Stochastic Cost Frontier and Inefficiency Estimatesof Public and Private Universities: DoesGovernment Matter?

G. Thomas Sav

Published online: 1 May 2012# International Atlantic Economic Society 2012

Abstract Stochastic frontier analysis is used to estimate operating cost inefficien-cies of public and private non-profit universities in the U.S. while also accountingfor the possible effects arising from differences in the degree of governmentownership. Using panel data for four academic years, 2005–2009, inefficienciesare estimated under two model specifications. Results indicate that public univer-sities are more cost efficient when environmental factors influence cost frontiers butprivate universities are the cost efficient institutions when those factors are deter-minants of inefficiency. Increased government funding does matter and increasesprivate sector inefficiency but offers some efficiency improvements among publicuniversities. Following the global financial crisis, there is evidence indicating aconsiderable slowdown in the inefficiency growth among both public and privateuniversities.

Keywords Cost inefficiency . Stochastic cost frontier . Government ownership .

Universities

JEL D2 . I21 . I22 . I23 . L3 . C33

Introduction

This paper employs stochastic frontier analysis to empirically estimate operating costinefficiencies for public and private non-profit universities in the U.S. The purpose isto determine whether or not and to what extent cost inefficiencies differ between thetwo ownership arrangements. That seems particularly relevant given the decadeof more declines in government funding of public higher education and the

Int Adv Econ Res (2012) 18:187–198DOI 10.1007/s11294-012-9353-4

G. T. Sav (*)Department of Economics, Raj Soin College of Business, Wright State University, Dayton, OH 45435,USAe-mail: tom.sav@wright.edu

internationally pervasive budget cuts brought about by the global financial crisis,all of which has stimulated interest in more market based or privatized educationsystems. But at the same time, it must be recognized that public universities differin the degree of government ownership that might be defined by differences in thedependency on government funding as a source of operating revenue. In this sense,the degree of so-called publicness can differ not only for public universities butalso for government funding dependent private universities. The paper additionallyexplores the possible effect of this publicness on the cost inefficiencies of bothpublicly and privately owned universities.

Stochastic frontier analysis has only recently been applied to investigate costinefficiencies in education.1 At the primary and secondary school levels, Chakrabortyand Poggio (2008) examined the inefficiencies pertaining to Kansas school districtsusing panel data for 2001–05. In higher education, Stevens (2005) provided a 1995–99 panel data study of 80 English and Welsh universities; McMillan and Chan (2006)did a 1992–93 cross section study of 45 Canadian universities; and Abbott andDoucouliagos (2009) examined seven New Zealand and 36 Australian universitiesfrom 1995 to 2003. Each study used different cost and inefficiency specifications thatmake comparisons difficult at best. For the present paper, the study by Stevens (2005)represents the closest in methodology for the empirical determination and reporting ofcost inefficiencies. However, unlike the present paper, none of the studies examinethe effect of public vs. private ownership or the effect of government funding differ-ences on cost inefficiencies. Rather, it is the public-private organization of U.S.higher education that offers the best opportunity for such an inquiry. A reasonablyexhaustive literature search indicates that the present paper represents the first to doso in applying stochastic frontier analysis.

Thus, stochastic cost frontiers are estimated for both public and private non-profituniversities using panel data covering four academic years, 2005–06 through 2008–09. Two alternative inefficiency models are employed to investigate the effects ofenvironmental factors, including the measure of publicness, on university cost fron-tiers and inefficiency measures. The focus is on Carnegie defined comprehensiveuniversities offering four-year degrees and engaged in graduate education at themaster’s degree level. A useable sample of 257 public and 297 private non-profituniversities are drawn from the national data base.

Literature Background Leading to Empirical Methodology

To begin, we employ the standard methodology of stochastic frontiers following thepioneering work of Aigner et al. (1977) and extended to panel data by Battese and

1 Outside of education, empirical applications of stochastic frontier analysis is not new. Production frontiersand efficiencies have been estimated, e.g., for the U.S. primary metals industry (Aigner et al. 1977), U.S.dairies (Kumbhakar et al. 1991), India paddy farms (Battese and Coelli 1992 and 1995), internationalairlines (Coelli et al. 1999), and U.S. electricity (Knittel 2002). Cost frontier research has been applied, e.g.,to the U.S. airlines industry (Kumbhakar 1991), insurance industry (Cummins and Weiss 1993), hospitalcare (Bradford et al. 2001), banking (Huang and Wang 2001), crime prevention (Barros and Alves 2005),and English football (Barros and Leach 2007).

188 G.T. Sav

Coelli (1995). The inclusion of the multiproduct dimension of universities leads to thegeneral form of total cost (C) for university i in time t as follows:

Cit ¼ C Yj;it;wk;it; zm;it; aj; bk ; dm� �þ vit þ uit i ¼ 1; . . . ;N ; t ¼ 1; . . . ;T ð1Þ

where the Yj,it are the j01,…, J outputs; wk,it are the k01,…, K input prices; zm,it arepossible m01,…, M environmental factors; αj, βk, and gm are parameters to beestimated; and vit+uit defines the combined error component (εit≡vit+uit). That is,university costs are subject to random variations, vit, due to factors outside the controlof the university, measurement error, and the usual statistical noise, as well aspossible inefficiency effects, uit, associated with managerial decisions, input charac-teristics, and other environmental factors. Thus, the uit≥1 measure the extent to whicha university operates on or above its minimum best practice cost frontier. As anexample, Stevens’ (2005) inefficiency estimates for English and Welsh universitiesrange from 1.007 to 2.011. The random component is generally assumed to beindependently and identically distributed as N(0,σv

2,) and independent of the uit.Assumptions underlying time varying inefficiency effects are more plentiful. Two areinvestigated here.

First, following the Battese and Coelli (1992) specification, the environmentalfactors, zm,it, are under the control of the university and directly alter the cost frontieras suggested by their inclusion in (1). The inefficiencies under this Model I aredetermined as:

uit ¼ uie�η t�Tð Þ ð2Þ

where the ui are independently and identically distributed as truncations at zero of N(μ,σu

2) and the uit monotonically increase (if η<0) or decreases (if η>0) or are timeinvariant. The alternative model specification rests upon the assumption that the costfrontier is free of the environmental effects, zm,it, and instead enter as determinants ofinefficiency. Following Battese and Coelli (1995), the inefficiency term under thisModel II is:

uit ¼ d0 þX

m

dmzm;it þ wit ð3Þ

where wit is the random component and uit is the truncation of the normal distributionwith mean δ0+Σδmzm,it and variance σu

2. Parameter estimates of the full models areobtained simultaneously through maximum likelihood estimation. Reparameterizationof σ2 ¼ σ2

v þ σ2u produces the estimate (gσu

2/σ2, 0≤g≤1, where g therefore measuresthe proportion of inefficiency in the overall variance (Battese and Corra 1977).

For empirical implementation, stochastic frontier studies have relied most heavilyon either the translog or Cobb-Douglas specifications. Although the translog can offergreater functional flexibility, it raised a number of issues in the present study andeventually gave way to the Cobb-Douglas.2 Thus, omitting the institutional (i) and

2 Evaluations of the translog produced estimates whereby more than half of the coefficients failed to meetany reasonable level of statistical significance and output and wage variables carried large negative costeffects that raised additional doubts concerning the appropriateness of the specification. Moreover, in onetranslog model scenario it was not possible to achieve convergence. In another model scenario, thelikelihood ratio test could not reject the Cobb-Douglas over the translog.

Stochastic Cost Frontier and Inefficiency Estimates 189

time (t) subscripts for expositional convenience, the university cost frontier to beestimated is:

C ¼ a0 þX

j

aj ln Yj þX

k

bk lnwk þX

m

dm ln zm;it þ vþ uð Þ ð4Þ

where the zm,it environmental variables are shifted to the inefficiency term (3) whenModel II is employed. The empirical implementation will include three outputs (J03), two input prices (K02), and four environmental factors (M04). Cost frontiers andinefficiencies are estimated for both public and private non-profit university sectors.3

Panel data for individual universities span four academic years (T04).

Data

Data for individual universities are taken from the U.S. Department of Education,National Center for Education Statistics, and the Integrated Postsecondary EducationData System (IPEDS). IPEDS changes periodically, thereby creating some longitu-dinal data problems. In addition, data releases occur with considerable annual lags.Here, data uniformity allowed for construction of a panel data set covering academicyears 2005–06 through 2008–09. The sample of universities are comprehensiveinstitutions and include Carnegie classified universities and colleges that offer a widerange of baccalaureate programs and engage in graduate education at the masterdegree level. In this respect, the sample is fairly homogeneous in terms of institutionalmissions. It is absent of the financing and cost allocation issues associated withuniversity medical schools and law and other professional schools common to thepublic and private flagship universities. By the same token, excluded are two-yearcommunity colleges heavily engaged in vocationally oriented education. Upon omit-ting universities that failed to complete the necessary survey, a balanced sample aroseand included 257 public and 297 private non-profit universities.

Table 1 lists the university cost and inefficiency variables along with their descrip-tive statistics. The total cost (C) measure along with the undergraduate teaching(UNGRAD), graduate teaching (GRAD), and research (RES) output measures areof fairly standard use in many higher education cost studies (e.g., beginning withCohn et al. 1989 and continuing through Koshal and Koshal 1999; Sav 2004, andLenton 2008, among others). These same studies provide a discussion of the caveatsassociated with these measures but, in the end, employ them with admission that theyare the best obtainable proxies that can be extracted from available data sets. Thesame applies to the use of an average faculty wage for the input price, except previousstudies have relied on a single wage whereas here there can be a potential contributionarising from incorporating a dual wage measure. The wage for nine month faculty(WAGE9) is generally applicable to teaching faculty on nine month contracts. The

3 Chow tests on the OLS estimates produced statistically significant F values that confirmed structuraldifferences in the public and private sectors: F(6, 2204)020.82 and F(9,2200)033.23 with and withoutenvironmental factors, respectively. Following the cost frontier implementations, structural differenceswere again confirmed: with 16 df, #2051 and 39 with and without environmental factors, respectively.The conclusion of structural differences supports previous findings (e.g., beginning with Cohn et al. (1989)and subsequently Koshal and Koshal (1999), Sav (2004), and Lenton (2008), among others).

190 G.T. Sav

twelve month wage (WAGE12) is more commonly applied to university administra-tors on twelve month contracts. And although this is the general application, there areinstances where the use of twelve month contracts are used merely as bookkeepingpractices or assigned to faculty working under research grant monies. Thus, somecaution may be owed in interpreting the empirical results obtained with respect to thetwelve month wage variable.

Four environmental factors are included to capture possible effects of varyingcharacteristics associated with students, faculty employment, and the degree ofgovernment ownership. As with Stevens (2005) and Chakraborty and Poggio(2008), data availability controls the selection of such variables. Presently, as withboth of those studies, the inefficiency term includes a control for minority enrollments(MINORITY). For universities, minority enrollments have created new academicopportunities but have also brought new challenges. Some universities may be moreefficient in terms of creating new programs and student centers focused on integratingdiversity into the academic curriculum and student life and, at the same time,attending to the need for implementing some remedial programs for underpreparedstudents arriving from lower income, underfunded minority school districts. Andwhile one can argue that universities engage in minority recruitment and, therefore,enrollments are at least partially under the control of the university, the assumptionhere is that they can be exogenously determined by immigration, migration, andgovernment provided minority and low-income educational grant opportunities.

In meeting enrollment demands and corresponding the teaching obligations, it isnot uncommon to find some universities employing greater proportions of non-tenuretrack instructors and part-time adjunct faculty. The extent of non-tenure track em-ployment may be limited by institutionally defined constraints (e.g., bylaws), exter-nally determined accreditation requirements, and access to non-tenure track facultylabor markets. But, as a group, non-tenure track faculty generally receive consider-ably lower wages relative to tenure track and tenured faculty and, therefore, theirrelative employment can affect cost and efficiency measures. However, a priori it isnot clear that their employment leads unambiguously to efficiency gains when as

Table 1 Variable means and standard deviations

Variable Description Public Private

Mean Std. Dev. Mean Std. Dev.

C Total cost (expenditures), $ 1.28E08 7.83E07 6.55E07 5.48E07

UNGRAD Undergraduate enrollment, FTE 7159.63 4694.98 2533.59 1940.57

GRAD Graduate enrollment, FTE 983.69 893.84 911.99 1372.40

RES Research grants, $ 1.43E07 1.39E07 2.73E06 4.89E06

WAGE9 Average 9-month faculty salary, $ 61521 10819 56254 16857

WAGE12 Average 12-month faculty salary, $ 60971 37185 49459 36479

MINORITY Percent minority student enrollment, % 37.99 25.84 34.16 18.27

NONTRACK Percent non-tenure track faculty, % 17.50 9.57 26.32 27.00

TENURED Percent faculty with tenure, % 49.53 13.17 37.06 22.39

GOVT Percent revenue from government, % 34.52 9.49 0.34 1.63

Stochastic Cost Frontier and Inefficiency Estimates 191

substitute for tenure track faculty there can be forgone research output that subse-quently leads to inefficiency increases. To examine part of the effect, the percent oftotal faculty employment under non-tenure track (NONTRACK) status is included inthe cost and inefficiency effect. At the same time, we wish to account for possiblecost or inefficiency effects that can be attributed to the tenure process, thus, theinclusion of the percent of total faculty employment that is tenured (TENURED).Certainly, it is not appropriate here to provide arguments for or against tenure or toattempt any sound review of the massive body of literature related to those argu-ments. Suffice it to say that from a cost perspective, there are those that claim tenurecreates inefficiencies due to so-called personnel inflexibilities and those that welcomethe cost saving efficiencies ingrained in the employment stability created by thetenure system. Perhaps the current empirical inquiry can help shed some light onthe matter.

The approach taken here provides separate sector estimates for public and privatenon-profit universities and therefore accounts for the underlying structural differencesbetween sectors. Those differences are attributed to the public vs. private ownershiparrangements. However, it seems additionally critical to recognize that all publicuniversities are not equal in their publicness nor are all private universities equallyprivate. Both public and private universities receive varying amounts of governmentlegislated appropriations and, therefore, compared to other revenue source dependen-cies can be said to differ in their degree of public and private ownership structure. Toinvestigate the extent to which this degree of publicness can alter cost frontiers andimpose cost inefficiencies or result in efficiency gains, the percent of total universityrevenues received from combined federal, state, and local government appropriatedfunding (GOVT) is included as an environmental effect. The measure includeslegislated appropriations for current operations and excludes government grants,contracts, and funding for capital improvements.

As indicated in Table 1, public compared to private sector universities are onaverage larger producers of both undergraduate education (nearly three times theUNGRAD) and research (more than five times the RES), but not substantiallydifferent regarding graduate education (GRAD) output. In addition, faculty on bothnine month and twelve month contracts receive higher wages in public compared toprivate sector employment; on average, nearly 10 % more for nine month faculty and23 % more for twelve month faculty. The proportion of non-tenure track facultyemployment is lower (17 % vs. 26 %) among public relative to private universities.On average, nearly 50 % of public university faculty is tenured compared to 37 %among private universities. As expected, private universities do not exhibit a highdegree of public ownership according to the measure of average government funding(GOVT); less than 1 %. However, the sample range (not shown) of 0 % to 22 %indicates considerable public ownership presence among a portion of private univer-sities. That compares to an average of 34 % with a range of 4 % to 70 % existingwithin the public university sector.

The 2005–09 panel data are pre- and post-global financial crisis and, therefore,could possibly capture the effects of such on university operating cost efficiencies. Todo so, the empirical implementation introduces academic year controls as environ-mental factors into the cost frontier and the inefficiency term, depending upon thespecified model.

192 G.T. Sav

Results

Table 2 presents the maximum likelihood estimates for both public and privateuniversities under the two efficiency models: Model I, with environmental factorsdirectly affecting university costs and Model II, with environmental factors asdeterminants of university inefficiency. In all cases, the likelihood ratios are highlysignificant, thereby rejecting the restricted OLS models. In addition, the g estimatesare significant and indicate that inefficiency can play an important role in universitycost analysis. Both models appear to perform extremely well in capturing eachsector’s underlying structure of cost and inefficiency.

Across the board, the output and wage coefficients are significant beyond the 5 %level with the vast majority reaching significance at better than 1 %. In addition, withthe exception of the private sector twelve month faculty wage, all the output and wagecoefficients carry positive signs, as might be expected. The negative twelve monthwage effect present in the private sector could be due to bookkeeping or accountingpractices suggested earlier or to real productivity effects associated with higher wage

Table 2 Cost frontier estimates for public and private universities

Variables Public Private

Model I Model II Model I Model II

α0 10.399 *34.02 9.322 *38.91 13.075 *78.13 10.379 *67.87

UNGRAD 0.681 *30.93 0.786 *53.95 0.298 *12.89 0.756 *40.42

GRAD 0.030 *2.78 0.090 *8.27 0.019 **2.05 0.132 *10.43

RES 0.005 *3.66 0.014 *4.82 0.003 **2.15 0.029 *7.63

WAGE9 0.086 *2.85 0.084 *5.78 0.033 *2.96 0.019 *2.67

WAGE12 0.026 *9.35 0.012 *7.23 −0.007 *−2.67 −0.008 *−4.82MINORITY 0.033 **2.35 0.066 *5.12 0.170 *12.13 1.021 *10.24

NONTRACK −0.029 *−2.59 −0.096 *−7.12 −0.020 **−2.36 −1.121 *−10.55TENURED 0.035 1.12 −0.031 −1.27 0.045 *4.97 −0.431 *−6.48GOVT −0.021 −1.18 −0.003 −0.17 0.035 ***1.80 1.060 *7.93

2006–07 0.073 *10.34 0.077 *3.71 0.085 *12.21 0.689 *5.57

2007–08 0.167 *15.37 0.188 *8.41 0.179 *20.66 1.612 *9.78

2008–09 0.187 *13.47 0.201 *8.93 0.219 *20.43 1.900 *10.23

δ0 0.575 **2.52 −5.331 *−9.43σ2 0.070 *8.40 0.043 *15.20 0.270 *17.40 1.341 *10.91

γ 0.955 *303.04 0.824 *3.02 0.983 *747.31 0.943 *138.84

η −0.004 −0.50 0.006 ***1.72

LL 911.60 182.44 709.96 −469.67LR Test *1461.38 *254.96 *2470.89 *245.78

N 1028 1028 1188 1188

Reported t values: asterisk, *denotes significance at the 1 %, **at the 5 %, and ***at the 10 %.

Stochastic Cost Frontier and Inefficiency Estimates 193

faculty. On either account, our data do not permit more precise investigation. Thus, inboth public and private universities, nine month relative to twelve month facultywages are estimated to have larger positive cost effects. Without exception, under-graduate education, relative to any output or wage, carries the largest cost impact.Under all model specifications, constant returns to scale is rejected. Under bothownership structures, we find significant economies of scale but the strength is notsymmetrical with respect to the model specifications, i.e., for the private sector,economies appear stronger in Model I compared to II, whereas in the private sectorthe reverse is true.

Turning to the significance of environmental factors in costs and inefficiency, thereis a slightly better showing in the private compared to the public sector. Within theformer, all the environmental coefficients except GOVT and NONTRACK, aresignificant at the 1 % level and better. However, even GOVT and NONTRACKbecome significant at the 5 % and 10 % level, respectively. In the public sector,GOVT and TENURED failed to reach the 10 % level of significance. Withoutexception, the results indicate that increased minority enrollments have both costincreasing and inefficiency increasing effects, while increases in the proportion ofnon-tenure track faculty employment generate reductions in both costs and ineffi-ciency. That’s in contrast to the tenured faculty effect. Tenure, while cost increasing,creates efficiency improvements. That would tend to support the notion that there arepossible efficiency gains to be realized in maintaining a stable labor force that isgranted through the tenure system. Based on the sign of TENURED, that conclusionholds for both public and private universities but is only supported by statisticalsignificance among the latter.

The control variables for academic years are all positive and statistically signifi-cant, therefore portraying a public and private sector industry trend of increasingcosts accompanied by increased operating inefficiencies. However, it is comforting tofind a substantial slowdown in the pace of both cost and inefficiency increases overthe academic years. For example, the academic year inefficiency effect (Model II) ineach sector more than doubled from 2007 to 2008 but from 2008 to 2009 it increasedonly 7 % in the public sector and 18 % in the private sector. Those inefficiencyslowdowns occurred despite the 2008 to 2009 academic year cost increases (Model I)of 12 % and 22 % in the respective sectors. In Model I, the estimated inefficiencydecay, η, indicates a relatively small but statistically insignificant efficiency loss forpublic universities. In the private sector, at the 10 % level of significance, η indicatesthat there occurred small efficiency gains.

Estimated inefficiency scores are provided in Table 3. Mean scores are presentedby academic year for each model. For public universities, the mean inefficiencyestimates are relatively insensitive to model choice. The major difference resides inthe rate of inefficiency change. By Model I estimates, inefficiency increased at anannual rate of 0.25 %. In comparison, Model II shows a substantial inefficiencyincrease from 2006–07 to 2007–08 of 11 % but followed by a 2008–09 inefficiencyslowdown of 2 % growth. In part, a different picture emerges in the private sector.There, the Model II mean inefficiency is less than half that of Model I; 1.444 vs.3.641. But as observed in the public sector, Model I shows private universitiesexperiencing a large inefficiency growth rate in 2007–08 that is more that cut in halfin 2008–09.

194 G.T. Sav

Overall, the results clearly indicate that any conclusions to be derived regardingpublic vs. private inefficiency differences must carefully consider the underlyingmodel assumptions. On average, public universities are more cost efficient by ModelI estimates while private universities are more efficient under the Model II specifi-cation. Also, the difference in public vs. private inefficiency varies considerably bymodel. In Model I, the mean private university inefficiency is 104 % greater than themean public inefficiency. In comparison, the Model II mean public university inef-ficiency exceeds by only 20 % the private inefficiency. However, in both cases thereis a statistically significant (at 1 % level) difference in the mean inefficienciesbetween the two sectors.

Returning to the effect of government funding or publicness on inefficiency, theModel II results for private universities indicated a significant and inefficiencyincreasing effect of GOVT. However, in the public sector, more GOVT was foundto be efficiency improving, although statistically insignificant. But the level ofgovernment funding in the sample of private universities reaches a maximum of22 % compared to 70 % for the public universities. Given the overall variationexisting in the public sector, it can be useful to divide the sample into differentgovernment funding levels. To investigate such, Model II was reestimated for publicuniversities divided into small, medium, and large institutions according to thepercentage of revenues received from government funding (GOVT) being less than30 %, 30 % but less than 40 %, and greater than or equal to 40 %. Table 4 presents thereestimated GOVT effect and the mean inefficiencies. For the small public universi-ties, GOVT remains positive but statistically insignificant. However, at the mediumand large public levels, the GOVT effect becomes efficiency improving and signif-icant at the 5 % level and better. Compared to the previous public sector meaninefficiency of 1.731, the reestimated mean inefficiencies are reduced for the small(1.335) and large (1.104) GOVT funded public universities and slightly increased forthe medium (1.794) level institutions. The reestimates suggest that the smaller andlarger GOVT funded public universities are on average less inefficient than theprivate sector universities (1.444), but that the medium GOVT funded publics thatcomprise 47 % of the sample remain more inefficient than the private universities. As

Table 3 Academic year inefficiencies for public and private universities

Public Private

Model I Model II Model I Model II

2005–06 1.771 1.538 3.691 1.399

2006–07 1.775 0.25 % 1.657 7.70 % 3.658 −0.90 % 1.396 −0.21 %

2007–08 1.778 0.25 % 1.845 11.39 % 3.625 −0.90 % 1.476 5.75 %

2008–09 1.784 0.25 % 1.884 2.11 % 3.592 −0.90 % 1.515 2.65 %

Median 1.727 1.679 2.993 1.221

Mean 1.778 1.731 3.641 1.444

N 1028 1028 1188 1188

Stochastic Cost Frontier and Inefficiency Estimates 195

with the previous estimates, the reestimates show substantial public sector growth inthe annual rates of inefficiency increases from the 2005–06 through the 2007–08 andthen a major decline in the percentage growth rate in the 2008–09 academic year.

Conclusions

This paper investigates the extent to which there exist differences in the operatingcost inefficiencies of publicly owned compared to privately owned non-profit uni-versities and how many of those differences could possibly be attributed to varyingamounts of publicness defined by government funded revenue dependency. Stochas-tic cost frontiers using panel data for U.S. comprehensive universities were estimatedunder two alternative time varying efficiency models. Panel data covered fouracademic years, 2005–06 through 2008–09, for 257 public universities and 297private non-profit universities.

The results indicate that including environmental factors along with output andfactor prices in the cost function, public universities are on average more costefficient than private universities. Yet when the identical environmental factors aremodeled as inefficiency determinants, then the results suggest that private com-pared to public universities are the more cost efficient institutions. Assuminguniversity decision-makers have less rather than more short-run control overenvironmental factors, then the latter modeling assumption and subsequent con-clusion would be more appropriate. A major thrust of the paper also recognizedthat public ownership as defined by the university’s revenue dependency ongovernment funding differs among public universities and also makes some privateuniversities partially public. Increased government funding or the degree of pub-licness was found to contribute to an increased inefficiency among private univer-sities but efficiency improvements among heavily government funded publicuniversities. Finally, regardless of the modeling assumptions, both public andprivate sectors were found to experience increased inefficiency growth rates foreach academic year from 2005–06 through 2007–08. However, the findings

Table 4 Re-estimated government effect and inefficiencies for public universities

Small (Govt<30 %) Medium (30 %≤Govt<40 %) Large (Govt≥40 %)

GOVT (t value) 0.015 (0.71) −0.437 (*−5.01) −0.335 (**−2.11)Inefficiencies

2005–06 1.224 1.580 1.080

2006–07 1.300 6.2 % 1.704 7.8 % 1.091 1.0 %

2007–08 1.389 6.8 % 1.925 13.0 % 1.113 2.0 %

2008–09 1.409 1.4 % 1.966 2.1 % 1.131 1.6 %

Median 1.292 1.714 1.045

Mean 1.335 1.794 1.104

N 332 32 % 480 47 % 216 21 %

Reported t values in ( ): asterisk, *denotes significance at the 1 % and **at the 5 %.

196 G.T. Sav

suggest a possible operating adjustment that led to a significant 2008–09 academicyear slowdown in the pace of inefficiency inflation for both public and private non-profit universities. That adjustment occurred following the global financial crisis.Thus, there is some evidence that both higher education sectors moved towardgreater cost efficiency. Whether or not that is sustainable will have to awaitadditional years of observed university production and costs.

At the time of the present research, a literature survey did not produce anycomparable studies of public vs. private U.S. university cost inefficiencies usingstochastic frontier methodologies. The study of English and Welsh universities byStevens (2005) remains the closest for comparative purposes. That study included afour year panel of 80 universities, but only up to 1999, and it could or did not accountfor public-private ownership or government funding differences. The English andWelsh inefficiency scores ranged from approximately 1.01 to 2.01 and averagedaround 1.2 to about 1.3 depending upon the model assumptions. Those inefficienciesare comparable to the inefficiencies found here for the small and large governmentfunded public universities but are considerably lower than the private universities andmedium government funded public universities. Other studies have employed differ-ent methodologies, specifications, and data that result in efficiency scores not directlycomparable to either the present work or that of Stevens (2005). For example, the1992–93 cross section study of 45 Canadian universities by McMillan and Chan(2006) does not seem comparable given technological changes occurring over nearlytwo decades. Finally, those studies along with the present research are plagued withthe usual measurement problems. In particular, there remains the elusive problemassociated with measuring educational quality on both the input and output sides. Inaddition, an aggregate measure of institutional research output and its quality is stillunavailable for large samples of universities. Any improvements on these accountswould be welcomed additions for future research. Moreover, while the present studyhas focused on public vs. private non-profit universities, the for-profit universitysector has been rapidly expanding within the U.S. and abroad. Although the for-profitentry is currently the largest at the vocational and two-year degree or certificateoffering level, the beginning of investigations into the relative efficiency of for-profitscould prove to be a useful and fruitful line of research inquiry.

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