Title

Split Sample Instrumental Variables

Author(s)

Joshua D. Angrist Joshua Angrist (Hebrew University and NBER)

Alan B. Krueger Alan Krueger (Princeton University and NBER)

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 use this estimate of the attenuation 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.

Creation Date

1993-10

Section URL ID

IRS

Paper Number

320

URL

https://dataspace.princeton.edu/bitstream/88435/dsp01tq57nr01r/1/320.pdf

File Function

Jel

C12

Keyword(s)

instrumental variables, split sample instrumental variables, compulsory schooling

Suppress

false

Series

1