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Location Properties of Point Estimators in Linear Instrumental Variables and Related Models

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  • Keisuke Hirano
  • Jack R. Porter

Abstract

We examine statistical models, including the workhorse linear instrumental variables model, in which the mapping from the reduced form distribution to the structural parameters of interest is singular. The singularity of this mapping implies certain fundamental restrictions on the finite sample properties of point estimators: they cannot be unbiased, quantile-unbiased, or translation equivariant. The nonexistence of unbiased estimators does not rule out bias reduction of standard estimators, but implies that the bias-variance tradeoff cannot be avoided and needs to be considered carefully. The results can also be extended to weak instrument asymptotics by using the limits of experiments framework.

Suggested Citation

  • Keisuke Hirano & Jack R. Porter, 2015. "Location Properties of Point Estimators in Linear Instrumental Variables and Related Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 720-733, December.
  • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:720-733
    DOI: 10.1080/07474938.2014.956573
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
    2. 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.
    3. Phillips, P C B, 1986. "The Distribution of FIML in the Leading Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 239-243, February.
    4. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    5. 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.
    6. 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.
    7. Kinal, Terrence W, 1980. "The Existence of Moments of k-Class Estimators," Econometrica, Econometric Society, vol. 48(1), pages 241-249, January.
    8. Carter, R A L, 1976. "The Exact Distribution of an Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 228-233, February.
    9. Ullah, Aman & Nagar, A L, 1974. "The Exact Mean of the Two-Stage Least Squares Estimator of the Structural Parameters in an Equation Having Three Endogenous Variables," Econometrica, Econometric Society, vol. 42(4), pages 749-758, July.
    10. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    11. 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.
    12. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    13. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    14. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    15. Anderson, T W & Sawa, Takamitsu, 1973. "Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions," Econometrica, Econometric Society, vol. 41(4), pages 683-714, July.
    16. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
    17. Fuller, Wayne A, 1977. "Some Properties of a Modification of the Limited Information Estimator," Econometrica, Econometric Society, vol. 45(4), pages 939-953, May.
    18. Sargan, J D, 1978. "On the Existence of the Moments of 3SLS Estimators," Econometrica, Econometric Society, vol. 46(6), pages 1329-1350, November.
    19. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Almost Unbiased Estimation in Simultaneous Equation Models With Strong and/or Weak Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 505-520, June.
    20. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    21. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    22. Hillier, Grant H & Kinal, Terrence W & Srivastava, V K, 1984. "On the Moments of Ordinary Least Squares and Instrumental Variables Estimators in a General Structural Equation," Econometrica, Econometric Society, vol. 52(1), pages 185-202, January.
    23. Maasoumi, Esfandiar, 1978. "A Modified Stein-like Estimator for the Reduced Form Coefficients of Simultaneous Equations," Econometrica, Econometric Society, vol. 46(3), pages 695-703, May.
    24. 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.
    25. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
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    Cited by:

    1. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R3, Cowles Foundation for Research in Economics, Yale University, revised Oct 2015.
    2. Isaiah Andrews & Timothy B. Armstrong, 2015. "Unbiased Instrumental Variables Estimation under Known First-Stage Sign," Cowles Foundation Discussion Papers 1984R2, Cowles Foundation for Research in Economics, Yale University, revised Sep 2015.

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