Housing Vouchers in Chicago

To begin, the housing voucher itself costs $8,383 per year (Jacob and Ludwig (2012), Table 1). Jacob and Ludwig (2012) document that receiving a housing voucher leads to a quarterly $328.95 reduction in earnings (s.e. 74.56). Hendren and Sprung-Keyser (2020) estimate that the earnings are taxed at a federal rate of 12.9% (inclusive of EITC), to which Hendren and Sprung-Keyser (2020) add 30% to correspond to the marginal tax rate on earnings imposed by the housing voucher program. This suggests a yearly tax revenue impact from the earnings reduction of $564. In addition to these earnings declines, Jacob and Ludwig (2012) document increases in receipt of public assistance, including TANF, Medicaid, and Food Stamps. Hendren and Sprung-Keyser (2020) multiply these changes by average costs of enrollment in these programs. Summing these changes suggests an increased cost of the voucher of $1,712. Combining, this suggests a yearly fiscal externality of $564 + $1,712 = $2,277. This implies that the net cost of the voucher is $8,383 + $2,277 = $10,660.

Combining, this implies an MVPF of $6,958 / $10,660 = 0.653 (95% CI [0.609, 0.704]).

A number of estimates for the willingness to pay for housing vouchers are summarized in Olsen (2003), ranging from 61% of cost to 92% of cost. The MVPF estimate is qualitatively similar if Hendren and Sprung-Keyser (2020) assume a different valuation. Even if housing vouchers are valued dollar-for-dollar, the MVPF falls below 1 due to the earnings reduction that reduces tax revenue.

The baseline specification in Hendren and Sprung-Keyser (2020) does not include any impacts on children. Jacob et al. (2014) document impacts on test scores, finding small statistically insignificant effects; Hendren and Sprung-Keyser (2020) use these estimates to assess the impact on the MVPF calculation. Jacob et al. (2014) find that a housing voucher leads to an increase of 0.0029SD (s.e. 0.0316) on females aged 0-6, 0.0634SD (s.e. 0.0325) on males aged 0-6, 0.0126SD (s.e. 0.0273) on males aged 6-18, and 0.03 (s.e. 0.0273) on females aged 6-18. To translate this to an earnings impact, Hendren and Sprung-Keyser (2020) take the assumption that a 1SD increase in test scores translates to a 10% increase in earnings from Kline and Walters (2016), who survey the literature on the impacts of test scores on earnings in their table A.IV. This implies a present discounted value impact of a voucher on children of $3,274 over the lifecycle, which corresponds to an impact of $655 on tax revenue. Hendren and Sprung-Keyser (2020) scale these effects by the average number of years on a housing voucher of 11, which implies 1 year of childhood housing vouchers correspond to a $60 increase in tax revenue. This implies a net cost of the voucher of $10,600 instead of the $10,660 measure above. For the willingness to pay, Hendren and Sprung-Keyser (2020) consider two cases: one where the after-tax impacts on children are included in WTP and one where they are not. Without including the child WTP, this implies an MVPF of 0.653 (95% CI of [0.609, 0.704]). Including child WTP implies an MVPF of 0.683 (95% CI of [0.610, 0.769]).

Hendren and Sprung-Keyser (2020) also consider an alternate specification where increases in transfers such as TANF and Food Stamp benefits are incorporated in willingness to pay. If receiving the housing voucher provided information about these other benefits and consequently induced take-up, then it might be appropriate to assume individuals value these new benefits at their resource cost. (By contrast, if these changes in benefits are the result of a household re-optimization in response to the voucher, then the application of the envelope theorem above is more appropriate.) This alternate specification along with the other baseline assumptions produces and MVPF of 0.816 with a 95% CI of [0.807, 0.826].