Patricia M. Anderson (Department of Economics, Dartmouth College) & Bruce D. Meyer (Harris School of Public Policy, University of Chicago) have published Unemployment Insurance Tax Burdens and Benefits: Funding Family Leave and Reforming the Payroll Tax, 59 Nat’l Tax J. 77 (2006).  Here is the abstract:

We examine the distributional consequences of the Unemployment Insurance (UI) payroll tax. Applying the ability–to–pay principle of equity, the UI payroll tax is quite regressive, while applying the benefits principle makes the UI program look quite good. We then simulate a revenue–neutral increase of the UI tax base to the OASDI tax base level, which appears equity–enhancing under the ability–to–pay principle, but has mixed effects under the benefits principle. Finally, providing family leave within the UI system would maintain the regressivity that violates the ability–to–pay principle of equity, but would agree much better with the benefits principle.