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Split Sample Instrumental Variables

Author

Listed:
  • Joshua D. Angrist
  • Alan B. Krueger

Abstract

Instrumental Variables (IV) estimates tend to be biased in the same direction as Ordinary Least Squares (OLS) in finite samples if the instruments are weak. To address this problem we propose a new IV estimator which we call Split Sample Instrumental Variables (SSIV). SSIV works as follows: we randomly split the sample in half, and use one half of the sample to estimate parameters of the first-stage equation. We then use these estimated first-stage parameters to construct fitted values and second-stage parameter estimates using data from the other half sample. SSIV is biased toward zero, rather than toward the plim of the OLS estimate. However, an unbiased estimate of the attenuation bias of SSIV can be calculated. We us this estimate of the attenutation bias to derive an estimator that is asymptotically unbiased as the number of instruments tends to infinity, holding the number of observations per instrument fixed. We label this new estimator Unbiased Split Sample Instrumental Variables (USSIV). We apply SSIV and USSIV to the data used by Angrist and Krueger (1991) to estimate the payoff to education.

Suggested Citation

  • Joshua D. Angrist & Alan B. Krueger, 1995. "Split Sample Instrumental Variables," NBER Technical Working Papers 0150, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0150
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    References listed on IDEAS

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    1. 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 353-366, July.
    2. 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.
    3. 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 125-140, January.
    4. Sargan, J D, 1974. "The Validity of Nagar's Expansion for the Moments of Econometric Estimators," Econometrica, Econometric Society, vol. 42(1), pages 169-176, January.
    5. 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.
    6. 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.
    7. Bekker, P.A., 1992. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Papers 512, Groningen State, Institute of Economic Research-.
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    More about this item

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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