Conditioning on the Probability of Selection to Control Selection Bias

33 Pages Posted: 1 Aug 2000 Last revised: 26 Sep 2010

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

Date Written: June 1995

Abstract

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.

Suggested Citation

Angrist, Joshua, Conditioning on the Probability of Selection to Control Selection Bias (June 1995). NBER Working Paper No. t0181. Available at SSRN: https://ssrn.com/abstract=225091

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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