C, we run another placebo test to directly check this concern

Despite these data limitations, when we ran estimates using total nonmortgage debt (measured at age 23 or 24, with the estimation sample restricted to the population for whom these data were available) as the endogenous variable, we get similar results

of the effect of the marginal dollar of debt on homeownership. 16 The full tables of results for our various specifications are presented in the appendix. The first stage is somewhat stronger, with a $1,000 increase in tuition causing an additional $200 to $350 dollars in total debt, as opposed to a range of about $100 to $200 in Table 3. In the second stage, estimates are somewhat attenuated relative to those in Table 4. Using the specification from column 6, we estimate that a $1,000 increase in total debt reduces the probability of homeownership by 1.2 percentage points at age 26, while this figure was 1.75 percentage points for our main results using federal student loan debt records.

E. Endogeneity of Tuition

Our identifying assumption that the instrument is exogenous to unobserved determinants of homeownership is not directly testable. We can, however, test for some plausible sources of endogeneity. For example, in-state tuition rates may be correlated with local housing and labor market conditions, which in turn affect homeownership rates. To see that such omitted variables are unlikely to bias our estimates, compare the estimates across columns 35 in Table 4. Column 4 differs from column 3 by the inclusion of yearly home statelevel economic controls: namely, the unemployment rate, log of average weekly wages, and the CoreLogic house price index, all measured in the subject’s home state at the age of 22. The estimated coefficient on student loan debt is stable across columns 3 payday loans in Oklahoma and 4, suggesting that these local economic conditions are not driving the results. Furthermore, column 5 includes home statebycohort fixed effects that should absorb the effects of all broad economic conditions at the state level. Again, the coefficient of interest is quite stable to this stricter set of controls, suggesting that our findings are not substantially biased by market-level factors.

Further evidence that tuition affects homeownership only through the student loan channel is provided by the absence of any clear effect of tuition on the control group

The estimated coefficient on tuition, which measures the partial effect on the control group’s homeownership rate, is small and changes sign across specifications. This can be seen by comparing columns 14 of Table 5. Since control group individuals do not pay tuition at public 4-year universities, their homeownership rates should not be correlated with that tuition except through omitted-variable bias. We find no evidence that such omitted variables are affecting the correlations between tuition and homeownership. This is essentially a placebo test, validating the contention that we are picking up an effect of tuition rather than the influence of some unobservable factor correlated with it.

We may still be concerned that the correlation between tuition and homeownership among the treatment group is being driven by factors specific to public 4-year universities, such as school quality. As we outlined in section IV. The test is motivated by Belley, Frenette, and Lochner (2014), whose findings suggest that the net tuition paid by lower-income students is less strongly tied to the sticker price due to the availability of need-based grants. While we do not observe family income in our data, we do observe Pell Grant receipt. We split the sample into those individuals who did and did not receive any Pell Grant aid before they turned 23. The former group received need-based aid, so their student debt burden should be less influenced by variation in the average in-state charged tuition. We have shown above that tuition is strongly relevant in explaining student loan debts among the treatment group in the non-Pell population (see Table 3). In contrast, the estimated first stage is smaller by half and not statistically significant for the population who received Pell Grant aid (results not shown, available on request).