CESifo Economic Studies

CESifo Economic Studies Advance Access originally published online on May 28, 2008
CESifo Economic Studies 2008 54(2):177-203; doi:10.1093/cesifo/ifn009

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Do Institutions Matter for University Cost Efficiency? Evidence from Germany

Gerhard Kempkes^* and Carsten Pohl

* Dresden University of Technology, Department of Business Management and Economics, 01062 Dresden, Germany, e-mail: gerhard.kempkes{at}gmail.com
Institute for Employment Research, IAB NRW, Josef-Gockeln-Straße 7, 40474 Düsseldorf, Germany, e-mail: carsten.pohl{at}iab.de

	Abstract

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
Efficiency analyses on higher education institutions have so far primarily focussed on the identification of inefficiency and less on the explanation of differences in efficiency performance. In this article, we study the impact of institutional factors on the efficiency of 67 publicly financed German universities for the years 1998–2003. We present some evidence that university costs and outputs are correlated with institutional settings such as the management structure of universities or the universities’ staff body. Furthermore, econometric evidence from a single-stage stochastic frontier model (based on a cost function) suggests that universities which are located in states with a comparatively liberal university legal framework are more efficient than those universities operating under more restrictive state regulation. (JEL codes: l28, L32, H72)

Key Words: Higher education • institutions • cost efficiency • stochastic frontier

	1 Introduction

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
Economic growth theory as well as a substantial body of empirical studies is important for its economic and non-economic well-being to a significant extent (OECD 2006). Human capital formation in turn is based on public higher education in many countries. In times of tight public budgets the efficient spending of public funds is receiving increasing attention in the economic-political debate. Despite the importance of the education sector for the economy, the question of efficient allocation of public resources in the university landscape has only recently been investigated for industrialized countries. Existing studies have predominantly focussed on the identification of differences in efficiency scores across universities (see Worthington 2001 for an overview). In contrast, there are only few empirical investigations that focus on the determinants of these inefficiencies. A prominent exception is a recent study, which finds university research performance and university efficiency to be related to university autonomy (Aghion et al. 2007).

Against this background, we first derive hypotheses with regard to the impact of institutional settings on university cost efficiency. Using a data set of 67 publicly financed German universities for the years 1998–2003 we study whether university costs and outputs are correlated to institutional settings and whether institutions may explain differences in cost efficiency performance across German universities. We present some evidence that university costs and outputs are correlated with the management structure of universities or characteristics of universities’ staff body. Furthermore, econometric evidence from a single-stage stochastic frontier model (based on a cost function) suggests that universities which are located in states with a comparatively liberal university legal framework are more efficient than those universities operating under more restrictive state regulation.

The remainder of this article is organized as follows. In section 2 the related literature on efficiency analysis of universities is surveyed. Based on this review we derive our hypotheses on the determinants of university inefficiency in section 3. In section 4, we provide descriptive statistics for our data set. In section 5, we first conduct a correlation analysis between university in-/outputs and institutional variables. Second, a single-stage stochastic frontier model, which is based on a cost function, is estimated in order to shed some light on causation of institutional settings on university efficiency. Section 6 concludes.

	2 Related literature

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
Early studies on university cost efficiency have predominantly focussed on single departments across universities since these can be assumed to have similar structures (e.g. Dundar and Lewis 1995; Johnes and Johnes 1995; Madden and Savage 1997 or Tomkins and Green 1988). More recent studies have evaluated entire universities because this often makes available panel data sets in the first place (e.g. Izadi et al. 2002 or Flegg et al. 2004). Empirical investigations on university cost efficiency have been conducted particularly for anglo-saxon countries such as the United Kingdom or Australia. In contrast, the efficiency of higher education institutions in Germany has only recently been studied by Warning (2004, 2005) for cross-section data as well as by Kempkes and Pohl (2007) in a panel data context. Since divergent institutional frameworks complicate cross-country comparisons there are only few investigations that have applied efficiency analysis on higher education institutions across countries (e.g. Agasisti and Pérez-Esparrells 2007 or Doucouliagos and Abbott 2007).

Whereas the large majority of existing studies reveal differences in cost efficiency across universities and/or single departments, little is known about the factors that drive these inefficiencies. In this context, the survey on frontier efficiency measurement in higher education by Worthington (2001) shows that early investigations have focussed primarily on the socio-economic background of students and/or parents since these characteristics have also been shown to be important determinants for educational achiement.¹ More recent studies do not only use characteristics of the enrolled students (proportion of female students, arts students, etc.) but also of university staff (age structure, proportion of professors, etc.). For instance, Stevens (2005) finds that a higher proportion of quality staff corresponds to more efficient universities. In line with this approach, Doucouliagos and Abbott (2007) include the ratio of non-academic to academic staff and the proportion of senior administrative employees as determinants of efficiency. The authors do not only find that a higher proportion of senior administrative staff is associated with higher levels of efficiency but also show the ratio of non-academic to academic staff is positively correlated with efficiency. Overall, these results suggest that (senior) administrative staff is able to disburden academics from time-consuming but unproductive administrative responsibilities.

However, due to endogeneity concerns, these results have to be interpreted with some caution due to endogeneity concerns. For instance, the causality between university cost efficiency and the share of professors in total staff might run both directions. On the one hand, a higher density of full professors might cause the university to operate more efficiently, but on the other hand, more efficient universities might simply choose to employ a higher density of full professors. For this reason, we suggest to include only variables that can—a priori—assumed to be strictly exogenous as explained in the hypotheses section.

Regarding institutional settings, Kuo and Ho (2007) investigate the impact of a university funding reform in Taiwan on university efficiency. The introduction of the University Operation Fund (UOF) in 1996 was intended to improve the cost efficiency of the Taiwanese university landscape. Comparing university efficiency before and after the introduction they conclude that the reform had a negative effect on the efficiency of public universities in Taiwan. Based on US state-level data and on evidence from OECD countries, Aghion et al. (2007) and Aghion (2007) suggest that university autonomy is not only associated with better research performance of universities but also with more efficient use of university funds.

Overall, the literature does not provide a clear-cut guidance on which set of explanatory variables should be included as determinants of cost inefficiency in an analysis on higher education institutions. Existing studies were instead driven by data availability for possible environmental variables. In particular, it is only recently that some evidence on the link between the efficiency of spending and institutional settings in universities and the governing public body or the corresponding legal frameworks has been presented.

In the next section, we derive hypotheses on the determinants of university efficiency focussing on institutional factors. As institutional variables we consider factors that are related to the management, the staff and student body, and the legal framework under which the university operates.

	3 Hypotheses

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
As argued previously, recent empirical evidence suggests that the autonomy of universities plays a significant role in determining the efficiency of university spending. Budget- and wage-setting autonomy in the German higher education system is rather low. However, the hiring autonomy is considered to be relatively high (Aghion et al. 2007).

Whereas the general institutional framework framework for the German university system is set by the federal government level ("Hochschulrahmengesetz"), higher education remains a core responsibility of the German states. The states define the institutional framework for higher education in more detail, which gives us the opportunity to exploit variation in the regulation of higher education across the German states.² State legislation for the universities encompasses a wide variety of aspects such as the allocation of university funds (e.g. the ability of universities to carry over year-end balances, lump-sum vs. line-item budgets), employment of professors (e.g. whether universities can autonomously decide on employment of professors without consulting state ministries), managerial power of the university management (power of decision of the rector/president as opposed to state intervention) and teaching (autonomous establishment of new university career programmes).

In 2000, the "Stifterverband für die Deutsche Wissenschaft", an influential think tank for the German university landscape, set up a commission of experts in order to evaluate the state laws for higher education which emerged after 1998. This evaluation has been conducted with an explicit focus on the autonomy of German universities.³ The Stifterverband (2002, p. 28) concludes with a final classification of state laws, dividing them into three groups: a "best-law" group, a "medium-law" group and a "worst-law" group with respect to self-governance and autonomy of universities, which is reported in Appendix 1.⁴ The category "best-law" stands for a relatively autonomous legal framework whereas "worst-law" corresponds to restrictive rules.

Given the evidence presented by Aghion et al. (2007), Aghion (2007) and related evidence from the literature on educational production functions (e.g. Wößmann 2007) and given the variation of university regulation across the German states, we formulate hypothesis 1:

Hypothesis 1: Universities located in states which allow universities more autonomy are more cost efficient than universities operating under a more restrictive regulatory framework.

Furthermore, it would be interesting to test the impact of performance-based funding mechanisms that have been implemented by some German states at the end of our sample period (2003). These mechanisms are often a means of increased budget autonomy for the universities. However, to this day "in many cases, performance-based funding only determines a marginal part of total budget allocations and discretionary, incremental funding dominates" (Orr, Jaeger and Schwarzenberger 2007).⁵ Thus, assessing these reforms is not very promising since the share of funding which is allocated based on university performance is marginal. Moreover, due to the time span of our data set, we cannot expect to measure any impact of these reforms.⁶

In Germany within the group of publicly financed universities there are universities which allow earning classical university degrees only whereas at so-called comprehensive universities both, classical university degrees as well as degrees of universities-of-the-applied-science—status may be earned. Note that the quality of the latter degrees is considered to be below the classical university degrees. Comprehensive universities have been established since the beginning of the 1970s. The idea was to have a unified organizational structure for universities and universities of applied science. In addition, the merger of scientific personnel between these two types of institutions was assumed to provide beneficial effects for teaching and research output. Hence, given this framework one may assume that comprehensive universities "produce" more graduates ceteris paribus and thus operate more efficiently than classical universities.

Hypothesis 2: Comprehensive universities are more cost efficient than classical universities.

Almost 20 years after German reunification, universities in Eastern and Western Germany have quite similar structures. However, evidence presented by Warning (2005) as well as Kempkes and Pohl (2007) suggests that universities in Western regions are more efficient than higher education institutions in Eastern Germany. In order to make sure that we are not only exploiting East/West differences with our institutional variables, we include the dummy variable EAST as a control.

Hypothesis 3: Universities in Western Germany are more cost efficient than universities in Eastern Germany.

The empirical literature on the link between demographic structure and public education spending finds for many countries that total education spending is not adjusted proportionately in response to varying sizes of the student cohort. Thus, spending per student rises if cohort size decreases and vice versa. (see e.g. Poterba 1997 for the US, Baum and Seitz 2003 for West Germany or Grob and Wolter 2007 for Switzerland). One of the main reasons for this phenomenon seems to be institutional inflexibility of public administration. Since the large majority of students in German universities are native from the state in which the university is located, one can expect university efficiency to increase (decrease) rather mechanically if the relevant age cohort (aged 18–35) in the respective state increases (decreases). Note that the source for this inefficiency is not rooted in the university but rather in state management of university funds.

Hypothesis 4: Universities can improve cost efficiency in times when demand for higher education in the state increases.

The Bologna process might be considered a further aspect in altering the efficiency performance of German universities. One key element is the introduction of internationally accepted bachelor and master degrees replacing national "Diplom"-degrees, which may be measured by the share of bachelor/master degrees out of total degrees. While some German universities have immediately followed the Bologna declaration other universities lag behind. Thus, efficiency could be improved/deteriorated by adapting to the requirements of the Bologna process; specifically universities adapting faster might boost their efficiency performance given that the Bologna declaration states inter alia that European higher education institutions should become more compatible and comparable in order to promote the exchange of students as well as the employability of citizens in the EU (van der Ploeg and Veugelers 2007). The reluctance of the remaining universities might be interpreted as an aversion to realize reforms, which suggests that these institutions are less efficient. However, it is rather obvious that it is not easy to identify causes and consequences in this case. Fast adapting universities may thereby boost efficiency but it may also be the case that more efficient universities adapt faster to the Bologna requirements. Our hypothesis is therefore restricted to correlation and does not suggest causation.

Hypothesis 5: Universities that rapidly adapted to the Bologna requirements are more efficient than slowly reforming higher education institutions.

Traditionally, German universities were managed by a university rector while younger universities are often operated by a university president. The differences between these two regimes are generally considered to be of minor importance. However, there are some differences, e.g. the minimum incumbency for presidents is four years, while rectors use to stay in office for shorter periods (Kühler 2005; Landfried 2000). Moreover, candidates who run for rectorate usually come from the inhouse-professorate, whereas university presidents may also come from external institutions (Kühler 2005). These differences lead to the common perception that university presidencies have somewhat more decision-making power and may thus lead a more professional university management.

Hypothesis 6: Universities managed by a president are more efficient than universities managed by a rector.

However, state legislation in some cases permits universities to choose between the presidential/rectoral regimes (Kühler 2005). Thus, we cannot completely rule out that the university regime is chosen contingent on the degree of university efficiency and that the university regime may have to be considered as endogenous.

With regard to the composition of university staff Duncombe, Miner and Ruggiero (1997) derive from public choice theory that tenure of public service employees is negatively associated with efficiency in public service provision. Since in Germany professors at universities have tenure we use the proportion of professors on total scientific staff as a determinant of university efficiency. However, Stevens (2005) finds that a higher share of qualified personnel (proportion of professors) has a positive influence on the efficiency of universities (net of the higher wages higher quality staff usually earns).⁷ Hence, there are ambiguous predictions from theoretical and empirical literature with regard to the efficiency in public service provision. Moreover, note that the staff composition of universities may merely be an indicator of efficient universities and that there may be no/little causal effect. Thus, we cannot even provide a clear-cut hypothesis on the correlation between the ratio of professors over total scientific staff and university efficiency.

University efficiency might also be influenced by the socio-demographic composition of enrolled students. As pointed out in the literature survey, previous studies investigating the determinants of university efficiency have predominantly focussed on this issue. In particular, Stevens (2005) as well as Doucouliagos and Abbott (2007) use the proportion of foreign students arriving at mixed results. Whereas Stevens (2005) does not find significant effects for British universities, Doucouliagos and Abbott's (2007) estimates suggest that a high proportion of overseas students is positively linked to efficiency performance in Australian universities. Following the literature, we also include the proportion of foreign students in our investigation. In Germany, international students are assumed to enrol in a particular university on purpose whereas native students predominantly study in the state they grew up. A priori, we assume that foreign students study at universities which offer the best education and/or which provide a good organization and thus permit to graduate faster. For this reason, the share of foreign students may be interpreted as a sign of quality and/or of efficiency of the university.⁸ Again, causation may run both directions: A positive correlation between the share of foreign students and the efficiency performance of universities may simply reflect the preference of foreign students to study in an efficient institution and thus may be far from showing a causal effect on university efficiency.

Hypothesis 7: Universities with a high share of foreign students are more efficient than universities with a lower share.

In summary, we derived seven hypotheses on the link between university cost efficiency and several institutional characteristics of universities and/or state regulation. Recall that we restrict hypotheses 4–7 to correlations.

	4 Data

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
We use data on 67 German public universities for the years 1998–2003.⁹ Private universities, universities of applied science, universities of the armed forces as well as specialized universities are excluded from our data set. These institutions are either oriented towards business management or medical studies, focus on teaching only or are not open to students without military background. Their inclusion would result in an even more heterogeneous data set. Our data set represents roughly 90 percent of students enrolled in German universities and about 65 percent of students enrolled in tertiary education (including universities of applied science, art colleges, conservatoires and theological universities).

Data on the cost function, i.e. on costs, third-party funds, graduates and on the number of students as well as on staff expenditures, the number of employees and on faculty composition have been provided by the Federal Statistical Office of Germany. Information on institutional variables such as the share of professors out of total scientific staff, the share of Bachelor/Master degrees awarded out of total degrees (without PhDs), the share of university-of-applied-sciences degrees out of total degrees has been provided by the Statistical Office as well. The management structure of universities has been taken from university homepages. Population data has been obtained from the Federal Statistical Office of Germany. Due to data availability problems, a wage variable is approximated by divding total personnel expenditures in a university by the total number of university's; staff (as in Stevens 2005). Monetary variables, i.e. costs, third-party funds and wages, have been deflated using the government consumption deflator published by the German Council of Economic Experts (2006). With regard to the self-governance and autonomy of the universities we use a study conducted on behalf of the "Stifterverband für die Deutsche Wissenschaft" (Stifterverband 2002), which evaluated state university laws.¹⁰ In line with these results we distinguish between three mutually exclusive groups: a "best-law" group, a "medium-law" group and a "worst-law" group. The ranking indicates that universities located in federal states which belong to the best-law-group operate under a relatively liberal legal framework when compared to other German federal states.

Table 1 reports descriptive statistics for our dependent and independent variables. There is considerable variation in the data. One important reason for this is the differing faculty composition of the universities. For instance, the university with the highest costs per student in the sample is the university with the highest share of students enrolled to cost intensive medical/veterinarian and agricultural faculties. On the other hand, the university with the lowest costs per student is a distance learning university.

View this table: [in this window] [in a new window]   Table 1 Descriptive statistics

 
The average individual wage for a university employee amounts to 35,741 EUR in the years 1998–2003. Note, however, the rather crude wage definition. Around one-third of the higher education institutions in Germany are run by a presidential regime (PRESIDENT). Interestingly, between 1998 and 2003 only 1.5 percent of all graduates in Germany received a bachelor or a master degree although the Bologna declaration was already signed in 1999. One-fifth of all considered universities are located in Eastern Germany (EAST). With respect to university regulation we find that 39 percent of the universities operate under a relatively liberal legal framework ("best-law" group), whereas 16 percent of all higher education institutions are located in federal states which are considered to have a rather restrictive university regulation ("worst-law" group).

	5 Empirical analysis

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
For the empirical investigation we follow two approaches. First, we provide a correlation analysis in order to show how the cost and output variables are related to all considered institutional variables. Second, using the single-stage stochastic frontier model proposed by Battese and Coelli (1995) we investigate the effect of institutional settings on university cost efficiency focussing on variables that may be considered exogenous.

5.1 Correlation analysis
The correlation matrix for the costs, output and the institutional variables are provided in Table 2. The share of students enrolled in MEDICINE-, SCIENCE-, ENGINEERING- or SOCIAL SCIENCES-careers are included as controls in the cost function since the university cost structure and endowment depend substantially on the faculty composition. As expected a high share of medical students in a university corresponds to higher costs per students (0.8109). A high share of students in natural science also corresponds to more cost intensive universities (0.4014). In contrast, a high share of social sciences (–0.3920) or engineering students (–0.1140) comes along with lower costs per student.

View this table: [in this window] [in a new window]   Table 2 Correlation analysis

 
With regard to the institutional variables we study correlations with the cost and two output variables. As explained in the previous section we distinguish between three groups of state regulation, i.e. "best-law" group, "medium-law" group and "worst-law" group. Interestingly, universities which operate under a relatively liberal legal framework display a significant, positive correlation with third-party funds and the number of graduates per student. In contrast, for universities located in a state that is classified in the "worst-law" group there is a positive and significant correlation with the cost variable. Finally, universities in the "medium-law group" show a negative correlation with third-party funds but also with the cost variable. Hence, these correlations suggest one specific property of "best-law" universities is the ability to "produce" a higher amount of outputs per student with an average amount of inputs (costs) per student.

In addition to the autonomy of universities, we consider the cohort size of individuals aged 18–35 (COHORT) living within the region of the university, the university type (APPLIED) as well as a regional dummy in order to account for differences between Eastern and Western Germany (EAST). The correlation matrix in Table 2 shows that universities in Eastern Germany are more cost-intensive than their counterparts in Western Germany. In addition, universities in the new federal states seem to generate fewer graduates per student than higher education institutions in the West. A large cohort size of individuals aged 18–35 is not associated with lower costs per student but it comes along with a higher number of graduates per student reflecting that students usually enrol in a university of the state where they obtained their high school diploma. Comprehensive universities (APPLIED) not only display on average lower costs per student but also a positive correlation with respect to the number of graduates per student suggesting that these universities offer shorter career-programmes.

Further, we study the correlations between the presidential regime (PRESIDENT), the adaptation to the Bologna requirements (BOLOGNA), the share of foreign students in the overall number of enrolled students (FOREIGN), the share of professors in the overall staff of the university (PROFS) and the cost/output variables. For the endogeneity concerns discussed earlier, we only included these variables in the correlation analysis. A presidential regime (PRESIDENT) is negatively associated with the cost variable (–0.1495). A possible explanation is the better management capacity discussed in hypothesis 6. However, this correlation might also simply show that less cost-intensive universities choose the presidential regime. With regard to the adaptation to the Bologna process no statistically significant relationship with regard to the cost level and third-party funds is found. However, there is a negative and significant correlation between the BOLOGNA variable and the number of graduates per student (–0.1538). This negative correlation may either show that universities with a low ratio graduates per student have opted first for the introduction of international degrees compared to universities with a higher turnover rate or that the early adaption of the Bologna requirements has induced somewhat slower graduation of students.

Universities with a higher share of professors in the overall staff also display higher costs per students (0.3115). A simple explanation could be that full time professors have an income above the average employee at a university. A higher share of professors is also positively associated with third-party funds. However, as explained in the hypotheses section it is far from evident whether the number of full time professor is the cause for higher expenditures per student or more third-party funds per student. Likewise, more third-party funds might require the employment of more full professors. With respect to the student body we find that a high share of foreign students is only marginally (negatively) correlated with the costs per student (–0.0173). Thus, a high or a low share of foreign students in the overall number of enrolled students is neither associated with increasing nor decreasing costs per student. Interestingly, FOREIGN is significantly correlated to third-party funds per student (0.3457). A possible explanation might be that foreign students prefer research-intensive universities. At the same time, FOREIGN is related to fewer graduates per student. Thus, descriptive analysis can neither reject nor confirm hypothesis 7.

5.2 Econometric analysis
Kumbhakar and Lovell (2000) compare and contrast various econometric models that permit to study the influence of environmental variables on efficiency performance. In the past, two-stage approaches have been quite popular, i.e. efficiency scores obtained from standard SFA settings in the first stage are regressed upon a set of environmental variables in the second stage. However, it is well known that this approach is problematic if explanatory and environmental variables are correlated: Efficiency scores obtained from the first-stage regression will be biased if relevant variables are omitted and only included in the second-stage.¹¹ Moreover, Wang and Schmidt (2002) report Monte-Carlo evidence that also the second-stage estimates are biased. This result holds even if environmental and explanatory variables are independent.

For these reasons, Wang and Schmidt (2002) strongly advocate single-stage procedures, in which efficiency estimates and the influence of environmental variables on the efficiency scores are estimated simultaneously. They find these approaches also to perform well in finite-sample settings. Such models have been proposed by Kumbhakar, Ghosh and McGuckin (1991), Reifschneider and Stevenson (1991) as well as Huang and Liu (1994) or Battese and Coelli (1995) among others (Kumbhakar and Lovell 2000).¹² We investigate the influence of our institutional variables on university cost efficiency using the single-stage model proposed by Battese and Coelli (1995).

As discussed in more detail in Kraus (2004), for German universities neither the behavioural assumption (cost minimizer or output maximizer) nor the assumption regarding the functional form is undisputed. However, applying the cost function approach has become standard in the empirical evaluation of higher education (e.g. Cohn, Rhine and Santos 1989; de Groot, McMahon and Volkwein 1991; Glass, McKillop and Hyndman 1995 or Izadi et al. 2002). Moreover, the evidence presented by Kempkes and Pohl (2007) suggests that—at least for the German university data—parametric efficiency analysis based on a translog cost function and standard non-parametric efficiency analysis lead to broadly similar efficiency predictions.

Based on this evidence, we argue that the translog cost function used in earlier studies is a proper starting point for assessing the influence of institutional factors on German university efficiency. We start from the following cost function:

(1)

The index i denotes the universities and t are the years. While represents a constant, t is a linear time trend to account for technological change. As cost variable C_it we choose university total costs net of the third-party funds the university has acquired, i.e. we take up the perspective of the German state governments by focussing on public costs.¹³ Universities produce j = 2 outputs (Q_jit). Acquired third-party funds are used as a proxy for the research output and the number of graduates is incorporated to capture the teaching output.¹⁴ Admittedly, our selection of output variables is mainly driven by data availability. Specifically, research and teaching quality is not accounted for. Moreover, third-party funds are of course only one dimension of the various possible measures of research (e.g. publications, citations, etc.). One consequence of this approach is that research output is biased towards certain types of research, namely towards science and medical research in contrast to social sciences. Another consequence is that research and teaching output are considered to be of homogeneous quality. It is a common perception in the German university landscape that this is of course a simplification with respect to third-party funds as well as to graduates. For these reasons, our study has to be interpreted with considerable caution.

The cost variable as well as both university outputs are normalized by the number of enrolled students (not graduated). To get a proxy for wages (w), we divide total staff expenditures by the number of employees in the university. Wages, total costs and third-party funds are deflated using the government consumption deflator published by the German Council of Economic Experts (2006). The specification of the translog function requires the inclusion of interaction terms between the two outputs as well as between the outputs and wages in order to account for substitution and complement effects. FACULTY represents shares of students enrolled to different faculty groups (m = 3): engineering careers (ENGINEERING), science careers (SCIENCE) and medical, veterinarian plus agrarian careers (MEDICINE). The share of students enrolled to social sciences and languages (SOCIAL) constitutes the base category. Thus, FACULTY controls for the faculty composition of universities because, as described in the previous section, different faculties have quite different cost structures (see also Kempkes and Pohl 2007).¹⁵

Based on the incremental funding mechanisms that have been used by the state governments in the sample period (see also Appendix 2), one may argue that the true model is not static but rather dynamic. Thus, the lagged cost variable should be included as a regressor. However, since most of the institutional variables are dummy variables or change little over time, the inclusion of the lagged endogenous variable is likely to create endogeneity problems because in this case, the time-invariant error components would be correlated with the lagged cost variable.

The classical error term is denoted by v_it, which is i.i.d. N(0, ) and also independent of u_it. The non-negative random variable u_it is assumed to display total economic inefficiency in the university production of teaching and research, i.e. technical inefficiency plus allocative inefficiency. This "inefficiency" error term u_it is assumed to be independently distributed and following a truncated normal distribution: N(µ_it, ). The environmental variables Z_it are assumed to determine µ_it (Battese and Coelli 1995 and Coelli 1996). This setup allows testing our hypotheses concerning the influence of the exogenous institutional variables (Z_it) on university efficiency (u_it):

(2)

BESTLAW and WORSTLAW capture whether a university operates under comparatively liberal or restrictive state regulation according to Stifterverband (2002). The variables are dummy variables that take the value of 1 if the university is located in a state with liberal (BESTLAW) or restrictive (WORSTLAW) state university regulation. Note that the classification of medium-ranking state laws represents the reference category. EAST accounts for differences in East/West German universities and takes the value of 1 if a university is located in the Eastern states. APPLIED accounts for the share of graduates who have been awarded degrees of the "university of applied sciences"—status. Thus, APPLIED is a proxy for the degree of comprehensive university. COHORT measures the share of population aged 18–35 at the state level.

We estimate three different specifications of the inefficiency term by subsequently adding more institutional variables. Since hypothesis 1 may be considered most important, we include BESTLAW and WORSTLAW in all specifications (models 1, 2 and 3). Based on the evidence presented in Kempkes and Pohl (2007), EAST is also included in all models; moreover, it may also be considered a control variable (hypothesis 3). APPLIED is included in models 2 and 3 to test hypothesis 2. COHORT is only included in model 3 (hypothesis 4). Each of these estimations is based on the same cost function as shown in Equation (1).

Finally, Equation (3) reports the share of deviations from the estimated cost function that is due to inefficiencies rather than noise. In Table 3, ² denotes the sum of and (see also Coelli 1996).

(3)

In Table 3 we present our empirical results. Estimations have been conducted using FRONTIER 4.1 (Coelli 1996).

View this table: [in this window] [in a new window]   Table 3 ML estimates of cost function coefficients and of institutional variable coefficients

 
The estimation results of the cost function indicate that the coefficients remain quite stable across the three alternative specifications. In particular, all models show that a high ratio of graduates/student is associated with lower public costs per student. Our results also suggest that there are economies of scope between teaching and research. The coefficient of the interaction term between the number of graduates and the amount of third party funds varies between –0.222 and –0.229 and is significant at the 1 percent level, which is consistent to Kempkes and Pohl (2007). In addition, we find evidence that wages have a positive impact on costs. This result contrasts previous findings presented by Kempkes and Pohl (2007). The reason for this is probably the more restrictive specification of the cost function in this article regarding the wage variable. Here, we control for faculty composition, but we do not control for interaction terms of wages with faculty controls. This different way of modelling the cost function is enforced by econometric concerns (see footnote 9). With respect to the faculty controls, we find that—as expected—universities with a higher share of medical as well as natural science students (MEDICINE and SCIENCE) operate on a higher cost level than higher education institutions with a high proportion of social science students (SOCIAL, base category). Our results also weakly suggest that universities with a high share of engineering students (ENGINEERING) have lower costs than universities with other foci. Of course, all of these findings are conditional on the absence of a measurement of teaching/research quality.

Focussing on the effect of the institutional variables, we find that indeed a state regulation favouring university autonomy (BESTLAW) has a positive effect on cost efficiency. The estimated coefficient lies between –0.422 and –0.394 and is significant at the 1 percent level in all three specifications. Note that this effect has to be interpreted relative to the reference category, which are the medium-ranking state laws. As expected, a rather restrictive state legal framework (WORSTLAW) seems to decrease university efficiency compared to the medium-ranking state laws. Again, this effect is significant at the 1 percent level in all three specifications and the coefficient is ranging from 0.239 to 0.258. These results are robust over the three models and are also robust to the exclusion of the East dummy variable (not reported here). In this respect, our econometric analysis confirms our findings from the correlation analysis.

The dummy variable for Eastern Germany (EAST) indicates that universities in the new federal states are significantly less efficient than their counterparts in Western Germany (0.322–0.346), which is consistent to previous findings (Warning 2005 as well as Kempkes and Pohl 2007). As expected, the results from models 2 and 3 suggest that comprehensive universities (APPLIED) are more efficient than "classical" universities (–0.836 to –0.845); yet the coefficient is not significantly different from zero. The population share aged 18–35 (COHORT) yields a positive coefficient, which is not in accordance with our hypothesis. However, the coefficient is insignificant. This is not surprising since it is a phenomenon of sluggish adjustment that is essentially based on time-series variation. Our estimation results, however, rely mainly on cross-sectional variation due to the structure of the data set and due to the nature of the benchmarking exercise.

Overall, the coefficients of the institutional variables are quite robust across the specifications. This suggests that there might indeed be beneficial effects of more liberal state regulation on university efficiency. In turn, restrictive university regulation seems to translate into less efficient universities. However, our models explain only a somewhat low fraction of the total variance in the error components. All three models suggest that roughly 7 percent of total variance of the v_it and the u_it is accounted for by our model of the inefficiency error (see gamma in Table 2) and more than 90 percent of deviations from the cost function are due to stochastic (or not explained) sources. Apart from institutions, other variables (e.g. regional GDP per capita) seem to explain more of the differences in efficiency performance (Kempkes and Pohl 2007). Thus, the effect of state regulation on university efficiency may be somewhat limited in scope; however, one has to bear in mind, that federal deregulation amendment was only passed in 1998. One would expect major impacts of deregulation to unfold with a considerable time lag.

Models 1, 2 and 3 may be compared to a model which includes only a constant term in the inefficiency specification based on their log(likelihood) functions (Berndt 1991). A likelihood-ratio test of the null hypothesis that the coefficients of all institutional variables are zero indicates strong joint significance in all models. Hence, although the institutional variables do not explain much of the deviations from the estimated cost function for German universities, models 1–3 do a much better job than a model without these variables. Moreover, models 1, 2 and 3 may be compared among one another. Likelihood-ratio tests of the null hypotheses that the coefficients of APPLIED and COHORT are indeed zero decide against models 2 and 3 at the 1 percent level of significance. Thus, model 1 is our preferred specifications.

	6 Conclusion

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
Recent empirical studies suggest that spending on higher education in the EU-15 countries including Germany is low compared to the United States or Switzerland (Aghion et al. 2007 and OECD 2006). Since public budgets are tight, the efficient spending of public funds in universities is receiving increasing attention in the economic-political debate. Previous research has predominantly focussed on the identification of inefficiencies in the university landscape instead of analysing the determinants of university efficiency.

Against this background, we tested the effects of institutional settings on university costs, outputs and efficiency based on a data set of 67 German universities for the years 1998–2003. In particular, we focussed on exploiting differences in university regulation across the German states that have emerged after the 1998 amendment of the federal university framework regulation in Germany ("Hochschulrahmengesetz").

Evidence from a single-stage stochastic frontier model suggests that characteristics of state university regulation have indeed a significant effect on university cost efficiency. More liberal state regulation is significantly linked to more efficient universities while a restrictive framework is associated with less efficient universities. This result can also be retraced by looking at the correlations of university costs and outputs with state regulation. Moreover, we find that presidential regimes are associated with lower costs, more teaching output, but less third-party funds. This may partly reflect that candidates from external institutions with a relatively long incumbency might have fewer concerns to adapt university structures to the requirements of tight public budgets; however we cannot rule out that more efficient universities simply choose the presidential regime.

This article has of course some important limitations. First, for policy relevance, it is of paramount importance to account for the quality of research and teaching outputs, which was—due to data availability—not possible in our investigation. In future studies it would be a good start to incorporate the number of publications and/or citations as indicators for the quality of research as well as graduate wages as a proxy for the quality of teaching. Second, the measure of research output has certainly to be broadened in order to account in a more encompassing way for the research in social sciences, which could also be accomplished by incorporating publications or citations as an additional research output. Third, in order to allow for a comprehensive evaluation of state legal frameworks in the German university landscape, the time-span of the data set should be increased. Here, changing accounting designs complicate things. Fourth, our analysis cannot answer the question by which channels more liberal state regulation translates into higher efficiency. The correlation analysis suggests that it affects both costs and outputs. However, it would be interesting to reveal the micro-channels by which efficiency is increased.

The empirical findings of our study may be relevant for political decision makers and also for the management of public universities, of course keeping in mind all the limitations mentioned supra. In particular, our results suggest that differences in cost efficiency within the German university landscape can be partly explained by—or are at least related to—institutional settings. Institutions are subject to political decisions and thus might be reconsidered in reforming the sector of higher education. Moreover, with regard to the higher education reform in the European Union and the renewed Lisbon Strategy it might not only be promising to assess the effect of institutions on university efficiency on a national level but also in a European context. The much richer cross-country variation in institutions across the European Union represents a good starting point in order to provide better founded empirical evidence which institutional settings benefit a cost efficient university landscape.

	Appendix 1

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 

Classification of state higher education laws as published by the Stifterverband für die Deutsche Wissenschaft

"Best-law-group" Baden-Wuerttemberg Bremen Hamburg Hesse Lower Saxony "Intermediate group" Bavaria Brandenburg Mecklenburg-Vorpomerania North Rhine Westphalia Saxony "Worst-law-group" Rhineland-Palatinate Saarland Saxony-Anhalt Schleswig-Holstein Thuringia

Source: Stifterverband für die Deutsche Wissenschaft (2002, p. 28).

	Appendix 2

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
Allocation of university funds in the German states. In Germany, the states (Bundesländer) are responsible for the university system and consequently, there is no uniform allocation mechanism for public university funding. In fact, the allocation mechanisms differ considerably from one state to another. Moreover, when compared to other countries, the allocation mechanisms for higher education in Germany can be characterized as highly complex (Leszczensky and Orr 2004, p. 2). However, one can observe some common patterns and trends over the states: University outputs only determine a marginal part of state grants, e.g. third-party funding determines about 2.5 percent of state grants to universities on average (max. about 7 percent in Baden-Württemberg) while graduates determine about 3 percent of state grants to higher education on average (max. about 8 percent in Brandenburg). PhDs determine less than 1 percent of state grants to universities on average and publications have only recently been taken into account by one state (Bavaria). In some states, gender equality or the share of foreign students also determine marginal parts of state university funding (Orr, Jaeger and Schwarzenberger 2007, p. 13).

However, the most important determinants of state grants are discretionary incremental components (e.g. previous year's budget adjusted for inflation, etc.) and the number of students who study still within the "regular study duration". Regular study duration ("Regelstudienzeit") denotes a subject-specific limit of semesters for a specific career that is fixed by the university examination regulations.

In the sample period, discretionary incremental components still dominated the allocation of state university funding; however, there is a clear trend towards indicator-based funding mechanisms (often relying on the number of students as the most important indicator), see Leszczensky and Orr (2004) and Orr, Jaeger and Schwarzenberger (2007).

	Acknowledgements

Top Abstract 1 Introduction 2 Related literature 3 Hypotheses 4 Data 5 Empirical analysis 6 Conclusion Appendix 1 Appendix 2 Acknowledgements References

 
We thank participants at the 5th International Industrial Organization Conference (IIOC) 2007 in Savannah, at the CESifo Summer Institute 2007 in Venice, at the 63rd Congress of the International Institute of Public Finance (IIPF) 2007 in Warwick as well as at the 34th Conference of the European Association for Research in Industrial Economics (EARIE) 2007 in Valencia for comments and discussion on a previous version of this article. Moreover, we thank Rick van der Ploeg, Heinz Schmalholz, Borge Hess, Helmut Seitz and especially Reinhilde Veugelers and an anonymous referee for very helpful remarks and suggestions.

	Footnotes

 
¹ In this context, Ortiz and Dehon (2008) show that the mother's level of education as well as the father's occupation are important factors of success at university.

² Specifically, in 1998 the federal government passed the framework legislation's fourth amendment. This amendment leaves the states more room for modifying or cutting university regulation with respect to organization and management of the universities (Stifterverband 2002). In addition, the federal government is currently planning to abolish federal framework legislation in October 2008 (Deutscher Bundestag 2007).

³ There are nine main characteristics of the state legislation, i.e. structure of the university, state-university cooperation, budget affairs, labour relations, management, foundation of new universities, teaching (establishment of new degree programmes), teaching evaluation and research. The state laws have been assessed with respect to the degree of autonomy that the universities enjoy in the nine categories presented above.

⁴ Most states changed their university frameworks in 1999. Some states lagged behind in the transformation of the legal frameworks for universities; however, Berlin was the only state that had not changed state legislation by 2002. In the empirical investigation, we could therefore not assess the effect of the state law on the three Berlin universities.

⁵ See Appendix 2 for a short outline of the mechanisms for allocating university funds in Germany.

⁶ Bagues, Labini and Zinovyeva (2008) as well as Kelchtermans and Verboven (2008) investigate reforms in the university funding system in Italy and in Belgium, respectively. The former study finds that an output-based funding system may create an incentive for underperforming universities to increase the number of exams passed and thus, generate less value added in economic terms. The latter article shows that the proposed system in Flanders may overall entail a loss in consumer surplus that exceeds the saving in fixed costs resulting from a reduction in the university's; programme diversity.

⁷ It may also be the case that professors are more/less efficient when they have more assistance from scientific and/or technical staff.

⁸ However, there are no data available on the quality of the enrolled students, e.g. grade of high school diploma, at single universities. Higher education institutions in Germany do not require the successful achievement of a standardized test for admission such as the SAT/ACT in the US.

⁹ Unfortunately, in 2004, the definition of medical students has been changed. As a result, student shares in some cases show dramatic increases/decreases. Consequently, 2004 and 2005 data cannot be compared with our sample period.

¹⁰ The three universities located in Berlin had to be excluded from our investigation since this state's university regulation has not been evaluated by Stifterverband (2002). The reason for this is that Berlin lagged behind in passing the amendment of the legal framework for universities. Thus, no reliable classification of the Berlin university regulation is available.

¹¹ Additionally, the two-stage approach postulates inconsistent econometric assumptions. While in the first-stage regression, efficiency scores (one component of the error term!) are assumed to be identically distributed, in the second stage, it is assumed that the environmental variables have a systematic effect on the efficiency scores.

¹² Another popular method to assess the influence of environmental variables on efficiency performance is to regress efficiency predictions from a non-parametric efficiency frontier on environmental variables. However, as Simar and Wilson (2007) point out, conventional confidence intervals of the second-stage regression are biased due to unknown serial correlation in the efficiency estimates. They propose a double-bootstrapping procedure to overcome these problems. The proposed procedure is shown to be related to single-stage econometric approaches (Simar and Wilson 2007, pp. 44–45). See also Daraio and Simar (2007) and Bonaccorsi, Daraio and Simar (2007).

¹³ Total costs include all current expenditures of the universities, e.g. salaries, administrative expenses, etc. Note that capital expenditures, i.e. construction of buildings, etc., are not included. Moreover, due to a peculiarity of the German public sector accounting system, pension payments for civil servants are not included either. Pension payments for public servants are reported in the general function "Allgemeine Finanzwirtschaft", which cannot be traced back to specific public functions.

¹⁴ There is an ongoing debate about using acquired third-party funds as a proxy for research output (see Worthington 2001 for an overview of the discussion). Some researchers have argued that third-party funds are actually inputs to the production process. However, we argue that these funds are basically earned by the universities on a competitive basis and that the amount of third-party funds that a university acquires can be interpreted as market revenue earned on a research market. Thus, third-party funds contain a quality dimension (the price that the university is able to charge for research activities) as well as a quantity dimension (the amount and size of projects the university can acquire).

¹⁵ Note that Kempkes and Pohl (2007) not only introduced faculty dummy variables but also interaction terms of the faculty dummies with university outputs and wages. This was possible due to the focus on the measurement of university efficiency rather than on the determinants of inefficiency. The present study focusses on the determinants of inefficiency, which calls for a more complex specification of the inefficiency term (see below, Equation 2). However, complex modelling of the cost function and the inefficiency term leads to overparameterization of the model, which is not uncommon in the application of stochastic frontier models (Fernández, Osiewalski and Steel 1997, p. 170: "... it is in the context of stochastic frontiers that the main problem referred to in this paper, namely overparameterization is most frequently encountered").

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