Alternative Methods of Statistical Inference

Table A.7 shows that the conclusions from inference on sticker price impacts are not sensitive to alternative error structures. Column 1 presents 90 percent condence intervals for the treatment eect for the preferred Within-Owner DID, column 2 presents estimates for an unweighted Within-Owner DID estimated over all states, and column 3 presents estimated for the preferred DDD specication. State-level clustering is intended to allow for arbitrary correlation between observations in the same state. Clustering within state-year cells pro-vides a more restrictive error structure that allows for correlation between observations in

51There may be an income eect from a reduction in average nancing costs that leads to increases on spending for normal goods, but it seems likely that this eect is of second-order importance relative to any price eects (including nancing costs).

the same state and year. Clustering within state-homeownership cells allows for correlation between homeowners in the same state and between renters in the same state (but does not allow correlation between homeowners and renters in the same state). The conclusions are unchanged across alternative error structures, and state clustering yields the most conser-vative condence intervals. Because clustered standard errors converge to their true values as the number of clusters increases, robustness of the conclusions to alternative error struc-tures (with greater numbers of clusters) mitigates any concerns that the conclusions may be impacted by small-sample bias in the standard errors.

While clustering is intended to allow for inference in the face of correlated errors, a more general concern is whether inference is based on the appropriate small-sample distribution.

Conley and Taber (2009) illustrate that for cases such as this where the policy change is restricted to a single cluster, the dierence-in-dierence estimator itself is inconsistent and thus subject to small-sample bias. They key idea behind their approach is that even though a consistent estimator of the treatment eect is unavailable, the larger number of control states can be used to estimate the distribution of the small-sample bias term (under the assumption of a common error distribution for treated and control states). The null hypothesis of no eect can then be rejected if the estimated treatment eect is a suciently unlikely event according to the empirical distribution derived from control states. This approach can provide an additional check on the robustness of the conclusions to alternative inference methods, by trading o assumptions about the appropriate small sample error distribution with the assumption of a common error distribution for treated and control states. Column 1 of Table A.7 shows that the 90% Conley-Taber condence interval is imprecisely estimated and does in fact include zero (though the one-tailed null hypothesis that the treatment eect is equal to 0 can be rejected with 90% condence). Because of small sample sizes within many states, however, this approach is ill-suited for the present application because it makes no adjustment for imprecisely estimated control states.

Figure A.1: Trends in Owner-Renter Income Inequality

Source: Author's calculations using data from the CPS March Supplements.

Figure A.2: Distribution of College Selectivity By Homeownership Status (Texas Colleges)

Source: Author's calculations using NPSAS data merged to the Barron's Selectivity Index.

Figure A.3: Tuition Trends

Source: Author's calculations using IPEDS data.

Figure A.4: Trends in Public College Funding Levels

Source: Author's calculations using IPEDS data.

Figure A.5: Owner-Renter Spending Gaps by Spending Type

Source: Author's calculations using Consumer Expenditure Survey data.

Table A.1: The Eect of HELOC-Eligibility on College Enrollment (All States)

Source: Author's calculations using the CPS analysis sample of 18-22 year olds, excluding the top 1% of the national income distribution.

Notes: Dependent variable is a dummy variable for college enrollment or any degree completion. All speci-cations include controls for the log of household income, state mortgage rates, the log of state housing prices and the 3-year change in state housing prices. Robust standard errors, clustered at the state level, are in parentheses. Observations are weighted by the CPS person-level supplement weight.

Table A.2: The Eect of HELOC-Eligibility on High School Enrollment (1) DDD (2)

Source: Author's calculations using the CPS analysis sample of 17 year olds.

Notes: ***Indicates signicance at the 1% level, **5%, and *10%. Dependent variable is a dummy for HS enrollment among 16 and 17 year olds. Controls include the log of household income, state mortgage rates, the log of state housing prices and the 3-year change in state housing prices. Robust standard errors, clustered at the state level, are in parentheses. Observations are weighted by the CPS person-level supplement weight.

Table A.3: The Eect of HELOC-Eligibility on College Sticker/Net Price (Levels)

DID: Within Owner DID: Within Renter DDD

Sticker Net Sticker Net Sticker Net

N 21,550 21,550 7,210 7,210 28,750 28,750

R-squared 0.232 0.189 0.163 0.119 0.249 0.199

Source: Author's calculations using the NPSAS analysis sample of aid applicants under the age of 26.

Notes: ***Indicates signicance at the 1% level, **5%, and *10%. The dependent variable is sticker price or net price. All specications include controls for the log of household income, state mortgage rates, the log of state housing prices and the 3-year change in state housing prices. Robust standard errors, clustered at the state level, are in parentheses. Observations are weighted by the CPS person-level supplement weight.

Table A.4: The Eect of HELOC-Eligibility on College Sticker/Net Price (All States)

DID: Within Owner DID: Within Renter DDD

Sticker Net Sticker Net Sticker Net

N 62,490 62,490 22,970 22,970 85,460 85,460

R-squared 0.291 0.169 0.241 0.217 0.310 0.207

Source: Author's calculations using the NPSAS analysis sample of aid applicants under the age of 26.

Notes: ***Indicates signicance at the 1% level, **5%, and *10%. The dependent variable is the log sticker price or net price. All specications include controls for the log of household income, state mortgage rates, the

Table A.5: The Eect of HELOC-Eligibility on Flagship Attendance

Source: Author's calculations using the NPSAS analysis sample of Texas aid applicants under the age of 26.

Notes: ***Indicates signicance at the 1% level, **5%, and *10%. Estimates are from the Within-Texas specication with controls for each class year. Robust standard errors are in parentheses. Observations are weighted by the NPSAS study weight, normalized to sum to one in each study wave.

Table A.6: The Eect of HELOC-Eligibility on Renter Attendance Intensity DID: Within Renters

Source: Author's calculations using the NPSAS analysis sample of aid applicants under the age of 26.

Notes: ***Indicates signicance at the 1% level, **5%, and *10%. Dependent variable is a dummy variable for exclusively attending college full-time. All specications include controls for the log of household income, state mortgage rates, the log of state housing prices and the 3-year change in state housing prices. Robust standard errors, clustered at the state level, are in parentheses. Observations are weighted by the CPS person-level supplement weight.

Table A.7: Comparing Alternative Inference ProceduresSticker Price

DID: Within Owner DDD

Reduced States All States Reduced States

(1) (2) (3)

Coecient estimate 0.141 0.227 0.147

Survey weights X X

90% condence interval

Cluster by state (0.034, 0.248) (0.140, 0.315) (0.026, 0.268) Cluster by state-year (0.067, 0.215) (0.165, 0.290) (0.065, 0.229)

Cluster by state-own   (0.048, 0.246)

Conley-Taber  (-0.083, 0.533) 

N 21,550 62,490 28,750

Source: Author's calculations using the NPSAS analysis sample of aid applicants under the age of 26.

Notes: For all columns, the dependent variable is the log of college sticker price. Column 1 presents estimates from the preferred Within-Owner specication over all states with dummies for class year, the standard set of controls, and xed eects for state and cohort. Column 2 relies on the same specication as Column 1 but is estimated over all states and without survey weights. Column 3 presents estimates from the preferred DDD specication over the reduced set of control states with dummies for class year, the standard set of controls, and xed eects for state-time, state-cohort, own-cohort and state-own cells. Conley-Taber condence intervals are estimated using publicly available Stata code used in Conley and Taber (2009) with 5% tails of the 90% condence interval computed from an empirical error distribution weighted by the number of observations within each control state. Observations are weighted by the NPSAS study weight (except for column 2), normalized to sum to one in each study wave.