# Using the MVPF

## Real World MVPF Calculation

In the introduction, we walked through a stylized example of an MVPF calculation for a college scholarship program. Now we apply that same logic to a real-world example to see how the MVPF is calculated. This explanation is designed to give you a sense of the way that a researcher might calculate the MVPF of a policy they’ve studied.

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We illustrate the MVPF construction for the admissions expansions at Florida International University (FIU), as studied by Zimmerman (2014). This analysis comes from Hendren and Sprung-Keyser (2020).

The cost from increased enrollment of admitting an additional student to FIU is \$11,403 per student admitted.

This data comes from the Delta Cost Project, a database constructed with information from the National Center for Education Statistics.

Students pay tuition that reduces the cost to the government by \$3,184.

Some students who enroll at FIU would have otherwise enrolled in community college. The reduced spending on community college by the government reduces the net cost of the policy by \$5,601.

While students are in school, they have lower earnings. These lower earnings reduce tax revenue by \$2,035, which increases the net cost of the policy to the government.

This calculation is based on the observed decline in earnings measured in Zimmerman 2014 and a calculation of the marginal tax and transfer rate based on estimates from the Congressional Budget Office.

After students graduate, they tend to obtain jobs with higher earnings trajectories. Between ages 26-33, we estimate that these higher earnings increase tax revenue by \$7,274.

By the time the beneficiaries are 33 years old, they have fully repaid the initial cost and returned \$2,621 back to the government.

The graph here shows how the net cost to the government varies with the age of the beneficiaries.

By the time the beneficiaries are 33 years old, they have paid back the initial cost to the government.

We do not observe incomes beyond age 33, but we can forecast those potential incomes by assuming that income profiles are proportional to the cross-sectional age distribution observed in the 2015 ACS, along with an assumption of 0.5% wage growth.

The graph shows the mean incomes by age for the 2015 ACS.

We first match the earnings of those not admitted to FIU to this pattern by noting it equals 97% of mean earnings at ages 26-33.

We assume these earnings for those not admitted remain at a constant 97% of mean ACS income over the life cycle.

Next, we incorporate the observed earnings of those admitted to FIU by adding the estimated impacts.

We then assume the earnings profile of those admitted to FIU follows a constant percentage of mean ACS earnings over the lifecycle.

Applying a tax and transfer rate of 18.9% (estimated using data from the Congressional Budget Office) suggests the original \$11,400 investment is fully repaid and actually returns an additional \$24,400 back to the government.

Because the policy “paid for itself”, the MVPF is infinite regardless of how much individuals are willing to pay (WTP) for being admitted to FIU.

For completeness, we walk through our construction of WTP here.

Our baseline WTP measure is given by the additional amount of additional money the beneficiaries have as a result of the policy.

Individuals admitted to FIU on average pay an additional \$2,900 in tuition costs.

This quantity is subtracted from their willingness to pay.

Admitted individuals have \$8,900 in reduced net earnings between the ages of 19-25. This is calculated by their reduction in pre-tax earnings, net of any tax payments owed on those earnings.

Admitted individuals have \$29,100 increased net earnings between the ages of 26-33. This is again calculated by taking the increase in earnings amongst the new enrollees and calculating their gains in post-tax income.

Forecasting to age 65, admitted individuals have \$95,500 in increased net earnings after taxes and transfers.

Summing, this implies an impact on net income of \$112,800 which we use as our measure of WTP. As noted above, the MVPF is infinite regardless of the measure of WTP.