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Alternative Approximations of the Bias and MSE of the IV Estimator Under Weak Identification With an Application to Bias Correction

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  • John Chao

    ()
    (University of Maryland)

  • Norman Swanson

    ()
    (Rutgers University)

Abstract

We provide analytical formulae for the asymptotic bias (ABIAS) and mean squared error (AMSE) of the IV estimator, and obtain approximations thereof based on an asymptotic scheme which essentially requires the expectation of the first stage F-statistic to converge to a finite (possibly small) positive limit as the number of instruments approaches infinity. The approximations so obtained are shown, via regression analysis, to yield good approximations for ABIAS and AMSE functions, and the AMSE approximation is shown to perform well relative to the approximation of Donald and Newey (2001). Additionally, the manner in which our framework generalizes that of Richardson and Wu (1971) is discussed. One consequence of the asymptotic framework adopted here is that consistent estimators for the ABIAS and AMSE can be obtained. As a result, we are able to construct a number of bias corrected OLS and IV estimators, which we show to be consistent under a sequential asymptotic scheme. These bias-corrected estimators are also robust, in the sense that they remain consistent in a conventional asymptotic setup, where the model is fully identified. A small Monte Carlo experiment documents the relative performance of our bias adjusted estimators versus standard IV, OLS, LIML estimators, and it is shown that our estimators have lower bias than LIML for various levels of endogeneity and instrument relevance.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200315.

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Date of creation: 21 Oct 2003
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Handle: RePEc:rut:rutres:200315

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Keywords: confluent hypergeometric function; Laplace approximation; local-to-zero asymptotics; weak instruments.;

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References

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  1. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  2. Jiahui Wang & Eric Zivot, 1998. "Inference on Structural Parameters in Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, Econometric Society, vol. 66(6), pages 1389-1404, November.
  3. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, Econometric Society, vol. 69(5), pages 1161-91, September.
  4. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
  5. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  6. Peter C.B. Phillips, 1982. "The Exact Distribution of LIML: I," Cowles Foundation Discussion Papers 658, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. Alastair Hall & Fernanda P. M. Peixe, 2000. "A Consistent Method for the Selection of Relevant Instruments," Econometric Society World Congress 2000 Contributed Papers 0790, Econometric Society.
  9. Richardson, David H & Wu, De-Min, 1971. "A Note on the Comparison of Ordinary and Two-Stage Least Squares Estimators," Econometrica, Econometric Society, Econometric Society, vol. 39(6), pages 973-81, November.
  10. John Shea, 1996. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," NBER Technical Working Papers 0193, National Bureau of Economic Research, Inc.
  11. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  12. Nelson, C. & Startz, R., 1988. "The Distribution Of The Instrumental Variables Estimator And Its T-Ratio When The Instrument Is A Poor One," Working Papers 88-07, University of Washington, Department of Economics.
  13. Alastair R. Hall & Glenn D. Rudebusch & David W. Wilcox, 1994. "Judging instrument relevance in instrumental variables estimation," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 94-3, Board of Governors of the Federal Reserve System (U.S.).
  14. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(02), pages 181-240, August.
  15. Nelson, C. & Startz, R., 1988. "Some Furthere Results On The Exact Small Sample Properties Of The Instrumental Variable Estimator," Working Papers 88-06, University of Washington, Department of Economics.
  16. Hahn, Jinyong & Hausman, Jerry, 2002. "Notes on bias in estimators for simultaneous equation models," Economics Letters, Elsevier, vol. 75(2), pages 237-241, April.
  17. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 173-80, January.
  18. Choi, In & Phillips, Peter C. B., 1992. "Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 113-150.
  19. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  20. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 13(2), pages 225-35, April.
  21. Hahn, Jinyong & Kuersteiner, Guido, 2002. "Discontinuities of weak instrument limiting distributions," Economics Letters, Elsevier, vol. 75(3), pages 325-331, May.
  22. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, Econometric Society, vol. 65(6), pages 1365-1388, November.
  23. 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, Econometric Society, vol. 52(1), pages 185-202, January.
  24. 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, Taylor & Francis Journals, vol. 21(3), pages 309-336.
  25. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, Econometric Society, vol. 62(3), pages 657-81, May.
  26. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2005. "Bias Corrected Instrumental Variables Estimation for Dynamic Panel Models with Fixed E¤ects," Boston University - Department of Economics - Working Papers Series WP2005-024, Boston University - Department of Economics.
  27. Jinyong Hahn & Jerry Hausman & Guido Kuersteiner, 2004. "Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 272-306, 06.
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Citations

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Cited by:
  1. Maurice Bun & Frank Windmeijer, 2010. "A comparison of bias approximations for the 2SLS estimator," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP07/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," NBER Technical Working Papers 0313, National Bureau of Economic Research, Inc.
  3. Berkowitz, Daniel & Jackson, John E., 2006. "Entrepreneurship and the evolution of income distributions in Poland and Russia," Journal of Comparative Economics, Elsevier, vol. 34(2), pages 338-356, June.
  4. David Neumark & Junfu Zhang & Stephen Ciccarella, 2005. "The Effects of Wal-Mart on Local Labor Markets," NBER Working Papers 11782, National Bureau of Economic Research, Inc.
  5. Maurice J.G. Bun & Frank Windmeijer, 2011. "A Comparison of Bias Approximations for the 2SLS Estimator," Tinbergen Institute Discussion Papers 11-088/4, Tinbergen Institute.
  6. Sonia Laszlo, 2005. "Self-employment earnings and returns to education in rural Peru," Journal of Development Studies, Taylor & Francis Journals, vol. 41(7), pages 1247-1287.
  7. Liu, Xiaodong & Lee, Lung-fei, 2010. "GMM estimation of social interaction models with centrality," Journal of Econometrics, Elsevier, vol. 159(1), pages 99-115, November.
  8. Zongwu Cai & Ying Fang & Henong Li, 2013. "Weak Instrumental Variables Models for Longitudinal Data," Papers 2013-10-14, Working Paper.
  9. Bun, Maurice J.G. & Windmeijer, Frank, 2011. "A comparison of bias approximations for the two-stage least squares (2SLS) estimator," Economics Letters, Elsevier, vol. 113(1), pages 76-79, October.
  10. Iglesias, Emma M. & Phillips, Garry D.A., 2011. "Almost Unbiased Estimation in Simultaneous Equations Models with Strong and / or Weak Instruments," Cardiff Economics Working Papers E2011/19, Cardiff University, Cardiff Business School, Economics Section.

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