From Andreas Mueller, Jesse Rotstein, and Till von Wachter:
Disability Insurance (DI) applications are awards are countercyclical. One potential explanation is that unemployed individuals who exhaust their Unemployment Insurance (UI) benefits use DI as a form of extended benefits. We exploit the haphazard pattern of UI benefit extensions in the Great Recession to identify the effect of UI exhaustion on DI application, using both aggregate data at the state-month and state-week levels and micro data on unemployed individuals in the CPS. We find no indication that expiration of UI benefits causes DI applications. Our estimates are sufficiently precise to rule out effects of meaningful magnitude.