To mitigate the selection problem, we control for school-specific fixed effects, as well as very flexible application-admissions pattern fixed effects.
Each regression also contains controls for parental education, family income by cohort, college, college selectivity tier by cohort, and UC application-admission pattern fixed effects that account for the intended major listed on each application.
Specifically, we control for very flexible application-admissions pattern fixed effects to account for student unobserved characteristics, as well as school-specific fixed effects to account for typically unobserved institutional characteristics that are plausibly correlated with peer quality and student outcomes.
Each regression also contains controls for race/ethnicity, SAT I math and verbal scores, UC-adjusted high school GPA, parental education, family income by cohort, college, college selectivity tier by cohort, and UC application-admission pattern fixed effects that account for the intended major listed on each application.
Each regression also contains controls for race/ethnicity, UC-adjusted high school GPA, parental education, family income by cohort, college, college selectivity tier by cohort, and UC application-admission pattern fixed effects that account for the intended major listed on each application.
Our empirical model includes a vector of observable student characteristics (X ic ) that control for SAT I math and verbal scores, high school GPA, parental education, and family income.9 We also include in our specification very flexible application-admissions pattern fixed effects (A ac ) to account for student unobservables.
Random = random effects model; Fixed = fixed effects model.
Fixed effects model the mean values of the response variable as a function of covariates, while random effects model any patterns in the residuals around these fixed effects, e.g. those generated by repeated observations on the same individual.
The independent variables were time trends (linear and quadratic effects), sinusoidal terms to account for seasonal patterns of ILI or influenza activity; fixed effects for geographic region, year, weeks with winter school breaks; and variables for each of the 3 weeks that immediately preceded or followed winter school breaks (Technical Appendix).
Because the fixed effects might not capture the pattern completely, an autoregressive error structure for residual variance was incorporated additionally to mitigate the potential effects of correlated residuals (model 3).
Treating base groups as fixed or random resulted in similar patterns, although they were more pronounced in the case of fixed effects.
