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Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables

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  • Davidson, Russell
  • MacKinnon, James G.

Abstract

We study several tests for the coefficient of the single right-hand-side endogenous vari- able in a linear equation estimated by instrumental variables. We show that writing all the test statistics—Student’s t, Anderson-Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)—as functions of six random quantities leads to a number of interesting results about the properties of the tests under weak- instrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice.

Suggested Citation

  • Davidson, Russell & MacKinnon, James G., 2008. "Bootstrap Inference in a Linear Equation Estimated by Instrumental Variables," Queen's Economics Department Working Papers 273633, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:273633
    DOI: 10.22004/ag.econ.273633
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    References listed on IDEAS

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    1. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," Harvard Institute of Economic Research Working Papers 2048, Harvard - Institute of Economic Research.
    2. JAMES G. MacKINNON, 2006. "Bootstrap Methods in Econometrics," The Economic Record, The Economic Society of Australia, vol. 82(s1), pages 2-18, September.
    3. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
    4. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
    5. 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.
    6. D.S. Poskitt & C.L. Skeels, 2005. "Small Concentration Asymptotics and Instrumental Variables Inference," Department of Economics - Working Papers Series 948, The University of Melbourne.
    7. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
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    9. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
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    11. Hillier, Grant, 2009. "Exact Properties Of The Conditional Likelihood Ratio Test In An Iv Regression Model," Econometric Theory, Cambridge University Press, vol. 25(4), pages 915-957, August.
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    14. 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.
    15. 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.
    16. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
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    18. Poskitt, D.S. & Skeels, C.L., 2007. "Approximating the distribution of the two-stage least squares estimator when the concentration parameter is small," Journal of Econometrics, Elsevier, vol. 139(1), pages 217-236, July.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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