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A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators

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  • Jinyong Hahn
  • Atsushi Inoue

Abstract

We examine empirical relevance of three alternative asymptotic approximations to the distribution of instrumental variables estimators by Monte Carlo experiments. We find that conventional asymptotics provides a reasonable approximation to the actual distribution of instrumental variables estimators when the sample size is reasonably large. For most sample sizes, we find Bekker[11] asymptotics provides reasonably good approximation even when the first stage R2 is very small. We conclude that reporting Bekker[11] confidence interval would suffice for most microeconometric (cross-sectional) applications, and the comparative advantage of Staiger and Stock[5] asymptotic approximation is in applications with sample sizes typical in macroeconometric (time series) applications.

Suggested Citation

  • Jinyong Hahn & Atsushi Inoue, 2002. "A Monte Carlo Comparison Of Various Asymptotic Approximations To The Distribution Of Instrumental Variables Estimators," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 309-336.
  • Handle: RePEc:taf:emetrv:v:21:y:2002:i:3:p:309-336
    DOI: 10.1081/ETC-120015786
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    Cited by:

    1. Paul A. Bekker & Jan van der Ploeg, 2000. "Instrumental Variable Estimation Based on Grouped Data," Econometric Society World Congress 2000 Contributed Papers 1862, Econometric Society.
    2. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    3. Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen & John C. Chao & Norman R. Swanson, 2012. "Instrumental variable estimation with heteroskedasticity and many instruments," Quantitative Economics, Econometric Society, vol. 3(2), pages 211-255, July.
    4. Carrasco, Marine & Tchuente, Guy, 2015. "Regularized LIML for many instruments," Journal of Econometrics, Elsevier, vol. 186(2), pages 427-442.
    5. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    6. Park, Albert & Brandt, Loren & Giles, John, 2003. "Competition under credit rationing: theory and evidence from rural China," Journal of Development Economics, Elsevier, vol. 71(2), pages 463-495, August.
    7. Neil Kellard & Denise Osborn & Jerry Coakley & Alastair R. Hall & Denise R. Osborn & Nikolaos Sakkas, 2015. "Structural Break Inference Using Information Criteria in Models Estimated by Two-Stage Least Squares," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 741-762, September.
    8. Abutaliev, Albert & Anatolyev, Stanislav, 2013. "Asymptotic variance under many instruments: Numerical computations," Economics Letters, Elsevier, vol. 118(2), pages 272-274.
    9. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    10. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    11. Chao, John & Swanson, Norman R., 2007. "Alternative approximations of the bias and MSE of the IV estimator under weak identification with an application to bias correction," Journal of Econometrics, Elsevier, vol. 137(2), pages 515-555, April.
    12. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    13. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    14. Richard Startz & Charles Nelson & Eric Zivot, 1999. "Improved Inference for the Instrumental Variable Estimator," Econometrics 9905001, University Library of Munich, Germany.
    15. Otilia Boldea & Alastair Hall & Sanggohn Han, 2012. "Asymptotic Distribution Theory for Break Point Estimators in Models Estimated via 2SLS," Econometric Reviews, Taylor & Francis Journals, vol. 31(1), pages 1-33.
    16. Otilia Boldea & Alastair Hall & Sanggohn Han, 2010. "Uncertainty, Entrepreneurship and the Organisation of Corruption," Centre for Growth and Business Cycle Research Discussion Paper Series 134, Economics, The University of Manchester.
    17. Joura, Essam & Xiao, Qin & Ullah, Subhan, 2021. "The impact of Say-on-Pay votes on firms' strategic policies: Insights from the Anglo-Saxon economy," International Review of Financial Analysis, Elsevier, vol. 73(C).
    18. Jan F. Kiviet & Jerzy Niemczyk, 2014. "On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490, Emerald Group Publishing Limited.
    19. Bekker, Paul A. & Crudu, Federico, 2012. "Symmetric Jackknife Instrumental Variable Estimation," MPRA Paper 37853, University Library of Munich, Germany.
    20. Kweh, Qian Long & Tebourbi, Imen & Lo, Huai-Chun & Huang, Cheng-Tsu, 2022. "CEO compensation and firm performance: Evidence from financially constrained firms," Research in International Business and Finance, Elsevier, vol. 61(C).
    21. Michael Christl & Monika Köppl‐Turyna & Dénes Kucsera, 2018. "Revisiting the Employment Effects of Minimum Wages in Europe," German Economic Review, Verein für Socialpolitik, vol. 19(4), pages 426-465, November.
    22. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2008. "Inference regarding multiple structural changes in linear models estimated via two stage least squares," MPRA Paper 9251, University Library of Munich, Germany, revised 20 Jun 2008.
    23. Kazuhiko Hayakawa, 2006. "Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present," Hi-Stat Discussion Paper Series d05-130, Institute of Economic Research, Hitotsubashi University.
    24. Kiviet, Jan F. & Niemczyk, Jerzy, 2007. "The asymptotic and finite sample distributions of OLS and simple IV in simultaneous equations," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3296-3318, April.
    25. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS

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    Keywords

    Many instruments; Weak instruments; JEL Classification : C31;
    All these keywords.

    JEL classification:

    • 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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