My last post discussed some implications of length-biased sampling for penal reform. In a follow-on post, I consider some implications of the same mathematics in the 1996 welfare reform. The figure to the right shows the probability that AFDC recipients would leave on or before a given year. The top line represents the distribution among all new entrants to the program. The bottom line performs the same calculations for the standing population of welfare recipients at a particular point in time.

As you can see, the two populations are really quite different. About 21 percent of new entrants into the welfare system are predicted to remain on the program more than five years—for most people, the identified limit on the receipt of federally-financed TANF aid. Within the standing population of current recipients, the comparable figure is 59 percent. The 20% requirement, perhaps reasonable for an entering cohort, is therefore quite punishing when applied to an existing population that inherently includes a much larger proportion of hard cases. If you haven’t seen Mary Jo Bane and David Ellwood’s work on welfare dynamics, have a peek here.