A Random Effects Panel Probit Model for Co-residence

In this section, I describe the random effects panel probit model for moving back home and report the regression estimates.

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I model the relationship between co-residence outcome and student loan debt with a random effects panel probit model.

𝐻_𝑖𝑡∗ = 𝑋𝑖𝑡𝛽 + 𝛾𝐸𝑖 + 𝛼𝑖 + 𝜀𝑖𝑡 𝑖 = 1,2, … , 𝑁; 𝑡 = 1,2, … , 𝑇 𝑤𝑖𝑡ℎ 𝐻_𝑖𝑡 = 1_{𝐻 𝑖𝑡∗>0} 𝛼_𝑖~𝑖. 𝑖. 𝑑. 𝑁(0, 𝜎_𝛼2_{); 𝜀} 𝑖𝑡~𝑖. 𝑖. 𝑑. 𝑁(0, 𝜎𝜀2) 𝜀_𝑖𝑡 𝑎𝑛𝑑 𝛼_𝑖 𝑎𝑟𝑒 𝑎𝑠𝑠𝑢𝑚𝑒𝑑 𝑡𝑜 𝑏𝑒 𝑟𝑎𝑛𝑑𝑜𝑚 𝛼𝑖 𝑎𝑛𝑑 𝜀𝑖𝑡 𝑎𝑟𝑒 𝑚𝑢𝑡𝑢𝑎𝑙𝑙𝑦 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑎𝑠 𝑤𝑒𝑙𝑙 𝑎𝑠 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑜𝑓 𝑋𝑖𝑡 𝑎𝑛𝑑 𝐸𝑖

where 𝐻_𝑖𝑡∗ _{is latent co-residence status, 𝐻}

𝑖𝑡 is the observed co-residence status which

indicates whether the individual is living at home or not in a given year. 𝐸𝑖 includes the

amount of student loan debt at the time of graduation, a measure of the parents’ income, an indicator for female, an indicator for Black, an indicator for Hispanic, an indicator of a master’s degree, indicator of a Ph.D. degree, and an indicator of professional degree. 𝑋_𝑖𝑡includes a measure of annual housing price in the MSA where the youth lives, annual marital status, annual income, full-employment status, and annual parental transfer. I include year dummies to control for macroeconomic factors. Considering the facts that younger adults are more likely to be living with parents than older ones and that younger adults are more likely to have attended school in more recent years when student loan burdens have increased, I also control for youths’ age at graduation. In the theoretical model, a youth moves back home to live with parents when his or her utility of living

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apart is less than the utility received when living in the parental home. Youths will differ in their tastes concerning living with parents. The term 𝜀_𝑖𝑡 from the regression model catches unobserved characteristics such as the youths’ tastes. Note that it is possible that a youth who has a higher tastes for living with parents decided in advance to move in with parents after graduation and therefore took more loans during college. However, I primarily focus on college graduates’ transition in parental co-residence after a period of independent living. I will interpret my results as reflective of the effect of student loan debt on parent-youth co-residence. It is outside the scope of this study to explain the mechanisms through which a youth becomes indebted. When we assume youths’ unobserved characteristics independent of variables in 𝑋_𝑖𝑡 and 𝐸_𝑖, 𝛽 and 𝛾 can be estimated consistently.

The estimation results of three different specifications of the model are reported in Tables 4, 5 and 6 respectively. Table 4 reports the results from the model with annual income controlled. Table 5 reports the results from the model with annual full- employment status controlled. Table 6 reports the results from the model with both of annual income and annual full-employment status controlled.

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Variable Coefficient

(Marginal Effect)

Standard Error

Amount of Student Loans/100 0.002* 0.001

Female 0.06 0.10 Black 0.42** 0.13 Hispanic 0.25* 0.11 Master’s degree -0.43** 0.19 Ph.D. degree -13.52 354.50 Professional degree -0.59 0.39 Housing Price/100 0.005** 0.002

Annual Marital Status -0.20* 0.10

Annual Income/100 -0.006*** 0.001

Parental Income/100 1.08 0.62

Annual Parental Transfer/100 -0.00 0.01

Note: The model include the youth’s age at graduation, a quadratic in age at graduation and year dummies. *Significant at 10 percent significance level; **Significant at 5

percent significance level; ***Significant at 1 percent significance level. Table 4. Random Effects Panel Probit Model for Co-residence (Controlling for

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Variable Coefficient

(Marginal Effect)

Standard Error

Amount of Student Loans/100 0.002* 0.001

Female 0.07 0.10 Black 0.44** 0.14 Hispanic 0.26* 0.12 Master’s degree -0.45** 0.17 Ph.D. degree -12.5 584.69 Professional degree -0.68 0.42 Housing Price/100 0.005** 0.002

Annual Marital Status -0.22* 0.10

Annual Full Employment Status -0.52*** 0.04

Parental Income/100 1.07 0.58

Annual Parental Transfer/100 -0.00 0.01

Note: The model include the youth’s age at graduation, a quadratic in age at graduation and year dummies. *Significant at 10 percent significance level; **Significant at 5

percent significance level; ***Significant at 1 percent significance level. Table 5. Random Effects Panel Probit Model for Co-residence (Controlling for

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Variable Coefficient

(Marginal Effect)

Standard Error

Amount of Student Loans/100 0.002* 0.001

Female 0.09 0.10 Black 0.41** 0.13 Hispanic 0.25* 0.10 Master’s degree -0.42** 0.13 Ph.D. degree -11.49 642.1 Professional degree -0.64 0.43 Housing Price/100 0.005** 0.002

Annual Marital Status -0.21* 0.10

Annual Full Employment Status -0.49*** 0.07

Annual Income/100 -0.005*** 0.001

Parental Income/100 1.05 0.56

Annual Parental Transfer/100 -0.00 0.01

Note: The model include the youth’s age at graduation, a quadratic in age at graduation and year dummies. *Significant at 10 percent significance level; **Significant at 5

percent significance level; ***Significant at 1 percent significance level. Table 6. Random Effects Panel Probit Model for Co-residence (Controlling for

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Under the specification of the third model in which both annual income and annual full-employment status are controlled (Table 6), the amount of student loan debt at the time of graduation has a significant effect on the outcomes of parent-youth co- residence. A one hundred dollar increase in the amount of loans owed would increase the probability of moving back home afterwards by 0.2 percent. Blacks and Hispanics are more likely to live at home after college. This reflects the facts that Blacks and Hispanics tend to live in extended households. As expected, youths who are married are less likely to live with parents after graduation. Having a master’s degree decreases the probability of living at the parental home by around 40 percent. This makes sense since youths with a more advanced degree are more likely to find a decent job after graduation and, hence, are more able to support themselves. The standard error of the Ph.D. degree variable is very large. This could be due to the fact that very few youths in my sample have received a Ph.D. Both labor market variables enter significantly in the regression. Working full- time decreases the probability of moving back home by around 50 percent. For employed youths, earnings have a statistically significant effect on co-residence. A one hundred dollar increase in income is associated with 0.5 percent decrease in the probabilities of living with parents. Parental transfers have small and insignificant effects on the probabilities of living at home. The measure of the housing price of the MSA in which a young adult reside is statistically significant. Housing price does play a role in determining the parent-youth co-residence outcome. A one hundred dollar increase in the

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housing price of the youth’s residential area is associated with 0.5 percent increase in the likelihood of living with parents.