The Scalability, Efficiency and Complexity of Universities and Colleges: A New Lens for Assessing the Higher Educational System

by   Ryan C. Taylor, et al.

The growing need for affordable and accessible higher education is a major global challenge for the 21st century. Consequently, there is a need to develop a deeper understanding of the functionality and taxonomy of universities and colleges and, in particular, how their various characteristics change with size. Scaling has been a powerful tool for revealing systematic regularities in systems across a range of topics from physics and biology to cities, and for understanding the underlying principles of their organization and growth. Here, we apply this framework to institutions of higher learning in the United States and show that, like organisms, ecosystems and cities, they scale in a surprisingly systematic fashion following simple power law behavior. We analyze the entire spectrum encompassing 5,802 institutions ranging from large research universities to small professional schools, organized in seven commonly used sectors, which reveal distinct regimes of institutional scaling behavior. Metrics include variation in expenditures, revenues, graduation rates and estimated economic added value, expressed as functions of total enrollment, our fundamental measure of size. Our results quantify how each regime of institution leverages specific economies of scale to address distinct priorities. Taken together, the scaling of features within a sector and shifts in scaling across sectors implies that there are generic mechanisms and constraints shared by all sectors which lead to tradeoffs between their different societal functions and roles. We particularly highlight the strong complementarity between public and private research universities, and community and state colleges, four sectors that display superlinear returns to scale.


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The original source of this data is the Integrated Postsecondary Education Data System, or IPEDS IPEDSDoc , where we use the 2013 Delta Cost Project DeltaDoc2017 refinement of the IPEDS data. Spanning nearly the entire U.S. higher education system, it includes over 20 million students, from + accredited universities. We use total enrollment (undergraduate and graduate) as our measure of size (see SI Appendix C). We supplement this main data source with several other databases Chettyetal2017 ; ScorecardDoc discussed below and in Appendix A, with the list and definitions of all variables in SI Table B1.

We use completion data from two of the most-widely reported U.S. sources as measures of educational output. First, we use the IPEDS Graduation Rate Survey, included in the Delta dataset DeltaDoc2017 . This dataset tracks six-year completions for cohorts of first-time first-year degree-seeking students (FTFT) (see SI Appendix G). Second, we use student outcome data on cohorts of Federal Student Aid-receiving (FSA) students which is collected via FAFSA reporting and managed through the Department of Education’s College Scorecard project ScorecardDoc . The Department of Education considers these data usable for research, but excludes them from their consumer tool due to possible reporting inaccuracies (ScorecardDoc p. 23-24). Both graduation rates describe cohorts that enrolled in 2007 and assess six-year outcomes by 2013 (excepting professional schools, where only a three-year rate was available). See SI Appendix E and G for details of the cross-dataset merging procedures and overall data limitations (specifically Table E1-E4 and G3 and Figures E1-E2 and G1-G2 on robustness of results to various aggregation problems). In particular, both FSA and FTFT cohorts used for our completion analysis can exclude or misrepresent portions of the IPEDS total enrollment, and may therefore introduce error into our analysis of overall institutional performance. Here we favor FSA results, because we assume that aid-receiving cohorts are less prone to systematically misrepresenting the student body composition than traditional student cohorts.

For our analysis of mid-career earnings we rely on the data provided by the Mobility Reports Card project, part of the broader Equality of Opportunity project Chettyetal2017 . Data on incomes were obtained from tax filings and linked to individual students. The data that is made available is aggregated at the school level. We use the mean 2014 incomes of students who attended the school for at least one year, focusing on the cohort born in 1984.

We gratefully acknowledge the support of the ASU-SFI Center for Biosocial Complex Systems and the National Science Foundation under Grant Number ACI-1757923. GBW would like to thank the Eugene and Clare Thaw Charitable Trust and the National Science Foundation under the grant PHY 1838420 for their generous support, and GBW and CPK thank CAF Canada for generous support. ML would like to acknowledge support from the Smart Family Foundation, Volkswagen Foundation and the National Science Foundation SBE 1656284. ML and CPK would like to thank the Omidyar Fellowship at the Santa Fe Institute for Supporting this work. We thank Sidney Redner, Paul LePore and John Miller for valuable feedback.

Author Contributions
CPK, MD, and GBW designed the concept of the study. RCT, XL, MD, and CPK performed the analysis. All authors discussed intermediate findings, interpreted results, and wrote the paper.

Competing Interest Statement
The authors declare no competing interests.


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