How does insurance eligibility affect labor supply?

There is a new paper by Craig Garthwaite, Tal Gross, and Matthew J. Notowidigdo, the abstract is this:

We study the effect of public health insurance eligibility on labor supply by exploiting the largest public health insurance disenrollment in the history of the United States. In 2005, approximately 170,000 Tennessee residents abruptly lost public health insurance coverage. Using both across- and within-state variation in exposure to the disenrollment, we estimate large increases in labor supply, primarily along the extensive margin. The increased employment is concentrated among individuals working at least 20 hours per week and receiving private, employer-provided health insurance. We explore the dynamic effects of the disenrollment and find an immediate increase in job search behavior and a steady rise in both employment and health insurance coverage following the disenrollment. Our results suggest a significant degree of “employment lock” – workers employed primarily in order to secure private health insurance coverage.  The results also suggest that the Affordable Care Act – which similarly affects adults not traditionally eligible for public health insurance – may cause large reductions in the labor supply of low-income adults.

The NBER version of this piece is here, ungated here.  Craig writes to me:

Applying our estimates to the ACA, this would mean a reduction in labor supply of about 0.3 to 0.6 percentage points (or about 500-900K people) just from this feature.

Is this a feature or a bug?  Reihan adds comment.