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Valid Confidence Intervals and Inference in the Presence of Weak Instruments

Author

Listed:
  • Charles R. Nelson

    (The University of Washington)

  • Richard Startz

    (The University of Washington)

  • Eric Zivot

    (The University of Washington)

Abstract

We investigate confidence intervals and inference for the instrumental variables model with weak instruments. Wald-based confidence intervals perform poorly in that the probability they reject the null is far greater than their nominal size. In the worst case, Wald-based confidence intervals always exclude the true paremeter value. Confidence intervals based on the LM, LR, and Anderson-Rubin statistics perform far better than the Wald. The Anderson-Rubin statistic always has the correct size, but LM and LR statistics have somewhat greater power. Performance of the LM and LR statistics is improved by a degrees-of- freedom correction in the overidentified ccase. We show that the practice of "pre-testing" by looking at the significance of the first - stage regression leads to extremely poor results when the instruments are very weak.

Suggested Citation

  • Charles R. Nelson & Richard Startz & Eric Zivot, 1996. "Valid Confidence Intervals and Inference in the Presence of Weak Instruments," Econometrics 9612002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpem:9612002
    Note: Type of Document - Adobe .pdf file; prepared on Mac; pages: 49; figures: 8, included in paper
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    References listed on IDEAS

    as
    1. Dufour, J.M., 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Cahiers de recherche 9539, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Jiahui Wang & Eric Zivot, 1996. "Inference on a Structural Parameter in Instrumental Variables Regression with Weak Instruments," Econometrics 9610005, University Library of Munich, Germany.
    4. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-298, May.
    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. Fuhrer, Jeffrey C. & Moore, George R. & Schuh, Scott D., 1995. "Estimating the linear-quadratic inventory model Maximum likelihood versus generalized method of moments," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 115-157, February.
    7. Newey, Whitney K & West, Kenneth D, 1987. "Hypothesis Testing with Efficient Method of Moments Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(3), pages 777-787, October.
    8. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    9. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 185-246, National Bureau of Economic Research, Inc.
    10. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    11. repec:fth:harver:1435 is not listed on IDEAS
    12. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    13. 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.
    14. 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.
    15. Shea, J., 1993. "Instrument Relevance in Linear Models: A Simple Measure," Working papers 9312, Wisconsin Madison - Social Systems.
    16. D. Klepinger & S. Lundberg & R. Plotnick, "undated". "Instrument selection: The case of teenage childbearing and women's educational attainment," Institute for Research on Poverty Discussion Papers 1077-95, University of Wisconsin Institute for Research on Poverty.
    17. 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.
    18. Rotemberg, Julio J, 1984. "Interpreting the Statistical Failures of Some Rational Expectations Macroeconomic Models," American Economic Review, American Economic Association, vol. 74(2), pages 188-193, May.
    19. Maddala, G S, 1974. "Some Small Sample Evidence on Tests of Significance in Simultaneous Equations Models," Econometrica, Econometric Society, vol. 42(5), pages 841-851, September.
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    More about this item

    Keywords

    confidence intervals; instrumental variables; pre-testing; weak instruments;
    All these keywords.

    JEL classification:

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

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