Split Sample Instrumental Variables

37 Pages Posted: 10 Jul 2000

See all articles by Joshua D. Angrist

Joshua D. Angrist

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

Alan B. Krueger

Princeton University - Industrial Relations Section; National Bureau of Economic Research (NBER); IZA Institute of Labor Economics

Date Written: June 1995

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

Angrist, Joshua and Krueger, Alan B., Split Sample Instrumental Variables (June 1995). NBER Working Paper No. t0150. Available at SSRN: https://ssrn.com/abstract=225130

Joshua Angrist (Contact Author)

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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IZA Institute of Labor Economics

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Alan B. Krueger

Princeton University - Industrial Relations Section ( email )

Princeton, NJ 08544-2098
United States
609-258-4046 (Phone)
609-258-2907 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

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