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An analysis of the performance of university-affiliated credit unions
Pergamon
0305-0548(95)00045-3
Computers Ops Res. Vol. 23, No. 4, pp. 375-384, 1996 Copyright © 1996 Elsevier ScienceLtd Printed in Great Britain. All rights reserved 0305-0548/96 $15.0+ 0.00
A N A N A L Y S I S OF THE P E R F O R M A N C E OF UNIVERSITY-AFFILIATED CREDIT UNIONS H . O. F r i e d , i t C. A . K . Lovell2:~§ a n d J. A. T u r n e r 3 ¶ IUnion College, Schenectady, New York, U.S.A., 2University of Georgia, Athens, Georgia, GA 30602, U.S.A. and 3Christensen Associates, Madison, Wisconsin, U.S.A.
Scope and Purpose--The objective of this paper is to evaluate the performance of university-affiliated credit unions, and to compare their performance with that of other credit unions. We use a mathematical programming technique known as Free Disposal Hull analysis, which generalizes a more popular linear programming technique known as data envelopment analysis. We then use a statistical technique known as seemingly unrelated regression analysis to attempt to attribute variation in performance to factors not under the control of management and factors that are under the control of management. Abstract--In this paper we analyze the operating efficiency of a group of university-affiliated credit unions in 1990. We use free disposal hull (FDH) techniques, which generalize data envelopment analysis (DEA) techniques by dispensing with the convexity assumption imposed in DEA, to measure the operating efficiency of university-affiliated credit unions and to compare their efficiency with that of credit unions not affiliated with a university. The purpose of the analysis is to test the hypothesis that university-affiliated credit unions, by virtue of the superior educational attainment of their members, some of whom sit on boards of directors that monitor managements, are thereby better managed and so perform better. In the second stage of the analysis we use seemingly unrelated regression (SUR) techniques to identify exogenous factors that might explain variation in operating efficiency among the university-affiliated credit unions.
1. I N T R O D U C T I O N I n 1990 t h e r e w e r e o v e r 14,000 c r e d i t u n i o n s in o p e r a t i o n in the U . S . C r e d i t u n i o n s are n o t - f o r - p r o f i t c o o p e r a t i v e s , b u t t h e y p r o v i d e m u c h t h e s a m e f i n a n c i a l services as p r o f i t - o r i e n t e d c o m m e r c i a l b a n k s , w h i c h a r e s u b s t a n t i a l l y l a r g e r b u t s o m e w h a t less n u m e r o u s . O f t h e s e c r e d i t u n i o n s 226 h a d a n e d u c a t i o n a l c o m m o n b o n d , a n d 148 o f t h e s e w e r e affiliated w i t h a c o l l e g e o r u n i v e r s i t y . T h e first o b j e c t i v e o f t h e s t u d y is t o m e a s u r e t h e o p e r a t i n g efficiency o f u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s , a n d t o c o m p a r e t h e i r p e r f o r m a n c e w i t h t h a t o f c r e d i t u n i o n s n o t affiliated w i t h a u n i v e r s i t y . T h e p u r p o s e is to test t h e h y p o t h e s i s t h a t u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s , b y v i r t u e o f t h e r e l a t i v e l y h i g h e d u c a t i o n a l a t t a i n m e n t o f m u c h o f t h e i r m e m b e r s h i p , s o m e o f w h o m sit o n the b o a r d s o f d i r e c t o r s t h a t m o n i t o r m a n a g e m e n t s , a r e t h e r e b y b e t t e r m a n a g e d a n d so o p e r a t e m o r e efficiently. T h e s e c o n d o b j e c t i v e o f the s t u d y is to q u a n t i f y t h e i m p a c t o f v a r i o u s e x o g e n o u s f a c t o r s t h a t m i g h t e x p l a i n v a r i a t i o n in o p e r a t i n g efficiency a m o n g the s u b s e t o f u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s . T h e p u r p o s e
"~H. O. Fried is Associate Professor of Economics at Union College. He received his Ph.D. in Economics from the University of North Carolina. He is the organizer of the Union College Workshop Series on the Measurement of Efficiency. He is a frequent contributor to professional journals, and he is co-editor of The Measurement of Productive Efficiency (Oxford University Press, 1993). :~C. A. K. Lovell is Terry Professor of Economics at the University of Georgia. He received his Ph.D. in Economics from Duke University. He is Editor-in-Chief of The Journal of Productivity Analysis, Associate Editor of Management Science, co-author of Production Frontiers (Cambridge University Press, 1994), co-editor of The Measurement of Productive Efficiency (Oxford University Press, 1993), and a frequent contributor to professional journals. §Author for correspondence. ¶J. A. Turner received her Ph.D. in Economics at the University of North Carolina. Her research interests involve the application of mathematical programming and econometric techniques to the measurement of efficiency and productivity in a wide variety of settings. 375
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here is to attempt to decompose operating inefficiency into an environmental component and a residual component reflecting managerial inefficiency. In the analysis we use two analytical techniques. In the first stage we use a mathematical programming technique, developed by Deprins et al. [1] and called free disposal hull (FDH) analysis, to measure operating efficiency. F D H generalised the more commonly used data envelopment analysis (DEA) technique by relaxing the convexity assumption of the latter. Despite the fact that F D H is a generalization of DEA, it is computationally somewhat simpler, since it is implemented by means of a straightforward vector comparison algorithm, while DEA requires the solution of a series of linear programs. In the second stage we employ seemingly unrelated regression (SUR) analysis to associate variation in operating efficiency with various exogenous variable capturing features of the operating environment beyond the control of management. This procedure enables us to decompose operating inefficiency into an environmental component and a residual component reflecting managerial inefficiency. The distinguishing feature of the second stage analysis is that we characterize the operating inefficiency to be explained on a variable-by-variable basis, which requires the use of SUR techniques, instead of the more conventional method which characterizes operating inefficiency by means of (one minus) the scalar-valued radial efficiency measure. Our approach includes all inefficiency, radial and non-radial, in the dependent variables, whereas the conventional approach attempts to explain only the radial component of inefficiency. Omitting non-radial slacks can be a serious problem in DEA [2], and is an even more serious problem in non-convex FDH, so a SUR approach that incorporates radial and non-radial slacks is essential for the achievement of an adequate explanation of operating inefficiency. Since F D H generalizes DEA, while retaining many of its other virtues, it is ideally suited for a performance analysis of credit unions. DEA was originally proposed by Charnes, Cooper and Rhodes [3] as an appropriate performance evaluation technique when: (i) the units being evaluated are not profit-oriented, as is the case in the public and not-for-profit sectors of the economy; (ii) services provided by these units are valued but not priced, or priced with distortion; and (iii) the units provide multiple services, making them difficult to evaluate using either ratio analysis or conventional econometric techniques. All 3 of these features are shared by credit unions. Credit unions are not-for-profit, cooperative enterprises owned by and operated for the benefit of their members. Benefit is not measured by profitability, but by the provision of savings and loan opportunities at favorable rates. These multiple services are valued by members, but not all of them are priced. In this context it is appropriate to use F D H in evaluating the ability of credit unions to provide maximum service to their members, given the resources at their disposal. In Section 2 of the paper we describe the first stage F D H technique used to evaluate the operating efficiency of credit unions, and we also describe the second stage SUR technique used to explain variation in measured operating inefficiency. In Section 3 we describe the data and the variables used in both stages of the analysis. Section 4 contains our empirical findings, and Section 5 concludes. 2. THE TWO-STAGE PERFORMANCE EVALUATION AND EXPLANATION TECHNIQUES We begin this section with a brief discussion of F D H and its relationship to DEA. The purpose of F D H is to evaluate the performance of a producer, first by identifying the set of all dominating producers, then by identifying a single most dominant producer, and finally by comparing the inputs and outputs of the producer being evaluated with those of the producer that most dominates it. The notions of "dominance" and "most dominant" will be explained shortly. Let producer i use resources x i = (x~ . . . . . x~) E N~_ to provide services yi = (y~ ..... y i ) E N~, and let there be i = 1. . . . . l producers. The data set is denoted T = {(xi, yi), i = 1. . . . . l}. A set of feasible production possibilities satisfying free disposal of the variables, but not convexity, is constructed from T by means of:
/(y) (;) (X/) ~m (0) (o} t yi
(xi'yi) e T U
j=l gj ej
0 'gJ >= O'vj > O "
/=1
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The set 7~ consists of all possible production activities having resources no smaller than, and services no larger than, those of each producer in the sample. Relative to 7~, producer o is undominated if there exists no other producer for which
Alternatively, producer o is dominated by all producers j for which
The number of dominating producers provides important insight into the performance of a producer. It provides the number and the identity of all producers who are performing at least as well in every dimension. This information is largely independent of the efficiency of a producer, since a producer may be relatively efficient and still be dominated by many other producers, or a producer may be relatively ineffÉcient and be dominated by very few other producers.t The most dominant of the producers that dominate producer o is identified by solving the following mathematical programming problem for producer o: 1
max0 °
s.t.
0°yf-<_ •L°yj
8o. ~o
j = 1,...,m
i= 1 l
E L°x~ < xs
j -- 1. . . . . n
i=l
=>0 l
E£°=
1
i=1
~o E {0, l},i---- l . . . . . 0 . . . . . I. This programming problem is the familiar DEA output-oriented variable returns to scale envelopment problem developed by Banker, Charnes and Cooper [4], with the addition of an extra constraint on the intensity vector L ° = (~°1, ...,Lo, ....L~). The additional constraint Lo E {0, 1) converts the D E A linear programming problem to an F D H mixed integer programming problem. More importantly, the additional constraint forces the program to identify, by means of the single non-zero element in ~o, the single most dominant producer relative to which the producer under evaluation is to be compared. This is in contrast to the DEA program, which identifies a fictitious convex combination of possibly non-dominating producers to which the producer under evaluation is to be compared. Thus in DEA a producer's role models may not dominate the producer being evaluated. In F D H a producer's role models dominate it by construction. If a producer is undominated, then at optimium (0 °)-1 = 1. Lo = 1, ~o = 0. Vi # 0, and slacks in all (m + n) functional constraints are zero. If a producer is dominated, then at optimum (0°) -1 _-< 1, Lo° = 0, L~ = 1 for the single most dominant producer k among the set of dominating producers, and total (radial plus non-radial) slacks are determined from the functional constraints by means of (L~y~ - y~),j = 1 , . . . . m . and (x~ - ;L~X~),j = 1. . . . ,n. Particularly in F D H , in which convexity is not imposed, a producer's performance is more accurately reflected in its (m + n)dimensional slack vector than in its radial efficiency score. F D H and DEA are illustrated in Fig. 1, where all producers are assumed to use the same input vector x E ~_ to produce different output vectors y = (Yl,Y2)E ~ . The F D H production possibilities set is bounded above by the solid staircase function constructed from the undominated producers A, B, C and D, and the free disposal assumption. The DEA production possibilities set is
tDominance informationis generatedautomaticallyin FDH analysis, but it is not inherentlylimitedto FDH. Althoughit has not been employed in DEA analysis, it can be, and it would provide valuable complementaryinsight into any DEA analysis of producer performance.
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A
•l
i
1 Yt Fig. 1. F D H and DEA.
bounded above by the piecewise linear function ABD reflecting convexity, and by horizontal and vertical extensions to the axes reflecting free disposal. Note that ~FDH C /~DEA.Producers A, B and D are each undominated, and rated technically efficient by both FDH and DEA. Producer C is also undominated, and called technically efficient by FDH. However it is dominated by a non-existent convex combination of producers B and D, and so it is called technically inefficient by DEA. Producer E is dominated, by producer B by all other producers located northwest of E in 20FDH. FDH assigns producer E a radial efficiency score of 0 -1 < 1, and finds non-radial slack in output Yl in the amount (ylB - 0y~). DEA assigns producer E a lower radial efficiency score of OE/OE', and finds no non-radial slack. Thus FDH, by dispensing with the convexity assumption maintained in DEA, creates a smaller production possibilities set that envelops the observed data more closely than does DEA. Consequently it generates higher radial efficiency scores. In the process of dispensing with convexity, however, FDH creates greater amounts of non-radial slack. The major difference between the 2 techniques is that FDH measures the efficiency of dominated producers relative to existing undominated producers, while DEA typically measures the efficiency of dominated producers relative to non-existent convex combinations of undominated producers. Having existing producers to score as role models is a feature of FDH that has proved to be attractive to management of dominated producers. The FDH problem is formulated as a mixed integer programming problem, but the solution algorithm is straightforward and computationally efficient. The solution algorithm, described in Tulkens [5] and Lovell and Vanden Eeckaut [6], has 2 steps. In the first step the set Do of dominating producers for producer o being evaluated is determined by means of a simple (m + n)-dimensional vector comparison: --X °
Oo
The second step begins by noting that the first set of functional constraints in the FDH problem can be rewritten as: /i\ 0o< ~ )o[YS~ j=l,...,m
-'eDo
\Y~J'
from which it follows that, at optimum
y( 0° = m a x ~ min ~ J ~ . L,=, .....
,,,ly:J J
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F r o m this maximum procedure an optimal radial efficiency score (0°) -1 is obtained for the producer under evaluation. The " m a x " part of the algorithm identifies the most dominant of the producers that dominate the producer under evaluation. Once the most dominant producer is identified, nonradial output slacks are calculated as (y~ -.0°y~), j = 1, ..., m. Total output slacks are calculated from the "rain" part of the algorithm as (y~ - y ~ ) , j = 1, ..., m. Total input slacks are determined directly from the data in this output-oriented problem.t To summarize, the F D H performance analysis generates 3 pieces of information for each producer: (i) the set, which may be empty, of all dominating producers, each of which can serve as a role model; (ii) the identity of the most dominant of the dominating producers; and (iii) an (m + n)-dimensional vector of total slacks measured relative to the performance of the most dominant of the dominating producers. A radial efficiency score is also generated, but in the absence of convexity the presence of so much non-radial slack renders the radial component of total slack of limited value. Once the performance of each producer is evaluated using the F D H technique, it is of interest to attribute variation in performance across producers to various causal factors. In DEA this is frequently accomplished by regressing producers' radial efficiency scores against a set of exogenous explanatory variables. Since in F D H non-radial slack is so important, performance is evaluated not in terms of radial efficiency scores, but in terms of an (m + n)-dimensional total slack vector. This requires that a single-equation explanatory regression be replaced by a system of equations of general form:
sji=fJ(z~,...,z~),+eji,
i=1,
.,l,
j=l,...,m+n,
where sji is total (radial plus non-radial) slack in variablej for producer i, z i = (z~, ..., z~) E ~t is a vector of exogenous variables for producer i, and eji is a 1 x (m + n) disturbance vector. This system of (m + n) equations could be estimated on an equation-by-equation basis, using ordinary least squares (OLS) separately on each equation. However it is likely that omitted exogenous variables also exert an influence on total slacks in the (m + n) equations. Since they are omitted, their influence shows up in the disturbance terms. This makes the system of equations only "seemingly" unrelated, and calls for a simultaneous estimation of the system. A seemingly unrelated regressions (SUR) approach was developed by Zellner [7] to deal with this situation, and we use this estimation technique. Estimation of the system of equations above generates two types of information. First, it signs and quantifies the effects of various exogenous variables thought to influence performance. Second, initial slacks can be adjusted (up or down) for environmental features to arrive at a clearer picture of management efficiency purged of the effects of varying environmental characteristics. Thus, for example, it is possible to predict the slacks that a dominant producer would have generated had it operated in the same environment as that of its most dominant producer. This exercise "levels the playing field," by putting the two producers in the same operating environment, and it may decrease or increase the predicted value of any given slack for the dominated producer.
3. THE CREDIT UNION DATA Input and service output data used in the first stage of this study are taken from the 1990 National Credit Union Administration Supervisors Yearend Call Report and the 1990 Credit Union National Association Yearbook Questionnaire. Exogenous variables used in the second stage are taken from the same sources, and from various other sources that provide information on universities with which some of the credit unions are affiliated. In the first stage the sample size is 8,954, about 62% of all credit unions in operation in 1990. Of the 148 university-affiliated credit unions in operation in
tFDH requiresonly that y C N~, i.e., that componentsof the output vectorbe non-negative.Howeverthe appearanceofyy in the denominator of the "rain" part of the maximin algorithm would appear to require strict positivityof all outputs for each producer being evaluated. Replacingzeros with a positive number smaller than any observedoutput in the data set resolves the problem without affectingthe optimal solution.
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1990, we have i n p u t a n d o u t p u t service d a t a for 135. In the second stage missing e x o g e n o u s variables reduce the university-affiliated credit u n i o n s a m p l e size f r o m 135 to 117.t V a r i a b l e s used in the first stage o f the analysis are defined as follows: The single i n p u t is t o t a l o p e r a t i n g expense, c o m p r i s e d in r o u g h l y equal shares o f e m p l o y e e c o m p e n s a t i o n a n d benefits, a n d o t h e r office-related expense. Six o u t p u t services are specified. T h e first 2 are q u a n t i t y variables, the t o t a l n u m b e r o f l o a n accounts, a n d the t o t a l n u m b e r o f d e p o s i t accounts. These are the 2 c o n v e n t i o n a l o u t p u t q u a n t i t y i n d i c a t o r s frequently e m p l o y e d in p e r f o r m a n c e v a l u a t i o n in the financial services sector. The next 2 are service price variables, the reciprocal o f the average l o a n rate, a n d the average d e p o s i t rate. The 2 rates are i n c l u d e d in the o u t p u t service vector because low l o a n rates a n d high d e p o s i t rates p r o v i d e benefits to m e m b e r b o r r o w e r s a n d savers. Inclusion o f these 2 price variables is a p p r o p r i a t e for b e n e f i t - m a x i m i z i n g n o t - f o r - p r o f i t c o o p e r a t i v e s like credit unions, a l t h o u g h their inclusion in the o u t p u t vector w o u l d n o t be a p p r o p r i a t e for p r o f i t - o r i e n t e d b a n k s . T h e fifth o u t p u t service, the n u m b e r o f share d r a f t (checking) accounts, is a transactions, o r t u r n o v e r , i n d i c a t o r . This v a r i a b l e is i n c l u d e d b e c a u s e the m o r e share d r a f t a c c o u n t s a credit u n i o n has, the m o r e p e r s o n n e l a n d o t h e r office expenses it incurs. The final o u t p u t service is a service v a r i e t y i n d i c a t o r , a simple c o u n t o f the n u m b e r o f 7 key services a credit u n i o n offers.:~ T h u s a credit u n i o n is viewed as using a single c o m p r e h e n s i v e resource to p r o v i d e 6 o u t p u t services to its m e m b e r s . T h e 6 o u t p u t services are specified so as to c a p t u r e the q u a n t i t y , price a n d variety d i m e n s i o n s o f overall service p r o v i s i o n . T h e s u m m a r y statistics r e p o r t e d in T a b l e 1 suggest t h a t by n e a r l y all m e a s u r e s university-affiliated credit u n i o n s are slightly large, a n d s o m e w h a t m o r e h o m o g e n e o u s t h a n o t h e r credit unions. T h e y also p r o v i d e s o m e w h a t greater service variety. T h e y offer lower average l o a n rates, an a d v a n t a g e p a r t l y offset b y slightly lower average d e p o s i t rates. V a r i a b l e s used in the s e c o n d stage o f the analysis are defined as follows. The d e p e n d e n t variables in the S U R m o d e l are the t o t a l (radial plus n o n - r a d i a l ) slacks in each o f the i n p u t a n d o u t p u t service variables. T h e e x p l a n a t o r y variables include: (i) the n u m b e r o f m e m b e r s in the credit union, a size i n d i c a t o r t h a t m a y c a p t u r e the effects o f scale e c o n o m i e s on p e r f o r m a n c e ; (ii) a d u m m y v a r i a b l e set to one i f the credit u n i o n has a state charter, a n d set to zero if it has a federal charter; (iii) the percent o f the s t u d e n t b o d y t h a t is non-white; (iv) a d u m m y v a r i a b l e set to one if the university is public, a n d set to zero if it is private; a n d (v) the r a t i o o f the value o f d e l i n q u e n t loans to the t o t a l value o f o u t s t a n d i n g loans. A l l b u t the last e x p l a n a t o r y v a r i a b l e are exogenous, while the d e l i n q u e n c y r a t i o is at least p a r t l y u n d e r the c o n t r o l o f m a n a g e m e n t . To the extent t h a t the d e l i n q u e n c y r a t i o reflects local e c o n o m i c c o n d i t i o n s , w h i c h are b e y o n d the c o n t r o l o f m a n a g e m e n t , it can be viewed as a n
Table 1. Summarystatisticsfor variablesused in the first stageof the analysis
University-affiliated (l = 135)
Mean S.D. Min Max
Not university-affiliated (l = 8,819)
Mean S.D. Min Max
Operating expense
Loan quantity
Loan price
($ooo)
(#)
(%)
692 1,171 1.9 6,370
3,347 5,948 25 37,669 2,437 7,128 1 254,457
591 1,681 1 49,614
Deposit quantity
Deposit price
Share drafts
Service variety
(#)
(%)
(#)
(#)
1t .36 1.16 8.77 18.21
9,813 16,617 111 85,902
5.89 1.00 2.88 10.79
2,320 4,710 0 23,015
3.19 2.49 0 7
11.76 1.49 5.02 31.65
7,081 19,540 1 591,840
6.25 1.15 2.51 14.68
1,282 4,306 0 76,093
2.61 2.23 0 7
tAdditional information on the sample and the specification of the services, resources and exogenous variables appears in Fried, Lovell and Vanden Eeckaut [9]. :~The 7 key services, with the percent of all credit unions offering each in parentheses, are certificates of deposit (53%), guaranteed student loans (14%), first mortgages (29%), direct deposit of Federal recurring payments (54%), credit cards (29%), ATM cards (24%), and travelers' checks (49%). The role of the variety indicator is to capture the range of services a credit union offers its members. Failure to offer a wide variety of financial services can lead to a decline in membership, and to a loss of deposit and loan accounts, as members take their business to other financial institutions. On this view variety is just as significant as the other, more conventional services a credit union can offer its members.
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exogenous variable. To the extent that the delinquency ratio reflects excessive risk-taking by credit union loan officers, it can be viewed as an endogenous variable. Although the true source of loan delinquency is unknown, we treat it as a proxy for exogenous local economic conditions. 4. EMPIRICAL
RESULTS
The first stage of the analysis consists of an FDH evaluation of the operating efficiency of all 8,954 credit unions in the sample. The purpose is to measure the efficiency with which credit unions utilize the operating expenses they incur to provide services to their members. The central hypothesis is that university-affiliatedcredit unions, which have a greater percentage of highly educated members, operate more efficiently than other credit unions. The linkage underlying this hypothesis is that educators supply a disproportionate share of the board of directors, which monitors the actions of the management of credit unions. To the extent that better-educated directors exert superior oversight, managerial performance in university-affiliatedcredit unions is expected to dominate that in other credit unions. (For more on the relationship between board of directors characteristics and credit union performance, see Hautaluoma et al. [8]). Results of the FDH analysis provide considerable support for the hypothesis that universityaffiliated credit unions operate more efficiently than other credit unions. Considering dominance first, on average the 135 university-affiliated credit unions are dominated by 15 credit unions, whereas on average the 8,819 other credit unions are dominated almost twice as often, by 30 other credit unions. Moreover, average radial efficiency scores are 94.2% for the 135 university-affiliated credit unions, and 91.4% for the 8,819 other credit unions. However as noted in Section 2, radial inefficiency is only one component of overall inefficiency, and it may be a misleading indicator of overall inefficiency when FDH is used to evaluate performance. This warning is emphasized by the results reported in Table 2, in which total slack, and its radial and non-radial components, is reported for each of 7 variables for both types of credit union. Three conclusions can be drawn from the results reported in Table 2. The first conclusion concerns the relative operating efficiency of university-affiliatedand other credit unions. Universityaffiliated credit unions have smaller total slacks, expressed in percentage terms, than other credit unions. This superior operating efficiency exists in each of the 7 variables, and in some variables the advantage is very large. The advantage suggested by average radial efficiency scores is reinforced by the inclusion of the non-radial component of total inefficiency. However the magnitude of overall inefficiency is substantially larger than the magnitude of the radial component of inefficiency for both types of credit union. Although it is not permissible to aggregate over slacks denominated in different units, it is permissible to aggregate over slacks expressed in percentage terms. On this basis, university-affiliatedcredit unions have on average approximately 9% slack in their operations, while other credit unions have on average approximately 17%, or twice as much, slack in their operations. The second and third conclusions relate to the analytical technique used to measure operating efficiency. Total slack, even when expressed in percentage terms, varies in magnitude over variables. Table 2. Operating efficiency in university-affiliated and other credit unions Total slack
Radial slack
Non-radial slack
4.23 15.62 4.89 8.98 7.02 9.11 16.09
-0.51 1.95 0.59 2.09 0.32 0.95
4.23 15.11 2.94 8.39 4.93 8.79 15.14
9.95 21.41 12.40 15.46 13.59 20.77 23.94
-3.02 8.72 3.24 8.55 2.30 4.25
9.95 18.39 3.68 12.22 5.04 18.47 19.69
(%)
(%)
(%)
University-affiliated (l = 135) Operating expense Loan quantity Loan price Deposit quantity Deposit price Share drafts Service variety
Not university-affiliated (1 = 8, 8t9) Operating expense Loan quantity Loan price Deposit quantity Deposit price Share drafts Service variety CAORZ3:4-F
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For both types of credit union slack is most severe in two service dimensions, loan quantity and service variety. This non-neutrality provides useful guidance to management by showing where there exists the greatest opportunity for improvement. Finally, as anticipated, radial slack is small compared to non-radial slack. This emphasizes the importance of reporting total inefficiency, rather than just the radial component of inefficiency, when analyzing operating performance. This is especially important in F D H , but it is also important in DEA. University-affiliated credit unions operate with half the slack of other credit unions. Nonetheless, they have slack ranging from 4% in operating expense to 16% in service variety, and it is of interest to see if these slacks can be attributed to various characteristics of their operating environment. To the extent that they can, performance of individual university-affiliated credit unions having these characteristics can be adjusted to obtain a clearer picture of the operating efficiency of their management. To explore this issue, a linear 7-equation SUR model was estimated, using 117 universityaffiliated credit unions.t Explanatory variables include the number of members in the credit union, a state charter dummy, a percent minority student population variable, a public university dummy, an urban location dummy, and a loan delinquency rate variable. Very low explanatory power was achieved, with a system-weighted R 2 = 0.0769. The SUR results appear in Table 3. Three exogenous variables (the state charter dummy, the public university dummy, and the urban location dummy) and 1 variable at least partly under the control of management (the loan delinquency rate) are statistically insignificant in each of the 7 equations. The percent minority variable is positive and statistically significance in the loan price and deposit price equations. This suggests that as the minority share of the student body (and perhaps faculty and staff) grows, university-affiliated credit unions offer less favorable deposit rates and less favorable loan rates to their members. These disadvantages are not offset by the provision of better service in the remaining 4 output dimensions. Finally, the number of members is statistically significant in 5 equations. As credit union size, measured by the number of members, increases, slack increases in the loan quantity, deposit quantity, and share draft dimensions, and declines in the loan price and deposit price dimensions. The first 3 results suggest that as university-affiliated credit unions grow, their members become less frequent users of their credit union's deposit and loan opportunities. The 2 price results suggest that
Table 3. SUR results for university-affiliatedcreditunions Independentvariables Dependentvariable Operatingexpense
Intercept
Numberof members
State charter
Percent minority
Public
- 136 (-0.25)
548 (0.03)
Urban
Delinquency ratio
23,499 (l.04)t
1.15 (1.12)
32,314 (1.52)
303 (0.62)
0.08 (3.54)
-218 (-0.46)
5.74 (0.48)
- 144 (-0.31)
-4,886 (-0.85)
89 (3.67
-0.003 (-2.46)
5.88 (-0.28)
1.04 (1.94)
-7.02 (-0.33)
-99 (-0.23)
242 (0.38)
0.11 (3.43)
365 (0.55)
0.81 (0.05)
49 (0.08)
64 (3.30)
- 0.002 (-2.82)
3.07 (0.18)
1.40 (3.30)
- 9.18 (-0.54)
-47 (-0.27)
0.03 (3.15)
90 (0.51)
2.20 (0.49)
101 (0.58)
0.79 (3.43)
-0.00+ (-1.58)
-0.31 (-1.35)
-0.001 (-0.17)
0.05 (0.22)
Loanquantity Loan price Deposit quantity Depositprice Share drafts Servicevariety
-27,407 (-1.73)
55 (0.15)
tt-statistics in parentheses.
tAlthough the FDH model is output-oriented, non-radial slackscan occurin both output and input dimensions. Accordingly we attempt to explain total (radial plus non-radial) inefficiencyin both output and input dimensions.
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Table4. Predictedslacks,expressedas percentof university-affiliatedcreditunion means, for a dominatedcreditunion Variable Operatingexpense Loan quantity Loan price Depositquantity Depositprice Share drafts Servicevariety
Predicted slacks(%), using actualdata 3.40 77.36 4.11 33.89 4.12 30.67 24.65
Predicted slacks(%), usingdata of most dominatingrole model 3.40 80.21 2.60 35.20 1.29 32.04 24.65
large university-affiliated credit unions have a smaller spread, offering lower loan rates and higher deposit rates to their members. The low explanatory power in the S U R model is disappointing, but enlightening.:~ The information conveyed by the low explanatory power suggests that variation in managerial performance across university-affiliated credit unions cannot be attributed to variation in the environment in which they operate. Virtually all of the performance variation revealed in the F D H model survives our attempt at explanation, or adjustment. We conclude that F D H provides an accurate portrayal of operating efficiency in university-affiliated credit unions, and that performance variation uncovered in the F D H analysis can be attributed almost exclusively to variation in managerial performance. While university-affiliated credit unions perform substantially better than other credit unions, some university-affiliated credit unions are better managed than others, regardless of variation in their operating environment. To illustrate how the results of the S U R analysis can be used to evaluate managerial performance, we conduct an experiment on 2 large university-affiliated credit unions. One is the most dominant of all the credit unions that dominate the other. We first use the S U R result to predict the slacks of the dominated credit union, using only statistically significant regressors. We then use the S U R results to predict the slacks the dominated credit union would have incurred had it operated in the same environment as its most dominant role model, using the statistically significant regressors of its role model. This analysis enables us to compare the predicted performance of the dominated credit union in 2 operating environments: its own, and that of its most dominant role model. Results appear in Table 4. It appears that had the university-affiliated credit union under evaluation enjoyed the operating environment of its most dominant role model, it would have fared no better in general. It would have performed the same in 2 dimensions, slightly better in the loan rate and deposit rate dimensions, and slightly worse in the 3 quantity dimensions. We conclude that it is not possible to attribute the weak performance of the university-affiliated credit union under evaluation to an operating environment less favorable than that of its most dominant credit union. The only possible explanations for its weak performance are a weak managerial performance, and potentially relevant explanatory variables omitted from the S U R model. 5. CONCLUSIONS In this paper we have employed a 2-stage combination of F D H and S U R in an effort to measure and explain the operating efficiency of university-affiliated credit unions. The contribution of the paper is partly methodological, and partly institutional. The methodological contribution of the paper is to demonstrate the feasibility and, in our judgement, the superiority, of the F D H / S U R combination over the more frequently employed D E A / O L S (or DEA/logit or DEA/tobit) combination. F G H generalizes D E A by dispensing the convexity. It emphasizes dominance, and associates role models with observed dominating producers, whereas the usual D E A models emphasize radial efficiency, and associates role models
;~Addingadditional variablesto the SUR system, such as the age of the credit union and the number of volunteers, yielded no statistically significant regressors and no appreciable improvement in explanatory power.
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with possibly n o n - d o m i n a t i n g producers. F D H measures performance in terms o f (m + n) total slacks measured relative to the operations o f a single m o s t d o m i n a n t producer, while D E A generally ignores non-radial slacks and measures performance in terms o f radial efficiency scores. Finally, variation in operating efficiency is explained by using (m + n) F D H total slacks as dependent variables in a S U R regression model, while the conventional a p p r o a c h seeks to explain operating efficiency by using a single D E A radial efficiency score as the dependent variable in an O L S (or a limited dependent variable) regression equation. The institutional contribution o f the paper has been to c o m p a r e the operating efficiency o f university-affiliated credit unions with that o f other credit unions. We have f o u n d considerable support for the hypothesis that university-affiliated credit unions, by virtue o f the higher educational attainment o f their membership, some o f w h o m sit on the b o a r d o f directors that oversees m a n a g e m e n t , operate m o r e efficiently than other credit unions. University-affiliated credit unions have considerably higher radial efficiency scores (i.e. values o f 0 closer to unity), and substantially smaller overall slacks in every dimension, than other credit unions. Moreover, we were unable to associate variation in university-affiliated credit u n i o n performance with variation in their operating environment, This strongly suggests that such performance variation as does exist c a n n o t be easily explained away, and so must be attributed to variation on managerial performance. Acknowledgements--The authors are indebted to the Filene Research Institute and the Credit Union National Association
for their generous financial support, and to Philippe Vanden Eeckaut for his helpful comments. REFERENCES 1. D. Deprins, L. Simar and H. Tulkens, Measuring labor-efficiency in post offices. In The Performance o f Public Enterprises: Concepts and Measurement (Edited by M. Marchand, P. Pestieau and H. Tulkens), North-Holland, Amsterdam (1989). 2. A. Bessent, W. Bessent, J. Elam and T. Clark, Efficiencyfrontier determination by constrained facet analysis. Ops Res. 36, 785-796 (1988). 3. A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiencyof decision making units. Eur. J. Opl Res. 2, 429-444 (1978). 4. R.D. Banker, A. Charnes and W. W. Cooper, Some models for estimating technical and scale efficiencies in Data Envelopment Analysis. Mgmt Sci. 30, 1078-1092 (1984). 5. H. Tulkens, On FDH efficiency analysis: some methodological issues and applications to retain banking, courts and urban transit. J. Prod. Analy. 4, 183-210 (1993). 6. C.A.K. Lovell and P. Vanden Eeckaut, Frontier Tales: DEA and FDH. In Mathematical Modelling in Economics (Edited by W. E. Diewert, K. Spremann and F. Stehling), Springer, Berlin (1993). 7. A. Zellner, An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Am. Statist. Assoc. $7, 348-368 (1962). 8. J.E. Hautaluoma, L. Jobe, B. Donkersgoed, T. Suri and R. Cropanzano, Credit Union Boards and Credit Union Effectiveness. Filene Research Institute, Madison, WI (1993). 9. H.O. Fried, C. A. K. Lovell and P. Vanden Eeckaut, Evaluating the performance of U.S. credit unions. J. Bank. Finance 17, 251-265 (1993).
0305-0548(95)00045-3
Computers Ops Res. Vol. 23, No. 4, pp. 375-384, 1996 Copyright © 1996 Elsevier ScienceLtd Printed in Great Britain. All rights reserved 0305-0548/96 $15.0+ 0.00
A N A N A L Y S I S OF THE P E R F O R M A N C E OF UNIVERSITY-AFFILIATED CREDIT UNIONS H . O. F r i e d , i t C. A . K . Lovell2:~§ a n d J. A. T u r n e r 3 ¶ IUnion College, Schenectady, New York, U.S.A., 2University of Georgia, Athens, Georgia, GA 30602, U.S.A. and 3Christensen Associates, Madison, Wisconsin, U.S.A.
Scope and Purpose--The objective of this paper is to evaluate the performance of university-affiliated credit unions, and to compare their performance with that of other credit unions. We use a mathematical programming technique known as Free Disposal Hull analysis, which generalizes a more popular linear programming technique known as data envelopment analysis. We then use a statistical technique known as seemingly unrelated regression analysis to attempt to attribute variation in performance to factors not under the control of management and factors that are under the control of management. Abstract--In this paper we analyze the operating efficiency of a group of university-affiliated credit unions in 1990. We use free disposal hull (FDH) techniques, which generalize data envelopment analysis (DEA) techniques by dispensing with the convexity assumption imposed in DEA, to measure the operating efficiency of university-affiliated credit unions and to compare their efficiency with that of credit unions not affiliated with a university. The purpose of the analysis is to test the hypothesis that university-affiliated credit unions, by virtue of the superior educational attainment of their members, some of whom sit on boards of directors that monitor managements, are thereby better managed and so perform better. In the second stage of the analysis we use seemingly unrelated regression (SUR) techniques to identify exogenous factors that might explain variation in operating efficiency among the university-affiliated credit unions.
1. I N T R O D U C T I O N I n 1990 t h e r e w e r e o v e r 14,000 c r e d i t u n i o n s in o p e r a t i o n in the U . S . C r e d i t u n i o n s are n o t - f o r - p r o f i t c o o p e r a t i v e s , b u t t h e y p r o v i d e m u c h t h e s a m e f i n a n c i a l services as p r o f i t - o r i e n t e d c o m m e r c i a l b a n k s , w h i c h a r e s u b s t a n t i a l l y l a r g e r b u t s o m e w h a t less n u m e r o u s . O f t h e s e c r e d i t u n i o n s 226 h a d a n e d u c a t i o n a l c o m m o n b o n d , a n d 148 o f t h e s e w e r e affiliated w i t h a c o l l e g e o r u n i v e r s i t y . T h e first o b j e c t i v e o f t h e s t u d y is t o m e a s u r e t h e o p e r a t i n g efficiency o f u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s , a n d t o c o m p a r e t h e i r p e r f o r m a n c e w i t h t h a t o f c r e d i t u n i o n s n o t affiliated w i t h a u n i v e r s i t y . T h e p u r p o s e is to test t h e h y p o t h e s i s t h a t u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s , b y v i r t u e o f t h e r e l a t i v e l y h i g h e d u c a t i o n a l a t t a i n m e n t o f m u c h o f t h e i r m e m b e r s h i p , s o m e o f w h o m sit o n the b o a r d s o f d i r e c t o r s t h a t m o n i t o r m a n a g e m e n t s , a r e t h e r e b y b e t t e r m a n a g e d a n d so o p e r a t e m o r e efficiently. T h e s e c o n d o b j e c t i v e o f the s t u d y is to q u a n t i f y t h e i m p a c t o f v a r i o u s e x o g e n o u s f a c t o r s t h a t m i g h t e x p l a i n v a r i a t i o n in o p e r a t i n g efficiency a m o n g the s u b s e t o f u n i v e r s i t y - a f f i l i a t e d c r e d i t u n i o n s . T h e p u r p o s e
"~H. O. Fried is Associate Professor of Economics at Union College. He received his Ph.D. in Economics from the University of North Carolina. He is the organizer of the Union College Workshop Series on the Measurement of Efficiency. He is a frequent contributor to professional journals, and he is co-editor of The Measurement of Productive Efficiency (Oxford University Press, 1993). :~C. A. K. Lovell is Terry Professor of Economics at the University of Georgia. He received his Ph.D. in Economics from Duke University. He is Editor-in-Chief of The Journal of Productivity Analysis, Associate Editor of Management Science, co-author of Production Frontiers (Cambridge University Press, 1994), co-editor of The Measurement of Productive Efficiency (Oxford University Press, 1993), and a frequent contributor to professional journals. §Author for correspondence. ¶J. A. Turner received her Ph.D. in Economics at the University of North Carolina. Her research interests involve the application of mathematical programming and econometric techniques to the measurement of efficiency and productivity in a wide variety of settings. 375
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here is to attempt to decompose operating inefficiency into an environmental component and a residual component reflecting managerial inefficiency. In the analysis we use two analytical techniques. In the first stage we use a mathematical programming technique, developed by Deprins et al. [1] and called free disposal hull (FDH) analysis, to measure operating efficiency. F D H generalised the more commonly used data envelopment analysis (DEA) technique by relaxing the convexity assumption of the latter. Despite the fact that F D H is a generalization of DEA, it is computationally somewhat simpler, since it is implemented by means of a straightforward vector comparison algorithm, while DEA requires the solution of a series of linear programs. In the second stage we employ seemingly unrelated regression (SUR) analysis to associate variation in operating efficiency with various exogenous variable capturing features of the operating environment beyond the control of management. This procedure enables us to decompose operating inefficiency into an environmental component and a residual component reflecting managerial inefficiency. The distinguishing feature of the second stage analysis is that we characterize the operating inefficiency to be explained on a variable-by-variable basis, which requires the use of SUR techniques, instead of the more conventional method which characterizes operating inefficiency by means of (one minus) the scalar-valued radial efficiency measure. Our approach includes all inefficiency, radial and non-radial, in the dependent variables, whereas the conventional approach attempts to explain only the radial component of inefficiency. Omitting non-radial slacks can be a serious problem in DEA [2], and is an even more serious problem in non-convex FDH, so a SUR approach that incorporates radial and non-radial slacks is essential for the achievement of an adequate explanation of operating inefficiency. Since F D H generalizes DEA, while retaining many of its other virtues, it is ideally suited for a performance analysis of credit unions. DEA was originally proposed by Charnes, Cooper and Rhodes [3] as an appropriate performance evaluation technique when: (i) the units being evaluated are not profit-oriented, as is the case in the public and not-for-profit sectors of the economy; (ii) services provided by these units are valued but not priced, or priced with distortion; and (iii) the units provide multiple services, making them difficult to evaluate using either ratio analysis or conventional econometric techniques. All 3 of these features are shared by credit unions. Credit unions are not-for-profit, cooperative enterprises owned by and operated for the benefit of their members. Benefit is not measured by profitability, but by the provision of savings and loan opportunities at favorable rates. These multiple services are valued by members, but not all of them are priced. In this context it is appropriate to use F D H in evaluating the ability of credit unions to provide maximum service to their members, given the resources at their disposal. In Section 2 of the paper we describe the first stage F D H technique used to evaluate the operating efficiency of credit unions, and we also describe the second stage SUR technique used to explain variation in measured operating inefficiency. In Section 3 we describe the data and the variables used in both stages of the analysis. Section 4 contains our empirical findings, and Section 5 concludes. 2. THE TWO-STAGE PERFORMANCE EVALUATION AND EXPLANATION TECHNIQUES We begin this section with a brief discussion of F D H and its relationship to DEA. The purpose of F D H is to evaluate the performance of a producer, first by identifying the set of all dominating producers, then by identifying a single most dominant producer, and finally by comparing the inputs and outputs of the producer being evaluated with those of the producer that most dominates it. The notions of "dominance" and "most dominant" will be explained shortly. Let producer i use resources x i = (x~ . . . . . x~) E N~_ to provide services yi = (y~ ..... y i ) E N~, and let there be i = 1. . . . . l producers. The data set is denoted T = {(xi, yi), i = 1. . . . . l}. A set of feasible production possibilities satisfying free disposal of the variables, but not convexity, is constructed from T by means of:
/(y) (;) (X/) ~m (0) (o} t yi
(xi'yi) e T U
j=l gj ej
0 'gJ >= O'vj > O "
/=1
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The set 7~ consists of all possible production activities having resources no smaller than, and services no larger than, those of each producer in the sample. Relative to 7~, producer o is undominated if there exists no other producer for which
Alternatively, producer o is dominated by all producers j for which
The number of dominating producers provides important insight into the performance of a producer. It provides the number and the identity of all producers who are performing at least as well in every dimension. This information is largely independent of the efficiency of a producer, since a producer may be relatively efficient and still be dominated by many other producers, or a producer may be relatively ineffÉcient and be dominated by very few other producers.t The most dominant of the producers that dominate producer o is identified by solving the following mathematical programming problem for producer o: 1
max0 °
s.t.
0°yf-<_ •L°yj
8o. ~o
j = 1,...,m
i= 1 l
E L°x~ < xs
j -- 1. . . . . n
i=l
=>0 l
E£°=
1
i=1
~o E {0, l},i---- l . . . . . 0 . . . . . I. This programming problem is the familiar DEA output-oriented variable returns to scale envelopment problem developed by Banker, Charnes and Cooper [4], with the addition of an extra constraint on the intensity vector L ° = (~°1, ...,Lo, ....L~). The additional constraint Lo E {0, 1) converts the D E A linear programming problem to an F D H mixed integer programming problem. More importantly, the additional constraint forces the program to identify, by means of the single non-zero element in ~o, the single most dominant producer relative to which the producer under evaluation is to be compared. This is in contrast to the DEA program, which identifies a fictitious convex combination of possibly non-dominating producers to which the producer under evaluation is to be compared. Thus in DEA a producer's role models may not dominate the producer being evaluated. In F D H a producer's role models dominate it by construction. If a producer is undominated, then at optimium (0 °)-1 = 1. Lo = 1, ~o = 0. Vi # 0, and slacks in all (m + n) functional constraints are zero. If a producer is dominated, then at optimum (0°) -1 _-< 1, Lo° = 0, L~ = 1 for the single most dominant producer k among the set of dominating producers, and total (radial plus non-radial) slacks are determined from the functional constraints by means of (L~y~ - y~),j = 1 , . . . . m . and (x~ - ;L~X~),j = 1. . . . ,n. Particularly in F D H , in which convexity is not imposed, a producer's performance is more accurately reflected in its (m + n)dimensional slack vector than in its radial efficiency score. F D H and DEA are illustrated in Fig. 1, where all producers are assumed to use the same input vector x E ~_ to produce different output vectors y = (Yl,Y2)E ~ . The F D H production possibilities set is bounded above by the solid staircase function constructed from the undominated producers A, B, C and D, and the free disposal assumption. The DEA production possibilities set is
tDominance informationis generatedautomaticallyin FDH analysis, but it is not inherentlylimitedto FDH. Althoughit has not been employed in DEA analysis, it can be, and it would provide valuable complementaryinsight into any DEA analysis of producer performance.
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A
•l
i
1 Yt Fig. 1. F D H and DEA.
bounded above by the piecewise linear function ABD reflecting convexity, and by horizontal and vertical extensions to the axes reflecting free disposal. Note that ~FDH C /~DEA.Producers A, B and D are each undominated, and rated technically efficient by both FDH and DEA. Producer C is also undominated, and called technically efficient by FDH. However it is dominated by a non-existent convex combination of producers B and D, and so it is called technically inefficient by DEA. Producer E is dominated, by producer B by all other producers located northwest of E in 20FDH. FDH assigns producer E a radial efficiency score of 0 -1 < 1, and finds non-radial slack in output Yl in the amount (ylB - 0y~). DEA assigns producer E a lower radial efficiency score of OE/OE', and finds no non-radial slack. Thus FDH, by dispensing with the convexity assumption maintained in DEA, creates a smaller production possibilities set that envelops the observed data more closely than does DEA. Consequently it generates higher radial efficiency scores. In the process of dispensing with convexity, however, FDH creates greater amounts of non-radial slack. The major difference between the 2 techniques is that FDH measures the efficiency of dominated producers relative to existing undominated producers, while DEA typically measures the efficiency of dominated producers relative to non-existent convex combinations of undominated producers. Having existing producers to score as role models is a feature of FDH that has proved to be attractive to management of dominated producers. The FDH problem is formulated as a mixed integer programming problem, but the solution algorithm is straightforward and computationally efficient. The solution algorithm, described in Tulkens [5] and Lovell and Vanden Eeckaut [6], has 2 steps. In the first step the set Do of dominating producers for producer o being evaluated is determined by means of a simple (m + n)-dimensional vector comparison: --X °
Oo
The second step begins by noting that the first set of functional constraints in the FDH problem can be rewritten as: /i\ 0o< ~ )o[YS~ j=l,...,m
-'eDo
\Y~J'
from which it follows that, at optimum
y( 0° = m a x ~ min ~ J ~ . L,=, .....
,,,ly:J J
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F r o m this maximum procedure an optimal radial efficiency score (0°) -1 is obtained for the producer under evaluation. The " m a x " part of the algorithm identifies the most dominant of the producers that dominate the producer under evaluation. Once the most dominant producer is identified, nonradial output slacks are calculated as (y~ -.0°y~), j = 1, ..., m. Total output slacks are calculated from the "rain" part of the algorithm as (y~ - y ~ ) , j = 1, ..., m. Total input slacks are determined directly from the data in this output-oriented problem.t To summarize, the F D H performance analysis generates 3 pieces of information for each producer: (i) the set, which may be empty, of all dominating producers, each of which can serve as a role model; (ii) the identity of the most dominant of the dominating producers; and (iii) an (m + n)-dimensional vector of total slacks measured relative to the performance of the most dominant of the dominating producers. A radial efficiency score is also generated, but in the absence of convexity the presence of so much non-radial slack renders the radial component of total slack of limited value. Once the performance of each producer is evaluated using the F D H technique, it is of interest to attribute variation in performance across producers to various causal factors. In DEA this is frequently accomplished by regressing producers' radial efficiency scores against a set of exogenous explanatory variables. Since in F D H non-radial slack is so important, performance is evaluated not in terms of radial efficiency scores, but in terms of an (m + n)-dimensional total slack vector. This requires that a single-equation explanatory regression be replaced by a system of equations of general form:
sji=fJ(z~,...,z~),+eji,
i=1,
.,l,
j=l,...,m+n,
where sji is total (radial plus non-radial) slack in variablej for producer i, z i = (z~, ..., z~) E ~t is a vector of exogenous variables for producer i, and eji is a 1 x (m + n) disturbance vector. This system of (m + n) equations could be estimated on an equation-by-equation basis, using ordinary least squares (OLS) separately on each equation. However it is likely that omitted exogenous variables also exert an influence on total slacks in the (m + n) equations. Since they are omitted, their influence shows up in the disturbance terms. This makes the system of equations only "seemingly" unrelated, and calls for a simultaneous estimation of the system. A seemingly unrelated regressions (SUR) approach was developed by Zellner [7] to deal with this situation, and we use this estimation technique. Estimation of the system of equations above generates two types of information. First, it signs and quantifies the effects of various exogenous variables thought to influence performance. Second, initial slacks can be adjusted (up or down) for environmental features to arrive at a clearer picture of management efficiency purged of the effects of varying environmental characteristics. Thus, for example, it is possible to predict the slacks that a dominant producer would have generated had it operated in the same environment as that of its most dominant producer. This exercise "levels the playing field," by putting the two producers in the same operating environment, and it may decrease or increase the predicted value of any given slack for the dominated producer.
3. THE CREDIT UNION DATA Input and service output data used in the first stage of this study are taken from the 1990 National Credit Union Administration Supervisors Yearend Call Report and the 1990 Credit Union National Association Yearbook Questionnaire. Exogenous variables used in the second stage are taken from the same sources, and from various other sources that provide information on universities with which some of the credit unions are affiliated. In the first stage the sample size is 8,954, about 62% of all credit unions in operation in 1990. Of the 148 university-affiliated credit unions in operation in
tFDH requiresonly that y C N~, i.e., that componentsof the output vectorbe non-negative.Howeverthe appearanceofyy in the denominator of the "rain" part of the maximin algorithm would appear to require strict positivityof all outputs for each producer being evaluated. Replacingzeros with a positive number smaller than any observedoutput in the data set resolves the problem without affectingthe optimal solution.
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1990, we have i n p u t a n d o u t p u t service d a t a for 135. In the second stage missing e x o g e n o u s variables reduce the university-affiliated credit u n i o n s a m p l e size f r o m 135 to 117.t V a r i a b l e s used in the first stage o f the analysis are defined as follows: The single i n p u t is t o t a l o p e r a t i n g expense, c o m p r i s e d in r o u g h l y equal shares o f e m p l o y e e c o m p e n s a t i o n a n d benefits, a n d o t h e r office-related expense. Six o u t p u t services are specified. T h e first 2 are q u a n t i t y variables, the t o t a l n u m b e r o f l o a n accounts, a n d the t o t a l n u m b e r o f d e p o s i t accounts. These are the 2 c o n v e n t i o n a l o u t p u t q u a n t i t y i n d i c a t o r s frequently e m p l o y e d in p e r f o r m a n c e v a l u a t i o n in the financial services sector. The next 2 are service price variables, the reciprocal o f the average l o a n rate, a n d the average d e p o s i t rate. The 2 rates are i n c l u d e d in the o u t p u t service vector because low l o a n rates a n d high d e p o s i t rates p r o v i d e benefits to m e m b e r b o r r o w e r s a n d savers. Inclusion o f these 2 price variables is a p p r o p r i a t e for b e n e f i t - m a x i m i z i n g n o t - f o r - p r o f i t c o o p e r a t i v e s like credit unions, a l t h o u g h their inclusion in the o u t p u t vector w o u l d n o t be a p p r o p r i a t e for p r o f i t - o r i e n t e d b a n k s . T h e fifth o u t p u t service, the n u m b e r o f share d r a f t (checking) accounts, is a transactions, o r t u r n o v e r , i n d i c a t o r . This v a r i a b l e is i n c l u d e d b e c a u s e the m o r e share d r a f t a c c o u n t s a credit u n i o n has, the m o r e p e r s o n n e l a n d o t h e r office expenses it incurs. The final o u t p u t service is a service v a r i e t y i n d i c a t o r , a simple c o u n t o f the n u m b e r o f 7 key services a credit u n i o n offers.:~ T h u s a credit u n i o n is viewed as using a single c o m p r e h e n s i v e resource to p r o v i d e 6 o u t p u t services to its m e m b e r s . T h e 6 o u t p u t services are specified so as to c a p t u r e the q u a n t i t y , price a n d variety d i m e n s i o n s o f overall service p r o v i s i o n . T h e s u m m a r y statistics r e p o r t e d in T a b l e 1 suggest t h a t by n e a r l y all m e a s u r e s university-affiliated credit u n i o n s are slightly large, a n d s o m e w h a t m o r e h o m o g e n e o u s t h a n o t h e r credit unions. T h e y also p r o v i d e s o m e w h a t greater service variety. T h e y offer lower average l o a n rates, an a d v a n t a g e p a r t l y offset b y slightly lower average d e p o s i t rates. V a r i a b l e s used in the s e c o n d stage o f the analysis are defined as follows. The d e p e n d e n t variables in the S U R m o d e l are the t o t a l (radial plus n o n - r a d i a l ) slacks in each o f the i n p u t a n d o u t p u t service variables. T h e e x p l a n a t o r y variables include: (i) the n u m b e r o f m e m b e r s in the credit union, a size i n d i c a t o r t h a t m a y c a p t u r e the effects o f scale e c o n o m i e s on p e r f o r m a n c e ; (ii) a d u m m y v a r i a b l e set to one i f the credit u n i o n has a state charter, a n d set to zero if it has a federal charter; (iii) the percent o f the s t u d e n t b o d y t h a t is non-white; (iv) a d u m m y v a r i a b l e set to one if the university is public, a n d set to zero if it is private; a n d (v) the r a t i o o f the value o f d e l i n q u e n t loans to the t o t a l value o f o u t s t a n d i n g loans. A l l b u t the last e x p l a n a t o r y v a r i a b l e are exogenous, while the d e l i n q u e n c y r a t i o is at least p a r t l y u n d e r the c o n t r o l o f m a n a g e m e n t . To the extent t h a t the d e l i n q u e n c y r a t i o reflects local e c o n o m i c c o n d i t i o n s , w h i c h are b e y o n d the c o n t r o l o f m a n a g e m e n t , it can be viewed as a n
Table 1. Summarystatisticsfor variablesused in the first stageof the analysis
University-affiliated (l = 135)
Mean S.D. Min Max
Not university-affiliated (l = 8,819)
Mean S.D. Min Max
Operating expense
Loan quantity
Loan price
($ooo)
(#)
(%)
692 1,171 1.9 6,370
3,347 5,948 25 37,669 2,437 7,128 1 254,457
591 1,681 1 49,614
Deposit quantity
Deposit price
Share drafts
Service variety
(#)
(%)
(#)
(#)
1t .36 1.16 8.77 18.21
9,813 16,617 111 85,902
5.89 1.00 2.88 10.79
2,320 4,710 0 23,015
3.19 2.49 0 7
11.76 1.49 5.02 31.65
7,081 19,540 1 591,840
6.25 1.15 2.51 14.68
1,282 4,306 0 76,093
2.61 2.23 0 7
tAdditional information on the sample and the specification of the services, resources and exogenous variables appears in Fried, Lovell and Vanden Eeckaut [9]. :~The 7 key services, with the percent of all credit unions offering each in parentheses, are certificates of deposit (53%), guaranteed student loans (14%), first mortgages (29%), direct deposit of Federal recurring payments (54%), credit cards (29%), ATM cards (24%), and travelers' checks (49%). The role of the variety indicator is to capture the range of services a credit union offers its members. Failure to offer a wide variety of financial services can lead to a decline in membership, and to a loss of deposit and loan accounts, as members take their business to other financial institutions. On this view variety is just as significant as the other, more conventional services a credit union can offer its members.
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exogenous variable. To the extent that the delinquency ratio reflects excessive risk-taking by credit union loan officers, it can be viewed as an endogenous variable. Although the true source of loan delinquency is unknown, we treat it as a proxy for exogenous local economic conditions. 4. EMPIRICAL
RESULTS
The first stage of the analysis consists of an FDH evaluation of the operating efficiency of all 8,954 credit unions in the sample. The purpose is to measure the efficiency with which credit unions utilize the operating expenses they incur to provide services to their members. The central hypothesis is that university-affiliatedcredit unions, which have a greater percentage of highly educated members, operate more efficiently than other credit unions. The linkage underlying this hypothesis is that educators supply a disproportionate share of the board of directors, which monitors the actions of the management of credit unions. To the extent that better-educated directors exert superior oversight, managerial performance in university-affiliatedcredit unions is expected to dominate that in other credit unions. (For more on the relationship between board of directors characteristics and credit union performance, see Hautaluoma et al. [8]). Results of the FDH analysis provide considerable support for the hypothesis that universityaffiliated credit unions operate more efficiently than other credit unions. Considering dominance first, on average the 135 university-affiliated credit unions are dominated by 15 credit unions, whereas on average the 8,819 other credit unions are dominated almost twice as often, by 30 other credit unions. Moreover, average radial efficiency scores are 94.2% for the 135 university-affiliated credit unions, and 91.4% for the 8,819 other credit unions. However as noted in Section 2, radial inefficiency is only one component of overall inefficiency, and it may be a misleading indicator of overall inefficiency when FDH is used to evaluate performance. This warning is emphasized by the results reported in Table 2, in which total slack, and its radial and non-radial components, is reported for each of 7 variables for both types of credit union. Three conclusions can be drawn from the results reported in Table 2. The first conclusion concerns the relative operating efficiency of university-affiliatedand other credit unions. Universityaffiliated credit unions have smaller total slacks, expressed in percentage terms, than other credit unions. This superior operating efficiency exists in each of the 7 variables, and in some variables the advantage is very large. The advantage suggested by average radial efficiency scores is reinforced by the inclusion of the non-radial component of total inefficiency. However the magnitude of overall inefficiency is substantially larger than the magnitude of the radial component of inefficiency for both types of credit union. Although it is not permissible to aggregate over slacks denominated in different units, it is permissible to aggregate over slacks expressed in percentage terms. On this basis, university-affiliatedcredit unions have on average approximately 9% slack in their operations, while other credit unions have on average approximately 17%, or twice as much, slack in their operations. The second and third conclusions relate to the analytical technique used to measure operating efficiency. Total slack, even when expressed in percentage terms, varies in magnitude over variables. Table 2. Operating efficiency in university-affiliated and other credit unions Total slack
Radial slack
Non-radial slack
4.23 15.62 4.89 8.98 7.02 9.11 16.09
-0.51 1.95 0.59 2.09 0.32 0.95
4.23 15.11 2.94 8.39 4.93 8.79 15.14
9.95 21.41 12.40 15.46 13.59 20.77 23.94
-3.02 8.72 3.24 8.55 2.30 4.25
9.95 18.39 3.68 12.22 5.04 18.47 19.69
(%)
(%)
(%)
University-affiliated (l = 135) Operating expense Loan quantity Loan price Deposit quantity Deposit price Share drafts Service variety
Not university-affiliated (1 = 8, 8t9) Operating expense Loan quantity Loan price Deposit quantity Deposit price Share drafts Service variety CAORZ3:4-F
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For both types of credit union slack is most severe in two service dimensions, loan quantity and service variety. This non-neutrality provides useful guidance to management by showing where there exists the greatest opportunity for improvement. Finally, as anticipated, radial slack is small compared to non-radial slack. This emphasizes the importance of reporting total inefficiency, rather than just the radial component of inefficiency, when analyzing operating performance. This is especially important in F D H , but it is also important in DEA. University-affiliated credit unions operate with half the slack of other credit unions. Nonetheless, they have slack ranging from 4% in operating expense to 16% in service variety, and it is of interest to see if these slacks can be attributed to various characteristics of their operating environment. To the extent that they can, performance of individual university-affiliated credit unions having these characteristics can be adjusted to obtain a clearer picture of the operating efficiency of their management. To explore this issue, a linear 7-equation SUR model was estimated, using 117 universityaffiliated credit unions.t Explanatory variables include the number of members in the credit union, a state charter dummy, a percent minority student population variable, a public university dummy, an urban location dummy, and a loan delinquency rate variable. Very low explanatory power was achieved, with a system-weighted R 2 = 0.0769. The SUR results appear in Table 3. Three exogenous variables (the state charter dummy, the public university dummy, and the urban location dummy) and 1 variable at least partly under the control of management (the loan delinquency rate) are statistically insignificant in each of the 7 equations. The percent minority variable is positive and statistically significance in the loan price and deposit price equations. This suggests that as the minority share of the student body (and perhaps faculty and staff) grows, university-affiliated credit unions offer less favorable deposit rates and less favorable loan rates to their members. These disadvantages are not offset by the provision of better service in the remaining 4 output dimensions. Finally, the number of members is statistically significant in 5 equations. As credit union size, measured by the number of members, increases, slack increases in the loan quantity, deposit quantity, and share draft dimensions, and declines in the loan price and deposit price dimensions. The first 3 results suggest that as university-affiliated credit unions grow, their members become less frequent users of their credit union's deposit and loan opportunities. The 2 price results suggest that
Table 3. SUR results for university-affiliatedcreditunions Independentvariables Dependentvariable Operatingexpense
Intercept
Numberof members
State charter
Percent minority
Public
- 136 (-0.25)
548 (0.03)
Urban
Delinquency ratio
23,499 (l.04)t
1.15 (1.12)
32,314 (1.52)
303 (0.62)
0.08 (3.54)
-218 (-0.46)
5.74 (0.48)
- 144 (-0.31)
-4,886 (-0.85)
89 (3.67
-0.003 (-2.46)
5.88 (-0.28)
1.04 (1.94)
-7.02 (-0.33)
-99 (-0.23)
242 (0.38)
0.11 (3.43)
365 (0.55)
0.81 (0.05)
49 (0.08)
64 (3.30)
- 0.002 (-2.82)
3.07 (0.18)
1.40 (3.30)
- 9.18 (-0.54)
-47 (-0.27)
0.03 (3.15)
90 (0.51)
2.20 (0.49)
101 (0.58)
0.79 (3.43)
-0.00+ (-1.58)
-0.31 (-1.35)
-0.001 (-0.17)
0.05 (0.22)
Loanquantity Loan price Deposit quantity Depositprice Share drafts Servicevariety
-27,407 (-1.73)
55 (0.15)
tt-statistics in parentheses.
tAlthough the FDH model is output-oriented, non-radial slackscan occurin both output and input dimensions. Accordingly we attempt to explain total (radial plus non-radial) inefficiencyin both output and input dimensions.
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Table4. Predictedslacks,expressedas percentof university-affiliatedcreditunion means, for a dominatedcreditunion Variable Operatingexpense Loan quantity Loan price Depositquantity Depositprice Share drafts Servicevariety
Predicted slacks(%), using actualdata 3.40 77.36 4.11 33.89 4.12 30.67 24.65
Predicted slacks(%), usingdata of most dominatingrole model 3.40 80.21 2.60 35.20 1.29 32.04 24.65
large university-affiliated credit unions have a smaller spread, offering lower loan rates and higher deposit rates to their members. The low explanatory power in the S U R model is disappointing, but enlightening.:~ The information conveyed by the low explanatory power suggests that variation in managerial performance across university-affiliated credit unions cannot be attributed to variation in the environment in which they operate. Virtually all of the performance variation revealed in the F D H model survives our attempt at explanation, or adjustment. We conclude that F D H provides an accurate portrayal of operating efficiency in university-affiliated credit unions, and that performance variation uncovered in the F D H analysis can be attributed almost exclusively to variation in managerial performance. While university-affiliated credit unions perform substantially better than other credit unions, some university-affiliated credit unions are better managed than others, regardless of variation in their operating environment. To illustrate how the results of the S U R analysis can be used to evaluate managerial performance, we conduct an experiment on 2 large university-affiliated credit unions. One is the most dominant of all the credit unions that dominate the other. We first use the S U R result to predict the slacks of the dominated credit union, using only statistically significant regressors. We then use the S U R results to predict the slacks the dominated credit union would have incurred had it operated in the same environment as its most dominant role model, using the statistically significant regressors of its role model. This analysis enables us to compare the predicted performance of the dominated credit union in 2 operating environments: its own, and that of its most dominant role model. Results appear in Table 4. It appears that had the university-affiliated credit union under evaluation enjoyed the operating environment of its most dominant role model, it would have fared no better in general. It would have performed the same in 2 dimensions, slightly better in the loan rate and deposit rate dimensions, and slightly worse in the 3 quantity dimensions. We conclude that it is not possible to attribute the weak performance of the university-affiliated credit union under evaluation to an operating environment less favorable than that of its most dominant credit union. The only possible explanations for its weak performance are a weak managerial performance, and potentially relevant explanatory variables omitted from the S U R model. 5. CONCLUSIONS In this paper we have employed a 2-stage combination of F D H and S U R in an effort to measure and explain the operating efficiency of university-affiliated credit unions. The contribution of the paper is partly methodological, and partly institutional. The methodological contribution of the paper is to demonstrate the feasibility and, in our judgement, the superiority, of the F D H / S U R combination over the more frequently employed D E A / O L S (or DEA/logit or DEA/tobit) combination. F G H generalizes D E A by dispensing the convexity. It emphasizes dominance, and associates role models with observed dominating producers, whereas the usual D E A models emphasize radial efficiency, and associates role models
;~Addingadditional variablesto the SUR system, such as the age of the credit union and the number of volunteers, yielded no statistically significant regressors and no appreciable improvement in explanatory power.
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with possibly n o n - d o m i n a t i n g producers. F D H measures performance in terms o f (m + n) total slacks measured relative to the operations o f a single m o s t d o m i n a n t producer, while D E A generally ignores non-radial slacks and measures performance in terms o f radial efficiency scores. Finally, variation in operating efficiency is explained by using (m + n) F D H total slacks as dependent variables in a S U R regression model, while the conventional a p p r o a c h seeks to explain operating efficiency by using a single D E A radial efficiency score as the dependent variable in an O L S (or a limited dependent variable) regression equation. The institutional contribution o f the paper has been to c o m p a r e the operating efficiency o f university-affiliated credit unions with that o f other credit unions. We have f o u n d considerable support for the hypothesis that university-affiliated credit unions, by virtue o f the higher educational attainment o f their membership, some o f w h o m sit on the b o a r d o f directors that oversees m a n a g e m e n t , operate m o r e efficiently than other credit unions. University-affiliated credit unions have considerably higher radial efficiency scores (i.e. values o f 0 closer to unity), and substantially smaller overall slacks in every dimension, than other credit unions. Moreover, we were unable to associate variation in university-affiliated credit u n i o n performance with variation in their operating environment, This strongly suggests that such performance variation as does exist c a n n o t be easily explained away, and so must be attributed to variation on managerial performance. Acknowledgements--The authors are indebted to the Filene Research Institute and the Credit Union National Association
for their generous financial support, and to Philippe Vanden Eeckaut for his helpful comments. REFERENCES 1. D. Deprins, L. Simar and H. Tulkens, Measuring labor-efficiency in post offices. In The Performance o f Public Enterprises: Concepts and Measurement (Edited by M. Marchand, P. Pestieau and H. Tulkens), North-Holland, Amsterdam (1989). 2. A. Bessent, W. Bessent, J. Elam and T. Clark, Efficiencyfrontier determination by constrained facet analysis. Ops Res. 36, 785-796 (1988). 3. A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiencyof decision making units. Eur. J. Opl Res. 2, 429-444 (1978). 4. R.D. Banker, A. Charnes and W. W. Cooper, Some models for estimating technical and scale efficiencies in Data Envelopment Analysis. Mgmt Sci. 30, 1078-1092 (1984). 5. H. Tulkens, On FDH efficiency analysis: some methodological issues and applications to retain banking, courts and urban transit. J. Prod. Analy. 4, 183-210 (1993). 6. C.A.K. Lovell and P. Vanden Eeckaut, Frontier Tales: DEA and FDH. In Mathematical Modelling in Economics (Edited by W. E. Diewert, K. Spremann and F. Stehling), Springer, Berlin (1993). 7. A. Zellner, An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias. J. Am. Statist. Assoc. $7, 348-368 (1962). 8. J.E. Hautaluoma, L. Jobe, B. Donkersgoed, T. Suri and R. Cropanzano, Credit Union Boards and Credit Union Effectiveness. Filene Research Institute, Madison, WI (1993). 9. H.O. Fried, C. A. K. Lovell and P. Vanden Eeckaut, Evaluating the performance of U.S. credit unions. J. Bank. Finance 17, 251-265 (1993).