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Table 4.
Panel Data Regression Models
Type of Institution
VariableAllResearchMastersBachelors
Enrollments (100s) 0.246*** −0.050 0.273*** 0.538*** 
 (0.064) (0.100) (0.063) (0.144) 
Squared enrollments −0.001*** −0.000 −0.001** −0.001** 
 (0.000) (0.000) (0.000) (0.000) 
ACT 75th percentile −0.334 0.055 −0.367 −0.119 
 (0.259) (0.598) (0.255) (0.238) 
No ACT score −1.338 6.361 −0.817 −0.551 
 (1.030) (4.240) (1.267) (1.071) 
Acceptance rate −0.022 −0.133 −0.004 −0.035 
 (0.025) (0.067) (0.019) (0.026) 
Yield rate −0.073** −0.326** −0.041 −0.098** 
 (0.025) (0.119) (0.024) (0.035) 
Percent undergrads 0.007 0.352 −0.033 −0.061 
 (0.057) (0.208) (0.061) (0.087) 
Percent revenue: Net tuition −1.611*** −1.458*** −1.302*** −1.639*** 
 (0.181) (0.182) (0.136) (0.258) 
Tuition discount rate −0.681*** −0.751* −0.421*** −0.595*** 
 (0.146) (0.321) (0.097) (0.129) 
Percent revenue: Appropriations −0.295 −0.349 −0.714* −0.883 
 (0.359) (0.221) (0.333) (0.669) 
Percent revenue: Grants −1.503*** −4.963*** −0.675*** −1.320*** 
 (0.243) (0.749) (0.168) (0.292) 
Percent revenue: Gifts 0.199 −0.979*** 0.461*** 0.071 
 (0.196) (0.276) (0.126) (0.111) 
Percent expense: Instruction 0.693*** 0.625* 0.726*** 0.509*** 
 (0.120) (0.258) (0.132) (0.140) 
Percent expense: Administration −0.109 0.676 0.293* −0.072 
 (0.207) (0.359) (0.134) (0.127) 
Percent expense: Student services 0.576** 1.521* 0.221 0.467*** 
 (0.202) (0.711) (0.150) (0.138) 
Percent expense: Research 1.202*** 3.180*** 0.333 0.747 
 (0.280) (0.583) (0.201) (0.550) 
Percent expense: Public service −0.004 0.351 0.061 −0.268 
 (0.458) (0.711) (0.353) (0.689) 
Percent expense: Academic support 0.379 −0.033 0.425** 0.329 
 (0.214) (0.337) (0.154) (0.231) 
Constant 93.751*** 94.043** 62.601*** 100.459*** 
 (14.291) (28.399) (15.605) (17.473) 
Sample size 8732 906 3164 4469 
R2 0.62 0.85 0.73 0.74 
Fixed effects vs. Pooled (F-test) 11.16*** 12.48*** 11.47*** 8.20*** 
Fixed vs. Random effects (χ2198.90*** 77.00*** 441.33*** 126.79*** 
Type of Institution
VariableAllResearchMastersBachelors
Enrollments (100s) 0.246*** −0.050 0.273*** 0.538*** 
 (0.064) (0.100) (0.063) (0.144) 
Squared enrollments −0.001*** −0.000 −0.001** −0.001** 
 (0.000) (0.000) (0.000) (0.000) 
ACT 75th percentile −0.334 0.055 −0.367 −0.119 
 (0.259) (0.598) (0.255) (0.238) 
No ACT score −1.338 6.361 −0.817 −0.551 
 (1.030) (4.240) (1.267) (1.071) 
Acceptance rate −0.022 −0.133 −0.004 −0.035 
 (0.025) (0.067) (0.019) (0.026) 
Yield rate −0.073** −0.326** −0.041 −0.098** 
 (0.025) (0.119) (0.024) (0.035) 
Percent undergrads 0.007 0.352 −0.033 −0.061 
 (0.057) (0.208) (0.061) (0.087) 
Percent revenue: Net tuition −1.611*** −1.458*** −1.302*** −1.639*** 
 (0.181) (0.182) (0.136) (0.258) 
Tuition discount rate −0.681*** −0.751* −0.421*** −0.595*** 
 (0.146) (0.321) (0.097) (0.129) 
Percent revenue: Appropriations −0.295 −0.349 −0.714* −0.883 
 (0.359) (0.221) (0.333) (0.669) 
Percent revenue: Grants −1.503*** −4.963*** −0.675*** −1.320*** 
 (0.243) (0.749) (0.168) (0.292) 
Percent revenue: Gifts 0.199 −0.979*** 0.461*** 0.071 
 (0.196) (0.276) (0.126) (0.111) 
Percent expense: Instruction 0.693*** 0.625* 0.726*** 0.509*** 
 (0.120) (0.258) (0.132) (0.140) 
Percent expense: Administration −0.109 0.676 0.293* −0.072 
 (0.207) (0.359) (0.134) (0.127) 
Percent expense: Student services 0.576** 1.521* 0.221 0.467*** 
 (0.202) (0.711) (0.150) (0.138) 
Percent expense: Research 1.202*** 3.180*** 0.333 0.747 
 (0.280) (0.583) (0.201) (0.550) 
Percent expense: Public service −0.004 0.351 0.061 −0.268 
 (0.458) (0.711) (0.353) (0.689) 
Percent expense: Academic support 0.379 −0.033 0.425** 0.329 
 (0.214) (0.337) (0.154) (0.231) 
Constant 93.751*** 94.043** 62.601*** 100.459*** 
 (14.291) (28.399) (15.605) (17.473) 
Sample size 8732 906 3164 4469 
R2 0.62 0.85 0.73 0.74 
Fixed effects vs. Pooled (F-test) 11.16*** 12.48*** 11.47*** 8.20*** 
Fixed vs. Random effects (χ2198.90*** 77.00*** 441.33*** 126.79*** 

Notes: Data were obtained from Integrated Postsecondary Education Data System for the years 2003—04 to 2006—07, 2009—10 to 2015—16 for private, four-year nonprofit institutions. Dependent variable is excess revenue as a percentage of expenses. Robust standard errors are shown in parentheses. Reference category for revenues is “other revenues.” Reference category for expenses is “other expenses.” Data from 2007—08 and 2008—09 were not included because they were not comparable to other years due to a change in financial reporting requirements.

*p < 0.05; **p < 0.01; ***p <0 .001.

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