168 J.A. Haslem et al. International Review of Economics and Finance 8 1999 165–182
The variable s
r
is the amount of slack foregone balance sheet output r, while the variable e
i
is the amount of excess balance sheet input i utilized. The values m
rl
and n
il
are shadow prices, or the marginal value of a unit of output or input. The analysis specifies bank specific bounds on the values of m
rl
and n
il
defined by Eq. 2: m
rl
5 1
y
rl
, r 5 1, . . . , s with n
il
5 1
x
il
, i 5 1, . . . , m 2
This procedure allows the projections and efficiency scores derived to be indepen- dent units invariant of the units of measurement for the data. This is a linear
programming problem with associated resource constraints and convexity conditions as discussed in Ali Seiford [1993].
The solution to the above problem identifies, for each bank, l, a projected point on the efficient frontier, xˆ
l
, yˆ
l
where the items x and y are the vectors of inputs and outputs. The particular form of the model allows for variable returns to scale. The
essence of the efficiency evaluation of a particular bank with an actual achieved combination of x
l
and y
l
is the identification of excesses in input utilization x
l
2 xˆ
l
and deficiencies in output yˆ
l
2 y
l
. A particular bank is deemed efficient if x
l
, y
l
5 xˆ
l
, yˆ
l
, the bank thus lying on the efficient frontier. Thus, one possible measure of inefficiency, delta or D
l
, can be defined by Eq. 3: D
l
5 m
l
yˆ
l
2 y
l
1 n
l
x
l
2 xˆ
l
3 Notice, that for efficient banks D
l
5 0.
As noted above, the base model was derived. This model embodies an approach consistent with the “systems-oriented” philosophy in banking where input and output
variables are simultaneously managed and determined. Two other oriented efficiency measures were used in the IDEAS model to provide
supplemental information on bank efficiency: iota and omicron. Any one of the three noted criteria could have been used to identify inefficient banks, but the interpretation
of inefficiency appropriately followed the primary criterion, delta. Iota and omicron measured bank efficiency in terms of proportional variable change.
14
3. InputOutput variables
The intermediation approach to defining bank output was used to specify the input output variables, where banks are considered intermediators of financial services
rather than producers of service accounts and transactions.
15
The variables selected and the device used to classify them as “inputs” or “outputs” followed Hancock 1986. In that study, the concept of “user cost” was used in a
methodology that identified individual financial assetsliabilities as inputs or outputs, where it is defined as the net price of holding one dollar unit of a variable during a
discrete time period. Those variables with negative user costs positive signsreturns were identified as output variables and those with positive user costs negative signs
returns were identified as input variables.
J.A. Haslem et al. International Review of Economics and Finance 8 1999 165–182 169
The variables that were used are defined in Appendix A, where they are classified as: 1 outputs, including domestic loans, foreign loans, total investments and noninterest
bearing deposits; and 2 inputs, including cash, labor expense, real capital, materials expense and total borrowed funds. The variables reflected the need to include foreign
and domestic loans independently and to minimize the number of variables in the analysis see Note11.
4. Sample construction
The data and definitions of the defined inputoutput variables Appendix A were obtained from Federal Reserve 1987, 1992, specifically the Federal Financial Institu-
tions Examination Council Form 031 reports of condition and income.
16
Form 031 was filed by all banks approved to operate both foreign and domestic offices. Further,
each sample bank was required to satisfy criteria that ensured it was substantively engaged in foreign banking.
17
These criteria generated a first 1987 sample of 62 banks from 256 and a first 1992 sample of 53 banks from 218. The banks had total assets that ranged from 45.8–
163.8 billion, and were thus much larger than those in the usual study of bank scale economies.
Fortunately, Shaffer and David 1991 had earlier estimated cost functions for the 100 largest banks. They found their efficient scale continued well into the multibillion-
dollar range of total assets, rather than the typical small bank sample estimate of less than 100 million. They used hedonic cost functions to adjust for the differences in
these large, complex organizations.
18
The model that included the variable business loans to total loans indicated that scale economies existed up to total assets of 37.2
billion. This model specification was most consistent with that used in the current study, which included both domestic and foreign loans. Thus, to ensure that all sample
banks had variable returns to scale, those with total assets greater than 37.2 billion were deleted from the 1987 and 1992 samples. This upper bound generated a second
1987 sample of 54 banks from 62 and a second 1992 sample of 47 banks from 53.
The second samples were also reduced in order to profile and summarize the input output efficiency of the banks that were efficient in 1987 and 1992 and inefficient in
1987, 1992, or both years. This required that each sample bank had operated in both years as the same legal entity, as identified by its charter number. These further
reductions resulted in final 1987 and 1992 samples of the same 33 banks.
This sample size was large enough to obtain reliable DEA results. This methodology differs from regression where the significance of the estimated equation’s explanatory
power is related to its degrees of freedom. More importantly, the sample size satisfied the heuristic set down by Charnes et al. [cited in Charnes, Cooper, Lewin Seiford
1994] that the number of DMUs should exceed the number of inputsoutputs by a ratio of at least three to one, respectively.
More important than sample size was the spatial distribution of the bank inputs outputs. Wide distribution could have reduced the number of strictly dominated banks
and thereby increased incorrectly the number identified as efficient. This was unlikely
170 J.A. Haslem et al. International Review of Economics and Finance 8 1999 165–182
here because the sample was truncated to ensure the banks shared the same form of production function. This resulted in a sample where, if anything, it was more difficult
to be incorrectly identified as efficient. This was not to say, for example, that the mix of activities represented by bank inputsoutputs did not differ. After all, it was these
inputoutput differences that were identified by DEA and provided the basis for normative guides to improved bank efficiency.
Another issue concerned the nonhomogeneity of the sample as measured by foreign domestic ownership of the banks Table 1. There was no a priori reason to believe
that this implied a difference in their underlying production function. Nonetheless, this issue was examined empirically and the findings are discussed below.
The year 1987 was selected because, as discussed above, this was the first year the unfolding LDC loan crisis was significantly recognized on bank financial statements.
And 1992 was selected as the “current” situation for purposes of analyzing bank efficiency. It was the latest year for which computer-ready data were available at the
time of the analysis.
5. Results of analysis
