The main analysis showed that institutions enrolling larger shares of Pell Grant recipients tend to produce lower median earnings ten years after entry. The percentage of Pell recipients is used here as a proxy for the socioeconomic composition of the student body. Institutions that enroll larger shares of Pell students also differ from other universities in several ways, including admissions selectivity, graduation outcomes, and levels of instructional spending. These institutional characteristics are often used to explain differences in earnings outcomes across institutions.
This extension examines whether the relationship between Pell share and earnings differs across institutional sectors. Separate regression models are estimated for public and private nonprofit institutions using the same set of predictors: the percentage of Pell Grant recipients, average SAT score, graduation rate, and instructional expenditure per student. Estimating the models separately allows the relationship between socioeconomic composition and earnings outcomes to be examined within each sector rather than assuming that the relationship operates in the same way across all institutions.
scorecard <- read.csv("collegescorecard.csv")
public_schools <- subset(scorecard, control == 1)
private_schools <- subset(scorecard, control == 2)
public_model <- lm(earn10yr ~ pctpell + sat_avg + grad_rate + instr_expend, data = public_schools)
summary(public_model)##
## Call:
## lm(formula = earn10yr ~ pctpell + sat_avg + grad_rate + instr_expend,
## data = public_schools)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18030 -3840 -1170 2816 35469
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.284e+04 5.114e+03 4.467 9.82e-06 ***
## pctpell -6.068e+01 3.291e+01 -1.844 0.06582 .
## sat_avg 8.167e+00 4.893e+00 1.669 0.09572 .
## grad_rate 2.063e+02 2.905e+01 7.102 4.27e-12 ***
## instr_expend 2.991e-01 9.055e-02 3.303 0.00103 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6156 on 497 degrees of freedom
## Multiple R-squared: 0.4334, Adjusted R-squared: 0.4289
## F-statistic: 95.06 on 4 and 497 DF, p-value: < 2.2e-16private_model <- lm(earn10yr ~ pctpell + sat_avg + grad_rate + instr_expend, data = private_schools)
summary(private_model)##
## Call:
## lm(formula = earn10yr ~ pctpell + sat_avg + grad_rate + instr_expend,
## data = private_schools)
##
## Residuals:
## Min 1Q Median 3Q Max
## -20842 -4764 -704 3674 70235
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.399e+04 4.526e+03 5.299 1.50e-07 ***
## pctpell -1.612e+02 2.978e+01 -5.413 8.15e-08 ***
## sat_avg 1.421e+01 4.458e+00 3.186 0.0015 **
## grad_rate 1.325e+02 3.262e+01 4.063 5.32e-05 ***
## instr_expend 2.177e-01 3.869e-02 5.626 2.53e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 8006 on 819 degrees of freedom
## Multiple R-squared: 0.4849, Adjusted R-squared: 0.4824
## F-statistic: 192.7 on 4 and 819 DF, p-value: < 2.2e-16Interpretation: The results show that the relationship between Pell share and earnings differs across sectors. Among public universities, the coefficient on Pell share is −60.68 and is not statistically significant at the conventional 0.05 level. This suggests that once graduation rates and instructional spending are taken into account, the share of Pell students does not independently explain differences in earnings outcomes across public institutions. Graduation rate emerges as the strongest predictor in the public sector model, with a coefficient of 206.32, indicating that institutions with higher completion outcomes tend to produce higher earnings ten years after entry.
Among private institutions, the relationship between Pell share and earnings remains strong and statistically significant. The coefficient on Pell share is −161.22, which implies that a ten percentage point increase in the share of Pell students corresponds to roughly $1,600 lower median earnings ten years after entry when the other variables in the model are held constant. Average SAT score, graduation rate, and instructional spending also remain positive predictors of earnings outcomes in the private sector model.
These results suggest that the relationship between socioeconomic composition and earnings outcomes operates differently across institutional sectors. In public universities, graduation rates account for much of the variation in earnings across institutions, while in private universities the share of Pell students remains strongly associated with earnings outcomes even when admissions selectivity, graduation rates, and instructional spending are considered. This pattern points to the importance of examining how the institutional structures of public and private higher education shape the relationship between class background and labor market outcomes. The regression models do not identify the mechanisms producing these differences, but they indicate that understanding how institutional structures interact with the socioeconomic composition of the student body is an important direction for further research.