TY  - JOUR
AU  - Angrist,Joshua D.
TI  - Conditioning on the Probability of Selection to Control Selection Bias
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 181
PY  - 1995
Y2  - June 1995
UR  - http://www.nber.org/papers/t0181
L1  - http://www.nber.org/papers/t0181.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
AB  - Problems of sample selection arise in the analysis of both experimental and non-experimental data.  In clinical trials to evaluate the impact of an intervention on health and mortality, treatment assignment is typically nonrandom in a sample of survivors even if the original assignment is random.  Similarly, randomized training interventions like National Supported Work (NSW) are not necessarily randomly assigned in the sample of working men.  A non- experimental version of this problem involves the use of instrumental variables (IV) to estimate behavioral relationships.  A sample selection rule that is related to the instruments can induce correlation between the instruments and unobserved outcomes, possibly invalidating the use of conventional IV techniques in the selected sample.  This paper shows that conditioning on the probability of selection given the instruments can provide a solution to the selection problem as long as the relationship between instruments and selection status satisfies a simple monotonicity condition.  A latent index structure is not required for this result, which is motivated as an extension of earlier work on the propensity score.  The conditioning approach to selection problems is illustrated using instrumental variables techniques to estimate the returns to schooling in a sample with positive earnings.
ER  -