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Jackknife Instrumental Variables Estimation

  • Angrist, J D
  • Imbens, G W
  • Krueger, A B

Two-stage-least-squares (2SLS) estimates are biased towards the probability limit of OLS estimates. This bias grows with the degree of over-identification and can generate highly misleading results. In this paper we propose two simple alternatives to 2SLS and limited-information-maximum-likelihood (LIML) estimators for models with more instruments than endogenous regressors. These estimators can be interpreted as instrumental variables procedures using an instrument that is independent of disturbances even in finite samples. Independence is achieved by using a 'leave-one-out' jackknife-type fitted value in place of the usual first stage equation. The new estimators are first order equivalent to 2SLS but with finite-sample properties superior, in terms of bias and coverage rate of confidence intervals, compared to those of 2SLS and similar to those of LIML, when there are many instruments.

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File URL: http://qed.econ.queensu.ca:80/jae/1999-v14.1/
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Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 14 (1999)
Issue (Month): 1 (Jan.-Feb.)
Pages: 57-67

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Handle: RePEc:jae:japmet:v:14:y:1999:i:1:p:57-67
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  1. Peter C.B. Phillips, 1982. "Exact Small Sample Theory in the Simultaneous Equations Model," Cowles Foundation Discussion Papers 621, Cowles Foundation for Research in Economics, Yale University.
  2. Nelson, Charles R & Startz, Richard, 1990. "The Distribution of the Instrumental Variables Estimator and Its t-Ratio When the Instrument Is a Poor One," The Journal of Business, University of Chicago Press, vol. 63(1), pages S125-40, January.
  3. Joseph G. Altonji & Lewis M. Segal, 1994. "Small Sample Bias in GMM Estimation of Covariance Structures," NBER Technical Working Papers 0156, National Bureau of Economic Research, Inc.
  4. Chamberlain, Gary & Imbens, Guido, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Scholarly Articles 3221489, Harvard University Department of Economics.
  5. Sawa, Takamitsu, 1973. "Almost Unbiased Estimator in Simultaneous Equations Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(1), pages 97-106, February.
  6. 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..
  7. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
  8. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  9. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  10. 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, vol. 13(2), pages 225-35, April.
  11. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  12. Angrist, Joshua D, 1990. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," American Economic Review, American Economic Association, vol. 80(3), pages 313-36, June.
  13. Maddala, G S & Jeong, Jinook, 1992. "On the Exact Small Sample Distribution of the Instrumental Variable Estimator," Econometrica, Econometric Society, vol. 60(1), pages 181-83, January.
  14. Joshua D. Angrist & Alan B. Krueger, 1990. "The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples," NBER Working Papers 3571, National Bureau of Economic Research, Inc.
  15. 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..
  16. Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc.
  17. Stoker, Thomas M., 1996. "Smoothing bias in the measurement of marginal effects," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 49-84.
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