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Instrumental Variables Regression with Weak Instruments

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  • Douglas Staiger
  • James H. Stock

Abstract

This paper develops asymptotic distribution theory for instrumental variables regression when the partial correlations between the instruments and the endogenous variables are weak, here modeled as local to zero. Asymptotic representation are provided for various statistics, including two-stage least squares and limited information maximum likelihood estimators, Wald statistics, and statistics testing overidentification and endogeneity. The asymptotic distributions provide good approximations to sampling distributions with ten-twenty observations per instrument. The theory suggests concrete guidelines for applied work, including using nonstandard methods for construction of confidence regions. These results are used to interpret J. D. Angrist and A. B. Krueger's (1991) estimates of the returns to education.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 65 (1997)
Issue (Month): 3 (May)
Pages: 557-586

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Handle: RePEc:ecm:emetrp:v:65:y:1997:i:3:p:557-586

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References

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  1. Mariano, Roberto S, 1982. "Analytical Small-Sample Distribution Theory in Econometrics: The Simultaneous-Equations Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 503-33, October.
  2. Charles R. Nelson & Richard Startz, 1988. "The Distribution of the Instrumental Variables Estimator and Its t-RatioWhen the Instrument is a Poor One," NBER Technical Working Papers 0069, National Bureau of Economic Research, Inc.
  3. 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.
  4. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
  5. Charles R. Nelson & Richard Startz, 1988. "Some Further Results on the Exact Small Sample Properties of the Instrumental Variable Estimator," NBER Technical Working Papers 0068, National Bureau of Economic Research, Inc.
  6. In Choi & Peter C.B. Phillips, 1989. "Asymptotic and Finite Sample Distribution Theory for IV Estimators and Tests in Partially Identified Structural Equations," Cowles Foundation Discussion Papers 929, Cowles Foundation for Research in Economics, Yale University.
  7. John Bound & David A. Jaeger & Regina Baker, 1993. "The Cure Can Be Worse than the Disease: A Cautionary Tale Regarding Instrumental Variables," NBER Technical Working Papers 0137, National Bureau of Economic Research, Inc.
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  1. An ivreg2 function for R
    by diffuseprior in DiffusePrioR on 2012-05-03 08:12:59
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