Turner (2011) uses difference-in-difference design to estimate the impact of the Hope Tax Credit on college attendance and persistence using data from the Census Bureau’s Survey of Income and Program Participation (SIPP). Turner (2011) estimates the marginal impact of tax credits on college attendance to be 0.00235 for first-year students and a 0.00210 increase in student persistence in the second year (that is, the effect of enrollment in a second-year of college conditional on having completed the first year). Hendren and Sprung-Keyser (2020) use these estimates to project the impact of the policy on lifetime earnings and tax revenue. They utilize estimates from Zimmerman (2014) on the impact of college attendance on earnings and assume that the returns to college are constant in percentage terms over the lifecycle.
MVPF = 12.6
Hendren and Sprung-Keyser (2020) calculate net costs beginning with the direct cost of the tax credit. Turner (2011) estimates the average subsidy amongst the eligible population to be $1,104. From this, Hendren and Sprung-Keyser (2020) calculate the direct program cost to be $431.05, which is a composition of the mechanical effect of those attending college in either the first or second year and the behavioral response of credits claimed by those induced into attending college (first year estimate) or persisting (second year estimate). Hendren and Sprung-Keyser (2020) then include two additional fiscal costs. First, Hendren and Sprung-Keyser (2020) estimate the cost of increased educational attainment net of private tuition by following the approach of Zimmerman (2014) in calculating government costs and net tuition per full-time enrollee based on data from the Delta Cost Project in 1998. This yields an enrollment cost of $288.30. Second, Hendren and Sprung-Keyser (2020) account for the changes in taxes paid and transfers received based on the earnings gain calculated in the willingness to pay section. This gives a $542.20 increase in government revenue. Adding that value to Hendren and Sprung-Keyser’s (2020) other costs components, Hendren and Sprung-Keyser (2020) get a total net cost of $180.53.
To calculate the willingness to pay, Hendren and Sprung-Keyser (2020) transform the effect of college attendance into additional years of schooling by assuming that individuals who enrolled in the second year of college (conditional on completing the first) complete an additional 1.5 years of college education on average, and add this to the single-year effect of increased enrollment in the first year. Hendren and Sprung-Keyser (2020) then use estimates from Zimmerman (2014) to estimate the impact on lifetime earnings. Hendren and Sprung-Keyser (2020) use the results from Zimmerman (2014) to estimate a decline in earnings in years 1-7 from college enrollment and then an increase in earnings over the rest of the lifecycle. Zimmerman (2014) observes earnings gains in years 8-14 and Hendren and Sprung-Keyser (2020) project those gains over the rest of the lifecycle. Hendren and Sprung-Keyser (2020) calculate post-tax and post-transfer earnings by assuming a tax and transfer rate of 20.0% during the bulk of the lifecycle. This figure comes from their calculation of the effective marginal tax rates based on estimates from the Congressional Budget Office. Hendren and Sprung-Keyser (2020) subtract out the individual contribution to tuition (including tax credits), which is estimated by the average tuition net of aid and tax credit subsidy using data from the Delta Cost Project for 2011. The projected earnings gains provide the willingness to pay for all individuals induced to change their behavior and receive more education as a result of the change in tax credits (i.e., the estimated impact of attendance). Hendren and Sprung-Keyser (2020) calculate total willingness to pay by summing those earnings gains with the simple value of the transfer for the fraction of individuals not induced to change their behavior. The resulting WTP is $2,271.
Combining these estimates, Hendren and Sprung-Keyser (2020) get an MVPF of 12.58. To obtain the confidence intervals, Hendren and Sprung-Keyser (2020) bootstrap the enrollment, earning and tax revenue outcomes. This leads to a fairly wide 95% confidence interval of [-24.72,\infty].
As an alternative specification, Hendren and Sprung-Keyser (2020) consider how the MVPF changes if one assumes that there is partial take-up of the tax credits amongst the eligible population, estimated at a lower bound of 63% by Maag and Rohaly (2007). This leads to an MVPF estimate of \infty (95% CI: [-52.83,\infty]).
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
Maag, Elaine and Jeffrey Rohaly (2007). “Who Benefits from the Hope and Lifetime Learning Credit?” Tax Policy Center, Urban Institute and Brookings Institution, Washington, DC.
Turner, Nicholas (2011). “The Effect of Tax-Based Federal Student Aid on College Enrollment.” National Tax Journal, 64(3), 839-61. DOI: https://dx.doi.org/10.17310/ntj.2011.3.04
Zimmerman, Seth D. (2014). “The Returns to College Admission for Academically Marginal Students.” Journal of Labor Economics, 32(4), 711-754. DOI: https://doi.org/10.1086/676661