Casey Mulligan would very much like you to believe it does.
“cutting unemployment insurance would increase employment, as it would end payments for people who fail to find work and would reduce the cushion provided after layoffs.”
Here’s one pretty well-done data point (several, actually) suggesting that he’s wrong:
In theory, greater employment protection should dampen the effects of output movements on employment and therefore reduce the Okun coefficient. In Figure 10 (right panel), we test this idea by plotting the coefficient against the OECD’s overall EPL index (averaged over 1985-2008, the period for which it is available). The relationship has the wrong sign, and it is statistically insignificant.
 For New Zealand, the EPL index is available over 1990-2008. We also find no relationship between the Okun coefficient and the various components of the EPL index.
Cross-posted at Asymptosis.