Inferring Disability Status from Corrupt Data

We investigate what can be learned about the prevalence of work disability using self-reported assessments of work capacity. Although health status is widely recognized as a crucial determinant of labor supply behavior and participation in public transfer programs, there is a long-standing debate about the reliability of self-reported indicators. Anderson and Burkhauser (1985), in fact, labeled the appropriate use of health controls “the major unsettled issue in the empirical literature on the labor supply of older workers,” and the debate has only grown stronger over time. Rather than focus on assumptions required to obtain point identi…cation, we take a step back to evaluate what can be inferred about disability rates under a variety of assumptions that are weaker but arguably more credible than those imposed in the existing literature. Extending the work on corrupt samples developed by Horowitz and Manski (1995), we develop a set of nonparametric bounds that, in the most basic setting, require only prior information restricting the fraction of persons who might misreport disability. These bounds inform the ongoing debate by e¤ectively constraining the range of uncertainty regarding the e¤ects of inaccurate reporting on inferences. The results clearly show that the strength of the conclusions one can draw depend directly on the strength of the assumptions one is willing to impose. Under minimal assumptions, the bounds are nearly uninformative. Tighter bounds can be obtained with additional assumptions. Under the assumption that the true disability rate is nondecreasing with age, our results imply that conventional participation models which presume valid self-reports may be misspeci…ed.