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.