Aid to Families with Dependent Children (AFDC) provided cash transfers to qualified families with sufficiently low income. These benefits traditionally come with term limits on the length of time a family can receive benefits. Grogger (2003) estimates the impact of changes in these term limits.
Grogger (2003) uses a difference in differences specification that exploits the fact that those without children under age 18 are not eligible for AFDC benefits. He studies the differences in welfare use and labor income for women with and without kids <= 13 years old who are subject to the 5-year time limit.
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To turn this into an MVPF, Hendren and Sprung-Keyser (2020) consider a thought experiment of relaxing term limits. There’s a mechanical cost savings for those who were on welfare longer than 5 years. In 1995, 34.6% of beneficiaries had been on welfare longer than 5 years (Pavetti, 1995). Absent any other changes, the 6.5% reduction in utilization which Grogger (2003) estimates implies a utilization rate of 28.1% without term limits. This 28.1%, multiplied by the average yearly welfare AFDC receipt, corresponds to the mechanical benefits and hence WTP for such a relaxation of term limits (= $1,496.13). The net cost to the government is then the total utilization incorporating the behavioral response, 34.6%, multiplied by the average yearly welfare AFDC receipt (= $1,839.33). Combining, this suggests an MVPF of term limits of $1,496.13 / $1,839.33 = 0.81, where the average AFDC yearly receipts in the numerator and denominator cancel each other out. This suggests the government imposes a welfare loss of $0.81 for every $1 of revenue it obtains from those on welfare beyond 5 years.
MVPF = 0.8
Grogger, Jeffrey (2003). “The Effects of Time Limits, the EITC, and Other Policy Changes on Welfare Use, Work, and Income among Female-Headed Families.” The Review of Economics and Statistics, 85(2), 394-408. DOI: http://www.jstor.org/stable/3211588
Hendren, Nathaniel and Ben Sprung-Keyser (2020). “A Unified Welfare Analysis of Government Policies.” The Quarterly Journal of Economics, 135(3): 1209–1318. DOI: https://doi.org/10.1093/qje/qjaa006
Pavetti, LaDonna (1995). “Who Is Affected by Time Limits?” Welfare Reform: An Analysis of the Issues, 31-34.