02577cam a22002537 4500001000600000003000500006005001700011008004100028100002300069245012000092260006600212490005100278500001500329520136000344530006101704538007201765538003601837690014901873690010002022710004202122830008602164856003702250856003602287t0181NBER20160824204244.0160824s1995 mau||||fs|||| 000 0 eng d1 aAngrist, Joshua D.10aConditioning on the Probability of Selection to Control Selection Biash[electronic resource] /cJoshua D. Angrist. aCambridge, Mass.bNational Bureau of Economic Researchc1995.1 aNBER technical working paper seriesvno. t0181 aJune 1995.3 aProblems 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC24 - Truncated and Censored Models • Switching Regression Models • Threshold Regression Models2Journal of Economic Literature class. 7aJ31 - Wage Level and Structure • Wage Differentials2Journal of Economic Literature class.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0181.4 uhttp://www.nber.org/papers/t018141uhttp://dx.doi.org/10.3386/t0181