The Quarterly Review of Economics and Finance 50 (2010) 424–435
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The Quarterly Review of Economics and Finance
journal homepage: www.elsevier.com/locate/qref
Estimating banking cost efficiency with the consideration of cost management
Chung-Hua Shen a , Ting-Hsuan Chen b,∗
a
b
Department of Finance, National Taiwan University, Taiwan, ROC
Department of Money and Banking, National Chengchi University, No. 64, Sec. 2, ZhiNan Rd., Wenshan District, Taipei City 11605, Taiwan, ROC
a r t i c l e
i n f o
Article history:
Received 1 October 2009
Received in revised form 12 July 2010
Accepted 3 August 2010
Available online 7 August 2010
JEL classification:
C23, G21
Keywords:
Bank
Cost efficiency
Economic provision for loan loss
Cost management
a b s t r a c t
This study re-investigates the bank cost efficiency by a combination of two strands of literature. The first
strand is related to bank cost efficiency; the other is related to earnings management. Employing the
findings reported in bank earnings management literature, this study argues that bank observed total
cost (“accounting cost”) may be the biased estimator of the true total cost. Using the biased total cost
may thus yield incorrect inferences from estimating bank cost efficiency. We propose a method to modify
accounting cost, which is referred to as “economic cost”, to be consistent with the economic theory; that is,
one that is free of cost management. Both accounting and economic costs are then adopted to analyze the
efficiency of 29 commercial banks in Taiwan banking industry. Our results show that estimated efficiency,
with the application of economic cost, offers results that are more reasonable results than those of the
accounting cost.
© 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
1. Introduction
Bank cost efficiency has received significant attention in the
recent years. Various studies have focused on topics like econometric issues (Altunbas, Liu, Molyneux, & Seth, 2000; Huang &
Kao, 2006; Pastor, 2002),1 international comparisons (Carvallo &
Kasman, 2005), risk of cost functions through non-performing
loans (Berger & DeYoung, 1997; Dongili & Zago, 2005; Mester,
1996),2 and mixed-cost functions (Shen, 2005a,b).
However, while studies of bank cost efficiency are abundant,
dramatically contrasting results have been observed when the
estimated efficiency of each bank is released. By employing the
banking industry in Taiwan as an example, Li (2002) estimated
cost efficiency based on the panel data of 43 commercial banks
in 1999, wherein Taitung Commercial Bank was the most efficient
∗ Corresponding author. Tel.: +886 2939 3091.
1
For example, Pastor (2002) proposed a new three-stage sequential analysis
based on the DEA model and decomposed total bad loans into two components:
bad loans due to bad management and due to theoretical environment. Altunbas
et al. (2000) investigated the impact of risk and quality factors on banks’ cost by
using the Fourier-flexible cost function. Huang and Kao (2006) estimated the joint
confidence interval for technical efficiencies by means of multiple comparisons.
2
For example, Mester (1996) used the stochastic frontier approach with the consideration of non-performing loan. Berger and DeYoung (1997) were the first to
investigate the relationship between bank efficiency and problem loans. Dongili and
Zago (2005) estimated Italian banks’ technical efficiency with the consideration of
problem loans.
while Kaohsiung Commercial Bank ranked 13th in overall ranking. However, nearly 30% of the loans of each of the two banks
were non-performing for that year. The two banks would later be
placed in receivership by the Taiwanese government. Incidentally,
these counter-intuitive results are not sporadic cases, as they are
often cited in Taiwan bank efficiency literature. As data on estimated individual bank efficiency from other countries are rarely
available,3 we can only guess the existence of these conflicts. Extant
studies on bank efficiencies seldom investigate the reasons for the
occurrences of the inconsistencies.4
The aim of this study is to resolve the counter-intuitive results
from the perspective of earnings management. Ahmed, Takeda, and
Thomas (1999), Laeven and Majnoni (2003), Cavallo and Majnoni
(2001), Kanagaretnam, Lobo, and Yang (2004), and Shen and Chih
(2005) to name a few, report their common observations in the
earnings management of banks. These studies claim that the provision for loan loss (PLL) is by far the largest and most important bank
accrual. Banks can accelerate recognition of accounting earnings
3
Past studies rarely report the efficiency of individual bank. Hence, it is difficult for us to offer more examples to justify the conflicting results. Earlier studies
typically report the efficiency of one type of banks, for example, the efficiency of
state-owned banks vs. private banks.
4
For example, the exceptions include Pastor (1999) and Altunbas et al. (2000).
The former used provision for loan loss as a risk factor to measure cost efficiency in
Spain. The latter used provision for loan loss as the output quality proxy to evaluate
X-inefficiency.
1062-9769/$ – see front matter © 2010 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.qref.2010.08.002
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
through current accruals by delaying the recognition of expenses
and vice versa. By identifying selectively the timing of PLL recognition, banks can control reported earnings by storing value in good
years and leasing it in lean years. In other words, the timing of PLL
recognition becomes the choice of bank managers, who focus more
on current earnings and are often more reluctant to recognize PLL.
This principal-agent problem fuels PLL manipulation, making the
PLL deviates from economic theory, but on the arbitrary decision
of mangers.
Bank total cost typically contains interest cost, non-interest
cost (operating expense/overhead cost), and PLL.5 Thus, the aforementioned accrual features of PLL cause the observed total cost
(hereafter, “accounting cost” or “A TC”) to fluctuate. Furthermore,
total cost is also likely to be manipulated by managers, making
accounting cost differ from theoretical total cost (hereafter, “economic cost” or “E TC”), as suggested by economic theory. Thus,
total cost is shifted between current and future periods either to
smoothen out income or to avoid loss. Wall and Koch (2000) surveyed a number of papers on bank loan losses accounting and
concluded that banks used loan loss accounting to manage earnings
and capital. Past studies using total cost, such as by Jordan (1998),
Rezvanian and Mehdian (2002), Carvallo and Kasman (2005), and
Berger, Hasan, and Zhou (2009), have not discussed this issue
(Table 1).
Our study is a combination of the two strands of literature. The
first strand is related to bank cost efficiency; the other is related to
earnings management. As the accrual features of PLL affect total
cost, we refer to it as “cost management”. The concept of cost
management is borrowed from earnings management literature,
which suggests that banks using PLL actively to engage in earnings
management could distort accounting cost in relation to cost (i.e.,
as defined in economic theory). We propose a method to modify
accounting cost; that is, one that is free of cost management. We
argue that PLL should be the sum of two components (expected
losses and accumulated PLL) in each period. This theoretical PLL
(hereafter, “economic PLL” or “E PLL”) is free of cost management.
We then use E PLL to replace reported PLL (hereafter, “accounting
PLL” or “A PLL”) in order to yield consistent values for economic
cost. In this study, we re-investigate bank cost efficiency by focusing on the resulting consistency in Taiwan.
Our study contributes to the literature in three aspects. First,
this is the first paper incorporating the concept of cost (earnings)
management into bank cost efficiency. As bank cost management is
found in accounting studies, cost efficient estimation may be biased
if it is ignored. Though we use Taiwan bank to illustrate the impact
of cost management on cost efficiency estimation, the application
to other countries is immediate. Our results confirm this further by
showing that cost efficient rankings could change when the total
cost is recalculated in view of the cost management effect.
Next, we not only emphasize that earnings management can
affect the definition of cost; we also provide a systematic method
on the retrieval of true total cost. Our approach shows that bank
total costs have been volatile for Taiwanese banks because of the
influence of the Asian Crisis in 1997 and the bailout plans in 2002.
Nevertheless, because this method is first in literature to attempt
retrieve economic cost, the method itself is still in its infancy;
hence, future studies are needed.
Finally, our study resolves the gap why some of the distressed
banks have been classified as among the relatively top-ranked
banks in literature. Generally, distressed banks under-provision
their loan loss in order to make the total cost appear substantially
5
See Koch and MacDonald (2002, p. 109).
425
lower than what is suggested economically. This counter-intuitive
result is solved in this study.
It is important to note that our study is different from those
that consider non-performing loans (NPL) in bank cost efficiency
literature. Berger and DeYoung (1997), Hughes and Mester (2008),
among other scholars, have discussed the advantages and weaknesses of NPL in bank cost functions in order to control loan quality.
However, the concept of NPL is different from PLL. NPL is likely to
be the defective output of loans, while PLL is somewhat similar to
expenses subtracted from revenues.
The paper proceeds as follows. In addition to the first section,
the next section discusses cost management. Section 3 shows how
to calculate economic cost. Section 4 introduces a cost efficiency
model. Section 5 provides the data sources. Section 6 reports the
empirical results, while Section 7 presents the conclusion.
2. Cost management
The accrual nature of PLL allows banks to manage total cost such
that it affects its earnings, resulting in covertly biased cost efficiency estimation.6 There are three possibilities wherein bank can
manage its cost.
First, banks can accelerate recognition of accounting earnings
through current accruals by delaying the recognition of expenses,
and vice versa. For example, when earnings are expected to be low,
bank managers have more likely delay the recognition of PLL in
order to mitigate the adverse effects of other factors on earnings.
Rules on accrual accounting under which banks operate require
the recognition of revenue (i.e., as it is earned) and expenses (i.e.,
as they are incurred), regardless of the timing of the actual cash
flows (Hasan and Wall, 2003). Moreover, the loss of writing off NPL
is recognized for up to 5 years. Thus, total cost could be shifted
between current and future periods wither to smoothen out income
or to avoid loss. Simply put, banks that actively use PLL to engage
in earnings management can distort accounting cost in relation to
cost (i.e., as defined in economic theory).
Next, PLL is affected substantially by government regulation
policy. When NPL is high and threatens the stability of financial markets, governments from many developing countries may
request that banks either write off NPL or inject funds into financial markets to help the banking sector overcome the economic
downturn. For example, Taiwanese authorities announced the First
Financial Reform in 2001 by asking banks to write off NPL down to
5% of all loans in 2 years.7 Thus, banks had to hold actively these
PLL in order to off-charge the huge accumulated NPL, as insufficient provisions were common in Taiwan before 2001. Total cost
suddenly rose that year owing to the rising PLL. It is not surprising to find that the total cost of the First Commercial Bank almost
quadrupled in 2001 because of PLL increases. Its accounting cost
increased from New Taiwan Dollar ($NT) 12,259 million in 2002:Q1
to $40,9688 million in 2002:Q2.
Third, bank total costs have been affected by a number of enterprise scandals, mainly because total cost contains PLL. As soon as
these enterprise scandals were recognized, lending banks immediately provided considerable loan loss reserves to write off the
6
In the academic field of accounting, PLL is often decomposed into nondiscretionary and discretionary PLL (Beaver and Engel, 1996; Ahmed et al., 1999;
Bouvatier and Lepetit, 2008). Unlike non-discretionary PLL, which relates systematically to total loans and non-performing loans, discretionary PLL is manipulated
by managers.
7
The First Financial Reform is also referred to as the 258 principles, since banks
have to write off the nonperformance loans down to 5% and have to increase the
capital adequacy ratio up to 8% in 2 years.
8
Our dollar unit refers to the New Taiwan Dollars throughout the paper.
426
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
Table 1
Definition of costs.
Paper
Cost definition
Summary
1. Total cost (interest cost + non-interest
cost + provision for loan loss)
Jordan (1998)
Total cost
This paper measures bank efficiency to achieve a better
understanding of the crisis in New England banks
between 1989 and 1992.
This paper uses a parametric and nonparametric
approach to examine cost structure and production
performance in Singapore.
A stochastic frontier model with country-specific
environmental variables was estimated for 481 banks
from 16 Latin American countries.
This paper helps predict the effect of financial reform
that partially privatizing and taking on minority
foreign ownership of three of its dominant “Big Four”
state-owned banks by analyzing the efficiency of
Chinese banks over 1994–2003.
Rezvanian and Mehdian (2002)
Total cost
Carvallo and Kasman (2005)
Total cost
Berger et al. (2009)
Total cost
2 Non-interest cost
Berger and DeYoung (1997)
Non-interest expense (operating
expense)
Kwan (2003)
Total operating cost
Bos and Schmiedel (2007)
Total operating cost
Valverde, Humphrey, and Paso (2007)
Operating cost = labor
expense + physical expense + material
expense
Podpiera and Weill (2008)
Total operating cost
3. Interest costs and non-interest costs
Altunbas et al. (2000)
Operating cost and financial cost
Bonin, Hasan, and Wachtel (2005)
Interest costs and non-interest costs
Fries and Taci (2005)
Interest expenses and operating
expenses
potential losses, thereby increasing total cost. For example, the
Taiwanese company, Rebar, which embezzled approximately $100
billion borrowed from banks, announced that it was in a “state of
default” in 2006. This type of embezzlement does not take place in a
day, but over years of operations. However, lending banks have not
established the necessary PLL. When the news of these scandals
broke out, PLL rose immediately,9 causing total cost to decrease
excessively low, even before the scandals became matters of public knowledge; once the scandals were finally publicized, and total
cost became excessively high.
3. An approach to calculate economic cost
Our cost function is estimated based on the economic total
cost (E TC) and not the accounting total cost (A TC). The relation
9
Mega Bank should increase $6 billion PLL and investment losses, and Chinese
Bank should increase $40 billion PLL and sale losses of NPL.
This paper addresses a little examined intersection
between the problem loan literature and the bank
efficiency literature.
After controlling for loan quality, liquidity,
capitalization, and output mix, per unit bank operating
costs are found to vary significantly across Asian
countries and over time.
This paper attempts to estimate comparable efficiency
scores for European banks operating in the Single
Market in the EU.
Looking at large banks across 10 countries, they find no
country seems to have a strong efficiency advantage. It
seems likely that state efforts to promote “national
champions” through favorable mergers which expand
scale and market share may determine the outcome.
This paper addresses the question of the causality
between non-performing loans and cost efficiency in
order to examine whether either of these factors is the
deep determinant of bank failures.
This paper investigates the impact of risk and quality
factors on banks’ cost to evaluate scale and
X-inefficiencies, as well as technical change for a
sample of Japanese commercial banks between 1993
and 1996.
They illustrate SFA to investigate the effects of
ownership on bank efficiency for eleven transition
countries.
This paper based on the stochastic frontier approach
(SFA) use a single-step procedure to examine the cost
efficiency in 15 East European countries.
between these two total costs is shown in Eq. (1) become
E TC = A TC − A PLL + E PLL,
(1)
E PLL = EL1 + EL2,
(2)
where E TC is economic total cost, E PLL is economic provision for
loan loss, A TC is accounting total cost, and A PLL is accounting
provision for loan loss.
Eq. (1) suggests that economic cost is equal to accounting cost
if accounting PLL is equal to economic PLL. However, because
accounting PLL is often not equal to economic PLL in reality, thus,
economic cost is not equal to accounting cost. Eq. (1) can be further
written as
E TC = CBPT + E PLL,
where CBPT = A TC − A PLL, and is the cost before provision and tax.
Eq. (2) suggests that E PLL is affected by expected losses and
adjusted accumulated PLL in each period, which are referred to
expected loss 1 (EL1) and expected loss 2 (EL2), respectively Shen
(2005a). They are described as follows.
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
3.1. EL1
The expected losses are determined by the current nonperforming loan (Current NPL). However, reported NPL is the stock
concept, we need to transform it into a flow concept, which is
referred to as “current non-performing loans” or “economic nonperforming loans.” The EL1 is defined as follows.
EL1 = k1 × current NPLt ,
(3)
where the Current NPL is defined as follows.
+ Sell offt ,
(4)
where NPL is the non-performing loan, Write off is net charge-off,
and Recovery is recovery of the written off loan. Sell off is the sale
of bad loans, including such sales to asset-management companies,
and k1 is the percentage of Current NPL.
Eq. (3) suggests that expected loss is the percentage of Current NPL. To illustrate this, loans are typically classified into five
categories, which are normal loans (0%), loans for observation (2%),
substandard loans (10%), doubtful loans (50%), and loan losses
(100%). The numbers in parentheses denote the percentage of loan
loss that should be provisioned for that category. PLL for the first
one category is referred to as general PLL where the bank has not
identified impairment. Also, the loan loss in the first category is
the concept of forward looking. By contrast, the last four categories belong to specific PLL where the bank will not recover the
non-performing loans in full. Also, the specific PLL is based on the
non-performing loans that have already occurred, and thus, PLL is
generated on the concept of backward looking. Because we do not
have data of these five classifications, we assume that the PLL is
simply a k percentage of newly created non-performing loans in
each period, where k is the weighted average number of the above
numbers. For simplicity, we assume k1 = 40%.10
Eq. (4) functions simply to transform the stock NPL to flow NPL.
Though this equation is simply based on an accounting identity,
banks do not disclose the amounts of sales of bad assets in detail,
and this scenario may yield a negative Current NPL. To overcome
this potential problem, we modify our Eq. (4) slightly as
If Current NPLt ≥ 0 (general condition)
Current NPLt = NPLt − NPLt−1 + Write offt + RECOVERYt ,
(5)
If Current NPLt < 0
Current NPLt = Min
Current NPL total loans
t
× total loant ,
coverage ratio be at least 40%, but that banks experiment with other
percentages in pursuit of robust checking. Once the consistent PLL
is obtained, the resulting total costs are generated.
The relation between RLL and PLL is:
RLLt = RLLt−1 + PLLt .
Thus, the accumulated PLL should cover a large percentage of
NPL, where we define the coverage ratio as RLL/NPL and recommend that
Coverage ratio =
Current NPLt = NPLt − NPLt−1 + Write offt + Recoveryt
EL2 = 0.4 × NPLt − (RLLt−1 + EL1t ).
PLL is also affected by the accumulated PLL (which is commonly
termed as reserve for loan loss, RLL) because the RLL may not be sufficient to cover non-performing loans. We define a coverage ratio
as the ratio of RLL over non-performing loans. When the coverage
ratio is low, banks should have a greater PLL. We suggest that the
10
This criterion was first used by Taiwan Financial Supervisory Commission (FSC).
In this study, we also try 50% and 60% to check the robustness of the results.
(6)
Once we obtain EL1 and EL2, we can calculate economic PLL by
summing them together.
4. Cost efficiency model
Frontier approach is the most often used approach to estimate bank cost efficiency (Mester, 1996; Pastor, 1999; Rezvanian &
Mehdian, 2002). Frontier approach comprises parametric and nonparameter approach, where the former include stochastic frontier
approach (SFA) and distribution-free approach (DFA) and the latter include data envelopment analysis (DEA). Parametric approach
generally separates out the effects of inefficiency and random error,
and the nonparametric approach does not. The methods have been
widely used in the literature; see Vennet (2002) and Maudos,
Pastor, Perez, and Quesada (2002) to name a few.
Two important factors, that is, the distribution of the error
term and the choice of functional form, must be determined in
applying frontier approaches. Regarding the former, we adopt
DFA approach11 which is relatively distribution free in the sense
that little of shape is imposed on the distributions of inefficiency
or random error. Namely, DFA eschews arbitrary distributions
by assuming that inefficiencies are stable over time while random error tends to average out. Regarding the latter, following
Rezvanian and Mehdian (2002), we use translog function12
ln TCit = ˛i +
M
am ln Ym,it +
m
+
+
3.2. EL2
RLLt
> k2,
NPLt
where k2 is another percentage. Assuming that current PLL is equal
to EL1, we argue that the past-accumulated PLL in conjunction
with the current PLL should cover the k2 percentage of NPL. That
is, RLLt−1 + EL1 > k2 × NPLt . Thus, additional loss from insufficient
coverage is
(5 )
where Min(Current NPL/total loans) denotes the minimum of the
new non-performing loan ratio during the whole sample period
for a bank. Thus, for a bank, whenever there is a negative Current NPL, we adopt the conservative principle by assuming the
negative Current NPL in that year be the same as the minimum
of the Current NPL/total loans in the whole sample year.
427
N
bn ln Wn,it
n
1 amn ln Yn,it ln Ym,it
2
M
N
m
n
1 bmn ln Wn,it ln Wm,it
2
M
N
m
n
11
Because the DFA cannot estimate cost frontier every quarter (see Berger &
Humphrey, 1991), we also use SFA to estimate individual quarterly cost function. However, the two methods may generate different results. For example, Weill
(2004) utilized data on European banking and reached different results by using
the two methods. Because the results yielded by DFA are more consistent with our
intuition and hypotheses, we draw our conclusions based on the DFA approach.
12
The translog has an advantage over earlier functional forms in that it allows
returns to scale to change with output or input proportions so that the estimated
cost curve can take on the familiar U-shape.
428
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
Table 2
Definition of variables.
Variable
Definition
Operational definition
1. Variables used for recovering economic PLL
Accounting total cost
A TC
NPL
Non-performing loans
PLL
Provision for loan loss
RLL
Reserve for loan loss
Write off
Net charge-off
Recovery
Recovery of the written off of the loan
Sell off
Sale of bad loans
Total loan
Total loan
2. Variables used for cost efficiency model
Economic total cost
E TC
W1
Fund price
Wage rate
W2
Fixed capital price
W3
Y1
Y2
Y3
Investments
Loans
Fee revenues
Q
Seasonal dummy
Interest cost + non-interest cost + A PLL
Non-performing loans + loan subject to observation
Same as left column
Same as left column
Same as left column
Same as left column
Same as left column
Total bills purchased, discounted and loans
A TC − A PLL +EL1 + EL2
Interest expense/(borrowings + deposits)
Salary expense/employees
(E TC − interest expense − salary expense)/(fixed
assets-accumulated depreciation)
Short-term investment + long-term investment
Total bills purchased, discounted and loans
Service fees + foreign exchange gain + security
brokerage revenue + commission revenues
Note: 1. A PLL: accounting provision for loan loss. 2. E TC is equal to A TC − A PLL +EL1 + EL2, where
EL1 = k1 × Current NPL
EL2 = 0.4 × NPLt − (RLLt−1 + EL1t ).
Current NPL is the flow non-performing loan, NPL is the stock non-performing loan and RLL is the reserve for loan loss. 3. Source: Taiwan Economic Journal database.
+
M N
m
abmn ln Wn,it ln Ym,it +
n
4
cq Qq + εit ,
(7)
q=1
where subscripts n is the nth inputs (n = 1, 2, 3) and m denotes
the mth outputs (m = 1, 2, 3), i is ith bank (i = 1, . . ., 29), TC is the
total cost, proxies by either accounting total cost or economic total
cost.13 Following Shen (2005b), three input prices are denoted
by fund price (W1 ), wage rate (W2 ), and fixed capital price (W3 ),
whereas the three outputs are investment amounts (Y1 ), loans
amounts (Y2 ) and fee revenues (Y3 ), and Qq (q = 1, 2, 3 and 4) are
seasonal dummies that take on the value of one for the qth season
and zero otherwise. See Table 2 for detailed definitions of variables.
For the distribution-free approach, we transform Eq. (7) into
ln Cit
= ln(Wit , Yit ) + ln εit
= ln(Wit , Yit ) + ln ui + ln vit ,
(8)
where error term ln εit specified here as ln εit = ln ui + ln it , that is,
the composite error ln εit includes both inefficiency ln ui (deviations
from the efficient frontier) and random error ln vit (measurement
error). No distributional assumptions are imposed on ui or vit .
To calculate X-efficiency (hereafter, EFF), we average the residuals from Eq. (8) for each bank over years. The key assumption is
that cost differences owing to average residual ln ûi for each bank,
an estimate of ln ui , is relatively stable and should persist over time,
while those owing to random error (ln vit ) is ephemeral and should
average out over time Berger and Hannan (1998). We transform
ln ûi into a normalized measure of efficiency,
EFF = exp(ln ûmin − ln ûi ),
(9)
13
Some studies also consider equity capital in the cost function. For example,
Dietsch and Lozano-Vivas (2000) used the ratio of equity capital to total assets as
proxy of environmental variable to measure regulatory condition. See also Kwan
(2003), Berger and Meter (1997), and Patti and Hardy (2005) to name a few. However, because equity capital changes slowly and its price is difficult to measure, and
because our study is to illustrate the influence of fluctuate PLL on cost efficiency, we
do not consider it.
where min indicates the minimum for all i. This approach corresponds with the conventional notion of efficiency as the ratio
of minimum resources needed for production to the resources
actually used, and ranges over (0,1], with higher values indicating
greater efficiency.
Once we obtain the estimated coefficients, the scale of
economies (SE) is obtained as follows.
SE =
3
∂ ln C
m=1
∂ ln Ym
= am +
3
n=1
amn ln Yn +
3
abmn ln Wn .
(10)
k=1
If SE is greater than one, the technology exhibits diseconomies
of scale. If SE is less than one, the technology exhibits economies of
scale. If SE is equal to one, the there are constant returns to scale.
5. Data sources
All variables are taken from the Taiwan Economic Journal (TEJ),
a private data vending company. Although the database contains
33 Taiwan commercial banks, our sample is comprised of only 29
because the remaining four banks (e.g., General Bank, DahAn Bank,
Cathay Bank, and Fubon Bank) have either been merged or consolidated. The sample period is 2001:Q2 to 2006:Q4. Please note that
the starting period of 2001:Q2 is determined because it is the date
that most of the banks in databank start to have the data of the
international definition for non-performing loans.
6. Empirical result
6.1. Basic statistics and recovery of the economic provision for
loan loss (E PLL)
Table 3 presents the average statistics of A TC, A PLL, cost before
provision and tax (CBPT), EL1, EL2, E PLL, and E TC for each bank
over the sample period. The first column corresponds to A TC,
wherein the highest value represents China Trust Bank, and followed by Chang-Hwa Bank and First Bank. The lowest A TC is for
Taitung Business Bank.
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
429
Table 3
Recover the economic PLL (each bank). Measure: million New Taiwan Dollars.
Bank
(A) A TC
Chang-Hwa
First
Hua-Nan
International Commercial Bank of China
HsinChu
Interna. Bank of Taipei
King’s Town
Taitung Business
Taichung
China Trust
Chiao Tung
Cathay
Taipei Fubon
Chinese
Taiwan Business
Kaohsiung
Cosmos
Union
SinoPac
E. Sun
Fu-Hwa
Tai-Shin
Far-Eastern
Ta Chong
En-Tie
Bo-Wa
Jih-Sun
Bank of Overseas Chinese
Taiwan Cooperative Bank
17,382
17,196
16,198
11,591
5004
4330
1848
1421
3505
21,196
5691
11,913
10,014
4326
12,186
1874
6081
5190
5755
5249
3252
14,718
4158
4531
3704
3097
4830
3891
17,154
(B) A PLL
−271
−93
109
135
192
12
23
37
17
582
−4
514
55
−88
−37
−8
298
26
189
−31
280
352
72
95
173
60
71
−74
−680
(C) CBPT = (A) − (B)
17,653
17,289
16,089
11,456
4813
4318
1825
1384
3488
20,614
5695
11,398
9958
4413
12,223
1882
5782
5164
5566
5279
2971
14,365
4086
4436
3531
3037
4758
3964
17,834
(D) EL1
548
679
727
466
235
137
84
137
61
1561
756
1483
786
225
671
52
939
306
379
406
198
1115
376
229
283
406
401
213
1644
(E) EL2
29,994
15,736
14,910
4333
4016
3755
4008
3725
9251
4167
5528
4040
4191
7624
24,090
1350
3820
2986
1473
1051
3519
1853
2346
4375
4464
12,430
4822
8292
21,269
(F) E PLL =(D) + (E)
30,542
16,415
15,637
4799
4251
3892
4092
3863
9312
5727
6284
5523
4977
7849
24,761
1402
4760
3292
1852
1457
3716
2968
2722
4604
4747
12,836
5223
8504
22,913
(G) E TC = (C) + (F)
48,195
33,703
31,726
16,255
9064
8210
5917
5247
12,800
26,341
11,979
16,922
14,935
12,262
36,984
3284
10,542
8456
7418
6736
6687
17,333
6808
9040
8279
15,873
9981
12,469
40,747
Note: 1. A TC: accounting total cost. A PLL: accounting provision for loan loss. 2. CBPT, which is the cost before provision and tax, is equal to (A TC − A PLL). 3. E PLL: economic
provision for loan loss, which is equal to EL1 + EL2. EL1 = k1 × Current NPLt , EL2 = 0.4 × NPLt − (RLLt−1 + EL1t ). E TC is economic total cost which is equal to CBPT + E PLL.
CBPT is defined as A TC minus A PLL. E PLL is the sum of EL1
and EL2, both of which are calculated based on the recovery of the
PLL provided earlier. Clearly, A PLL is overwhelmingly smaller than
E PLL (A PLL < E PLL), suggesting that banks are typically underprovisioned. This results in an overestimation of the profits. For
example, the A PLL and E PLL of Hua-Nan Bank are $109 and
$15,637 million, respectively. With A PLL much lesser than E PLL,
we see that the observed total cost is considerably underestimated.
The last column corresponds to E TC, of which the highest value
is represented by Chang-Hwa Bank, and followed by Taiwan Cooperative Bank and Taiwan Business Bank. Kaohsiung Bank obtains
the lowest E TC. Typically, A TC < E TC suggests that banks manage their earnings to lower provisions, thereby increasing profit.
Accordingly, the use of accounting cost may overestimate the efficiency, given the same inputs.
Table 4
Recover the economic PLL (each quarter). Measure: million New Taiwan Dollars.
Quarter
(A) A TC
(B) A PLL
(C) CBPT = (A) − (B)
(D) EL1
(E) EL2
(F) E PLL = (D) + (E)
2001:Q3
2001:Q4
2002:Q1
2002:Q2
2002:Q3
2002:Q4
2003:Q1
2003:Q2
2003:Q3
2003:Q4
2004:Q1
2004:Q2
2004:Q3
2004:Q4
2005:Q1
2005:Q2
2005:Q3
2005:Q4
2006:Q1
2006:Q2
2006:Q3
2006:Q4
5979
5400
5098
10,290
7087
10,783
4668
5994
8051
9424
4496
6348
7988
10,346
5070
7572
9624
15,339
6502
7135
7759
8688
−59
1337
−4470
5004
1308
2162
−8182
1284
2018
1667
−4211
750
700
1121
−2699
1195
1166
4203
−5644
462
111
1237
6038
4063
9568
5286
5779
8621
12,850
4710
6033
7757
8707
5598
7288
9225
7769
6377
8458
11,136
12,146
6673
7649
7451
765
1186
645
713
1396
928
240
702
1291
1276
234
715
849
840
808
856
1424
731
369
1623
836
960
12,964
11,298
13,688
12,065
10,753
8594
8864
8175
7581
6048
7736
6535
6104
4862
5030
3900
3070
2641
1492
2182
3519
3225
13,729
12,484
14,332
12,778
12,149
9522
9104
8877
8871
7323
7970
7250
6953
5702
5838
4756
4494
9910
14,972
3804
4355
4185
(G) E TC = (C) + (F)
19,767
16,547
23,900
18,064
17,928
18,143
21,954
13,587
14,904
15,080
16,677
12,848
14,241
14,927
13,607
11,133
12,952
21,046
27,118
10,477
12,004
11,636
Note: see notes in Table 3. CBPT, which is the cost before provision and tax, is defined as accounting total cost minus provision for loan loss (A TC − A PLL). E PLL is the sum
of EL1 and EL2, and they are respectively calculated based on the expected cost which comprises the flow (from new non-performing loan) and stock (from the accumulated
PLL) parts. E TC is economic total cost which is CBPT adds E PLL.
430
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
Table 5
Descriptive statistics.
Variable
Mean
SD
Min
Max
A TC (million)
E TC (million)
Fund price
Wage rate (ten thousand)
Fixed capital price
Investments (million)
Loans (million)
Fee revenues (million)
7710
15,481
0.03
18.5
0.45
358,502
89,809
907
7434
15,946
0.36
8.6
1.01
298,106
105,234
1247
−6536
2076
0.01
4.6
0.01
30,126
312
37
70,312
136,363
0.71
47.6
8.18
1,713,910
434,747
8220
Note: Mean, SD, Min and Max denote the average, the standard deviation, minimum
and; A TC is accounting total cost. E TC is economic total cost. Three prices of inputs
are fund price, wage rate, and fixed capital price. Three outputs comprise investments, loans, and fee revenues. The detail definition of input price and outputs are
in Table 2.
Table 4 presents further the summation of each variable across
banks for each quarter. The highest A TC is in 2005:Q4. Note that
CBPT, which is the total cost before provisions and taxes, should
be smaller than the A TC. However, we find that CBPT is greater
than A TC in 2002:Q1, as A PLL is negative. Meanwhile, the negative A PLL for that quarter is an effect of bank provisions that are less
in the first three quarters than in the fourth quarter, which is commonly employed to manipulate earnings; Liu (1999) referred to this
as evidence of earnings manipulation. Once our consistent measure
on PLL is adopted, the E PLL become positive ($14,332 million) in
2002:Q1, whereas it decrease to $9522 million in 2002:Q4.
Fig. 2. accounting PLL (accounting cost) vs. economic PLL (economic cost).
Table 5 presents the mean, standard deviations, and the minimum and maximum values of A TC, E TC, fund price, wage rate,
fixed capital price, investments, loans, and fee incomes. The mean
and the standard deviation of A TC are $7710 and $7434 million,
respectively, whereas they are $15,481 and $15,946 million for
E TC, respectively. The mean and standard deviation of A TC are
only half of E TC; hence, banks minimize their accounting cost and
Fig. 1. accounting cost (solid line) vs. economic cost (dash line).
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
431
Table 6
Translog function.
Constant
ln Y1
ln Y2
ln Y3
ln P1
ln P2
ln P3
(ln Y1 )2
2
(ln Y2 )
(ln Y3 )2
(ln P1 )2
(ln P2 )2
2
(ln P3 )
ln Y1 × ln Y2
ln Y1 × ln Y3
ln Y2 × ln Y3
ln P1 × ln P2
A TC
E TC
580.873**
(4.460)
−59.126**
(−5.015)
10.423**
(3.590)
5.606*
(1.699)
0.630
(0.426)
11.448**
(3.312)
2.013*
(1.913)
2.846**
(4.649)
−0.461**
(−2.973)
−0.189
(−1.425)
−0.013
(−0.588)
0.172
(0.449)
0.002
(0.084)
−0.199
(−0.860)
−0.344*
(−1.719)
0.264**
(2.856)
0.076
(1.125)
338.917**
(4.828)
−27.789**
(−4.259)
4.891**
(2.672)
−0.660
(−0.328)
2.328**
(2.472)
−2.767
(−1.251)
−0.561
(−0.839)
1.143**
(3.203)
−0.238**
(−2.436)
0.103
(1.246)
−0.031**
(−2.191)
0.222
(0.909)
0.030**
(2.504)
0.014
(0.094)
−0.111
(−0.890)
0.034
(0.583)
−0.049
(−1.147)
ln P1 × ln P3
ln P2 × ln P3
ln Y1 × ln P1
ln Y1 × ln P2
ln Y1 × ln P3
ln Y2 × ln P1
ln Y2 × ln P2
ln Y2 × ln P3
ln Y3 × ln P1
ln Y3 × ln P2
ln Y3 × ln P3
Q1
Q3
Q4
A TC
E TC
0.001
(0.063)
−0.023
(−0.477)
−0.016
(−0.176)
−0.705**
(−3.032)
−0.155**
(−2.376)
−0.041
(−0.846)
0.140
(1.132)
0.112**
(3.409)
0.017
(0.595)
0.166*
(1.688)
−0.029
(−0.812)
0.162
(1.193)
0.142
(1.052)
−0.002
(−0.050)
−0.001
(−0.124)
0.009
(0.300)
−0.150**
(−2.579)
−0.023
(−0.152)
0.047
(1.134)
0.062**
(2.023)
−0.003
(−0.04)
0.001
(0.050)
0.013
(0.695)
0.115*
(1.819)
−0.032
(−1.435)
−0.003
(−0.028)
0.047
(0.135)
−0.107*
(−1.745)
Note: 1. The model is estimated by the following equation.
ln TCit = ˛i +
M
am ln Ym,it +
m
N
n
bn ln Wn,it +
1
2
N
M
m
amn ln Yn,it ln Ym,it +
1
2
n
N
M
m
n
bmn ln Wn,it ln Wm,it +
N
M
m
abmn ln Wn,it ln Ym,it +
n
4
cq Qq + εit ,
q=1
where TCit is the total cost, proxies by either total accounting cost or economic total cost. Three input prices (W) are denoted by fund price, wage rate, and capital price. The
three outputs (Y) are investment, loans, and fee revenues. Qq is a seasonal dummy. 2. **and* represent respectively significant at 5% and 10%level. Numbers in parentheses
are t-value.
its variations. The mean values of the price of funds, wages, and
capital are 3%, $185,000, and 45%, respectively.
Fig. 1 plots the graphs of A TC and E TC for each bank. The plots
show that most banks have higher E TC (denoted by dashed lines)
than A TC (denoted by solid lines). We can classify the total cost patterns in Fig. 1 into three groups. In the first group, A TC and E TC
move closer over time; an example for this is First Bank. One possible reason for this phenomenon is government requests. Beginning
2002, there is sufficient PLL after Taiwan’s First Financial Reform
(see footnote 7). First Bank has sufficient provisions. In the second
group, A TC and E TC move up and down proportionally; the pattern of Taipei Fubon Bank reflects this phenomenon. In the third
group, the difference between A TC and E TC increase over time;
Chang-Hwa Bank is a good example of this group.
Fig. 2 compares the graph of A PLL (A TC) with the graph of
E PLL (E TC) in terms of averages. E PLL is higher than A PLL, and
E TC is also higher than A TC. The fluctuation of E TC is larger than
that of A TC because of the fluctuation of PLL. Based on the above
results, true costs should increase with accurate PLL, indicating that
understating PLL undeniably causes misestimated in total costs.
random-effect model is used because of insignificant Hausman
statistics.14
The coefficients of A TC and E TC are largely the same, but
with some minor differences. For example, the coefficients of ln Y3
change from positive to negative, whereas those of ln Y1 × ln P3
changes from negative to positive, though they are insignificant.
Also, the significant coefficients of (ln P3 )2 when using E TC become
insignificant when using A TC. While coefficients change slightly,
both their effects on X-efficiency and the resulting rankings of each
bank resist easy direct evaluation. Eq. (9) is employed for this purpose.
The coefficients of seasonal dummies are considerably different
when varying total costs are used as dependent variables. The coefficients are 0.162 and −0.003 for A TC and E TC in the first quarter,
respectively. The coefficients for the fourth quarter are negative for
both of the specifications, but this is only significant when E TC is
used as a dependent variable.
Once we obtain the estimated coefficients, we judge the economic scale of each bank. In Table 7, banks are divided into five
6.2. Cost efficiency
14
Hausman (1978) suggests using the Chi square test to examine the null hypothesis of random effects vs. the alternative of the fixed-effects panel model. The Chi
square 2(30) is found to be 5.927, which does not undermine the null hypothesis of
Table 6 presents the estimated results using A TC and
E TC as the dependent variables in our translog function. The
random effects given that the critical value is 43.773.
432
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
Table 7
Economic scale.
Total assets (thousand)
A TC
E TC
Bank group
Less 200,000
0.148
−0.081
200,000–400,000
0.629
−0.222
400,000–600,000
−0.295
0.896
600,000–800,000
800,000–1,000,000
1.569
0.931
0.625
0.212
King’s Town Bank, Taitung Business Bank, Taichung Bank, Chinese
Bank, Kaohsiung Bank, Cosmos Bank, Union Bank, Fuh-Wa Bank,
Far-Eastern Bank, Ta-Chong Bank, En-Tie Bank, Bo-Wa Bank, Jih-Sun
Bank, and Bank of Overseas Chinese
HsinChu Bank, International Bank of Taipei, Taipei Fubon Bank,
SinoPac Bank, E. Sun Bank, and Tai-Shin Bank
International Commercial Bank of China, China Trust Bank, Chiao Tung
Bank, and Cathay Bank
Taiwan Business Bank
Chang-Hwa Bank, First Bank, Hua-Nan Bank, and Taiwan Cooperative
Bank
Note: 1. A TC is accounting total cost. E TC is economic total cost. 2. Bank Group lists banks name of each group based on total assets.
groups based on total assets. When A TC is used as the dependent
variable, around two-thirds of the economic scale of the banks
are lower than 1, suggesting economies of scale. Diseconomies
of scale start to appear in the fourth group, suggesting that cost
increases faster than production in this group. For example, the
scale economies of Chang-Hwa Bank comprised of 1.23 in 2003:Q4;
the asset size is around $400–600 million. When E TC is used the
dependent variable, all the scale economies of the banks are lower
than 1, indicating potential economies of scale by expanding further their assets. Thus, the optimal size might have exceeded the
current asset size of all banks.
Fig. 3 presents the plot of the economic scale obtained using
A TC as the dependent variable, wherein the horizontal and vertical axes represent fixed assets and economic scale, respectively.
Results suggest that most banks are in the stage of economies of
scale, and that a few banks are in the stage of diseconomies of scale.
Fig. 4 is similar with Fig. 3, but obtained using E TC as the dependent variable. Results are also similar to those wherein A TC is the
dependent variable, but the number of banks falling within the
range of diseconomies of scale is smaller. In other words, most
banks would enjoy economies of scale after adjusting for the provision for loan loss.
Table 8 presents the estimated X-efficiency of the 29 banks. The
rankings change dramatically when different total cost measures
are used. First, some top-ranked banks drop in their standings considerably, and since then have been identified as among the least
efficient banks. For example, by using A TC as the dependent variable, Bo-Wa Bank, which previously is the second most efficient
bank, become the least efficient bank (rank 29) when E TC is used.
Fig. 3. Economic scale—accounting cost.
Fig. 4. Economic scale—economic cost.
Bo-Wa Bank was classified as a distressed bank and was taken over
by Taiwan through Resolution Trust Corporation (RTC)15 in August
2007 because of the bank’s worsening net worth and substantial
NPL of 13%. Consequently, the results of the least efficient yield by
E TC are consistent with our intuition, indicating that E TC is preferable over A TC. The same argument applies to Taitung Business
Bank, which was also taken over by RTC in 2006. Its rank dropped
from seventh to eighth when the two measures were used. The rank
of Bank of Overseas Chinese, whose non-performing ratio reached
10.96% and average non-performing ratio at 9.41%, also saw major
changes, dropping from its first-place ranking in efficiency (i.e., by
using A TC) to the 27th standing (i.e., by using E TC). The ranking
of Chang-Hwa Bank exhibits the most drastic change, falling from
fourth to 26th, the drop of which is also consistent with intuition.
This consistency reflects the bank’s non-performing ratio, previously at 4.85%; its average ratio is 4.32%, which is higher than the
average of 2.78%, in 2004.16
15
The RTC is a government company that was established to take over distressed
banks whose net worth is negative or whose capital-adequacy ratio is less than 2%.
Bo-Wa Bank’s assets reached a negative level of NT$24.7 billion in 2007, and the
bank’s non-performing ratio hit a high of 13%. It was taken over by the RTC in 2007
and then sold to Development Bank Singapore (DBS) through an auction.
16
The Taiwan government decided to sell Chang-Hwa Bank through global depository receipts at the end of 2004. However, because the bidding price was low, the
bank was not sold. After the failed attempt to sell the bank through global depository
receipts (GDR), the government auctioned it on the market in June 2005. Taishin
Financial Holding Company purchased 22.5% of the bank’s special equity shares,
becoming the largest shareholder of the bank.
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
433
Table 8
X-Efficiency and rank (A TC and E TC).
A TC
E TC
Value
Chiao Tung
Cathay
King’s Town
Far-Eastern
Fu-Hwa
E. Sun
SinoPac
Taitung Business
Ta Chong
Interna. Bank of Taipei
Kaohsiung
Tai-Shin
Taiwan Cooperative Bank
Union
Cosmos
Taiwan Business
Hua-Nan
En-Tie
Taipei Fubon
International Commercial Bank of China (ICBC)
Taichung
Hsinchu
Jih-Sun
First
China Trust
Chang-Hwa
Bank of Overseas Chinese
Chinese
Bo-Wa
Rank
0.97683
0.94199
0.96948
0.96815
0.97350
0.96574
0.96328
0.97308
0.96808
0.96652
0.96881
0.96880
0.96879
0.96878
0.96442
0.99073
0.95723
0.96746
0.97255
0.96605
0.96790
0.95810
0.96385
0.96315
0.95454
0.97755
1.00000
0.96178
0.99756
5
29
9
14
6
20
23
7
15
18
10
11
12
13
21
3
27
17
8
19
16
26
22
24
28
4
1
25
2
Value
Rank
1.00000
0.98591
0.97601
0.97421
0.97390
0.97375
0.97276
0.96903
0.96851
0.96755
0.96733
0.96732
0.96731
0.96730
0.96688
0.96663
0.96609
0.96600
0.96583
0.96574
0.96573
0.96567
0.96554
0.96411
0.96404
0.96360
0.95816
0.94822
0.93953
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
Note: 1. A TC is accounting total cost. E TC is economic total cost. 2. The spearman correlation coefficient (Rs ) of two efficient measures is 0.0601.
Table 9
X-Efficiency and rank (operating cost).
A TC
Value
Chiao Tung
Cathay
King’s Town
Far-Eastern
Fu-Hwa
E. Sun
SinoPac
Taitung Business
Ta Chong
Interna. Bank of Taipei
Kaohsiung
Tai-Shin
Taiwan Cooperative Bank
Union
Cosmos
Taiwan Business
Hua-Nan
En-Tie
Taipei Fubon
International Commercial Bank of China (ICBC)
Taichung
Hsinchu
Jih-Sun
First
China Trust
Chang-Hwa
Bank of Overseas Chinese
Chinese
Bo-Wa
0.97683
0.94199
0.96948
0.96815
0.97350
0.96574
0.96328
0.97308
0.96808
0.96652
0.96881
0.96880
0.96879
0.96878
0.96442
0.99073
0.95723
0.96746
0.97255
0.96605
0.96790
0.95810
0.96385
0.96315
0.95454
0.97755
1.00000
0.96178
0.99756
E TC
Rank
5
29
9
14
6
20
23
7
15
18
10
11
12
13
21
3
27
17
8
19
16
26
22
24
28
4
1
25
2
Operating expense
Value
Rank
Value
Rank
1.00000
0.98591
0.97601
0.97421
0.97390
0.97375
0.97276
0.96903
0.96851
0.96755
0.96733
0.96732
0.96731
0.96730
0.96688
0.96663
0.96609
0.96600
0.96583
0.96574
0.96573
0.96567
0.96554
0.96411
0.96404
0.96360
0.95816
0.94822
0.93953
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1.00000
0.92990
0.93413
0.93947
0.93564
0.93511
0.93067
0.92549
0.93197
0.93297
0.93832
0.93303
0.94580
0.93303
0.92187
0.94326
0.92874
0.93493
0.93102
0.93130
0.92970
0.93524
0.93283
0.92246
0.92348
0.93644
0.93767
0.93450
0.93001
1
23
13
4
8
10
21
26
18
16
5
14
2
15
29
3
25
11
20
19
24
9
17
28
27
7
6
12
22
434
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
Table 10
X-Efficiency and rank (outlier).
E TC
Chiao Tung
Cathay
King’s Town
Far-Eastern
Fu-Hwa
E. Sun
SinoPac
Taitung Business
Ta Chong
Interna. Bank of Taipei
Kaohsiung
Tai-Shin
Taiwan Cooperative Bank
Union
Cosmos
Taiwan Business
Hua-Nan
En-Tie
Taipei Fubon
International Commercial Bank of China (ICBC)
Taichung
Hsinchu
Jih-Sun
First
China Trust
Chang-Hwa
Bank of Overseas Chinese
Chinese
Bo-Wa
Delete outlier
Value
Rank
Value
Rank
1.00000
0.98067
0.97149
0.95542
0.94910
0.94784
0.94781
0.94780
0.94736
0.94394
0.94262
0.94164
0.94057
0.93996
0.93327
0.92589
0.92571
0.91773
0.91175
0.91150
0.89806
0.89674
1.00000
0.98067
0.97149
0.95542
0.94910
0.94784
0.94781
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1.00000
0.99523
0.98897
0.98680
0.98649
0.98728
0.98519
0.98157
0.98225
0.98066
0.98157
0.98157
0.98157
0.98157
0.98129
0.98091
0.98165
0.98148
0.97336
0.97788
0.98077
0.97978
0.98069
0.97977
0.97852
0.97872
0.97467
0.96798
0.96667
1
2
3
5
6
4
7
11
8
20
12
13
14
10
16
17
9
15
27
25
18
21
19
22
24
23
26
28
29
In contrast, some of the least efficient banks can now be viewed
as the most efficient banks. For example, Cathay Bank, which
ranked as the worst bank (rank 29) when A TC serves as the dependent variable, becomes the second most efficient bank when E TC is
used. Cathay Bank constantly exhibits outstanding performance in
terms of profit. However, in late 2005, it acquired PLL of $9 million
to solve its NPL problem acquired from Taiwan’s double-card crisis
(credit and cash cards). This provision led its earnings to fall from
$13,879 million in 2004 to $2852 million in 2005. Nevertheless,
the lower earnings resulting from the huge provisions do not represent inefficiency for that specific year, but a decision to remove
bad loans. Other banks also suffered substantial losses during this
crisis. E. Sun Bank’s rank fell from the top 20 to rank 6 due to the
same set of factors. The bank charged off $7600 million in late 2002.
Third, the rankings of some banks remain the same. For example,
First Bank maintains its ranking as twenty-four, regardless of the
dependent variable measures used.
Our empirical studies demonstrate that using E TC as the dependent variable provides for a more reasonable result.
6.3. Robust testing
We consider two robust testing in this subsection. First, we use
operation expenses as the cost measure. Berger and Humphrey
(1991) suggested that operating expense (non-interest cost) have
been shown to comprise the bulk of cost inefficiency at banks.
In particular, the operating cost may be less influenced by cost
management even though it is only part of the total cost. Thus,
also we estimate the X-efficiency by using operating expenses as
the dependent variable. In Table 9, our results show that the correlation coefficient between operating expense and E TC is 0.57,
but is only 0.34 between operation expense and A TC. The results
using E TC are actually more consistent with those using operating
expenses.
Next, we winzorize observations that fall in the top and bottom
one percentile of all variables (Table 10). When the outliers are
deleted, our results change little, that is, the efficiency rankings
remain similar to previous results even though the absolute values
of bank efficiency scores increase.
7. Conclusion
This study suggests that A TC is identified often as the biased
estimator of true total cost, primarily because banks manipulate
provision for loan loss. In this paper, we propose a new measure for total cost, which is designed to act consistently with
economic theory. This new total cost argues that banks manage earnings by highlighting revenues while concealing losses,
making the conventional measure of A TC misleading. In particular, banks report higher accounting earnings by providing less
PLL. Our E TC overcomes these weaknesses to reflect true total
cost.
Both A TC and E TC are used to calculate bank cost efficiency.
We have examined which of the estimated efficiency is consistent
with intuition. We have defined our intuition as follows: Banks
that have been taken over by the government due to their negative net worth, high non-performing loans, or substantial negative
profit, as observed over years of operations, should display strong
inefficiency. Otherwise, banks that exhibit high efficiency but yield
receivership of government are contradicts economic theory, as
well as yields wrong predictions from the perspective of bank
development.
Our results also show that E TC is higher than A TC, suggesting
that banks typically under-provision their loan loss. In addition,
because the Taiwan banking industry suffered the enterprise crisis in 2002, the second wave of financial reforms in 2004, and the
double-card crisis in November 2005, the total cost should have
fluctuated significantly as a result of the fluctuation of PLL. Our
C.-H. Shen, T.-H. Chen / The Quarterly Review of Economics and Finance 50 (2010) 424–435
results demonstrate that the fluctuation of E TC is larger than that
of A TC, another scenario consistent with our intuition.
Our results show that estimated efficiency, with the application
of new total cost, offers results that are more reasonable. For example, the distressed banks that were taken over by RTC are ranked
close to the top when A TC is used, but ranked close to the bottom
when E TC is employed. Similar conditions apply to banks with
very high non-performing loans. Overall, our proposed measure is
a simple method, not only in terms of adjusting earnings management, but also in calculating total cost and the resulting efficiency
measure.
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