The Performance of Universities in North Rhine- Comparison of a Distribution Solution and the Performance Criteria of a Data Envelopment Analysis

Günter Fandel, Hagen*

A. Introduction

In the last few years a variety of approaches have been developed for recording the efficiency and the success of universities (HIS 1997, A9/97 and A10/97; Wüstemann et al. 2000; Andersen et al. 2001; Ziegele 2001). The purpose of this is the distribution of funds among universities on the basis of performance and success.

The present concept of budget distribution among universities in North Rhine-Westphalia allots correspondingly more funds to universities with higher numbers of students in the first four semesters and a larger number of academic personnel, with otherwise the same number of graduates, and to those with higher outside funding expenditure with otherwise the same number of doctorates (Fleischer 1997). This has the effect of rewarding poorer input-output shares, which is not exactly sensible from the aspect of the efficient output of services. In addition, the aggregation of figures over all subject groups in a university, i.e. by looking at their totality, hides the subject groups are characterised by the efficient output of services and those are not.

The redistribution criteria that are used can be interpreted on the other hand as input or output variables and therefore be used as elements of a Data Envelopment Analysis. The different subject groups in universities in North Rhine-Westphalia, and the universities as a whole, can then be studied with regard to the relative efficiency of their output of services in this year on the basis of the same data material towards which the redistribution was oriented in 1997. These results of the efficiency analysis can then be compared directly with those of the redistribution, to examine how far the redistribution was economically rational, i.e. was in harmony with the performance criteria.

* Prof. Dr. Günter Fandel, Lehrstuhl für Betriebswirtschaft, FernUniversität, Universitätsstraße 41, D-58084 Hagen. E-Mail: [email protected]. I would like to thank in particular my academic assistant Dipl.-Kfm. Steffen Blaga for his support for the calculations. 2

It is not intended to discuss further here the output of services by universities from a general theory of production aspect. This would go beyond the boundaries of the arguments in this paper. For analyses of this type from the aspect of content and perspective see Albach et al. (1978) and Fandel/Paff (2000) and the literature referred to there.

B. Performance-oriented redistribution of funds for teaching and research among the universities in North Rhine-Westphalia

I. Redistribution

At the behest of the parliament of North Rhine-Westphalia the Ministry of Science and Research started a redistribution among the region's fifteen universities of part of the funds available for teaching and research on the basis of defined performance and success criteria. In 1997 the redistribution budget amounted to DM 148.58 million and was provided by the universities themselves from their own funds for the appropriate title groups for teaching and research.

The criteria used as the basis for the distribution were different for the two areas of teaching and research. For teaching they were:

(1) the shares of posts for academic personnel,

(2) the shares of students in semesters 1 to 4; in deviation from this in the case of the FernUniversität in addition half of all part-time students in semesters 1 to 8, because, together with their occupations, they have double the standard length of study with half the study load, in comparison with full-time students, and (3) the shares of graduates, with the analogously modified conversion of the graduates in part-time degree courses at the FernUniversität as under (2), in the respective universities, whereby (a) to calculate the numbers or shares under (1) to (3) the subject groups Humanities and Social Sciences, Natural Sciences and Engineering Sciences were weighted in the ratio 2:5:5, and (b) the numbers or shares of graduates for the calculation under (3) were discounted in dependence on the length of time by which the graduates had exceeded the standard length of the degree course. 3

The following criteria were used for the redistribution to record performances and successes in research: (4) the shares of third-party funding and (5) the shares of doctorates in each university, whereby (c) a moving average for the last three years was determined for the shares of third-party funding under (4), and the subject groups Humanities and Social Sciences, Natural Sciences and Engineering Sciences were given a weighting of 7:2:1 for their third- party funding, and (d) the subject groups were given the weighting shown under (a) for the shares of doctorates.

Medicine is not included in this redistribution, and also remains outside all further considerations. The data on (1) referred to the sum of the academic personnel in the universities over the years 1993 to 1995, ascertained in each case on 1 October in each of these years. The data for (2) were based on the surveys for winter semester 1995/96. The figures for (3) and (5) resulted from the sum of graduates and doctorates respectively over the examination years 1992 to 1994, and the three-year average of the actual expenses in the budget years 1992 to 1994 served to record the third-party funding under (4). The aim of the selected periods and data volumes was to minimise the annual randomness in the differences between the universities.

The redistribution that was sketched above can be described using the data compiled in Table 1. Column 1 lists the universities in North Rhine-Westphalia included in the redistribution of funds for teaching and research, and they are numbered consecutively in Column 2 with i, i = 12,,...,15. Columns 3 to 7 contain the shares aij of the universities i in the redistribution cri- teria j, j = 12,,...,5, in accordance with the information provided in (1) to (5) and the supplementary explanations (a) to (d).

Col. 8 shows the sum of the weighted shares

5 S Pi =⋅∑ g jia j, i =1,...,15, j1= for each university, which, as an aggregated percentage rate, was relevant for the target

I distribution of funds B (Col. 9), which the universities provided from the budgets Bi of the actual distribution (Col. 11 total, percentages in Col. 10). If the shares aij in accordance with (1) 4 to (5) or (a) to (d) are specified, the aggregated percentage rates then only depend on which weightings g j are assigned to the redistribution criteria j, j =1,...,5, on the basis of higher- education policies. This allocation was the result of a negotiation process (Fandel/Gal 2001) between the universities and the ministry:

max z(g) = ()z11(g),...,z 5(g) ' with 5 ⎛⎞I zii(g) =⋅ ⎜⎟∑ a jg jB −Bi , i =1,...,15, ⎝⎠j1=

5 ⎧⎫5 g ∈=G ⎨⎬g ∈IR 0 ≤g jj≤1, j =1,...,5 , and ∑ g =1 , ⎩ j1= ⎭ which resulted after several iterations in the weighting vector

g ==(g15,...,g ) (0,2;0,2;0,35;0,2;0,05), as shown in the heading of Table 1 above Cols. 3 to 7.

However, a certain amount of leeway is removed from this negotiation process if the curricular standard values under (a) favour the scientific and technical subject groups in such a way in four criteria that this cannot be compensated through the weightings under (c) for calculating the shares of outside funding.

The gains and losses in the redistribution for the universities (difference between Cols. 9 and 11) are shown in Col. 13 and their changes with regard to the actual distribution can be read off in Col. 12. Particular attention in respect of the subsequent comparison with the efficiency results of the Data Envelopment Analysis should be directed here to the gains made by the universities of and and to the losses suffered by those in and Münster. 5

Table 1: Initial data in 1996 for the redistribution in 1997 (Fandel/Gal 2001)

Criteria j Target distribution Actual distribution Gain/loss Positions Stud. Grad. Outside Doct.

Weights gj Sum of the 0,2 0,2 0,35 0,2 0,05 weighted No Unweighted shares aij shares DM mill. Ratio DM mill. in % of DM mill. University S SS I II I SI i ai1 ai2 ai3 ai4 ai5 Pi BPii=⋅B Pi BPii=⋅B Bi BBii− 123456 7 8 9 10 11 12 13 1 13,46 10,30 15,33 15,40 20,34 14,21 21,12 13,76 20,44 3,31 0,68 Bielefeld 2 5,24 5,58 3,61 10,31 4,70 5,72 8,50 5,01 7,44 14,31 1,06 3 10,66 8,74 8,84 11,17 10,95 9,76 14,49 10,20 15,16 -4,40 -0,67 4 9,89 9,18 11,89 12,96 15,95 11,37 16,88 11,58 17,20 -1,84 -0,32 5 8,61 8,52 7,70 5,00 7,26 7,48 11,12 6,92 10,28 8,15 0,84 Düsseldorf 6 4,51 5,42 2,88 4,70 5,94 4,23 6,29 4,02 5,97 5,29 0,32 Cologne 7 8,17 11,98 10,61 8,71 10,81 10,03 14,89 10,65 15,82 -5,85 -0,93 Münster 8 9,29 10,86 12,26 9,15 10,47 10,67 15,86 11,60 17,23 -7,96 -1,37 DSH Köln 9 1,08 1,62 2,10 1,17 0,37 1,53 2,27 1,21 1,80 26,07 0,47 10 4,86 3,70 3,92 2,17 2,82 3,66 5,44 3,90 5,80 -6,28 -0,36 11 5,97 6,56 5,00 3,23 3,12 5,06 7,51 4,97 7,39 1,68 0,12 12 6,03 5,49 6,34 3,68 2,40 5,38 7,99 5,24 7,79 2,58 0,20 13 4,60 4,00 3,72 4,04 2,02 3,93 5,84 4,07 6,04 -3,31 -0,20 Wuppertal 14 5,50 5,50 4,44 4,39 2,17 4,74 7,04 4,56 6,78 3,87 0,26 FU Hagen 15 2,13 2,56 1,36 3,92 0,66 2,23 3,31 2,31 3,43 -3,37 -0,12 Total 100,00 100,01 100,00 100,00 99,98 100,00 148,56 = B 99,99 148,58 = B / -0,01

II. Material arguments

k The multiplication of the shares aij of the various subject groups k, k =1,2,3, in a university i in a criterion j by the curricular standard values ck under (a), or by the weights dk under (c), and their subsequent summation for the calculation of the share values aij , i.e.

3 kk aij =⋅∑ c aij , j=1,2,3,5, k1=

3 kk adij =⋅∑ aij ,j=4, k1=

i =1,...,15, conceals efficiencies or inefficiencies in the output of services by subject groups in a university, which do not appear through the selected aggregation of the data. It can happen here that a university is classified on the whole as efficient in the Data Envelopment Analysis (DEA), but that individual subject groups are characterised by inefficiency. The reason for this is found in the definition of the performance characteristic and the construction of the DEA, and its methodology cannot be contested. What is more critical is the phenomenon that a university may be inefficient in all subject groups, but appears as a whole to be efficient on the basis of the weighting of the data specific to the subject groups with the curricular standard values. As 6 alternative calculations show, this would be the case for the University of Essen, if the numbers of graduates in the Humanities and Social Sciences in Table 2 were increased by 39. An disorientation from practical understanding of this nature is an argument against the aggregation over all subject groups in the way this was carried out in the redistribution of funds. The ministry obviously shares these misgivings. Because redistribution following an inspection of the university departments by a committee of experts, whose main objective was to transfer positions from inefficient to efficient faculties within a university, or gather them in completely "to fulfil the quality pact".

The shares of students in the first four semesters as a redistribution criterion make it clear that the redistribution is in part aligned towards input variables which were formally treated or rewarded as performance results. To justify this it could be said that, in the services production of the universities, the numbers of students served in the system of the university are indirectly an indication that, where a large number of students study, a great number of lectures, the actual output of the universities concealed behind this, are offered, and that this should be rewarded to a greater extent. However, this is countered by the political requirement for universities to show why they have dropout rates that are continuously bemoaned, i.e. why students are not turned into graduates. The idea, based on the theory of production, comes through here that students are regarded as the input and graduates as the output of universities, as seems obvious. From the aspect of service production students represent external factors (Kleinaltenkamp/Haase 1999;

Stuhlmann 1999; Corsten 2000), which, in accordance with the definition, are subject to disposition by the university to a limited extent only - and this includes their success!

The academic personnel employed are undoubtedly an input of the university's service production. The questionable practice of still assessing this positively during redistribution follows from the manifest calculation of not wishing to generate massive departures of personnel from established and extremely well-equipped universities through a purely results-oriented redistribution, or to pre-program the inefficient employment of personnel by not providing funds for personnel.

As with students in the first four semesters, in the case of the actual expenditure of outside funding as a redistribution criterion the question arises whether it is not in fact input for teaching and research, rather than a performance output for universities. It may be objected here that outside funding that universities attract is an expression of the successful efforts of the academic personnel, and as such should be treated as the output of these efforts. However, if the 7 circumstances are examined more closely, it is seen that a good deal of outside funding, for example, the Universities Renewal Programme (HEP) and the Universities Supporting Programme (HSP), was allocated by ministries without any noticeable efforts on the part of the universities and was earmarked for teaching purposes. In contrast, outside funding for research which a university attracts tends to conform to the output character which was addressed above, but on the other hand is also used for doctorates and other higher degrees, and its successful use is carefully monitored by the providers of the outside funding. Insofar it would also be input; this time for research.

Because the share of outside funding in the period in which data were collected was mainly earmarked for teaching, and because it is impossible to calculate the outside funding from research promotion agencies from the statistics, with the DEA applied here this paper follows the method of interpreting this outside funding as inputs, in full awareness of the methodological reservations.

Following the observations, in the further analysis it will be assumed with the help of the DEA that positions for academic personnel, students in the first four semesters and outside funding are inputs in the university for teaching and research, and that the number of graduates and doctorates represent output. This means that, with the same data material, the efficiency of the production of services by the universities can be compared with the effects of redistribution.

C. Assessment of the efficiency of universities in North Rhine-Westphalia using the DEA

I. Methodological considerations

Here is not the place to spread out and discuss the methodological aspects of DEA models and the associated forms of measuring efficiency. For this purpose reference is made here among others to Charnes et al. (1978); Banker et al. (1984); Dyckhoff/Allen (2001) and Kleine (2002). It must also be said here that DEA applications are already traditional in the field of education (Johnes/Johnes 1995; Kirjavainen/Loikkanen 1998; Korhonen et al. 2001, Chakraborty et al. 2001). However, some methodological considerations will be presented briefly which may serve to make clear why a certain DEA approach in a defined version was selected to evaluate the efficiency of universities in their subject groups and as a whole, namely the model from Banker 8 et al. (1984) with the assumption of variable returns on scale (VRS) in the alignment of the input orientation.

The input orientation in considerations of efficiency, i.e. minimising the inputs of universities with given outputs, is supported by the behaviour of those responsible for taking education and scientific policy decisions to make savings in university budgets, i.e. to reduce the number of positions for academic personnel and to be more reserved when awarding outside funding. Applying input orientation to students in the first four semesters could also be interpreted as unfriendly towards students, but, given fixed support shares for seminar and examination outputs, is a direct consequence of input orientation in the use of academic personnel. The counterpart would be output orientation with graduates with the same number, or with an increase in the number of academic personnel. An educational policy dilemma shows through here, namely that the number of students in the Federal Republic of increased by about 73% in the years 1977 to 1990, but that personnel capacities were increased by only 6% (Fandel 1998). This was followed by a reduction in the number of positions without a noticeable fall in the number of students. Another problem of output orientation is the quality of the students as a characteristic of the input, which cannot be assumed to have remained the same with a growing proportion of students from their corresponding age groups.

There is a plausible reason for applying the model from Banker et al. (1984) with variable returns on scale (VRS), i.e. the modification of the approach by Charnes et al. (1978), which starts from the assumption of constant returns on scale (CRS). There is practically no sense in wanting to increase or reduce the input-output levels of efficient universities arbitrarily. As giant universities they would be unable in any case to take over the teaching and research work of all other universities, because there are location problems for students and academic personnel. Mini-universities neglect the fact that the service process cannot fall below defined minimum levels if it is to be successful. These minimum levels are found in the number of chairs required, which depends on the subject, and their endowment with academic personnel and secretariats. However, with the assumption of variable economies of scale in contrast to one of constant economies of scale, the efficiency analysis requires on the one hand fragmentation of subject groups for which there is less demand over several university locations, which would be concentrated in a few universities with constant economies of scale.

In general the DEA presumes that the input-output combinations of the decision-making units (here the subject groups within the universities or the universities as a whole), which were 9 examined jointly as to their relative efficiency, are combinable in any convex way and that the convex hull of these combinations is a subset of the same unknown technology as defined by Koopmans's activity analysis (see Fandel 1991). This is certainly not tenable from the aspect of an examination of university operations based on production theory, because, strictly speaking, the goods at the different universities are not homogeneous and the performance processes are not the same. This argument on the basis of management-theory may be easily ignored from the perspective of macroeconomically aggregated production. However, with a federative education policy only universities from the same federal state, for which there is a uniform political educational establishment, may then be compared with one another.

II. Application of the DEA and results

For the application of the DEA model from Banker et al. (1984), with variable economies of scale and input-oriented efficiency measuring of the services production of the different subject groups Humanities and Social Sciences, Natural Sciences and Engineering Sciences at universities in North Rhine-Westphalia, and their production of services in general, it is necessary to go back to the absolute figures for the criteria used on redistribution, which are shown in Table 1 in shares only. Some obvious modifications of the source data were carried out here:

(1') in the case of academic personnel those working in central institutions (library, computer centre and the like) are not included, because on redistribution they were assigned on a percentage basis to the subject groups without this corresponding to their actual provision of services.

(4') The same procedure as under (1') was used for the valuation of outside funding, whereby, however, in addition the three-year average was altered to the sum of the funds over the three years.

(a') and (c') The weighting of the subject group Humanities and Social Sciences at the Deutsche Sporthochschule (DSH) in Cologne, which deviated from the uniform principle of the redistribution, of 3.5 in the case of graduates, doctorates, students and academic personnel and 4.5 in the case of outside funding, was transformed into the weighting under (a) and (c), corrected to 2 and 7 respectively. 10

The input and output data of the different subject groups in the universities that were examined and their total values aggregated in accordance with their weightings in (a) or (c) are listed in k Tables 2 - 5. In addition, the last columns show the respective performance criteria θi , k =1,2,3,4, i =1,...,15, for the services production for the subject groups k (k =1,2,3) and aggregated (k = 4) for the university i in accordance with the approach from Banker et al. (1984). These performance criteria are compiled in Table 6 for a better comparison. A dash in the columns indicates that the appropriate subject group is not represented at this university. The efficiency calculations were carried out with the help of the program DEAP, Version 2.1 (Coelli 1996).

Table 2: Calculation Humanities and Social Sciences (k = 1)

VRS Output Input Efficiency No. x1 x1 r1 r1 r1 University 1i 2i 1i 2i 3i i Outside 1 θi Graduates Doctorates Students Personnel funding in DM '000 Aachen 1 1410 108 3365 569 8537 1,000 Bielefeld 2 2528 250 5995 1188 40164 0,795 Bochum 3 4129 331 7301 1730 29422 0,805 Bonn 4 5775 524 8358 1651 34415 1,000 Dortmund 5 2517 135 5173 912 5562 1,000 Düsseldorf 6 928 115 5235 707 16348 0,799 Cologne 7 9878 760 15347 2598 25950 1,000 Münster 8 8502 446 10939 2332 36026 1,000 DSH 9 1696 44 1698 447 11146 1,000 Cologne Duisburg 10 1602 70 3561 703 3756 1,000 Essen 11 2349 58 5397 881 7105 0,931 Paderborn 12 1658 58 2531 647 6905 1,000 Siegen 13 1638 75 2677 790 15048 0,814 Wuppertal 14 1490 35 3071 661 7457 0,894 FU Hagen 15 1218 62 2695 424 7845 1,000 11

Table 3: Calculation Natural Sciences (k = 2)

VRS Output Input Efficiency No. x2 x2 r2 r2 r2 University 1i 2i 1i 2i 3i i Outside 2 θi Graduates Doctorates Students Personnel funding in DM '000 Aachen 1 1919 496 2239 1340 76788 0,857 Bielefeld 2 1025 256 1704 904 59949 0,772 Bochum 3 1749 487 2026 1304 72719 0,902 Bonn 4 4233 1008 3244 2000 142734 1,000 Dortmund 5 1543 242 2284 962 37852 0,875 Düsseldorf 6 1251 405 1885 1013 39898 1,000 Cologne 7 2035 583 2662 1284 87893 0,985 Münster 8 3462 600 3513 1672 56044 1,000 DSH 9 ------Cologne Duisburg 10 477 90 556 490 15938 1,000 Essen 11 646 168 1381 720 23940 0,803 Paderborn 12 986 110 1358 688 36828 0,873 Siegen 13 330 92 549 464 22799 1,000 Wuppertal 14 338 97 729 565 53820 0,826 FU Hagen 15 224 10 665 272 4535 1,000 Table 4: Calculation Engineering Sciences (k = 3) VRS Output Input Efficiency No. x3 x3 r3 r3 r3 University 1i 2i 1i 2i 3i i Outside 3 θi Graduates Doctorates Students Personnel funding in DM '000 Aachen 1 6168 1031 3980 2277 412132 1,000 Bielefeld 2 ------Bochum 3 1584 225 1470 922 82768 0,940 Bonn 4 167 18 156 128 4588 1,000 Dortmund 5 1795 255 1905 1121 79675 1,000 Düsseldorf 6 ------Cologne 7 ------Münster 8 55 1 85 15 3 1,000 DSH 9 ------Cologne Duisburg 10 1093 99 736 614 33316 1,000 Essen 11 1234 60 1276 636 22722 0,911 Paderborn 12 1925 60 1662 713 30543 1,000 Siegen 13 1114 55 1316 541 12141 1,000 Wuppertal 14 1569 44 2085 765 27758 0,822 FU Hagen 15 55 18 141 128 5405 1,000 12

Table 5: Calculation of all subject groups (weighted sums) (k = 4)

VRS Output Input Efficiency No. x4 x4 r4 r4 r4 University 1i 2i 1i 2i 3i i Outside 4 θi Graduates Doctorates Students Personnel funding in DM '000 Aachen 1 43252 7851 37825 19223 625467 1,000 Bielefeld 2 10179 1780 20510 6896 401046 0,655 Bochum 3 24924 4222 32082 14590 434160 0,802 Bonn 4 33548 6178 33716 13942 530961 1,000 Dortmund 5 21723 2755 31291 12239 194313 1,000 Düsseldorf 6 8113 2255 19895 6479 194232 1,000 Cologne 7 29933 4435 44004 11616 357436 1,000 Münster 8 34591 3897 39868 13099 364273 1,000 DSH 9 3393 88 3396 894 78022 1,000 Cologne Duisburg 10 11049 1085 13582 6926 91484 1,000 Essen 11 14098 1256 24079 8542 120337 0,994 Paderborn 12 17872 966 20162 8299 152534 1,000 Siegen 13 10496 885 14679 6605 163075 0,771 Wuppertal 14 12515 775 20212 7972 187597 0,693 FU Hagen 15 3832 264 9420 2848 69390 1,000

Table 6: Comparative overview of the VRS efficiencies

Humanities and Engineering All subject No. Natural Sciences University Social Sciences Sciences groups i 1 2 3 4 θi θi θi θi Aachen 1 1.000 0.857 1.000 1.000 Bielefeld 2 0.795 0.772 --- 0.655 Bochum 3 0.805 0.902 0.940 0.802 Bonn 4 1.000 1.000 1.000 1.000 Dortmund 5 1.000 0.875 1.000 1.000 Düsseldorf 6 0.799 1.000 --- 1.000 Cologne 7 1.000 0.985 --- 1.000 Münster 8 1.000 1.000 1.000 1.000 DSH 9 1.000 ------1.000 Cologne Duisburg 10 1.000 1.000 1.000 1.000 Essen 11 0.931 0.803 0.911 0.994 Paderborn 12 1.000 0.873 1.000 1.000 Siegen 13 0.814 1.000 1.000 0.771 Wuppertal 14 0.894 0.826 0.822 0.693 FU Hagen 15 1.000 1.000 1.000 1.000

13

k The efficiency criteria θi are the results of the optimising problems (Banker et al. 1984):

k min θi subject to

15 kk −+xx1i ∑ 1i ' ⋅λi' ≥0, i'=1

15 kk −+xx2i ∑ 2i' ⋅λi' ≥0, i'=1

15 kk k θ⋅i1rri−∑ 1i'⋅λi' ≥0, i'=1

15 kk k θ⋅i2rri−∑ 2i'⋅λi' ≥0, i'=1

15 kk k θ⋅i3rri−∑ 3i'⋅λi' ≥0, i'=1

15 ∑ λ=i' 1, i'=1

λ≥i' 0, i' =1,...,15,

i ==1,...,15 and k 1,...,4.

They can be interpreted as Farrell criteria (Coelli et al. 1998, p. 134 ff.) in the sense that they

kkk indicate the most the input bundle (r1i ,r2i ,r3i ) of university i can be reduced in study case k for

kk kk kk k k the corresponding vector (−θi1ri,r−θi2i,r−θi3i,x1i,x2i)' to just lie in the set of feasible production activities

15 15 M =vkkv ≤ λ⋅vkwith λ=1, λ≥0, i =1,...,15, { ∑∑iii i i1==i1 kkkkkk and vi1=−( r i,−r2i,−r3i, x1i, x2i) '}

k which is generated by the convex combinations of the observed vi and those which are

k inefficient as compared with them. The efficiency criteria θi lie between zero and one and just reach the value one if the university i is efficient in M for the observed case k (Humanities and Social Sciences, Natural Sciences, Engineering Sciences, aggregated overall consideration).

14

III. Discussion of the findings

There are numerous opportunities for a discussion of the findings if the results in Table 6 are compared with the consequences of redistribution in Table 1. The discussion will be concentrated below on five points.

(i) In the shares of the criteria on which the redistribution is based the RWTH Aachen displays almost overwhelming values in comparison with all other universities, i.e. it can wait complacently for the negotiation process for determining the weights vector g. On the basis of the DEA it can be seen that its services production in Natural Sciences is relatively inefficient. This does not have an effect on the aggregated consideration because the overwhelming successes in Engineering Sciences compensate for this circumstance.

(ii) In the case of the University of Siegen the relative inefficiency in Humanities has a greater effect on the overall consideration, because it takes place on a significantly higher production level for it to be cushioned by the successes in Natural Sciences and Engineering Sciences.

(iii) The universities of Bielefeld and Wuppertal should not have gained in the redistribution, because they displayed inefficiencies in all considerations (for example in comparison with the University of Münster, which lost out on redistribution).

(iv) The universities of Münster and Cologne should not have lost on redistribution because they are efficient practically throughout, with a negligible exception in Cologne in Natural Sciences.

(v) After an inspection of the committee of experts the FernUniversität recently had to accept a reduction of positions in Natural Sciences and Engineering Sciences for which there is no rational explanation on the basis of the efficiency criteria. In addition, this affects an educational technology which, from the input side of students, cannot be so directly compared with that of other universities in North Rhine-Westphalia as is implied by the assumptions of the DEA. 15

The discussion of the redistribution receives a completely new dimension when we look at the personnel dispositions that are possible on the basis of the DEA efficiency analyses in accordance with subject groups and as a whole for the universities that were examined, as shown in Table 7. According to this, the universities of Bonn, Münster, DSH Cologne, Duisburg and Hagen are the only universities which would not have to give up personnel for a redistribution; also the University of Cologne would remain unaffected to some extent.

It may be objected that it is an illusion to discuss the redistribution of a total of 2602 positions for academic personnel. However, when we consider that the average annual salary is to be put at about DM 100,000, this corresponds to a redistribution budget of around DM 260 million. This is not even twice the material resources budget that was redistributed in 1997, which was in fact then increased in the following years by an additional 50% - 100%.

Table 7: Personnel dispositions

No. Humanities and Natural Engineering All subject University i Social Sciences Sciences Sciences groups Aachen 1 0 192 0 192 Bielefeld 2 243 206 0 450 Bochum 3 521 160 68 749 Bonn 4 0 0 0 0 Dortmund 5 0 120 0 120 Düsseldorf 6 142 0 0 142 Cologne 7 0 20 0 20 Münster 8 0 0 0 0 DSH Cologne 9 0 0 0 0 Duisburg 10 0 0 0 0 Essen 11 61 142 82 285 Paderborn 12 0 88 0 88 Siegen 13 252 0 0 252 Wuppertal 14 70 98 136 305 FU Hagen 15 0 0 0 0 Total / 1289 1026 287 2602

Of their nature, positions can be less flexibly distributed among universities than material resources. This was possibly the reason why the ministry did not initially consider a corresponding solution for the redistribution. In addition, personnel dispositions cannot be discussed without a corresponding redistribution of students among universities. 16

D. Conclusion

The comparison of the results showed that the solution of the redistribution among the universities in North Rhine-Westphalia in 1997 was not in harmony with the efficiencies of services production which applied at the time in these universities. Consequently, the question is whether it would have been possible to generate a redistribution solution of the negotiation problem through a parallel efficiency consideration on the basis of the DEA, which would have corresponded more to the prevailing efficiencies and inefficiencies in the universities, and in the subject groups they offer. There is no isomorphism between the two problem structures. However, if it had been possible to take account of the results of the efficiency considerations in the negotiation problem in such a way that, through the introduction of appropriate restrictions, it was ensured that universities which are better than others in their performance criteria no longer lose through the redistribution, or that the latter do not receive more than the former from the redistribution. This would have limited the solution space for the negotiation problem still further and in certain circumstances the results would have been a different weights vector for the redistribution criteria as the solution. We may question whether the Science Ministry of North Rhine-Westphalia would have wanted to approve such an open determination of the weights vector. This meant that redistribution consequences were pre-programmed which are not in harmony with the discussed efficiency criteria.

A further question is the one regarding the randomness and stability of the discussed solutions. The data material on the redistribution and production variables initially avoids the randomness of certain solutions by basing all variables on average values or on total values over several years. Annual data could have led to very sensitive displacements in the redistributions, which were not wanted by either the political decision-makers or the universities. On the other hand, with moving averages of these variables the values of the redistribution criteria and of the associated input and output variables change from year to year. This alters the efficiency criteria and at the same time the redistributions within the negotiation problem. However, the available data material is not sufficient for a sensitivity analysis at this level.

Finally it must be said that the universities and subject groups respectively are interpreted in the DEA as DMUs: decision making units. This is certainly permissible for the university as a whole, because in the framework of the global budgets it can determine the internal distribution of funds itself, within the limits of statutory provisions. With regard to the subject groups, a 17 decision-making competence of this nature cannot be detected at first. However, it is found in the same measure as with the university as a whole in the distribution of the funds allocated to them within a group of subjects in accordance with load criteria in such a way that efficient allocations are generated.

Bibliography

Albach, H., Fandel, G., and Schüler, W: Hochschulplanung, Baden-Baden 1978.

Andersen, U., Minssen, H., Molsich, B., and Wilkesmann, U.: Kontextsteuerung von Hoch- schulen durch veränderte Modi der Mittelzuweisung, Diskussionspapier No. 01-1, Institut für Arbeitswissenschaft der -Universität Bochum, Bochum 2001.

Banker, R.D., Charnes, A., and Cooper, W.W.: Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis, in: Management Science, 30, 1984, pp. 1078-1092.

Chakraborty, K., Biswas, B., and Lewis, C.: Measurement of Technical Efficiency in Public Education: A Stochastic and Nonstochastic Production Function Approach, in: Southern Economic Journal, 67, 2001, pp. 889-905.

Charnes, A., Cooper, W.W., and Rhodes, E.: Measuring the Efficiency of Decision Making Units, in: European Journal of Operational Research, 2, 1978, pp. 429-444.

Coelli, T.: DEAP Version 2.1, http://www.une.edu.au/econometrics/cepa.htm, 1996.

Coelli, T., Prasada Rao, D.S., and Battese, G.E.: An Introduction to Efficiency and Productivity Analysis, Boston u.a. 1998.

Corsten, H.: Der Integrationsgrad des externen Faktors als Gestaltungsparameter in Dienst- leistungsunternehmungen - Voraussetzungen und Möglichkeiten der Externalisierung und Internalisierung, in: Bruhn, M. (ed.): Dienstleistungsqualität: Konzepte – Methoden – Erfahrungen, 2000, pp. 145-168.

Dyckhoff, H., and Allen, K.: Measuring Ecological Efficiency with Data Envelopment Analysis, in: European Journal of Operational Research, 132, 2001, pp. 312-325. 18

Fandel, G.: Funktionalreform der Hochschulleitung, in: Zeitschrift für Betriebswirtschaft, 68,

1998, pp. 241-257.

Fandel, G.: Theory of Production and Cost, et al. 1991.

Fandel, G., and Gal, T.: Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia, in: European Journal of Operational Research, 130, 2001, pp. 111-120.

Fandel, G., and Paff, A.: Eine produktionstheoretisch fundierte Kostenrechnung für Hochschulen, in: Zeitschrift für Betriebswirtschaft, Ergänzungsheft 3/2000, pp. 191 – 204.

Fleischer, W.: Modelle und Erfahrungen aus Nordrhein-Westfalen, in: HIS (1997), S. 7-18.

HIS (ed.): Symposium: Staatliche Finanzierung der Hochschulen – Neue Modelle und Erfah- rungen aus dem In- und Ausland, Teil 1 (A9/97): Modelle – Ausland, und Teil 2 (A10/97): Modelle – Deutschland, Hannover 1997.

Johnes, J., and Johnes, G.: Research Funding and Performance in U.K. University Departments of Economics: A Frontier Analysis, in: Economics of Education Review, 14, 1995, pp. 301-314.

Kirjavainen, T., and Loikkanen, H.: Efficiency Differences of Finnish Senior Secundary Schools: An Application of DEA and Tobit Analysis, in: Economics of Education Review, 17, 1998, pp. 377-394.

Kleinaltenkamp, M., and Haase, M.: Externe Faktoren in der Theorie der Unternehmung, in: Albach, H. (ed.): Die Theorie der Unternehmung in Forschung und Praxis, 1999, pp. 167- 194.

Kleine, A.: DEA-Effizienz, 2002.

Korhonen, P., Tainio, R., and Wallenius, J.: Value efficiency analysis of academic research, in: European Journal of Operational Research, 130, 2001, pp. 121-132.

Stuhlmann, S.: Die Bedeutung des externen Faktors in der Dienstleistungsproduktion, in: Corsten, H. (ed.): Wettbewerbsfaktor Dienstleistung: Produktion von Dienstleistungen – Produktion als Dienstleistung, 1999, pp. 23-58. 19

Wüstemann, G., Weber, H., Brixner, H.C., and Dämmrich, Th.: Leistungsorientierte Mittelzu-

weisung an Hochschulen im Land Hessen, Hessisches Ministerium für Wissenschaft und Kunst, Wiesbaden 2000.

Ziegele, F.: Grundlagen und Merkmale eines neuen Modells der staatlichen Mittelvergabe in , CHE Centrum für Hochschulentwicklung, Gütersloh 2001.