Byunghoon Kang, 2017. "Inference in Nonparametric Series Estimation with Data-Dependent Undersmoothing," Working Papers 170712442, Lancaster University Management School, Economics Department.
    7. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    8. Federico Crudu & Giovanni Mellace & Zsolt Sandor, 2017. "Inference in instrumental variables models with heteroskedasticity and many instruments," Department of Economics University of Siena 761, Department of Economics, University of Siena.
    9. Victor Chernozhukov & Christian Hansen & Martin Spindler, 2015. "Valid Post-Selection and Post-Regularization Inference: An Elementary, General Approach," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 649-688, August.
    10. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    11. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    12. Jonas Andersson & Jarle Møen, 2016. "A Simple Improvement of the IV-estimator for the Classical Errors-in-Variables Problem," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 78(1), pages 113-125, February.
    13. Alexandre Belloni & Victor Chernozhukov & Christian Hansen & Damian Kozbur, 2016. "Inference in High-Dimensional Panel Models With an Application to Gun Control," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 590-605, October.
    14. Hansen, Christian & Kozbur, Damian, 2014. "Instrumental variables estimation with many weak instruments using regularized JIVE," Journal of Econometrics, Elsevier, vol. 182(2), pages 290-308.
    15. Damian Kozbur, 2017. "Testing-Based Forward Model Selection," American Economic Review, American Economic Association, vol. 107(5), pages 266-269, May.
    16. Shi, Zhentao, 2016. "Econometric estimation with high-dimensional moment equalities," Journal of Econometrics, Elsevier, vol. 195(1), pages 104-119.
    17. Bekker, Paul & Wansbeek, Tom, 2016. "Simple many-instruments robust standard errors through concentrated instrumental variables," Economics Letters, Elsevier, vol. 149(C), pages 52-55.
    18. repec:eee:econom:v:204:y:2018:i:1:p:86-100 is not listed on IDEAS
    19. John Chao & Jerry Hausman & Whitney Newey & Norman Swanson & Tiemen Woutersen, 2013. "Combining Two Consistent Estimators," Departmental Working Papers 201310, Rutgers University, Department of Economics.
    20. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    21. Antonia Diaz & Luis A. Puch, 2016. "Investment, Technological Progress and Energy Efficiency," Working Papers 909, Barcelona Graduate School of Economics.
    22. Yoonseok Lee & Yu Zhou, 2015. "Averaged Instrumental Variables Estimators," Center for Policy Research Working Papers 180, Center for Policy Research, Maxwell School, Syracuse University.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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