Bounding the joint distribution of disability and employment with contaminated data

Understanding the relationship between disability and employment is critical and has long been the subject of study. However, estimating this relationship is difficult, particularly with survey data, since both disability and employment status are known to be misreported. Here, we use a partial identification approach to bound the joint distribution of disability and employment status in the presence of contaminated data. Allowing for a modest amount of contamination leads to bounds on the labor market status of the disabled that are not overly informative given the relative size of the disabled population. Thus, absent further assumptions, even a modest amount of contamination creates much uncertainty about the employment gap between the non-disabled and disabled. However, additional assumptions considered are shown to have some identifying power. For example, under our most stringent assumptions, we find that the employment gap is at least 15.2% before the Great Recession and 22.0% afterwards.