TY  - JOUR
AU  - Angrist,Joshua D.
AU  - Krueger,Alan B.
TI  - Split Sample Instrumental Variables
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 150
PY  - 1995
Y2  - June 1995
UR  - http://www.nber.org/papers/t0150
L1  - http://www.nber.org/papers/t0150.pdf
N1  - Author contact info:
Joshua Angrist
Department of Economics
MIT, E52-353
50 Memorial Drive
Cambridge, MA  02142-1347
Tel: 617/253-8909
Fax: 617/253-1330
E-Mail: angrist@mit.edu

Alan B. Krueger
Industrial Relations Section
Firestone Library
Princeton University
Princeton, NJ 08544
Tel: 609/258-4046
Fax: 609/258-2907
E-Mail: akrueger@princeton.edu
AB  - 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.
ER  -