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Jackknife Instrumental Variables Estimation

  • Joshua D. Angrist
  • Guido W. Imbens
  • Alan Krueger

Two-stage-least-squares (2SLS) estimates are biased towards 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 to those of 2SLS and similar to LIML when there are many instruments. Moreover, the jackknife estimators appear to be less sensitive than LIML to deviations from the linear reduced form used in classical simultaneous equations models.

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File URL: http://www.nber.org/papers/t0172.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0172.

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Date of creation: Feb 1995
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Publication status: published as Journal of Applied Econometrics, Vol. 14, no. 1 (January-February 1999): 57-67.
Handle: RePEc:nbr:nberte:0172
Note: LS
Contact details of provider: Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
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  1. Gary Chamberlain & Guido W. Imbens, 1996. "Hierarchical Bayes Models with Many Instrumental Variables," Harvard Institute of Economic Research Working Papers 1781, Harvard - Institute of Economic Research.
  2. Altonji, Joseph G & Segal, Lewis M, 1996. "Small-Sample Bias in GMM Estimation of Covariance Structures," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 353-66, July.
  3. 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.
  4. 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.
  5. Joshua Angrist & Alan Krueger, 1990. "Does Compulsory School Attendance Affect Schooling and Earnings?," Working Papers 653, Princeton University, Department of Economics, Industrial Relations Section..
  6. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  7. Buse, A, 1992. "The Bias of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 60(1), pages 173-80, January.
  8. Joshua Angrist & Alan Krueger, 1993. "Split Sample Instrumental Variables," Working Papers 699, Princeton University, Department of Economics, Industrial Relations Section..
  9. 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.
  10. Joshua Angrist, 1989. "Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records," Working Papers 631, Princeton University, Department of Economics, Industrial Relations Section..
  11. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  12. 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.
  13. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May.
  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. Stoker, Thomas M., 1996. "Smoothing bias in the measurement of marginal effects," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 49-84.
  16. 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..
  17. 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.
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