Are Public Master’s Institutions Cost Efficient? A Stochastic Frontier and Spatial Analysis

Abstract

The current study examines costs, measured by educational and general (E&G) spending, and cost efficiency at 252 public master’s institutions in the United States over a nine-year (2004–2012) period. We use a multi-product quadratic cost function and results from a random-effects model with a first-order autoregressive (AR1) disturbance term to calculate economies of scale with regard to undergraduate enrollment, graduate enrollment, and research. We also employ a slightly modified version of Kumbhakar et al. (J Prod Anal 41(2):321–337, 2014) multi-step approach, involving the use of stochastic frontier analysis (SFA) and taking into account spatial interdependency, to decompose cost efficiency into long-term stable (persistent) and short-term (residual) efficiency. The key results of this study include evidence that: (1) regional clustering of costs exists; (2) there are economies of scale in undergraduate education and diseconomies of scale in graduate education; (3) relatively few institutions are cost inefficient; and (4) cost inefficiency tends to be long-term and persistent rather than short-term and residual. This research also identifies public master’s institutions that are the most cost efficient. Our inquiry has implications for future research as it points towards specific institutions, which may be engaged in effective practices to keep costs low, for possible follow-up case studies. Going forward, the techniques used in this study could be applied to examine economies of scale and scope as well as cost efficiency among other types of higher education institutions, such as public or private research universities, baccalaureate institutions, and community colleges.

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Notes

  1. 1.

    This was computed using IPEDS data (which includes latitudinal and longitudinal coordinates) and the Stata “nearstat” routine.

  2. 2.

    Cheslock and associates (2016) identified other but less commonly used theoretical frameworks and perspectives that include cost disease, the positional arms race, and the principal-agent model. Cost disease is utilized to explain why costs rise faster in higher education, compared to other industries. The positional arms race perspective seeks to explain why costs increase over time within certain higher education institutions that are competing for top students and faculty. In the principal-agent model, costs are posited to be a result of the extent to which the interests of the principals (i.e., students, parents, alumni, donors, and taxpayers) diverge from those of the agents (i.e., faculty members, staff, administrators, and trustees) and tend to focus on costs in specific areas (e.g., administrative) versus total costs.

  3. 3.

    Each higher education institution should only offer one type of output (undergraduate education, graduate education, or research).

  4. 4.

    One higher education institution is producing all outputs.

  5. 5.

    DEA is a nonparametric technique, based on linear programming methods to derive a non-parametric piece-wise surface (or frontier). DEA methods do not require distributional assumptions regarding deviations from the frontier. However, DEA has several limitations that include measurement error and outliers that may influence the shape and position of the frontier. For an introduction to DEA, see Thanassoulis (2001).

  6. 6.

    When estimating a SFA model, it is assumed that the distribution of the inefficiency component of the error (u i ) is usually half normal, truncated normal, exponential, or normal gamma. In this study, the SFA models were estimated assuming a half-normal of u i . SFA models with the truncated distribution did not converge. In this research, efficiency scores generated from SFA models with an exponential distribution are highly correlated (e.g., r = 0.97, p < 0.001) with efficiency scores generated from SFA models with a half-normal of u i and, consequently, were not included in the analyses. The gamma distribution, an extension of the exponential distribution of u i , has not been used extensively in the SFA literature and requires a complex or simulated log-likelihood function. Therefore, the gamma distribution is not used in this study.

  7. 7.

    The v is assumed to be independent and identically distributed as N(0, δ 2), independent of the u, which is an unobservable nonnegative random variable assumed to be independent and identically distributed (i.i.d) as a truncation at zero of N(µ, δ 2). As in OLS regression models, the independent variables are assumed to be independent of the random error (v).

  8. 8.

    This method is based on the following formula:

    \(E[\exp (u_{i} )\left| {e_{i} } \right.] = \frac{{1 - \varPhi \left( {\delta + \left( {\frac{{\gamma e_{i} }}{\delta }} \right)} \right)}}{{1 - \varPhi \left( {\frac{{\gamma e_{i} }}{\delta }} \right)}} \cdot { \exp }\left( {\gamma e_{i} + \left( {\frac{{\delta^{2} }}{2}} \right)} \right)\)

    where Φ is the cumulative density function, δ = δu. δu/δ, γ = δ 2u 2, and e i  = v i − u i .

  9. 9.

    A detail description of this three-step analysis can be found in the book by Kumbhakar et al. (2015). A practitioner's guide to stochastic frontier analysis using Stata. New York, NY: Cambridge University Press.

    We modified the Stata code provided by Kumbhakar et al. (2015) at https://sites.google.com/site/sfbook2014/to apply to our study.

  10. 10.

    In our study, we used a maximum distance band that would also include public master’s institutions in the US, including Alaska but excluding Hawaii.

  11. 11.

    As of January 1st, 2015, 29 states and the District of Columbia have minimum wage laws well above the federal level, thus implicitly pushing all other wages in the respective states upward. See http://www.dol.gov/whd/minwage/america.htm.

  12. 12.

    Following the literature, we first define the average incremental cost (AIC) for undergraduate output (FTE undergraduate students) as AICU = [TC{QU,QG,QR} − TC{0,QG,QR}]/QU, where TC{QU,QG,QR} is the total cost of producing QU units of undergraduate students, QG units of graduate students and QR units of research; and TC{0,QG,QR} is the total cost when output for QU (FTE undergraduate enrollment) is zero. We then define average incremental costs for graduate and research outputs in a similar manner. Next, we calculate the marginal cost (MC) of increasing the undergraduate FTE enrollment by one student by simply taking the first order derivative of the total cost function with respect to the undergraduate FTE enrollment: MCU = ∂TC/∂QU. We then define and calculate marginal costs for graduate FTE enrollment and research outputs in a similar manner. Economies of scale are said to exist for a product when the ratio of these two measures (AICi/MCi) is greater than one. If the ratio of AICi/MCi is less than one, diseconomies of scale exist.

  13. 13.

    Although this was not a part of our study, we allowed for heterogeneity in the cost inefficiency term and estimated the determinants of residual (i.e., short-term) and persistent (i.e., long-term) cost inefficiency. More specifically, we explored the relationship between (1) short-term cost inefficiency and some of the variables in our AR1 random-effects model and (2) long-term cost inefficiency and several of the variables in our AR1 random-effects model. Preliminary results showed that short-term cost inefficiency is negatively influenced by faculty salary (beta = −4.19, p < 0.001), positively associated with student-to-faculty ratio (beta = 0.84, p < 0.01) and positively related to offering a doctoral degree (beta = 1.96, p < 0.001). Persistent cost inefficiency is positively related to the student-to-faculty ratio (beta = 7.80, p < 0.001) and the presence of an affiliated medical school (beta = 3.64, p < 0.01) and negatively related to faculty salaries (beta = −4.46, p < 0.001) and the university offering doctoral degrees (beta = −2.46, p < 0.001). In future research, we plan to further pursue this particular line of inquiry in a more comprehensive and systematic way.

  14. 14.

    The complete lists of all 252 institutions ranked by persistent cost efficiency scores generated by all four models are available from the authors upon request.

References

  1. Agasisti, T., & Salerno, C. (2007). Assessing the cost efficiency of Italian universities. Education Economics, 15(4), 455–471.

    Article  Google Scholar 

  2. Anselin, L. (1988). Spatial econometrics: Methods and models. Berlin: Kluwer Academic Publishers.

    Google Scholar 

  3. Anselin, L. (1996). Global Moran’s I Algorithm used in GeoDa: The Moran scatterplot as an ESDA tool to assess local instability in spatial association. In M. Fischer, H. Scholten, & D. Unwin (Eds.), Spatial analytical perspectives on GIS in environmental and socio-economic sciences (pp. 111–125). London: Taylor and Francis.

    Google Scholar 

  4. Arifeen, S., & Mamun, K. (2012). Stochastic estimation of cost frontier: Evidence from Bangladesh. Education Economics, 22(2), 211–227.

    Google Scholar 

  5. Battese, G. E., & Coelli, T. J. (1995). A model for technical inefficiency effects in a stochastic frontier production for panel data. Empirical Economics, 20(2), 325–332.

    Article  Google Scholar 

  6. Baumol, W. J., Panzar, J. C., & Willig, R. D. (1982). Contestable markets and the theory of industry structure. New York: Harcourt Brace Jovanovich.

    Google Scholar 

  7. Boehner, J. A., & McKeon, H. P. (2003). The college cost crisis (Report of U.S. House Committee on Education and the Workforce and U.S. House Subcommittee on 21st Century Competitiveness). Washington, DC: U.S. Government Printing Office.

  8. Brewer, D. J., Gates, S. M., & Goldman, C. A. (2002). In pursuit of prestige: Strategy and competition in U.S. higher education. New Brunswick: Transaction.

    Google Scholar 

  9. Cheslock, J. J., Ortagus, J. C., Umbricht, M. R., & Wymore, J. (2016). The Cost of Producing Higher Education: An Exploration of Theory, Evidence, and Institutional Policy. In M. B. Paulsen (Ed.), Higher education: Handbook of theory and research (Vol. 31, pp. 349–392). Dordrecht: Springer.

    Google Scholar 

  10. Cohn, A., Rhine, S., & Santos, M. (1989). Institutions of higher education as multi-product firms: Economies of scale and scope. The Review of Economics and Statistics, 71(2), 284–290.

    Article  Google Scholar 

  11. de Groot, H., McMahon, W. W., & Volkwein, J. F. (1991). The cost structure of American research universities. Review of Economics and Statistics, 73, 424–431.

    Article  Google Scholar 

  12. Doyle, W. (2015). Efficiency in degree production among public comprehensive universities. In M. Schneider & K. C. Deane (Eds.), The university next door: What is a comprehensive university, who does it educate, and can it survive? (pp. 93–120). New York: Teachers College Press.

    Google Scholar 

  13. Dundar, H., & Lewis, D. R. (1995). Departmental productivity in American universities: Economies of scale and scope. Economics of Education Review, 14(2), 199–244.

    Article  Google Scholar 

  14. Forbus, P., Newbold, J. J., & Mehta, S. S. (2011). A study of non-traditional and traditional students in terms of their time management behaviors, stress factors, and coping strategies. Academy of Educational Leadership Journal, 15(2), 109–125.

    Google Scholar 

  15. Fryar, A. H. (2015). The comprehensive university: How it came to be and what it is now. In M. Schneider & K. C. Deane (Eds.), The university next door: What is a comprehensive university, who does it educate, and can it survive? (pp. 19–42). New York: Teachers College Press.

    Google Scholar 

  16. Fu, T.-T., Huang, C. J., & Tien, F. F. (2008). University cost structure in Taiwan. Contemporary Economic Policy, 26(4), 651–662.

    Article  Google Scholar 

  17. Green, W. H. (2005). Fixed and random effects in stochastic frontier models. Journal of Productivity Analysis, 23(1), 7–32.

    Article  Google Scholar 

  18. Gros Louis, K. R. R., & Thompson, M. (2002). Responsibility center budgeting and management at Indiana University. In D. M. Priest, W. E. Becker, D. Hossler, & E. P. St. John (Eds.), Incentive-based budgeting systems in public universities (pp. 93–107). Cheltenham: Edward Elgar.

    Google Scholar 

  19. Harcleroad, F. F., & Ostar, A. W. (1987). Colleges and universities for change: America’s comprehensive public state colleges and universities. Washington, DC: AASCU Press.

    Google Scholar 

  20. Hashimoto, K., & Cohn, E. (1997). Economies of scale and scope in Japanese private universities. Education Economics, 5(2), 107–115.

    Article  Google Scholar 

  21. Hearn, J. C., Lewis, D. R., Kallsen, L., Holdsworth, J. M., & Jones, L. M. (2006). “Incentives for managed growth”: A case study of incentives-based planning and budgeting in a large public research university. Journal of Higher Education, 77(2), 286–316.

    Article  Google Scholar 

  22. Hedrick, D. W., Wassell, C. S, Jr., & Henson, S. E. (2009). Administrative costs in higher education: How fast are they really growing? Education Economics, 17(1), 123–137.

    Article  Google Scholar 

  23. Henderson, B. D., & Kane, W. D. (1991). Caught in the middle: Faculty and institutional status and quality in state comprehensive universities. Higher Education, 22(4), 339–350.

    Article  Google Scholar 

  24. Izadi, H., Johnes, G., Oskrochi, R., & Crouchley, R. (2002). Stochastic frontier estimation of a CES cost function: The case of higher education in Britain. Economics of Education Review, 21(1), 63–71.

    Article  Google Scholar 

  25. Jaquette, O., & Parra, E. E. (2014). Using IPEDS for panel analyses: Core concepts, data challenges, and empirical applications. In M. B. Paulsen (Ed.), Higher education: Handbook of theory and research (Vol. XXIX, pp. 467–533). Dordrecht: Springer.

    Google Scholar 

  26. Jaquette, O., Parra, E., Hillman, N. W., & Curs, B. R. (2013). Using organizational, local, and state-level panel data to conduct policy analyses of organizational change (symposium). Paper presented at the annual meeting of the Association for the Study of Higher Education.

  27. Johnes, G. (1996). Multiproduct cost functions and the funding of tuition in UK universities. Applied Economics Letters, 3(9), 557–561.

    Article  Google Scholar 

  28. Johnes, G. (1997). Costs and industrial structure in contemporary British higher education. Economic Journal, 107(442), 727–737.

    Article  Google Scholar 

  29. Johnes, G., & Johnes, J. (2009). Higher education institutions’ costs and efficiency: Taking the decomposition a further step. Economics of Education Review, 28(1), 107–113.

    Article  Google Scholar 

  30. Johnes, G., & Schwarzenberger, A. (2011). Differences in cost structure and the evaluation of efficiency: The case of German universities. Education Economics, 19(5), 497–499.

    Article  Google Scholar 

  31. Johnstone, B. D., & Marcucci, P. N. (2010). Financing higher education worldwide: Who pays? Who should pay?. Baltimore, MD: The Johns Hopkins University Press.

    Google Scholar 

  32. Koshal, R. K., & Koshal, M. (1999). Economies of scale and scope in higher education: A case of comprehensive universities. Economics of Education Review, 18(2), 269–277.

    Article  Google Scholar 

  33. Koshal, R. K., & Koshal, M. (2001). Multi-product total cost function for higher education: A case of Bible Colleges. Economics of Education Review, 20(3), 297–303.

    Article  Google Scholar 

  34. Kumbhakar, S., Lien, G., & Hardaker, J. B. (2014). Technical efficiency in competing data models: A study of Norwegian grain farming. Journal of Productivity Analysis, 41(2), 321–337.

    Article  Google Scholar 

  35. Kumbhakar, S. C., Wang, H., & Horncastle, A. P. (2015). A practitioner’s guide to stochastic frontier analysis using Stata. New York, NY: Cambridge University Press.

    Google Scholar 

  36. Kuo, J., & Ho, Y. (2008). The cost efficiency impact of the university operation fund on public universities in Taiwan. Economics of Education Review, 27(5), 603–612.

    Article  Google Scholar 

  37. Laband, N., & Lentz, F. (2003). New estimates of economies of scale and scope in higher education. Southern Economic Journal, 70(July), 172–183.

    Article  Google Scholar 

  38. Lenton, P. (2008). The cost structure of higher education in further education colleges in England. Economics of Education Review, 27(4), 471–482.

    Article  Google Scholar 

  39. Lewis, D. R., & Dundar, H. (1995). Economies of scale and scope in Turkish universities. Education Economics, 3(2), 133–157.

    Article  Google Scholar 

  40. Longlong, H., Fengliang, L., & Weifang, M. (2009). Multi-product total cost functions for higher education: The case of Chinese research universities. Economics of Education Review, 28(4), 505–511.

    Article  Google Scholar 

  41. McMahon, W. W. (2009). Higher learning, greater good: The private and social benefits of higher education. Baltimore, MD: The Johns Hopkins University Press.

    Google Scholar 

  42. McMillan, M. L., & Chan, W. H. (2006). University efficiency: A comparison and consolidation of results from stochastic and non-stochastic methods. Education Economics, 14(1), 1–30.

    Article  Google Scholar 

  43. Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1), 17–23.

    Article  Google Scholar 

  44. Morphew, C. (2002). A rose by any other name: Which colleges became universities. The Review of Higher Education, 25(2), 207–224.

    Article  Google Scholar 

  45. Morphew, C. C., & Baker, B. D. (2004). The cost of prestige: Do new research I universities incur higher administrative costs? The Review of Higher Education, 27(3), 365–384.

    Article  Google Scholar 

  46. Nelson, R., & Heverth, K. T. (1992). Effect of class size on economies of scale and marginal costs in higher education. Applied Economics, 24, 473–482.

    Article  Google Scholar 

  47. O’Meara, K. (2007). Striving for what? Exploring the pursuit of prestige. In J. C. Smart (Ed.), Higher education: Handbook of theory and research (Vol. XXII, pp. 121–179). Dordrecht: Springer.

    Google Scholar 

  48. Robst, J. (2001). Cost efficiency in public higher education institutions. The Journal of Higher Education, 72(6), 730–750.

    Article  Google Scholar 

  49. Schneider, & Deane, K. C. (Eds.). (2015). The university next door: What is a comprehensive university, who does it educate, and can it survive?. New York: Teachers College Press.

    Google Scholar 

  50. Selingo, J. (2015, February 5). Regional public colleges–the ‘middle children of higher ed’–struggle to survive. The Washington Post. Retrieved from http://www.washingtonpost.com/news/grade-point/wp/2015/02/09/regional-public-colleges-the-middle-children-of-higher-ed-struggle-to-survive/.

  51. Stevens, P. A. (2005). A stochastic frontier analysis of English and Welsh universities. Education Economics, 13(4), 355–374.

    Article  Google Scholar 

  52. Stocum, D. L., & Rooney, P. M. (1997, September/October). Responding to resource constraints: A departmentally based system of responsibility center management. Change: The Magazine of Higher Learning.

  53. Strauss, J. C., & Curry, J. R. (2002). Responsibility center management: Lessons from twenty- five years of decentralized management. Washington, DC: NACUBO.

    Google Scholar 

  54. The College Board. (2014). Trends in college pricing. Retrieved from http://trends.collegeboard.org/college-pricing.

  55. Thanassoulis, E. (2001). Introduction to the theory and application of data envelopment analysis: A foundation text with integrated software. New York: Springer.

    Google Scholar 

  56. Titus, M., & Eagan, K. (2016). Examining production efficiency in higher education: Theutility of stochastic frontier analysis. In M. B. Paulsen (Ed.), Higher education: Handbook of theory and research (Vol. 31, pp. 441–512). Dordrecht: Springer.

    Google Scholar 

  57. U. S. Department of Education. (2015). Institution of Education Sciences, National Center for Education Statistics.

  58. Whalen, E. L. (1991). Responsibility center budgeting. Bloomington, IN: Indiana University Press.

    Google Scholar 

  59. Yin, M. L. (2015). Rethinking student outcomes: Constructing predicted and adjusted graduation and retention rates for comprehensive universities. In M. Schneider & K. C. Deane (Eds.), The university next door: What is a comprehensive university, who does it educate, and can it survive? (pp. 121–148). New York: Teachers College Press.

    Google Scholar 

  60. Zumeta, W. (2001). Public policy and accountability in higher education: Lessons from the past and present for the new millennium. In D. E. Heller (Ed.), The states and public higher education policy: Affordability, access, and accountability (pp. 155–197). Baltimore: The Johns Hopkins Press.

    Google Scholar 

  61. Zumeta, W., Breneman, D. W., Callan, P. M., & Finney, J. E. (2012). Financing higher education in the era of globalization. Cambridge, MA: Harvard Education Press.

    Google Scholar 

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Acknowledgments

This study acknowledges Ozan Jaquette (University of Arizona), who provided access to the dataset used in this research, Kevin Eagan (UCLA), who helped to extract key variables, Manuel S. Gonzalez Canche (University of Georgia), who provided code and assistance to help create spatial maps, and the suggestions of two anonymous reviewers. Any errors are our own.

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Correspondence to Marvin A. Titus.

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Titus, M.A., Vamosiu, A. & McClure, K.R. Are Public Master’s Institutions Cost Efficient? A Stochastic Frontier and Spatial Analysis. Res High Educ 58, 469–496 (2017). https://doi.org/10.1007/s11162-016-9434-y

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Keywords

  • Public master’s institutions
  • Cost efficiency
  • Stochastic frontier analysis
  • Spatial analysis