In our preferred specification we include controls for educational outcomes (specifically school sector, degree attained, and major choice) because these covariates could affect earnings and homeownership conditional on tuition. However, it may also be possible that these outcomes are affected by tuition. As such, controlling for them could then introduce a different bias (although we would not expect tuition at public 4-year schools to have much effect on some of the covariates, such as the choice between all other education sectors). We therefore show specifications both with and without these controls (compare cols. 1 and 2 of Table 4). The results are broadly similar regardless of whether education controls are included, so neither source of bias seems to be of much concern. In section IV.F we show that there is little evidence that our measured educational outcomes are affected by movements in tuition.

It is worth keeping in mind that tuition changes could affect homeownership via channels not directly measured by student loan debt. If students (or their parents) have assets they draw down to pay for college, a higher tuition leaves them with less left over for an eventual down payment on a house. This behavior would tend to bias our estimates of the effect of debt away from zero.

Table 5 presents results of regressing homeownership directly on the instrument and usual vectors of controls. Looking across the columns, every additional $1,000 of tuition (charged over a 4-year period) leads to a 0.20.4 percentage point lower homeownership rate for the treatment group at age 26. In contrast, as illustrated in columns 14, tuition does not appear to be negatively correlated with homeownership for the control group.

Stripping away the assumed channel of student loan debt, we can look directly at the reduced-form effect of tuition on homeownership for the treatment and control groups

Stripping away the assumed channel of student loan debt, we can look directly at the reduced-form effect of tuition on homeownership for the treatment and control groups

Note. This table reports probit estimates of the effect of the interaction between tuition and an indicator variable for whether the individual ever attended a public 4-year college before age 23 on homeownership, measured at age 26. Marginal probabilities (defined as the average marginal effect across individuals) are reported. See Table 1 for variable definitions. Sample selection and specification details in cols. 17 are the same as in Table 3. Column 8 is restricted to the population that received some Pell Grant aid before age 23. Tuition is recorded in thousands of 2014 dollars. Standard errors are in parentheses (clustered at the home state level). PSE = postsecondary education.

It is not surprising that the reduced-form effect of tuition is considerably smaller than the estimated effect of debt. Debts do not rise one-for-one with tuition hikes, for several reasons. First, not all students attend school full time for four straight years after high school. On average, individuals in our treatment group were enrolled at a public 4-year university for 570 days in the 4 years following their eighteenth birthday-approximately half of the potential school days, excluding summer and winter breaks. Furthermore, according to the Digest of Education Statistics, approximately 30% of undergraduates at public 4-year universities were attending only part time during the 1990s (the relevant time period for our sample). Second, not all students pay the sticker price of tuition. For example, many students receive scholarships or need-based grants. Based on annual national averages over the period 19972017 (using data from Ma et al. 2017), every $1,000 increase in real posted tuition at public 4-year universities was associated with a $350 increase in the net price paid by their students. For all these reasons, imposing an additional $1,000 of debt on students would likely affect their homeownership rate more than the 0.20.4 percentage points estimated in the reduced-form specification. Third, students may pay for some increases in the remaining net cost of college through methods other than borrowing-for example, work study or reducing consumption-further reducing the pass-through of sticker-price tuition to student loan debt. As we showed in Table 3, about $150 of every $1,000 increase in tuition passes through to students’ debt.