Journal
of Banking
and Finance
Evaluating
unions*
Harold
17 (1993) 251-265.
North-Holland
the performance
of US credit
0. Fried
Union College, Schenectady, NY 12308, USA
CA.
Knox Love11
University of North Carolina, Chapel Hill, NC 27599, USA
Philippe
Vanden
Eeckaut
CORE, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium
Credit unions are small, cooperative,
not-for-profit
institutions,
which distinguishes
them from
other financial intermediaries.
In this study we conduct
a performance
evaluation
of credit
unions. The criteria respect the unique organizational
and institutional
features of credit unions,
without losing sight of the fact that they must compete with other financial intermediaries.
We
use nonparametric,
nonstochastic
techniques
to measure performance,
and we use parametric,
stochastic
techniques
to attribute
performance
variation
to features of credit unions and their
operating environment.
Our sample consists of two-thirds of all active credit unions in 1990.
1. Introduction
Credit unions are different from other US financial intermediaries.
They
are not-for-profit
cooperatives,
operated to provide service to their members.
Their not-for-profit
cooperative
structure gives them certain advantages,
as
well as certain disadvantages,
vis-a-vis competing
financial
intermediaries.
Their cooperative
nature restricts their size, with over 95% of them having
less than $100 million in assets. This limits their ability to exploit the costCorrespondence to: C.A. Knox Lovell, Department
of Economics,
University
of North
Carolina at Chapel Hill, CB No. 3305, Chapel Hill, NC 27599-3305, USA. Telephone: 919-9665372, Fax: 919-966-4986.
*We are grateful to Dr. Albert E. Burger, Director, Center for Credit Union Research, School
of Business University
of Wisconsin-Madison,
for his guidance,
and to the Filene Research
Institute for its financial support. We are indebted to Paul Bauer, Allen Berger, Rolf Fare, Bill
Hampel, David Humphrey,
Marc Ivaldi, Juan Rodriguez, Henry Tulkens and Larry White for
many helpful comments. A more detailed version of this paper is available under the same title
as Working paper no. 92-3, Department
of Economics,
University of North Carolina,
Chapel
Hill, NC 27599-3305, USA.
H.O. Fried et al., PerJormance of US credit unions
252
reducing benefits of economies
of scale and scope. However, their not-forprofit status, in conjunction
with their ability to transact
only with their
members,
gives them a tax advantage,
which provides an offsetting cost
reduction.
Perhaps
because of their small size and small share in most
services in the financial intermediation
sector, and perhaps because of their
unconventional
organizational
structure,
credit unions have not been the
subject of much theoretical
or empirical
research.’
The purpose
of this
paper is to conduct an empirical investigation
into credit union performance.
In section 2 we develop a mode1 of credit union performance.
The mode1 is
consistent
with the stated objective of credit unions, to provide maximum
benefits to their members. We define benefits as the saving and loan services
a credit union offers, and we define these services as having quantity,
price
and variety components.
Such a construction
is consistent
with the not-forprofit cooperative
status of credit unions, yet offers considerable
overlap with
the services provided by other competing
financial intermediaries.
In section
3 we described
our data sources, and we construct
the data set and the
variables used in the empirical analysis. The variables include two resources,
six services, and 20 other variables characterizing
the operating environment,
for 8,947 credit unions that were active in 1990. In section 4 we describe our
performance
evaluation
methodology.
We use nonparametric,
nonstochastic
techniques
to construct
the free disposal hull of the observed data, which
represents the production
possibilities
set of the credit unions in the sample.
This is used to assign credit unions to one of two sets: undominated,
bestpractice
credit
unions,
and dominated
credit
unions.
Performance
is
evaluated
in terms of dominance
relationships
and productive
efficiency
measures. Our empirical analysis is conducted
in section 5. In the first stage
of the analysis we find a substantial
amount of domiance, and a considerable
amount
of productive
inefficiency,
with inefficient credit unions providing
about 20% less service than best practice credit unions do. In the second
stage of the analysis we explain a small but statistically
significant
part of
measured performance
variation in terms of various features of the operating
environment
of credit unions. We attribute
the remainder
to unmeasured
environmental
characteristics,
and to variation
in managerial
performance.
Section 6 concludes.
2. The organization
and objectives of credit unions
Credit unions accept savings from members, and so have some features of
a producer cooperative.
They also provide loans to members, and so have
some features of a consumer cooperative.
Since credit unions are owned and
operated by members, the objective of credit unions can be thought of as
‘Much
of the extant
research
is surveyed
by Overstreet
and Ruvin (1991).
H.O. Fried et al., Performance of US credit unions
253
maximizing
services provided to members. This immediately
suggests that
profit maximization
is not an appropriate
objective, since there are no nonmember suppliers or customers to exploit. It also suggests that the interests
of saver/members
(high interest rates) are in conflict with those of borrower/
members (low interest rates), and this lack of unanimity
renders producer
cooperative models and consumer cooperative models, both of which assume
unanimity
in member objectives and a group of non-members
to exploit in
an effort to meet those objectives,
inappropriate
models of credit union
behavior. Finally, since the interests of saving members are neither more nor
less important
than those of borrowing
members, it is desirable to avoid
attaching a priori weights to the saving services and the borrowing services a
credit union offers its members.
These and other features of credit unions call for care in the specification
of a behavioral
model with which to evaluate
performance.
It is not
appropriate,
for example, to treat credit unions like commercial
banks, and
evaluate their performance
on the basis of their ability to maximize profit
[e.g., Fixler and Zieschang (1992), Berger et al. (1993)]. On the other hand, it
is not appropriate
to ignore the services offered by other financial
intermediaries when developing
a behavioral
model for credit unions, since they
compete in many of the same markets. In light of these features, we evaluate
the performance
of credit unions on the basis of a model that is in part much
more general than conventional
models of producer behavior, and in part
very idiosyncratic,
tailored to their special characteristics.
We treat credit
unions as seeking to maximize benefits of membership
in a credit union,
Maximum
benefit is expressed as maximum
service provision,
subject to
resource
availability
and in a given operating
environment.
Since this
framework involves only the ‘production’ aspect of credit union operation, it
is more basic than, and hence more general than, any behavioral
model of
the credit union.’
What remains is to specify the services credit unions
provide, the resources they employ, and the environment
in which they
operate.
Credit unions use three types of resource: human resources, other variable
operating expenditures,
and volunteer labor and sponsor-donated
resources,
The first two are paid for, and are relatively easy to measure with some
degree of accuracy. The third is almost impossible to measure accurately.
The services credit unions provide their members
can be classified as
‘In this respect our modelling philosophy
is consistent with that adopted by Charnes et al.
(1978) to study the not-for-profit
sector of the economy, where prices are either non-existent
or
unreliable indicators of value. It is also consistent with the approach
advocated by Pestieau and
Tulkens (1991) for comparing
the performance
of public and private providers,
who have
different objectives and different constraints.
Our motivation
is different, however, in that we
believe that credit unions seek to provide maximum services, subject to their resource base. In
this respect our model is similar to the indirect production
approach
proposed
by Shephard
(1974) and extended by Fare and Grosskopf (1991).
254
H.O. Fried et al., Performance
of US credit
unions
saving services provided to depositors
and loan services provided to borrowers. Within
each classification
there are three types of service. They
include the number of savings and loan accounts, the interest rates paid on
saving accounts
and charged on loan accounts,
and the variety or convenience features offered to lenders and borrowers. The number of accounts
captures the quantity
dimension
of service provision.
Interest rates are not
interpreted
as prices with which to aggregate type of accounts, but rather as
another dimension
of the services a credit union provides its members, since
depositors
seek high saving rates and lenders desire low loan rates. The
variety indicators
measure the range of loan and saving services a credit
union offers, and are intended
to capture the conveniences
dimension
of
service provision.
The environment
in which a credit union operates is characterized
by a
long list of features, many of which are subject to managerial
influence at
one level or another. Among the more prominant
environmental
variables
are the size of the credit union, the nature of its common bond, the type of
character, and the branching
structure of the credit union.
3. Data sources and variable construction
All data used in this study come from two primary sources. One is the
National
Credit Union Administration
(NCUA) Supervisors
Yearend Call
Report for the year 1990. The other is the Credit Union National
Association (CUNA) Yearbook Questionnaire,
also for the year 1990.
Two variable
inputs are identified.
The labor input is defined as the
number of full-time employees plus half the number of part-time employees.
Other operating expense is defined as total operating
expense, less employee
compensation
and benefits, and less provision
for loan losses, provision
for
investment
losses, and member insurance.
We have created six output variables, three designed to characterize
loan
services and three designed to characterize
deposit services. One pair of
variables measures quantity,
the second pair measures price, and the third
pair measures
variety. A loan quantity index is constructed
as the total
number
of outstanding
loans of all types, excluding
loans to other credit
unions because they provide no direct service to the borrower-members
of
the credit union making the loan. A loan price index is constructed
as the
reciprocal
of net interest on loans divided by the value of all outstanding
loans. This construction
implies that a lower interest
rate on loans is
associated with better performance.
The Yearbook lists 36 different types of
loan and insurance
services that a credit union might offer. A loan variety
index is created by weighting whether or not a credit union offers a loan type
by the proportion
of all credit unions in its class that do offer the service,
dividing this weighted (0,l) variable by the maximum
value observed in its
H.O. Fried et al., Performance of US credit unions
Table
Summary
statistics
255
1
for variables.
Variable
Mean
Std. dev.
Min.
Max.
Labor (no.)
Operating expense (S)
Loan quantity (no.)
Loan price (YJ
Loan variety (0, 1,000)
Saving quantity (no.)
Saving price (“/,)
Saving variety (0, 1,000)
10.2
251541.8
2,45 1.3
11.75
684.4
I, 124.6
6.25
708.9
32.3
740.207.0
7,115.2
0
1
1
5.02
0
1
2.5 I
7
1,730
27,359,345
254,457
31.65
Loo0
591,840
14.68
LOO0
1.08
88.4
19,508.O
1.15
118.6
class, and summing
over all 36 loan types. A credit union’s
class is
determined by its asset size and its common bond category, defined below. A
saving quantity index is constructed
as the total number of share and deposit
accounts. A saving price index is constructed
by dividing net interest paid by
the value of all share and deposit accounts. This construction
implies that a
higher interest rate on deposits is associated
with better performance.
The
Yearbook lists 40 different types of saving and related services that a credit
union might offer its members.
A saving variety index is constructed
in
exactly the same way the loan variety index is constructed.
Summary
statistics for the eight variables appear in table 1.3
The Call Report and the Yearbook contain data that allow the construction of several environmental
variables.
These variables
may account
for
observed performance
variation
of credit unions, and they may be manipulated by credit union management
or the national
leadership
to enhance
performance.
Both sources contain
information
on the yearend
value of
current assets, from which five assets size class categories are defined. Nearly
83% of the credit unions in our sample are in the three smallest asset size
classes, having less than $20 million
in assets. The Yearbook
lists the
common bond of a credit union at the time of its formation. On this basis a
credit union is assigned to one of three common bond categories: associational, occupational
or residential. The occupational
common bond category
accounts for 82% of the credit unions in our sample. A credit union typically
receives some sort of support from its sponsor, the organization
with which
it is allied, in the form of donated resources that are not reported in either
the Call Report or the Yearbook. Although existence of sponsorship
can be
difficult to discern, and extent of sponsorship
impossible
to determine,
the
3The creation of a data set of 8,947 observations
from the nearly 14,000 credit unions active
in 1990 results from a careful screening of the original data for missing variables and suspect
entries, and from lengthy discussions
with CUNA personnel.
Thus we are satistied with the
selection and the accuracy of the variables we are using, although the operating expense variable
may contain undesirable price variation in addition to quantity variation, It is unfortunately
not
possible to disentangle the two components
of expense variation.
256
H.O. Fried et al., Performance of US credit unions
Call Report does contain sufficient information
to permit the construction
of
a sponsorship
indicator.
A binary (0,l) sponsorship
variable
identifies
a
credit union as being sponsored if any one of the following variables is zero:
employee compensation
and benefits, office occupancy
expense, and office
operations
expense. On this criterion one-third
of the credit unions in our
sample show evidence of sponsorship.
Additional
environmental
variables include (1) the number of members; (2)
the ratio of the number of members to the number of potential
members;4
(3) the type of charter (1 if state, 0 if federal); (4) the age of the credit union
(‘new’ if organized
since 1987, ‘recent’ if organized
197&1986, ‘old’ otherwise); (5) branching (1 if at least one branch, 0 if no branches); (6) geographic
location; (7) asset size group (1 if asset size class is above $100 million, 0
othewise); (8) loan size (the ratio of the value of loans to the number
of
loans); (9) saving size (the ratio of the value of savings to the number
of
saving accounts);
(10) delinquency
(the ratio of the number
of dilinquent
loans to the number of loans); (11) investment
ratio (the ratio of the value of
investments
to the value of loans); (12) real estate (the ratio of the value of
real estate loans to the value of loans).
4. The performance evaluation
methodology
We evaluate the performance
of credit unions on the basis of their ability
to provide
maximum
service with their given resources,
in their given
operating environment.
To this end we construct
a free disposal hull of the
observed service/resource
data, and evaluate performance
on the basis of two
criteria: dominance
and efficiency. We then use environmental
variables to
explain measured
performance
variation.
Here we outline the performance
analysis methodology.5
Credit union k uses resources
xk =(x7,. . . ,xi) E R”, to provide
services
y”=(y:,....y;)~[W:,
k=l ,. . . ,l. The data set is denoted
T = {(yk,xk), k=
1,. . . ,I). From this data set a set of feasible production
possibilities
is
constructed
as
‘%ome credit unions have a broadly
defined field of membership
that makes eligible for
membership
relatives of members, other unrelated groups, and former members. Others have a
much more narrowly defined held of membership.
The ratio of actual to potential members thus
serves as a capacity
utilization
indicator
that provides a more or less severe constraint
on
growth.
‘The technique
is nonparametric
and nonstochastic,
and goes by the name FDH, for ‘free
disposal hull.’ It was introduced
by Deprins et al. (1984) and is more fully developed in Tulkens
(1993). It is in fact a generalization
of the variable returns to scale data envelopment
analysis
(DEA) model of Banker et al. (1984).
H.O. Fried et al., Performance of US credit unions
257
Y2
A
YT E
D-
0
y2
/
/
/
0
/
:
D
0
)
C
.__~‘~__-~_________~
4
D
Yl
B
Yl
Fig. 1. Dominance,
radial efficiency,
and slack.
..
(1)
The set F consists of all possible production
activities having resources no
smaller than, and services no larger than those of each credit union in the
sample. T satisfies free disposal of all variables, but it is not convex. Fig. 1
illustrates, for the case of live credit unions using the same resource vector to
provide different service vectors.
A credit union is undominated if no other credit union uses no more of
each resource to provide no less of each service. In fig. 1 credit unions A, B
and C are undominated.
Credit union B dominates
credit unions D and E.
Dominance
relationships
are good preformance
indicators.
The more credit
unions a particular
credit union dominates,
the more impressive
is its
performance,
while the more often a credit union is dominated,
the less
impressive is its performance.
On the other hand, having losts of dominating
credit unions means having lots of role models to emulate, thereby enhancing
the possibility
of learning
and improving
performance.
A credit union is
efficient if it is undominated,
and inefficient if it is dominated.
In fig. 1 credit
unions A, B and C are efficient, while credit unions D and E are ineffkient.
Efficient credit unions A and C do not dominate any other credit union; they
are ‘efficient by default’. Inefficient credit union D dominates
credit union E.
Thus dominance
is neither necessary nor sufficient for efficiency. The two
criteria provide independent
information
on performance.
Dominance
is
measured using a vector comparison
technique that provides a simple count
H.O. Fried et al., PerJormance
258
of US credit unions
of all credit unions for which (y’, -x’) 2(yk, - xk), or for which (y’, -xi) I
(yk, -xk), where credit union k is being evaluated
and i # k, i = 1,. . ,I,’
Credit unions for which neither inequality holds are not comparable
to credit
union k on the dominance
criterion.
Efficiency is measured radially, after which slacks are considered.
In fig. 1
credit unions A, B and C are incapable
of radial expansion
of the services
they provide. They are undominated,
and efficient. Credit unions D and E
are dominant,
and radially inefficient. The radial efficiency of credit union D
is given by the ratio yy/yy = yy/y: < 1. In addition, credit union D has slack
in service y, in the amount (y;-4’;).
It has no slack in service y,. The radial
efficiency of each credit union in the sample is obtained as the solution to a
mixed integer programming
problem. For credit union k the problem can be
expressed
minimize
subject
Ok
with respect to {Ok,i.f,i=
l,...,
I}
(2)
to
k
yi<
Ok
I
=
i;,
‘%
ii1i_fxfgxr,
A!20,
j=l,...,m,
j=l
i=l ,...,
,...,n,
19
At optimum,
Ok* 5 1 provides the radial efficiency score for credit union k.
Slacks in (m +n) dimensions
are inferred from the optimum
inequalities
in
the first (m+n) constraints,
with equality meaning no slack and inequality
showing existence and magnitude
of slack. Together,
the two constraints
involving the vector Ak imply that (I - 1) elements of this vector are zero, and
the one non-zero element identifies the best practice credit union that most
dominates credit union k, and against which the radial efficiency and slack of
credit union k are measured. It is the constraint
nf E {0,1) that distinguishes
our FDH model from the variable returns to scale DEA model of Banker et
al. (1984). Our non-convex
feasible set is a subset of the convex DEA feasible
set, and is the smallest feasible set consistent
with the observed data and
satisfying free disposability.
‘The vector inequality
‘2’ means ‘2’ but not = ,’ and similarly
for the vector inequality
‘<‘.
H.O. Fried et al., Performance of US credit unions
259
Table 2
Dominance
relationships
in the sample.
Asset size class and common
bond categories
[O)..., 11 [l,..., 51 [S )..., 201 [20 ,...,
million
million
million
million
loo]
Cl10 ,... [
million
Row sums
Associational
Dominated (no.)
Undominated
(no.)
Efficient by default (no.)
451
246
205
43
389
322
67
9
193
160
33
6
81
65
16
6
I
2
5
2
1,121
795
326
66
Occupational
Dominated (no.)
Undominated
(no.)
Efficient by default (no.)
1,550
1,075
475
67
2,589
2,183
406
30
1,889
1,639
250
33
1,035
757
278
72
280
115
165
73
7,344
5,769
1,574
275
Residential
Dominated
(no.)
Undominated
(no.)
Efficient by default (no.)
90
56
34
10
125
110
15
1
134
124
10
2
111
80
31
10
23
12
11
8
483
382
101
31
Column sums
Dominated (no.)
Undominated
(no.)
Ellicient by default (no.)
2,09 I
1,377
714
120
3,103
2,615
488
40
2,116
1,923
193
41
1,227
902
325
88
310
129
181
83
8,947
6,946
2,001
372
-
5. Evaluating the performance of credit unions
We are now prepared to apply the methodology
developed in section 4 to
the data described in section 3 to evaluate the performance
of credit unions.
Each of 8,947 credit unions is evaluated on the basis of its ability to utilize
the two variable resources at its disposal to provide maximum
amounts of
six services to its members. Evaluation
is based on dominance
and efficiency,
the latter having radial and slack components.
Dominance
relationships
are summarized
in table 2, in which credit unions
are cross-classified
by their asset size class and their common bond category.
Roughly 78% of all credit unions are dominated
by at least one other credit
union. Of the undominated
credit unions, only 4% have such a unique
services mix or resource mix that they are efficient by default and dominate
no other credit union. There are over 150,000 instances of dominance
in the
sample, meaning that each dominated
credit union has on average about 22
dominating
credit unions to serve as role models.
Radial efficiency scores are summarized
in table 3. The mean radial
efficiency score in the sample is 91.6%. This implies that on average credit
unions are capable of providing
9.2% more of all six services with the
variable
resources
at their disposal.
However,
2,001 credit unions
are
undominated,
and so cannot achieve any equiproportionate
increase in the
services they provide with the resources
they use. Deleting
these credit
260
H.O. Fried et al., Performance
of US credit unions
Table 3
Radial
efkiency
scores in the sample.
Asset size class and common
bond categories
[O)..., l]
million
[l,...) 51
million
[5 )..., 201 [20 ,...,
million
million
Associational
Total (%)
Inetlicient (%)
95.0
90.8
90.3
88.3
91.5
89.7
92.2
90.2
98.6
95.1
92.6
89.5
Occupational
Total (%)
Inefficient (%)
93.0
89.9
90.1
88.3
90.5
89.1
92.9
90.3
91.3
93.5
91.5
89.2
Residential
Total (%)
Inefficient (%)
93.4
87.3
87.2
85.4
88.8
81.9
93.6
91.1
97.1
94.4
90.7
88.3
93.4
90.0
88.2
90.5
89.1
92.9
90.4
97.3
93.6
91.6
89.2
Column means
Total (%)
Inefficient (X)
90.0
1001
[loo ,...,
million
[
Row means
unions, the remaining
dominated
credit unions have a mean radial efficiency
score of 89.2%. These credit unions are capable of providing a 12.1% increase
in all services with no increase in resources. Neither of these radial efficiency
scores exhibits any meaningful
variation
across common
bond categories.
They do vary across asset size class, with the largest size class exhibiting
relatively high radical efficiency. The 310 credit unions with assets in excess
of $100 million outperform
all other groups of credit unions by a wide
margin on the basis of the radial efficiency criterion. Recall, however, that 83
of these credit unions are efficient by default. Nonetheless,
the generally
superior performance
of large credit unions provides encouraging
evidence of
their competitive
viability in the larger financial intermediation
market.
Radial efliciency is but one component
of overall productive
efficiency.
Even after radial inefficiency has been accounted
for, slack in the form of
exessive utilization
of resources or underprovision
of services in up to seven
dimensions
(=six services+ two resources
- 1) can remain. In table 4 total
inefficiency is decomposed
into its radial and slack components.
Since slack
cannot be aggregated across variables measured in different units, results are
reported for each variable. Results are presented in terms of percentages,
the
ratio of radial slack to best practice and the ratio of non-radial
slack to best
practice, respectively. Results are averages over all 8,947 credit unions.
On average
the labor input is overutilized
by 22x, and all of the
inefficiency
is attributed
to slack since radial efficiency measurement
is
output-oriented.
There is even greater
inefficiency
in the use of other
operating expense. Underprovision
of services varies in severity from 33% of
best practice for the loan quantity index to 14% of best practice for the loan
H.O. Fried et al., Performance of US credit unions
261
Table 4
Efficiency results in the sample.
Variable
Total
slack (%)
Radial
slack (%)
Non-radial
slack (%)
x,: Labor
x2: Operating expense
y,: Loan quantity
y2: Loan price
y3: Loan variety
y,: Saving quantity
ys: Saving price
y,: Saving variety
225
30.5
32.6
14.4
16.2
20.0
15.9
14.5
n.a.
na.
4.2
8.2
8.0
5.1
7.8
7.8
22.5
30.5
28.4
6.2
8.2
14.9
8.1
6.7
n.a.: not applicable.
price index and the saving variety index. Although
aggregation
across
variables is inappropriate,
it appears that assigning a productive
inefficiency
of approximately
20% of best practice to credit unions would not be too far
off the mark.7
Two features of this overall efficiency evaluation
deserve emphasis. First,
inefficiency is non-neutral
across variables. Credit unions do a much better
job of keeping up with best practice in the quality dimensions
of service
provision than in the quantity dimension. The l&16% slack in the price and
variety indicators
is considerably
less than the 20-33x
slack in the quality
indicators.
Second, non-radial
slack is an important
component
of overall
inefficiency. This suggests that studies which report only radial inefficiency
may be deficient in two ways. They understate
overall inefficiency, and they
call it neutral when it is not.
The next task is to explain
the observed
variation
in credit union
preformance,
by attributing
variation in efficiency to characteristics
of credit
unions and the environment
in which they operate. We use two regressionbased approaches. In the first approach a logistic regression of general form
RI, = f(z;,
. . , z&J,
i=l , . . ,8,947,
is estimated, where R&= 1 if the ith credit union is dominated
inefficienct, and R&=0 if the ith credit union is undominated
and radially
and radially
‘While not directly comparable,
this figure of 2004 overall inefficiency relative to best practice
is not out of line with results reported for banking by Ferrier and Love11 (1990), Berger and
Humphrey
(1991), Bauer et al. (1993) and Berger (1993). There appears
to be considerable
operating inefficiency in both segments of the financial intermediation
sector. It should be noted,
however, that our findings refer to credit unions only, and the cited results generally refer to
banks only. Thus the credit union segment could be more or less efftcient than the banking
segment. We have no evidence to report on this issue, but the great size disparity between the
two segments makes such a comparison
difficult, since most credit unions would be noncomparable
to most banks.
262
H.O. Fried et al., Performance of US credit unions
efficient. In this approach the radial efficiency status of the ith credit union is
posited to depend on a vector of environmental
variables (~1,. . . ,zio) that
characterizes
the ith credit union. The second approach
seeks to explain
overall, radial plus slack, inefficiency in each credit union. Since slacks, and
hence overall inefficiency,
cannot
be aggregated
across noncommensurate
variables, this approach
is conducted
on a variable-by-variable
basis. This
requires estimation
of equations of general form
TI,= f’(~i,. . . , z\O, dj),
i=l ,...I 8,947,
j=l,...,
8,
where TI,, is total, radial plus slack, inefficiency in the observed amount of
variable j in the ith credit union. This inefficiency is posited to depend on a
vector of environmental
variables (z;, . . . , ~1,) that characterizes
the ith credit
union. The dummy variable df=O if there is no inefficiency, radial or slack,
in the jth variable in the ith credit union, and d\= 1 otherwise. Since these
eight relationships
are unlikely
to be independent,
it is appropriate
to
estimate them as a system. Thus our second approach to explaining efficiency
variation
involves estimation
of a system of eight equations,
one for each
variable, using 20 explanatory
variables and 8,947 credit unions.
Results are summarized
in table 5.8 The logistic regression (3) shows the
radial component
of inefficiency to vary significantly
with a large number of
included explanatory
variables. Radial efficiency is generally higher for credit
unions having an associational
common bond, with sponsorship
as we have
defined it, with a large number of members and a high ratio of members to
potential members, with a state charter that was granted between 1970 and
1986, with large assets, with a high delinquency
ratio, a high ratio of
investments
to loans, a low ratio of real estate loans to total loans, and no
branches.
The seemingly
unrelated
regression
model (4) generates
results broadly
similar to those of the logistic regression,
although
significance
levels are
somewhat lower and there is some variation
in sign and significance
across
equations.
Overall efficiency in the utilization
of resources and the provision
of services is generally
higher for credit unions
with an associational
common bond, with sponsorship,
with a high ratio of members to potential
members, having a state charter, having no branch offices, having a high
investment-to-loan
ratio and with few real estate loans. The remaining
aThe functions f’( .) and S’( .) are specified as being linear in the variables. Complete results
are available on request. As Larry White has pointed out to us, heteroskedasticity
may occur
when estimated
parameters
are used as dependent
variables
in a second stage explanatory
regression model, and GLS estimation
techniques
should improve efficiency in estimation.
Since
we use calculated slacks instead of estimated parameters
as dependent variables, this point is not
directly relevant. Moreover,
the GLS correction
is unavailable
to us, since our calculated
slacks
do not have estimated variances. Nonetheless
the spirit of this argument
is relevant, and may
explain why so few of our second stage regression coefficients are statistically
significant.
‘* Significant at 90x,
** Signiticant at 95%.
+(**I
-(**I
Intercept
Associational
Residential
Sponsorship
I. No. of members
2. Ratio mem.
3. Charter status
4. Age
Recent
New
5. Branching
6. Geo
Northeast
Atlantic
South
Lake
Central
7. Asset size
8. Loan size
9. Saving size
10. Delinquency
11. Investment
12. Real estate
-(**I
+f**)
I(**,
Zf*,
-(**I
__
-(**I
-(**I
-(**I
+(**I
-(**I
-
I;::;
‘jl:;
Radial
inefficiency
Dependent
variable
Model
_Logistic
-
Table
+(**I
-(**I
+
-(**I
+(**I
-Y*)
Operating
expense
slack
____
unrelated
_(**)
-(**)
-(**)
+(**)
-(**)
-(**)
-
+(**I
-
+
_(**)
-(**I
+t**j
-(**I
-
_(*I)
-(**)
-(**)
5
+(**)
_
_
_
_
+(**I
~__
I;::;
_
_
-(**I
+(**I
$1
_
_
+(**I
-(**I
+(**I
-(**I
+(**I
1;::;
+(**I
I,**,
+
_
+(**I
+
+(**)
_
+(**I
_
+(*I
-(**I
1;::;
price
variation.
-__
___
+(**I
-(**I
+
-(**I
efficiency
regression
-__Loan
quantity
Loan
slack
slack
of overall
$**, z(**,
+(**I
-(*I
+(**I
-
Labor
slack
__-__
+(**)
-
Seemingly
Determinants
___
,i::;
-(*I
I,**,
+
_
+
+
-(**I
-(*)
+
+(**I
+
+(**I
+
-(**)
+(**)
-(**)
-(**)
I,**,
_
+
-(*I
I;::;
_(**)
I(**,
+
+(**)
+
-
A*,
I,**,
-(**)
+(**)
_
+
_
+(**I
+(*)
+
+
+
_(**)
-(**)
-
_
_
-(**)
-(*a)
-(**)
_(*t)
,;r:;;;::;
+(**)
+(**)
+(**)
-(**I
Saving
variety
slack
___-__
Saving
Saving
quantity
price
slack
slack
I;::; ,;;;I
_
-(**I
+(**I
4’“)
+
Loan
variety
slack
.____
___
264
H.O. Fried et al., Performance
of US credit unions
explanatory
variables are either rarely significant
or have conflicting
effects
on performance.
It is particularly
interesting
to note that, although we have
allowed for variable
returns
to scale, size has no apparent
independent
impact on performance.
The number of members has conflicting
effects, as
does the asset size dummy.
This finding
contrasts
with the significant
favorable effect of size on radial efficiency revealed by the single equation
logit regression. This may be due to the fact that the logit regression ignores
the nonradial
component
of overall inefficiency. Other discrepancies
between
the two sets of results may be attributable
to the same feature, and these
discrepancies
generate a strong preference for the more inclusive seemingly
unrelated regression model.
We have identified
several significant
influences
on credit union performance. Some are amenable
to influence by individual
credit union managements. Others may be used by the national
leadership
to improve credit
union performance
and to enhance
the competitive
viability of the credit
union
segment
of the financial
intermediation
sector of the economy.
However they are conditional
on our specification
of resources and services.
The use of a different set of variables
might generate
different
results,
although we doubt that they would be significantly
different in light of our
large sample size. Moreover,
the seemingly
unrelated
regression
model
explains only 25% of the variation
in efficiency. Much variation
in performance is left unexplained,
and at this point must be attributed
to unmeasured environmental
variation
or, suggestively,
to variation
in managerial
performance.
6. Summary and conclusions
The purpose of this study has been to evaluate the performance
of credit
unions.
To that end we have assumed
that credit unions have as their
objective the provision of maximum
benefits to their memberships.
We have
defined the benefits credit unions provide as having a quantity dimension,
a
price dimension,
and a variety
or convenience
dimension.
Given
the
resources at their disposal, we have measured their performance
in terms of
their ability to provide maximum
amounts
of service of each type. Performance is evaluated
in terms of dominance
relationships
and productive
efficiency.
We have found lots of dominance,
which implies the existence of lots of
potential
role models for each inefficient credit union. We have also found
about 20% productive inefficiency on average, which implies lots of room for
improvement.
Finally, we have found considerably
more room for improvement in the quality dimension
than in the price and variety dimensions.
This
implies that credit unions can improve their performance
by getting more
members
from their pool of potential
members,
and by getting
more
H.O. Fried et al., Performance of US credit unions
265
accounts per member. We have explained a small but statistically
significant
portion of performance
variation.
Among the important
explanatory
variables are some that should
be informative
to individual
credit union
managers and the national leadership alike.
There are at least two ways in which this research might be extended.
First, it might be useful to merge this data set with complarable
data on
small banks, to see how the two types of financial intermediary
compare. A
difficulty with such an exercise would be that proprietary
banks and not-forprofit cooperative
credit unions have different objectives, which would make
the selection of a common set of variables and a fair performance
critierion a
daunting
task. A second extension would involve creating a panel of credit
unions observed
over a period of several years. This would enable the
calculation
of productivity
growth
rates, which would provide
another
ctiterion on which to evaluate the performance
of credit unions.
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