Persistent inefficiency in the higher education sector: evidence from Germany

ABSTRACT

Utilizing panel data and taking heterogeneity and persistent inefficiency into account, we show the limitations of standard efficiency analysis for higher education institutions. It is the first time that the concept of long-term inefficiency is considered in the analysis of traditional universities. This inclusion allows for more accurate estimations and more purposeful policy recommendations. The new specification improves the accuracy of the heterogeneity assumption and exposes inefficiency’s tendency to be persistent. Thus, this paper finds that an efficiency increase can be achieved only if future measures aim at long-term conditions, which are presumably determined outside of individual institutions.

KEYWORDS:

• Efficiency
• higher education
• stochastic frontier analysis
• persistent inefficiency
• heterogeneity
• Germany

JEL CLASSIFICATION:

• C14
• C23
• D61
• I22
• I23
• H52

Acknowledgments

I am grateful for the valuable comments from Tommaso Agasisti, Heike Auerswald, Alexander Kemnitz, Marcel Rentsch, Silke Übelmesser and two anonymous referees. Moreover, I thank the participants of the 4th Workshop on Efficiency in Education (2016) for an inspiring discussion. I acknowledge support from the Federal Statistical Office of Germany, especially Marco Threin, for providing the data and helpful remarks.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Sabine Gralka http://orcid.org/0000-0001-8303-4297

Notes

1. The Battese and Coelli (1992) specification is seen as the standard approach to efficiency estimation due to its wide application.

2. Master’s institutions are thereby classified as teaching-oriented institutions that confer mainly bachelor’s and master’s degrees and account for less than 1% of doctoral degrees conferred (see Titus, Vamosiu, and McClure (2016) for a detailed discussion).

3. The terms ‘East’ and ‘West’ thereby refer to institutions located in the two separate German areas before the reunification in 1990, with Brandenburg, Mecklenburg-Vorpommern, Saxony-Anhalt, Saxony and Thuringia being part of the former German Democratic Republic (so-called ‘East’ Germany).

4. See for example Johnes and Johnes (2009) for the UK, Sav (2012) for the US, Zoghbi, Rocha, and Mattos (2013) for Brazil, Longlong, Fengliang, and Weifang (2009) for China and Bolli et al. (2016) for an EU country comparison.

5. See for example Johnes and Johnes (2009) and Johnes and Schwarzenberger (2011). Exceptions are the recent studies from Bolli et al. (2016), who looked at a ten-year period, and Titus, Vamosiu, and McClure (2016) who examined a nine-year period.

6. An alternative concept of including heterogeneity relaxes the assumption that all units must face the same underlying cost function. The ‘Random-Parameter’ model developed by Tsionas (2002) and Greene (2005a) allows the parameters of the function to vary across institutions, while the institution-specific parameters are constrained to be constant over time. Using panel data, the model has been applied for the HE sector of selected countries (see for example Johnes and Johnes (2009) for the UK and Johnes and Schwarzenberger (2011) for Germany). The model entails a complex econometrical implementation (Kumbhakar, Wang, and Horncastle 2015).

7. See for example Johnes and Johnes (2009) for the English HE sector, Agasisti and Johnes (2015) for the Italian HE sector and Johnes and Schwarzenberger (2011) for the German HE sector. An extended review of the models can be found in the survey by Greene (2008).

8. Along with Kumbhakar, Lien, and Hardaker (2014), similar models were developed simultaneously by Colombi et al. (2014) and Filippini and Greene (2016). Kumbhakar and Heshmati (1995) proposed the first estimation specification that includes the idea of persistent inefficiency. They assumed that the time-invariant component is due entirely to long-term inefficiency and thereby neglect the notion of heterogeneity.

9. See for example Filippini, Greene, and Masiero (2016) for an application to the electricity distribution area and Heshmati, Kumbhakar, and Kim (2016) for an analysis of international airlines.

10. Due to a substantial merger within the period, the universities ‘U Duisburg-Essen’, ‘Brand. TU Cottbus-Senftenberg’, and ‘HafenCity U Hamburg’ are omitted from the sample. It must be noted that almost all universities have undergone smaller restructurings, which are not explicitly discussed.

11. Amongst other distortions, the predefined smaller size of universities of applied science could lead to seemingly more efficient universities, assuming economies of scale in the HE sector (as ascertained by Koshal and Koshal (1999) and Olivares and Wetzel (2014), for example). It should be pointed out to the reader that this exclusion could also naturally lead to distortion.

12. The exclusion of medicine-related factors is common in the efficiency estimation of German universities, as shown in Kempkes and Pohl (2010), because university hospitals in Germany, which teach the subject of human medicine, are associated with a university but possess their own management, teaching facilities, budgets and accounting systems. This strong delimitation allows the German Federal Statistical Office to provide separate, university-hospital-specific data.

13. A comprehensive view of possible input and output factors can be found in De Witte and López-Torres (2017) and Warning (2007), with special attention to the German HE sector.

14. Instead of the amount of students, the number of graduates can be used in the estimation. We follow the argumentation from Olivares and Wetzel (2014) and reason that students are cost drivers and increase their human capital before completing their degrees.

15. Ph.D. students are not included as an output variable in order to avoid bias from double counting. Within the German HE sector, the majority of Ph.D. students work as research associates and are hence considered in the wage rate. Additionally, Frässdorf and Frässdorf (2016) note that the data from the Federal Statistical Office are not without issues and can represent only around half of doctoral candidates in Germany.

16. General science contains mathematics, natural sciences, veterinary medicine, agricultural, forest and nutritional sciences and engineering. Non-science subjects are courses related to art, economics, law, sports and culture.

17. Third-party funds encompass contributions from the German public domain (primarily the federal government, federal states, the federal labor office and municipalities) and contributions from the European Union and the German Research Foundation, as well as funds from private and industrial foundations and investors.

18. The Federal Statistical Office defines scientific employees primarily as professors, lecturers and research associates. Technical employees are employees within the administration and libraries and technicians, caretakers and care staff.

19. This step allows us to – among other things – control for the fact that HE institutions experience strongly varying non-completion rates (for more details, see Johnes (2014)). Furthermore, Agasisti and Haelermans (2016) showed that the sole consideration of students or graduates leads to strongly varying efficiency results.

20. Not all applied models are available within a statistical package; hence, the model by Greene (2005a) is conducted in LIMDEP, while the others are executed in STATA.

21. Recently, the (multi-) input/output distance functions have gained popularity within the efficiency estimation (Abbott and Doucouliagos 2009; Bolli et al. 2016). In the present study, we follow the argument of Kempkes and Pohl (2010), who choose to estimate a cost function compared to a distance function, as the interpretation of the coefficients are more intuitive in the context of a cost function.

22. To verify the assumption for the present dataset, a skewness test on the ordinary least squares residuals was conducted and found to be significant, providing support for the cost frontier specification of the model.

23. The literature emphasized the difficulty of choosing a cost function and highlighted three functions that make sense in the general multiproduct context. Baumol et al. (1982) were the first to determine the requirements and propose the constant elasticity of substitution and the quadratic and translog specifications. The first of these is known to present some conceptual difficulties (Johnes 2004; Titus, Vamosiu, and McClure 2016). The second, which is used by most studies implementing the heterogeneity aspect, has the disadvantage of depending on numerous assumptions. The last is demanding both in terms of data and it’s highly non-linear specification but has the advantage of having a sufficiently flexible form.

24. In principle, efficiency could follow any non-normal distribution such that it can be separated out from the other residual term, but a common assumption is that it follows a half-normal distribution. For a comparison of the most frequently used distributions and their impact, see Eagan and Titus (2016).

25. It has been argued that there is endogeneity in this model caused by the explanatory variables being related to the error term. The existence of inefficiency could lead firms to change their production decisions (O’Donnell 2014). We follow the argumentation from Johnes and Tsionas (2016) and reason that universities are inflexible regarding certain inputs due to government restrictions.

26. A similar model was proposed by Kumbhakar (1990). The specifications differ only in the form of the time-varying component, where the mentioned model has one additional parameter. The estimation of both models and a subsequent likelihood-ratio test showed that the extra parameter is not warranted, and hence, the Battese and Coelli (1992) model is selected.

27. It can be argued that the four error component model is inefficient relative to a maximum likelihood estimation method, as shown by Heshmati, Kumbhakar, and Kim (2016). We deliberately choose the component model due to its relatively straightforward estimation procedure compared to the simulated maximum likelihood method and the opportunity to verify the estimation results in every step.

28. For a discussion of the relatively new model and a detailed simulation, see Badunenko and Kumbhakar (2016).

29. Kumbhakar, Wang, and Horncastle (2015) argued that the estimation results should be expected to vary among the three methods.

30. The implications of the cost function for economies of scale and scope in university production are not the main thrust of this study and are therefore not considered in any depth.

31. The value implies that universities could decrease their costs by approximately 66% without reducing their output.

32. It must be noted that inclusion of the dummy implies the assumption that East and West Germany differ in their production technology.

33. This is caused by the high amount of (interaction) terms in the translog regression specification relative to the small sample size.