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Non-asymptotic inference in instrumental variables estimation

Author

Listed:
  • Joel L. Horowitz

    (Institute for Fiscal Studies and Northwestern University)

Abstract
This paper presents a simple method for carrying out inference in a wide variety of possibly nonlinear IV models under weak assumptions. The method is non-asymptotic in the sense that it provides a finite sample bound on the difference between the true and nominal probabilities of rejecting a correct null hypothesis. The method is a non-Studentized version of the Anderson-Rubin test but is motivated and analyzed differently. In contrast to the conventional Anderson-Rubin test, the method proposed here does not require restrictive distributional assumptions, linearity of the estimated model, or simultaneous equations. Nor does it require knowledge of whether the instruments are strong or weak. It does not require testing or estimating the strength of the instruments. The method can be applied to quantile IV models that may be nonlinear and can be used to test a parametric IV model against a nonparametric alternative. The results presented here hold in finite samples, regardless of the strength of the instruments.

Suggested Citation

  • Joel L. Horowitz, 2018. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP52/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:52/18
    as

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    File URL: https://www.ifs.org.uk/uploads/cemmap/wps/CWP521818.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    3. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(4), pages 667-709, August.
    4. Holly, A & Phillips, P C B, 1979. "A Saddlepoint Approximation to the Distribution of the k-Class Estimator of a Coefficient in a Simultaneous System," Econometrica, Econometric Society, vol. 47(6), pages 1527-1547, November.
    5. Nelson, Charles R & Startz, Richard, 1990. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 58(4), pages 967-976, July.
    6. Rothenberg, Thomas J., 1984. "Approximating the distributions of econometric estimators and test statistics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 15, pages 881-935, Elsevier.
    7. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    8. Whitney K. Newey & Frank Windmeijer, 2009. "Generalized Method of Moments With Many Weak Moment Conditions," Econometrica, Econometric Society, vol. 77(3), pages 687-719, May.
    9. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2012. "Measuring the price responsiveness of gasoline demand: Economic shape restrictions and nonparametric demand estimation," Quantitative Economics, Econometric Society, vol. 3(1), pages 29-51, March.
    10. Andrews, Donald W.K. & Soares, Gustavo, 2007. "Rank Tests For Instrumental Variables Regression With Weak Instruments," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1033-1082, December.
    11. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    12. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
    13. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    14. 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.
    15. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages 125-140, January.
    16. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    17. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, May.
    18. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    19. Guido W. Imbens & Richard H. Spady & Phillip Johnson, 1998. "Information Theoretic Approaches to Inference in Moment Condition Models," Econometrica, Econometric Society, vol. 66(2), pages 333-358, March.
    20. 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.
    21. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    22. 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.
    23. Daron Acemoglu & Simon Johnson & James A. Robinson, 2001. "The Colonial Origins of Comparative Development: An Empirical Investigation," American Economic Review, American Economic Association, vol. 91(5), pages 1369-1401, December.
    24. Andrews, Donald W.K. & Marmer, Vadim, 2008. "Exactly distribution-free inference in instrumental variables regression with possibly weak instruments," Journal of Econometrics, Elsevier, vol. 142(1), pages 183-200, January.
    25. Moreira, Marcelo J., 2009. "Tests with correct size when instruments can be arbitrarily weak," Journal of Econometrics, Elsevier, vol. 152(2), pages 131-140, October.
    26. Marine Carrasco & Guy Tchuente, 2016. "Regularization Based Anderson Rubin Tests for Many Instruments," Studies in Economics 1608, School of Economics, University of Kent.
    27. Jun, Sung Jae, 2008. "Weak identification robust tests in an instrumental quantile model," Journal of Econometrics, Elsevier, vol. 144(1), pages 118-138, May.
    28. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 66(6), pages 1389-1404, November.
    29. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    30. Chernozhukov, Victor & Hansen, Christian & Jansson, Michael, 2009. "Finite sample inference for quantile regression models," Journal of Econometrics, Elsevier, vol. 152(2), pages 93-103, October.
    31. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    32. Phillips, P.C.B., 1983. "Exact small sample theory in the simultaneous equations model," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 8, pages 449-516, Elsevier.
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    More about this item

    Keywords

    Weak instruments; normal approximation; finite-sample bounds;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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