Do undesirables matter on the examination of banking efficiency using stochastic directional distance functions

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G Model

ARTICLE IN PRESS

QUAECO-983; No. of Pages 18

The Quarterly Review of Economics and Finance xxx (2016) xxx–xxx

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The Quarterly Review of Economics and Finance journal homepage: www.elsevier.com/locate/qref

Do undesirables matter on the examination of banking efﬁciency using stochastic directional distance functions Tai-Hsin Huang a,∗ , Ming-Tai Chung b a b

Department of Money and Banking, National Chengchi University, Taiwan, R.O.C. Taiwan Academy of Banking and Finance, Taiwan, R.O.C.

a r t i c l e

i n f o

Article history: Received 13 January 2016 Received in revised form 5 September 2016 Accepted 26 September 2016 Available online xxx JEL classiﬁcation: D24 G21 G28 Keywords: Technical efﬁciency Directional technology distance function Undesirable outputs Public banks Private banks Financial holding company

a b s t r a c t This paper aims to gain further insights into whether the First Financial Restructuring (FFR) policy improves the technical efﬁciency of Taiwan’s banks during the period 1999–2012, using the directional technology distance function (DDF). DDF simultaneously allows for the expansion of the desirables and the contraction of the undesirables, which is able to depict a bank’s true production activities. We ﬁnd that the banks have a lower technical inefﬁciency with the preferred model compared to the other models. Before 2002, the technical inefﬁciency exhibits a gradual upward trend and then posts a downward trend during the FFR period, due to enhanced banking and beneﬁts obtained from compliance with FFR. The inefﬁciency scores deteriorate sharply, during the “credit card and cash card crisis” in 2006 and “the subprime mortgage crisis” in 2008. Public and ﬁnancial holding company (FHC) banks are respectively more efﬁcient than private and non-FHC banks. © 2016 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.

1. Introduction There has been increasing interest in the relationship between regulatory reforms and technical efﬁciency of the banking industry. To enhance the banking industry’s competitive viability and to restructure the ﬁnancial system, Taiwan authorities launched a series of ﬁnancial reforms, referred to as “First Financial Restructuring (henceforth, FFR)” from 2002 to 2003. The current study adopts the parametric stochastic frontier approach (SFA) in the context of the directional technology distance function (DDF) to examine the production efﬁciency of Taiwan’s banks. We then investigate whether the FFR policy does improve the technical efﬁciency of banks in Taiwan. In particular, we split the sample period into four sub-periods: pre-reform period (1999–2001), reforming period (2002–2003), post-reform period I (2004–2007), and postreform period II (2008–2012). In our research case, during the process of granting various loans to their customers, banks some-

∗ Corresponding author. E-mail addresses: [email protected] (T.-H. Huang), [email protected] (M.-T. Chung).

times experience loan defaults that result in non-performing loans (NPLs), which are a form of undesirable outputs. We include undesirable outputs in DDF to depict a bank’s true production activities along with environmental variables to account for the impacts from various macro- and micro-factors, as proposed by Battese and Coelli (1995). This allows one to estimate the shadow price of the nonmarketable bad output. For the purpose of comparison, we also estimate a stochastic DDF without environmental variables. To further highlight the role of the undesirable outputs in the application of the banks’ frontier model emphasized herein, we simultaneously subsume the estimation results of the stochastic DDF, which ignores the undesirable outputs as the comparison group. Moreover, the conventional stochastic input distance function is estimated with and without connecting a set of environmental variables with the inefﬁciency term. It is well-known that the standard input and output distance functions are unable to consider bad outputs. Consequently, their efﬁciency estimates may fail to reﬂect the real managerial abilities of bank managers. Desirable and undesirable outputs are jointly produced. The former are often marketable, but the latter are not, and their disposal is frequently subject to regulation. Thus, it is necessary to explicitly

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model the effects of producing both forms of outputs. Since there are, in general, no markets for undesirables, their (shadow) prices must be estimated and contain valuable information. The estimation of DDF allows us to calculate the shadow price of undesirables. Färe, Grosskopf, Noh, and Weber (2005) are the ﬁrst to use DDF to measure environmental efﬁciency and estimate the shadow price of the undesirable output. Fukuyama and Weber (2008) and Ke, Li, and Chiu (2011) employ the method of Färe et al. (2005) to estimate the shadow price of problem loans via a parametric DDF. This paper follows these previous works to examine the shadow price of NPLs using the stochastic DDF. About three decades ago, banks in Taiwan were rigorously regulated by the government with total assets of state-owned banks taking up more than three quarters of the entire banking industry. At the outset of the 1990s, Taiwan’s government took steps to privatize public banks and liberalize the ﬁnancial market by allowing the new entry of private and foreign banks. As a result, the degree of competition in the industry largely intensiﬁed, which is expected to prompt the performance of domestic banks. These policies appear to have helped Taiwan’s banking sector successfully weather the Asian ﬁnancial crisis in 1997–1998, but over-banking has caused excessive competition and lowered interest margins, such that the existing banks suffer from a low level of proﬁts. Even worse, the quality of loans has deteriorated in order for the banks to seize and keep a larger market share. The aftermath of the Asian crisis saw soaring NPLs and declining capital adequacy ratios, hurting asset quality and proﬁtability within the banking sector. Among them, high NPLs are thought to be the most serious problem, substantially reducing the liquidity of some banks and bringing them to the edge of insolvency. The major target of the FFR aims to write off the NPLs of ﬁnancial institutions. Many important laws on regulating ﬁnancial institutions were legislated and revised at the same time, which are designed to enhance the performance of commercial banks. The ratio of NPLs to total loans largely dropped after the enforcement of the “2-5-8 policy”.1 A bank is said to be technically efﬁcient if it can produce maximum output from a given set of inputs (an output-oriented measure) or can employ a minimum input mix to manufacture the same output level (an input-oriented measure). SFA and the nonparametric data envelopment analysis (DEA) are two major frontier techniques suitable for measuring the efﬁciency and productivity change of ﬁrms. However, there is no consensus on the preferred method (Berger & Humphrey, 1997). Frontier efﬁciency is useful for ﬁnancial institution managers and industry consultants to assess performance. Many researchers apply either SFA or DEA to study the effects of ﬁnancial deregulation on the efﬁciency and productivity gains of banks and insurance ﬁrms, as well as the effects of mergers and acquisitions and capital regulations on banks’ profitability and performance. The results may provide valuable policy implications to regulatory analysis. A bank has to spend additional resources to disentangle itself from these NPLs. This lowers either its input-oriented efﬁciency score due to the fact that the extra input usage curtails the amount of undesirable NPLs, instead of raising quantities of desirable outputs, or cuts its output-oriented efﬁciency score since parts of input quantities are used toward the disposal of the undesirables. The implication is that the conventional radial measures of technical efﬁciency may not be able to reﬂect the true managerial abilities of banks due to the presence of undesirables that are not freely disposable. In other words, undesirable outputs are not allowed to be

1 The Taiwan government enacted the 2-5-8 policy, which requires all banks within 2 years to reduce their NPL ratio to be less than or equal to 5% and to maintain a capital adequacy ratio above 8%.

disposed of costlessly. “Cleaning up” these outputs requires a reallocation of inputs away from the production of desirable outputs. To date, the recently developed DDF appears to be the sole model that is useful to explicitly model the effects of producing both desirable and undesirable outputs, taking into account their characteristics and their interactions. Speciﬁcally, DDF allows one to measure a ﬁrm’s technical efﬁciency along with a given direction that measures how much quantities of outputs (desirables and/or undesirables) and inputs should be increased and decreased, respectively, to reach the efﬁcient frontier. The Shephard’s (1953) input and output distance functions can be viewed as special cases of DDF. Dorfman and Koop (2005) point out that the undesirable output is one of the major issues in the ﬁeld of the measurement of efﬁciency and productivity growth under the framework of multiple inputs and outputs. The ﬁrst research utilizing DDF is attributed to Chambers, Chung, and Färe (1996) who generalize the model of Luenberger (1992, 1995) to a beneﬁt function. DDF has three salient features. First, in contrast to Shephard’s (1953) output distance function that seeks to increase both desirable and undesirable outputs, DDF simultaneously allows for the expansion of the desirables and the contraction of the undesirables (and/or inputs). Second, DDF has an additive structure such that the efﬁciency indices of individual ﬁrms can be aggregated into the industry level. Third, when a functional form is required to be speciﬁed for DDF neither the dependent nor the explanatory variables have to be transformed by taking the natural logarithm, which avoids the calculation with respect to non-positive entries for some observations. So far, most empirical studies employ DEA, except for Feng and Serletis (2014) and Huang, Chiang, and Tsai (2015), to estimate efﬁciency in the context of DDF. See, for example, Färe, Grosskopf, and Hernandez-Sancho (2004), Färe et al. (2005), Färe, Grosskopf, and Weber (2006), Hsiao, Chang, Cianci, and Huang (2006), Koutsomanoli-Filippaki, Margaritis, and Staikouras (2009b), and Park and Weber (2006). DEA is function-free and hence is advantageous in that it does not suffer from the possible speciﬁcation error on the production frontier. Nevertheless, the main shortcoming of DEA comes from its omission of the random disturbance, so that the resulting efﬁciency estimates tend to be confounded with noises (Berger & Humphrey, 1997; Das & Ghosh, 2006; O’Donnell & Coelli, 2005). Conversely, a particular functional form has to be speciﬁed to represent the production technology if SFA is employed. This approach is able to separate the effects of noises on estimated efﬁciency scores and, more importantly, environmental variables can be easily incorporated and linked with technical efﬁciencies. The rest of this paper is organized as follows. Section 2 brieﬂy reviews the literature. Section 3 introduces the background of Taiwan’s banking industry. Section 4 speciﬁes a parametric DDF to be estimated, and Section 5 describes the data set. Section 6 discusses the empirical ﬁndings, while the last section concludes the paper.

2. Literature review 2.1. Effects of regulation on banking efﬁciency Many researchers have investigated the nexus of deregulation and banking efﬁciency, but the results are mixed (Berger & Humphrey, 1997). Das and Ghosh (2006) ﬁnd that medium-sized Indian public banks performed reasonably well and the efﬁciency scores of the banking sector are quite high during the period 1992–2002. Isik and Hassan (2003) conclude that the performances of all types of Turkish banks, with the exception of state-owned banks, have recorded signiﬁcant improvements after deregulation,

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driven mainly by efﬁciency gains rather than technical progress. Sturm and Williams (2004) explore the effect of foreign bank entry on Australian bank efﬁciency during the post-reform period 1988–2001 and ﬁnd an increase in technical efﬁciency after the ﬁnancial reform. Hasan and Marton (2003) attain the same conclusion for Hungarian banks that experienced a similar deregulation process as in Australia. Some researchers contrarily claim that ﬁnancial deregulation has uncertain effects on banks’ technical efﬁciencies, because the ﬁnancial industries of different countries face heterogeneous environments that affect, e.g., market competition and the decision-making of bank managers. Speciﬁcally, deregulation in Spain has led to a negative impact upon savings banks’ efﬁciency (Grifell-Tatjé & Lovell, 1996), while Elyasiani and Mehdian (1995) conclude that banking efﬁciency in the United States is unchanged after the deregulation of the early 1980s. Halkos and Salamouris (2004) apply DEA to study the performance of Greek commercial banks and point out that the mean efﬁciency level ﬂuctuates over time. Many other studies attain similar results to the above works, such as Fukuyama and Weber (2002) for Japanese banks and Fu and Heffernan (2009) for Chinese banks. Several investigators have applied DDF to measure efﬁciency and productivity in the banking industry. Park and Weber (2006) show that the efﬁciency score of Korean banks decreases from 1992 to 1998, rises in 1998 and 1999, and declines from 2000 to 2002. Koutsomanoli-Filippaki et al. (2009a, 2009b) note that the bank efﬁciency and productivity of 10 Central and Eastern European countries rise in the period 1998–2003, using SFA and DEA, respectively. They argue that the highest proportion of proﬁt inefﬁciency is attributed to allocative inefﬁciency and productivity change, driven by technological change. Hsiao et al. (2010) appear to be the ﬁrst to apply DDF to explore the efﬁciency of Taiwan’s banking industry using DEA. They ﬁnd that banks present a lower operating efﬁciency during the FFR reform period compared to the pre-reform period, but have a higher operating efﬁciency in the post-reform period. Koutsomanoli-Filippaki, Margaritis, and Staikouras (2012) present estimates of proﬁt efﬁciency in the 25 European Union (EU) member states over the period 1998–2008. DDF has been employed to evaluate other industries than banking, such as airports (Yu, 2004), paper (Chung, Färe, & Grosskopf, 1997), electric utilities (Färe et al., 2005; Lee, Park, & Kim, 2002), and manufacturing (Zaim, 2004), as well as multiple industries (Watanabe & Tanaka, 2007). These articles are primarily concerned about the production process that transforms a range of inputs into several desirable outputs, together with polluting by-products. Because the disposal of these undesirables consumes resources, they should be explicitly considered in the model insofar as to correctly measure a ﬁrm’s performance. This is particularly important for heavily pollutant industries; or the resulting efﬁciency estimates are apt to be overestimated arising from the omission of undesirables. 2.2. The input- and output-oriented distance functions The distance function has been widely applied in the past literature of banking performance. Färe and Primont (1995) provide a detailed survey on the use of this function to estimate banking efﬁciency. English, Grosskoft, Hayes, and Yaisawarng (1993) employ the translog output distance function to calculate the output allocative and technical efﬁciencies of small U.S. banks in 1982 and ﬁnd that these banks are output inefﬁcient. Subsequently, several studies choose the deterministic output distance frontier to estimate technical efﬁciency. For instance, Iqbal, Ramaswamy, and Akhigbe (1999) show that minority-owned banks in the U.S. produce less output quantities than non-minority-owned banks, when they employ the same input mix. Kumbhakar and Wang (2007)

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use the input distance function to examine the impact of ﬁnancial deregulations on banking efﬁciency and total factor productivity change in China. The evidence exhibits that joint-equity banks are more efﬁcient than wholly state-owned banks. Li, Hu, and Chiu (2004) employ a similar method to English et al. (1993) to estimate the technical efﬁciency of 43 Taiwan banks over the period 1997–1999. Their results support that public banks are more efﬁcient than private banks and mixed ownership helps improve the technical efﬁciency of public banks. Li, Hu, and Liu (2009) apply the output distance function to examine the relationship between banks’ efﬁciency and non-performing loans in Taiwan. They argue that new banks consume almost twice as much resources to reduce the same amount of NPLs in comparison with old banks established before 1991. 2.3. Regulatory changes in Taiwan’s banking industry East Asian countries have achieved remarkable economic success in the 1980s and 1990s, as their governments undertook the major responsibility for the promotion of economic growth (Stiglitz, 1996). Starting from 1980 to 1990, Taiwan’s government implemented a series of ﬁnancial modernization aiming at the removal of some restrictions on its ﬁnancial market so as to strengthen the competition and efﬁciency of the market. The deregulation policies liberalized the settings of foreign exchange rates and interest rates, capital inﬂow and outﬂow, and the establishment of ﬁnancial institutions (Chuang & Hölscher, 2008; Liu & Hsu, 2006; Yang, 2001). In 1991 there were 11 state-owned banks and 11 private banks—i.e., 50% of banks were owned by the government. New banks were not allowed to enter and the establishment of new branches by existing banks was also under government control. The lack of competition appeared to result in poor operations for the state-owned banks. That same year in 1991, the New Banking Law was passed and enacted. Sixteen new commercial banks were launched to compete with state-owned and original private banks in the period 1991–1993. In addition, the government permitted the transformation of a few investment and trust companies and a number of credit co-operative associations into commercial banks. The ﬁnancial reform successfully enhanced the performance of Taiwan’s banks, which weathered the Asian ﬁnancial crisis that erupted in mid-1997 and suffered smaller losses than other Asian countries (Liu & Hsu, 2006). The deregulation policy, however, caused a rapid increase in both the number of banks and bank branches, which intensiﬁed the degree of competition and largely lowered interest margins and proﬁtability. The problem of “over-banking” curbs the operational scale of banks such that they are unable to reduce average costs by enjoying economies of scale and product diversiﬁcation (scope economies). In addition, due to keen competition in the ﬁnancial industry, local companies that may not earn proﬁts ﬁnd it easier to obtain loans from banks. Consequently, the ratio of non-performing loans (NPLs) to total loans for banks in Taiwan soared swiftly from 3.82% in 1997 to 4.88% in 1999 and reached a maximum value of 11.74% in March 2002. Taiwanese banks are facing harsh challenges from their rivals and from clients who fail to repay their loans. In order to solve the over-banking problem, the government of Taiwan passed “the Financial Institutions Merger Act” in December 2000 and “the Financial Holding Company Act” in July 2001.2 To

2 At the same time, the government passed the “Act for the Establishment and Administration of the Financial Restructuring Fund”, “Act Governing Bills Finance Business”, and “Value-added and Non-value-added Business Tax Act” and revised the “Deposit Insurance Act” and “Insurance Act”. See, for example, Chuang and Hölscher (2008) and Yeh (2005).

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shrink the amounts of NPLs, the authorities revised the Business Tax Act to reduce the business tax rate from 5% to 2%. Banks can use this tax cut to write off their NPLs. The government also established a ﬁnancial restructuring fund in July 2001 for the purpose of integrating and stabilizing the ﬁnancial market. As a result, the overall ratio of NPLs fell from 8.85% at the end of 2002 to 2.24% at the end of 2005. 3. Methodologies 3.1. The DDF and the shadow prices of undesirables N denote an N-vector of inputs employed Let x = (x1 , ..., xN ) ∈ R+ M by a bank to jointly produce desirable outputs y = (y1 , ..., yM ) ∈ R+ I . We deﬁne the techand undesirable outputs b = (b1 , ..., bI ) ∈ R+ nology as:

T (x, y, b) =

P(x) =

u = z + W ≥ 0.

(3)

Here, W is assumed to be a normal random variable with mean zero and constant variance u2 , is a vector of unknown coefﬁcients to be estimated, and z is a vector of environmental variables that affect banks’ efﬁciency. The estimated coefﬁcients of Eq. (2) can then be used to calculate the shadow prices of undesirables using formula (A10) in Appendix A. 3.2. The input distance function To highlight the importance of undesirables on examining banks’ performance, we alternatively estimate the translog input distance function with M outputs and J inputs. After imposing symmetry and homogeneity restrictions, the following translog input distance function is estimated:

(x, y, b) : x can producey and b

and the output set can be expressed as:

See Appendix A for detailed derivation of Eq. (2). Following Battese and Coelli (1995), the inefﬁciency term of u can be related to a set of exogenous variables as:

(y, b) : x can produce y and b .

We deﬁne the directional technology distance function as3 :

T (x, y, b; gx , gy , g ) = sup ˇ : (x − ˇgx , y + ˇgy , b − ˇg ) ∈ T , D b b

−ln x3 = a0 +

J−1

aj ln xj /x3

N, g ∈ where the directional vector is g = (gx , gy , gb ) with gx ∈ R+ y M , and g ∈ RI . If g = 0, then DDF reduces to the directional outR+ x b + put distance function, whereas DDF reduces to the directional input distance function, provided gy = 0. Following Koutsomanoli-Filippaki et al. (2009a), we specify g = (gx , gy , gb ) = (1, 1, 1), which implies that the bank under study should simultaneously decrease inputs and undesirable outputs by ˇ ≥ 0 units and increase desirable outputs by ˇ ≥ 0 units along with the speciﬁed direction g. Therefore, ˇ measures the gap between the efﬁcient frontier and the bank’s actual production level and reﬂects the bank’s technical inefﬁciency. The larger the value of ˇ is, the less efﬁcient the bank is. A value of ˇ = 0 means that the bank is already producing on the production frontier. To empirically gauge technical (in)efﬁciency under the framework of the stochastic frontier approach, we choose to estimate the quadratic directional distance function as follow4 :

−x3 = ˛0 +

N−1

˛n (xn − x3 ) +

n=1 N−1 N−1 1

+

2

1 2

I I

+

n=1

m=1

(xn −

x3 ) (xn

− x3 ) +

ii (bi − x3 ) (bi − x3 ) +

M M 1

2

M N−1

n=1

ni (bi − x3 ) (xn − x3 ) +

nt n=1

(xn − x3 ) +

M

m=1 l=1

j=1 k=1 J−1 M

+

M

cjm ln xj /x3 ln ym + j0 t

j=1 m=1

1 jt t ln xj /x3 + mt t ln (ym ) + V − U + j00 t 2 + 2 J−1

M

j=1

m=1

(4)

which is illustrated by Appendix A. Here, U is a truncated normal random variable,5 reﬂecting technical inefﬁciency of a bank and it is independent of the disturbance term of V. Following Battese and Coelli (1995), we specify the inefﬁciency term is as: U = z + W ≥ 0,

0, U2

(5)

, is a vector of unknown parameters to be where estimated, and z is a vector of environmental variables.

i (bi − x3 )

4. Data description ˇmm

(ym +

x3 ) (ym

+ x3 )

M

I

m=1

i=1

M

m=1

mn (ym + x3 ) (xn − x3 )

m=1

i=1 N−1

++

W ∼N +

m=1 m =1

I

1 + ı2 t 2 + 2

I

1 1 ajk ln xj /x3 ln xk /x3 + bml ln ym ln yl 2 2 J−1 J−1

i=1

i =1

i=1 N−1

ˇm (ym + x3 ) +

n =1

n=1

+

˛nn

M

bm ln ym

m=1

j=1

(1)

M

mi (bi − x3 ) (ym + x3 ) + ı1 t

m t (ym + x3 ) +

I

i t (bi − x3 ) + v − u. (2)

i=1

3 Chambers, Chung, and Färe (1996) and Färe and Grosskopf (2004) give a thorough discussion on the properties of the directional technology distance function. 4 Chambers (2002) suggests using this functional form, followed by Färe et al. (2005), Fukuyama and Weber (2008), Feng and Serletis (2014), Huang et al. (2015), and Koutsomanoli-Filippaki et al. (2009a).

4.1. Input and output variables We compile a total of 52 commercial banks in Taiwan spanning 1999–2012, before the enforcement of IFRS, based on the Taiwan Economic Journal database and Financial Institutions Major Business Statistics. The resulting unbalanced panel data contain 589 bank-year observations. We identify three inputs, three outputs, and an undesirable according to the intermediation approach that views banks as ﬁnancial intermediaries employing labor, capital, and deposits (borrowed funds) to produce loans, other earning assets (investments), and non-interest revenue. Input borrowed funds (x1 ) include various deposits and borrowed money, capital (x2 ) is deﬁned as the value of net ﬁxed assets, and labor (x3 ) is deﬁned as the number of full-time equivalent employees. The three

5 This paper also estimates the speciﬁcation of Uit = Ui exp [− (t − T )] for the ith bank in period t, as proposed by Battese and Coelli (1992).

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Table 1 Variable deﬁnitions and descriptive statistics. Variables

Deﬁnitions

Mean

Standard deviation

Inputs Borrowed funds (x1 ) Physical capital (x2 ) Labor (x3 )

Total deposits, money market funding and other funding (million NTD) Fixed assets minus accumulated depreciation (million NTD) Number of full-time equivalent employees

536,244.82 11,567.88 3042.95

594,308.96 15,147.36 2351.76

Desirable outputs Investments (y1 ) Loans (y2 ) Non-interest revenues (y3 )

Total of other earning assets minus deposits with banks (million NTD) Total loans plus deposits with banks (million NTD) Fee income plus commission income (million NTD)

110,224.08 409,099.65 2704.73

149,784.48 454,003.29 3623.01

Undesirable outputs Non-performing loans (b1 )

Non-performing loans (million NTD)

11,028.86

16,224.98

Environmental variables Real GDP per capita (z1 ) Population density (z2 )

Ratio of GDP to the number of inhabitants (million NTD) Ratio of inhabitants per square kilometer (person/km2 )

0.55 629.73

0.04 10.33

Bank-speciﬁc factors Deposits per branch (z3 ) Average return on equity (z4 ) Herﬁndahl-Hirschman index (z5 )

Total deposits to the number of branches (million NTD) Average return over equity (%) Herﬁndahl–Hirschman index of total assets

6236.97 4.64 504.38

722.35 4.67 41.17

Note: All dollar-valued variables have been deﬂated by the consumer price index with base year 2011.

desirable outputs are investments (y1 ), composed of government and corporate securities, the sum of short- and long-term loans (y2 ), and non-interest revenues (y3 ), comprising services charges on loans, transactions, and income from renting and ﬁduciary activities, and commissions. Moreover, we classify non-performing loans (b) as the single undesirable output that is a by-product of various forms of loans granted by the bank to its customers. All of the above variables, except for labor, are measured in terms of millions of New Taiwan dollars (NTD) and are deﬂated by the GDP deﬂator of Taiwan with the base year of 2011. 4.2. Environmental variables Following Allen and Rai (1996), Dietsch and Lozano-Vivas (2000), Huang, Shen, Chen, and Tseng (2011), Lozano-Vivas, Pastor, and Hasan (2001), and Lozano-Vivas, Pastor, and Pastor (2002), this study identiﬁes macroeconomic variables, regulatory conditions, as well as the availability of bank services as environmental variables that affect banks’ efﬁciency. Speciﬁcally, we associate ﬁve environmental variables with the inefﬁciency term as follows. 4.2.1. Real GDP per capita (IC) Ratio of Taiwan’s real GDP to its population. This macroeconomic variable serves as an indicator of overall economic conditions, inﬂuencing deposits, loans, and off-balance activities. Therefore, it may contribute to an increase or decrease in bank efﬁciency. A higher IC value shows that banks are facing a favorable atmosphere, because the demand for banks’ services and supply of loanable funds are increasing, prompting interest and proﬁt margins of the banks and managerial efﬁciencies as well. Conversely, banks in countries with higher IC usually face ﬁercer competition in charging interest rates and proﬁt margins, which incur higher operating costs and lower efﬁciency. Thus, the expected sign of IC on efﬁciency is ambiguous. 4.2.2. Population density (PD) Inhabitants per square kilometer. Lozano-Vivas et al. (2001, 2002) assume that a higher PD value tends to lower banks’ operating costs, prompting a bank’s efﬁciency. 4.2.3. Deposits per branch (DB) Ratio of total amounts of deposits to the number of branches. The expected sign of DB on efﬁciency is mixed. Lozano-Vivas et al. (2001, 2002) assume that a higher DB implies higher banking efﬁ-

ciency levels. However, a higher DB level tends to lower a bank’s proﬁt due to higher interest expenditures and/or lower interest rate spreads, which in turn reduce technical efﬁciency. For example, Rojas-Suarez (2001) argues that low spreads in developing countries may signal risky institutions.

4.2.4. Average return on equity (ROE) This variable is calculated across all sample banks for each year, which exhibits the proﬁtability of the entire banking industry in that year, arising possibly from higher technical efﬁciency. Therefore, this indicator is expected to be positively correlated with banks’ efﬁciencies.

4.2.5. Herﬁndahl–Hirschman index (HHI) This standard HHI reﬂects the degrees of market competition and is calculated with respect to total assets. It can have either a positive or negative effect on technical efﬁciency. If market concentration reﬂects consolidation through the survival of more efﬁcient banks and markets remain contestable, then market concentration should be associated with higher efﬁciency (Fries & Taci, 2005; Koutsomanoli-Filippaki et al., 2009a). Conversely, if market concentration reﬂects market power for some banks, then it may increase the costs of the sector due to slack and inefﬁciency. The negative relationship between market power and efﬁciency is known as the “quiet life” hypothesis.6 In sum, variables IC, DB, and HHI exert ambiguous effects on banks’ efﬁciency, while positive effects are expected for the remaining variables of PD and ROE. Table 1 provides variable deﬁnitions and their descriptive statistics. Since most of these variables have relatively large standard deviations, the scale of sample banks differs substantially.

6 Hicks (1935) ﬁrst stressed the “quiet life” hypothesis, and it means that ﬁrms with higher market power put less effort at pursuing cost efﬁciency. The evidence of some empirical studies provides support for this hypothesis, e.g., Berger and Hannan (1997, 1998), whereas some studies are contrary to those of Berger and Hannan’s, e.g., Fu and Heffernan (2009) and Maudos and de Guevara (2007).

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Table 2 Parameter estimates with undesirable outputs. Variable

Parameter

Model I

Model II Coefﬁcient

t-ratio

Intercept x1 x2 x3 x12 x22 x32 x1 x2 x1 x3 x2 x3

˛0 ˛1 ˛2 ˛3 ˛11 ˛22 ˛33 ˛12 ˛13 ˛23

−44.909 −0.004*** −0.007 – 0.006*** 7.7E − 05 – −0.303*** – –

−0.477 −3.650 −0.489 – 4.356 0.065 – −11.676 – –

391.693*** −0.004*** −4.7E − 04 – 0.006*** −9.7E − 05 – −0.312*** – –

4.729 −4.639 −0.038 – 4.823 −0.109 – −14.528 – –

Desirable outputs

y1 y2 y3 y12 y22 y32 y1 y2 y1 y3 y2 y3

ˇ1 ˇ2 ˇ3 ˇ11 ˇ22 ˇ33 ˇ12 ˇ13 ˇ23

−0.009 1.4E − 08*** −3.0E − 08 5.2E − 07 −2.3E − 10 1.6E − 08*** −2.7E − 08 2.0E − 08*** −1.5E − 07*

−1.396 3.972 −0.755 0.833 −0.029 3.544 −0.344 5.536 −1.881

−0.010* 7.6E − 09*** 3.3E − 08 −1.5E − 07 8.4E − 09 1.9E − 08*** −1.6E − 07*** 1.2E − 08*** −2.8E − 07***

−1.799 3.156 1.148 −0.340 1.479 6.132 −2.772 4.924 −5.034

Undesirable output

b1 b21

1 11

1.8E − 05*** −1.0E − 07

7.396 −0.692

1.5E − 05*** −1.5E − 07

9.114 −1.308

Inputs–outputs

y1 x1 y1 x2 y1 x3 y2 x1 y2 x2 y2 x3 y3 x1 y3 x2 y3 x3 b1 x1 b1 x2 b1 x3 b1 y1 b1 y2 b1 y3

11 12 13 21 22 23 31 32 33 11 12 13 11 12 13

−1.3E − 08*** 5.9E − 08* – −1.6E − 08*** 4.3E − 08 – 1.2E − 07 −2.1E − 06* – 2.6E − 08 2.8E − 07 – −1.3E − 07*** −1.9E − 08 −2.4E − 08

−2.756 1.835 – −4.798 1.244 – 1.488 −1.653 – 0.969 1.141 – −3.454 −0.631 −0.026

−1.6E − 08*** 4.8E − 08*** – −9.1E − 09*** −2.4E − 08 – 2.8E − 07*** −3.6E − 06*** – −1.8E − 09 6.3E − 08 – −6.5E − 08*** −3.9E − 09 3.6E − 06***

−4.997 2.140 – −4.030 −0.963 – 4.856 −3.836 – −0.095 0.324 – −2.396 −0.189 4.100

Technical change

t t2 tx1 tx2 tx3 ty1 ty2 ty3 tb1

ı1 ı2

1 2 3 1

−45.588* 7.890** 3.3E − 04*** −0.003** – −2.1E − 04 −2.1E − 04 −0.015*** 0.003***

−1.699 2.053 2.477 −2.044 – −1.549 −1.534 −4.681 2.973

−100.244*** 11.535*** 1.7E − 04* −0.001 – −1.5E − 04 −8.2E − 05 −0.009*** 0.002***

−5.493 4.761 1.719 −0.882 – −1.531 −0.847 −4.015 2.474

Constant IC PD DB ROE HHI

z0 z1 z2 z3 z4 z5

4.186*** 21.499*** −9.606*** 0.437 −66.127* 5.895

2.825 2.771 −3.296 0.687 −1.938 0.682

2

200,000.050*** 0.228***

1,314,726.200 3.873

100,226.080*** 0.286*** 0.076***

255.766 8.499 7.381

Inputs

Zs

Other ML parameters

1 2 3

Coefﬁcient

t-ratio

Number of observations Log-likelihood function * ** ***

589 −4365.048

589 −4270.939

Denotes signiﬁcance at the 10% level. Denotes signiﬁcance at the 5% level. Denotes signiﬁcance at the 1% level.

5. Empirical results 5.1. Efﬁciency estimates We estimate the quadratic form of DDF that includes the undesirable output, under the framework of Battese and Coelli (1992, 1995), respectively. The former is referred to as Model I and the

latter as Model II. Models III and IV are similar to the ﬁrst two models, but exclude the undesirable output from DDF. Using Frontier 4.1 software (Coelli, 1996), we estimate (6) and (15). Table 2 presents the parameter estimates of the stochastic DDF of (6). More than one half of the parameter estimates attain statistical signiﬁcance at least at the 10% level.

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The coefﬁcient of the variable IC has a positive sign, implying that a large IC deteriorates banking efﬁciency. This may be attributed to the fact that the more developed the economy is, the higher the operating and ﬁnancial costs banks incur when supplying a given level of services (Dietsch & Lozano-Vivas, 2000). The variable of population density (PD) is found to be signiﬁcantly and negatively correlated with technical inefﬁciency, which is consistent with Lozano-Vivas et al. (2001, 2002). Deposits per branch (DB) have a positive effect on technical inefﬁciency. A higher amount of deposits per branch reduces banking efﬁciency, due possibly to the substantial decrease in the interest rate spreads in Taiwan during the sample period. The net interest margin in Taiwan is quite stable and ranges from 2.90% in 1997 to 2.99% in 2000. It reaches a maximum value of 3.15% in 2002, but then descends swiftly to 1.23% in 2009. ROE is signiﬁcantly and negatively correlated with the inefﬁciency term, implying that higher proﬁtability causes higher efﬁciency. Moreover, HHI is positively associated with inefﬁciency, suggesting that banks in a more concentrated market are operating less efﬁciently, which supports the quiet life hypothesis. The evidence is not consistent with Fu and Heffernan (2009) and Maudos and de Guevara (2007), who claim that an increase in the degree of market concentration leads to market selection and consolidation through the survival of the most efﬁcient ﬁnancial institutions. However, this ﬁnding is consistent with Berger and Hannan (1997, 1998). Table B1 in Appendix B presents coefﬁcient estimates of Models III and IV. Two-thirds of the parameter estimates are signiﬁcant, and the signs of the environmental variables in Model III are the same as those in Model I. Table 3 presents technical inefﬁciency scores for each sample T (x, y, b; 1, 1, 1) is equal to year. The estimated mean value of D 70.91 in Model I. Given our directional vector g = (1, 1, 1), this mean inefﬁciency value indicates that desirable outputs should be expanded by 70.91 units (measured by number of employees), while inputs and the undesirable output should be contracted by 70.91 units, if the representative bank operates efﬁciently. It is apparent that the average inefﬁciency estimates of Models I and II are lower than those of Models III and IV, respectively, implying that the exclusion of economic bad outputs from DDF tends to overestimate the inefﬁciency scores. In addition, the average inefﬁciency measure of Model I is less than that of Model II, implying that the omission of environmental variables is apt to exaggerate managerial inefﬁciency. The foregoing reﬂects the importance of including both undesirables and the environment in DDF. Fig. 1 draws those average inefﬁciency measures for the four models. Models I and III show that the average technical inefﬁciency peaks in 2002, 2006, and 2009. The ratio of NPLs to total loans of Taiwan’s banking sector rose from 0.93% in 1990 to 7.48% in 2001, due to the domestic ﬁnancial crisis in 1999 and the dot-com bubble in 2001. To boost the performance of banks, Taiwan’s authorities launched “FFR” from 2002 to 2003, which appears to help reduce the inefﬁciency measure from 2003 to 2005. During 2005–2006, a number of private banks encountered serious bad debts due to the over-issuance of credit cards and cash cards to unqualiﬁed people. This eroded those banks’ proﬁts and deteriorated efﬁciency. The increase in inefﬁciency level from 2007 to 2009 reﬂects the subprime mortgage crisis.7 Models II and IV reveal that average technical inefﬁciencies are decreasing over time, while Models I and III show reverse trends. In 2006, the average inefﬁciency scores of Models II and IV peaked at 318.65 and 481.11, respectively. FFR (2002–2003) appears to have

7 These banks are almost all private, medium, or large and FHC banks (e.g., Taishin and Chinatrust).

7

Table 3 Average inefﬁciency scores by year. Year

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 1999–2012

With undesirable outputs

Without undesirable outputs

Model I

Model II

Model III

Model IV

40.39 39.70 39.36 85.35 44.83 30.85 42.51 101.14 98.16 138.95 154.46 80.93 81.65 69.96 70.91

565.96 457.90 411.68 352.35 339.18 293.42 302.70 318.65 261.34 232.14 202.20 157.14 158.44 153.54 315.86

164.44 157.88 151.39 214.98 175.75 145.76 194.44 291.45 270.90 295.26 320.77 268.78 290.71 281.13 221.75

520.98 433.78 409.26 381.87 402.16 370.82 426.68 481.11 417.42 388.11 352.67 294.37 318.71 318.72 399.13

a beneﬁciary effect on technical efﬁciency in the short run, except for Model IV. 5.2. The input distance function To highlight the advantage of DDF, we estimate the conventional input distance frontier of (13) with the results shown in Table 4.8 Most of the coefﬁcient estimates are accurately estimated. As far as the environmental variables are concerned, the signs of variables IC, PD, DB, and HHI differ from those of DDF, and the coefﬁcient of DB is found to be insigniﬁcant. The effect of ROE on technical inefﬁciency is signiﬁcantly negative, which is consistent with Cavallo and Rossi (2002) for German and Italian banks. This suggests that in these countries higher proﬁtability improves efﬁciency. These ﬁgures indicate two empirical implications. One is associated with the model speciﬁcation. In contrast to the conventional output distance function that seeks to increase both desirable and undesirable outputs (if any), DDF simultaneously allows for the expansion of the desirables and the contraction of the undesirables. The other one is that the omission of an important explanatory variable, i.e., the undesirable output, may bias the parameter estimates (Chen, 2012). The overall average values of technical efﬁciency for Models V and VI are equal to 0.9034 and 0.8461, respectively, and the annual average efﬁciency scores are reported in Table 5. These two models give somewhat close mean efﬁciency measures, as opposed to the DDF Models I and II. To be fully efﬁcient, sample banks are suggested to reduce 10.69% and 18.19% of their current input mix. Similar to Hsiao et al. (2010), the mean efﬁciency value of Model V during the pre-reform period is equal to 0.9033, worsens to 0.8771 during the reform period, and improves to 0.9064 and 0.9151 during the post-reform periods I and II, respectively. Fig. 2 draws the annual average technical efﬁciency scores for Models V and VI. The average efﬁciency scores of Model V oscillate in a wide scope between 0.8614 in 2001 and 0.9428 in 2007 over the transition period without a clear trend. Conversely, the efﬁciency scores of Model VI show a gradually increasing trend. Since estimates in Tables 3 and 5 are not directly comparable, we transform the average inefﬁciency scores implied by Table 5 into the same units as in Table 3, i.e., the number of employees.9 Table 6

8 We also estimate the output distance frontier, but the results are not shown due to their similarity to the input distance frontier. 9 Battese et al. (2000) and Kumbhakar et al. (2002) adopt a translog stochastic frontier labor-use model to estimate the labor-use requirements. They ﬁnd that the technical inefﬁciencies of labor use in Swedish banks are apparent, and the overall mean inefﬁciency is estimated to be about 12–16%.

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Model I

Model II

Model III

Model IV

600 500 400 300 200 100 0 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Fig. 1. Average inefﬁciency estimates over time.

Table 4 Stochastic input distance function estimations. Variable

Parameter

Coefﬁcient

t-ratio

Coefﬁcient

t-ratio

Intercept ln x˜ 1 ln x˜ 2 2 (ln x˜ 1 ) 2 (ln x˜ 2 ) (ln x˜ 1 ) × (ln x˜ 2 )

a0 a1 a2 a11 a22 a12

−4.473*** 0.181 −0.451* 1.221*** −0.654*** −0.589***

−3.861 0.549 −1.655 9.702 −2.672 −3.413

−10.962*** −1.232*** −0.022 0.150 1.847*** −0.581***

−11.274 −4.368 −0.101 1.536 8.378 −4.204

Outputs

ln y1 ln y2 ln y3 2 (ln y1 ) 2 (ln y2 ) 2 (ln y3 ) (ln y1 ) (ln y2 ) (ln y1 ) (ln y3 ) (ln y2 ) (ln y3 )

b1 b2 b3 b11 b22 b33 b12 b13 b23

0.335*** 0.057 −0.144*** 0.141*** −0.118*** −0.005 −0.096*** 0.153*** −0.115***

5.933 1.043 −2.831 10.028 −5.013 −0.410 −2.536 5.600 −5.712

0.170*** −0.005 −0.068* −0.012 0.050*** −0.004 −0.434*** 0.118*** −0.060***

4.284 −0.119 −1.837 −1.226 2.826 −0.525 −12.501 5.858 −3.947

Inputs–outputs

(ln (ln (ln (ln (ln (ln

x˜ 1 ) (ln x˜ 1 ) (ln x˜ 1 ) (ln x˜ 2 ) (ln x˜ 2 ) (ln x˜ 2 ) (ln

c11 c12 c13 c21 c22 c23

−0.247*** 0.189*** −0.077** 0.007 0.036 −0.028

−8.519 4.058 −2.037 0.314 1.060 −1.171

−0.141*** 0.263*** −0.073*** 0.023 0.011 −0.037***

−6.708 6.640 −2.621 1.614 0.421 −2.228

Technical change

t t2 (ln (ln (ln (ln (ln

x˜ 1 ) t x˜ 2 ) t y1 ) t y2 ) t y3 ) t

j0 j00 1 2 1 2 3

−0.128*** 3.3E − 04 −0.009 −0.004 −0.004* 0.025*** −0.014***

−4.275 0.335 −1.241 −1.007 −1.897 5.713 −4.964

−0.115*** 0.003*** −0.004 0.005 2.0E − 04 0.013*** −0.009***

−5.609 3.545 −0.791 1.531 0.107 4.179 −4.512

Constant IC PD DB ROE HHI

z0 z1 z2 z3 z4 z5

−98.021*** −38.232*** 0.209*** −1.4E − 04 −0.034*** −0.028***

−3.757 −3.349 3.685 −0.915 −3.173 −2.992

2

0.298*** 0.951***

4.608 83.931

0.038*** 0.788*** 0.013***

23.159 81.749 2.253

Inputs

Zs

Other ML parameters

Number of observations Log-likelihood function * ** ***

y1 ) y2 ) y3 ) y1 ) y2 ) y3 )

Model V

588 250.757

Model VI

588 411.450

Denotes signiﬁcance at the 10% level. Denotes signiﬁcance at the 5% level. Denotes signiﬁcance at the 1% level.

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Fig. 2. Average technical efﬁciency in Models V and VI.

Table 5 Average technical efﬁciency estimates by year. Year

Model V

Model VI

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.9259 0.9239 0.8614 0.8650 0.8901 0.8939 0.8804 0.9158 0.9428 0.9167 0.9010 0.9292 0.9167 0.9118 0.9033 0.8771 0.9064 0.9151 0.9034

0.8294 0.8330 0.8346 0.8351 0.8421 0.8484 0.8480 0.8467 0.8530 0.8547 0.8581 0.8598 0.8614 0.8630 0.8324 0.8385 0.8489 0.8594 0.8461

Table 6 Average technical inefﬁciency over time. Year

Model I

Model II

Model V

Model VI

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 1999–2012

40.39 39.70 39.36 85.35 44.83 30.85 42.51 101.14 98.16 138.95 154.46 80.93 81.65 69.96 70.91

565.96 457.90 411.68 352.35 339.18 293.42 302.70 318.65 261.34 232.14 202.20 157.14 158.44 153.54 315.86

149.20 163.45 294.21 309.89 298.73 313.55 401.28 280.22 205.82 299.51 390.88 281.71 312.12 340.64 284.85

365.50 369.57 370.76 389.63 433.71 471.97 539.91 562.43 599.15 577.80 569.98 587.31 596.21 590.00 488.06

lists the average technical inefﬁciency measures in terms of number of employees for Models I, II, V, and VI. On the basis of Models V and VI, the average technical inefﬁciency scores are respectively 284.85 and 488.06, which exceed the corresponding mean values of 70.91 and 315.86 from Models I and II, respectively. Again, the stan-

dard input distance function is inclined to overestimate technical inefﬁciencies, due partially to its failure to allow for the expansion of desirable outputs and the contraction of undesirable outputs. 5.3. Efﬁciency scores for various classiﬁcations To gain further insights into the impact of a bank’s ownership and organizational structure on efﬁciencies, we classify the entire sample into two different forms of ownership and organizational structure, respectively.10 5.3.1. Ownership effects on efﬁciency To eliminate the size effect, we translate the inefﬁciency value to the efﬁciency score, which is calculated as one minus the ratio of inefﬁciency value to labor. Fig. 3 shows the average efﬁciency scores over time for different types of ownership. Both models of I and III show that public banks are more efﬁcient than private banks, especially during the post-FFR II period, and their differences are statistically signiﬁcant, as shown in Table 7. Our results are congruent with Huang et al. (2011), Li et al. (2004), Liang, Yao, Hwang, and Wu (2008), Peng and Wang (2004), and Wu (2008). Li et al. (2004) and Liang et al. (2008) indicate technical efﬁciencies of (completely or partially) government-owned banks are higher than those of purely private-owned banks. Peng and Wang (2004) and Wu (2008) show that government-owned or controlled banks are the most cost efﬁcient. Huang et al. (2011) also ﬁnd similar evidence in East European (transition) countries. 5.3.2. The effect of organizational structure on efﬁciency On the basis of organizational structure, we split our sample banks into two groups: ﬁnancial holding companies (FHC) and nonﬁnancial holding companies (non-FHC). Banks belonging to FHC are expected to operate more efﬁcient than those of non-FHC, since the former belongs to a large conglomerate. Table 8 conﬁrms the above expectation. The average efﬁciency measure of the FHC banks is signiﬁcantly higher than that of the non-FHC banks. Fig. 4 shows the efﬁciency scores over time across different forms of banking organizational structure. The time patterns of efﬁciency scores for the two types of banks nearly synchronously move

10 We do not list the sample banks by bank ownership and organizational structure. The lists are available upon request from the authors.

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Table 7 The efﬁciency scores and bank ownership. Period

Model I with undesirable output

Model III without undesirable output

Public

Private

Public

Private

Pre-FFR period (1999–2001) Mean No. of banks t-test: Public vs. Private

0.9868 39 5.31*** [0.00]

0.9606 111

0.9492 39 5.57*** [0.00]

0.8478 111

FFR period (2002–2003) Mean No. of banks t-test: Public vs. Private

0.9794 26 3.62*** [0.00]

0.9410 72

0.9422 26 4.27*** [0.00]

0.8257 72

Post-FFR period I (2004–2007) Mean No. of banks t-test: Public vs. Private

0.9835 48 3.81*** [0.00]

0.9557 117

0.9462 48 4.57*** [0.00]

0.8508 117

Post-FFR period II (2008–2012) Mean No. of banks t-test: Public vs. Private

0.9756 55 4.52*** [0.00]

0.9275 121

0.9332 55 4.77*** [0.00]

0.8003 121

Whole period (1999–2012) Mean Std. dev. No. of banks t-test: Public vs. Private

0.9810 0.0208 168 7.69*** [0.00]

0.9464 0.0568 421

0.9420 0.0544 168 9.08*** [0.00]

0.8312 0.1544 421

t-test: Pre-FFR vs. FFR t-test: FFR vs. Post-FFR I t-test: Post-FFR I vs. Post-FFR II

3.27*** [0.00] −2.15** [0.03] 3.37*** [0.00]

1.16 [0.25] −1.33 [0.18] 2.14** [0.03]

Note: The ﬁgures in the brackets stand for p-value. * Denotes signiﬁcance at the 10% level. ** Denotes signiﬁcance at the 5% level. *** Denotes signiﬁcance at the 1% level.

Table 8 The efﬁciency scores and organizational structure. Period

Model I with undesirable output

Model III without undesirable output

Non-FHC

FHC

Non-FHC

FHC

Pre-FFR period (1999–2001) Mean No. of banks t-test: non-FHC vs. FHC

0.9674 147 0.03 [0.97]

0.9669 3

0.8745 147 0.30 [0.77]

0.8560 3

FFR period (2002–2003) Mean No. of banks t-test: non-FHC vs. FHC

0.9451 70 −1.98* [0.05]

0.9665 28

0.8385 70 −2.24** [0.03]

0.9018 28

Post-FFR period I (2004–2007) Mean No. of banks t-test: non-FHC vs. FHC

0.9566 106 −2.87*** [0.00]

0.9767 59

0.8571 106 −2.93*** [0.00]

0.9171 59

Post-FFR period II (2008–2012) Mean No. of banks t-test: non-FHC vs. FHC

0.9226 99 −4.60*** [0.00]

0.9682 77

0.7890 99 −4.62*** [0.00]

0.9097 77

Whole period (1999–2012) Mean Std. dev. No. of banks t-test: non-FHC vs. FHC

0.9505 0.0553 422 −4.38*** [0.00]

0.9709 0.0377 167

0.8441 0.1490 422 5.16*** [0.00]

0.9100 0.1127 167

t-test: Pre-FFR vs. FFR t-test: FFR vs. Post-FFR I t-test: Post-FFR I vs. Post-FFR II

3.27*** [0.00] −2.15** [0.03] 3.37*** [0.00]

1.16 [0.25] −1.33 [0.18] 2.14** [0.03]

Note: The ﬁgures in the brackets stand for p-value. * Denotes signiﬁcance at the 10% level. ** Denotes signiﬁcance at the 5% level. *** Denotes signiﬁcance at the 1% level.

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Model I_Public

Model I_Private

Model III_Public

Model III_Private

11

1.00

0.95

0.90

0.85

0.80

0.75

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Fig. 3. Average efﬁciency scores by ownership in Models I and III.

1.00

Model I_Non-FHC

Model I_FHC

Model III_Non-FHC

Model III_FHC

0.95

0.90

0.85

0.80

0.75 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Fig. 4. Average efﬁciency scores by bank organizational type in Models I and III.

together, and the difference in average efﬁciency score becomes broader after the FFR period in both models.

5.4. The shadow price The shadow price of NPLs can be viewed as the cost that the bank has to spend to deal with the NPLs, measured by the same unit as either Pm or Wn (see Eq. (12)). A higher value of the shadow price leads to a higher cost of NPL disposal, which tends to hurt banks’ performance. We use the price of loans, P2 , to calculate the shadow price of the bad output.11 Table 9 shows that the average shadow prices during the four periods are equal to 0.0019, 0.1310, 0.2882, and 0.3602, respectively. The average shadow price in the pre-FFR period is the lowest among the four periods. Since we do not impose the monotonicity T /∂b1 ≥ 0 for each observarestriction on the bad output, i.e., ∂D T /∂b1 takes tion, as Färe et al. (2005) do, the partial derivative of ∂D

11 We also apply other output and input prices to calculate the shadow price, based on (12). The results are not shown in order to save space.

negative values for a few observations.12 In these cases the ratio of T /∂b1 /∂D T /∂y2 is set to be equal to zero, which leads the shadow ∂D prices of the undesirables to be equal to zero. Moreover, there are T /∂y2 ≤ 0, where the corresponding several observations with ∂D values of the shadow prices are also set to be equal to zero. Since the zero shadow prices mainly occur between 1999 and 2001, we will not discuss the pre-FFR period (1999–2001). Taiwan underwent its own domestic ﬁnancial crisis in 1999, joined WTO, and then faced the challenges of international competition in ﬁnancial markets and the dot-com bubble in 2001. The ratio of NPLs to total loans in Taiwan’s banking industry rose rapidly during this time. After that, the “Financial Holding Company Act” was implemented, and the government revised the “Value-added and Non-value-added Business Tax Act”, cutting the business tax from 5% to 2%. Moreover, the government enforced negotiations between banks and

12 Fukuyama and Weber (2008) also do not impose this non-negativity restriction on bad outputs, i.e., they allow their output frontier to be either positively or negatively sloped with respect to b1 . Feng and Serletis (2014) impose the monotonicity and curvature conditions on the directional output distance function, which is commonly estimated by Bayesian stochastic frontier approach.

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Table 9 Estimates of the shadow price and its components. Period

Shadow price

P2

Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.0019 0.1310 0.2882 0.3602 0.2037

0.0883 0.0641 0.0548 0.0387 0.0610

/∂b ∂D T 1 /∂y ∂D T 2

−0.0246 −2.1821 −5.5385 −10.1609 −4.7491

shadow price

T /∂y2 ∂D

y2

T /∂b1 ∂D

b1

−0.0002 −0.0009 −0.0009 −0.0018 −0.0010

278,837 292,681 362,850 469,464 357,529

3.84E − 05 0.0025 0.0079 0.0171 0.0074

17,987 16,132 7764 3440 10,775

P2

0.60 0.50 0.40 0.30 0.20 0.10 0.00 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 -0.10 Fig. 5. The shadow price and price of loans (P2 ).

debtors, aiming at reducing the operating risk and technical inefﬁciency of banks. These policies helped banks have more resources to eliminate NPLs and promote their managerial abilities. The implementation of these policies is likely to hinder the estimated values T /∂b1 from being non-negative. of ∂D T /∂y2 , Note that the shadow price consists of three items: P2 , ∂D and ∂DT /∂b1 . Table 9 shows the individual estimates. From the FFR T /∂y2 remains constant, ∂D T /∂b1 period to post-FFR period I, ∂D enlarges around three times, while P2 decreases slightly. Summing up the three components, we see that the average shadow price T /∂y2 rises sharply in post-FFR period I. In the last period, both ∂D and ∂DT /∂b1 go up more than twice as much as the former period, accompanied by a decrease in P2 . The overall effect is that the average value of the shadow price increases from 0.2882 to 0.3602. We conclude that the main source stimulating the shadow price comes T /∂b1 , rather than ∂D T /∂y2 . from ∂D Fig. 5 shows that the average price of loans is around 5% and decreases over time. Conversely, the average shadow price of NPLs grows with time until 2008 and then decreases sharply. During the FFR period (2002–2003), the shadow price increases from 0.1087 in 2002 to 0.1553 in 2003. After that period, the shadow prices continue to climb and reach another peak in 2006 due to the “credit card and cash card crisis”. The “credit card and cash card debt crisis” was the result of the over-issuance of credit cards and cash cards by Taiwan banks since 2004, arising from ﬁerce competition in the industry. The bad debts of credit cards and cash cards amounted to NT$800 billion in 2005 and 2006. The average shadow price of NPLs peaks in 2008 and is equal to 0.6587, and then drops to 0.2972 in 2012. The subprime mortgage crisis in the U.S. is the major reason for the rise of the shadow prices, and this has affected Taiwanese banking sectors greatly. When these external events happen, the shadow prices of NPLs could accurately reﬂect the cost of NPLs.

5.4.1. Ownership effects on the shadow price We classify the sample banks on the basis of ownership (private vs. public) and members of a ﬁnancial holding company (FHC) to see

their differences in average shadow prices. Fig. 6 draws the average shadow prices across time for these two forms of banks. The average shadow prices of private banks are more stable and higher than those of public banks, except in 2008 when the U.S. subprime crisis happened. Table 10 shows that the highest average shadow price of private banks is equal to 0.3330 in post-FFR period I, meaning that the “credit card and cash card crisis” hit private banks severely. Post-FFR period II has the second highest shadow price for private banks with a slightly lower average value of 0.3201, while the highest average shadow price for public banks is equal to 0.4954. The average shadow price is lower for public banks, except for post-FFR period II. Our ﬁndings are not consistent with the previous ﬁndings of Li et al. (2009), who note that public banks have to spend more resources than private banks to cut their NPLs. A possible reason is that public banks have already operated for a long time and have great credit, and so they have to compete for loans. They pay a lower cost for NPLs and have better operating efﬁciency. Moreover, public banks have a longer operating life, having abundant experiences to achieve their maximum proﬁt target and to lower shadow price. Based on the above discussion, an increase in the ratio of T /∂b1 to ∂D T /∂y2 would result in an enhancement of the shadow ∂D T /∂b1 /∂D T /∂y2 price. In the FFR period, the absolute value of ∂D is equal to 1.3087 for public banks, which is notably lower than 2.4896 for private banks. Consequently, the shadow price for public banks is about 0.0671 that is signiﬁcantly lower than 0.1535 for private banks. Similar results are found in post-FFR period I. However, the reverse results are reached in post-FFR period II. The T /∂b1 /∂D T /∂y2 for private banks increases to absolute value of ∂D 8.2584, and that of public banks rises substantially to 16.5751. This raises the shadow price of public banks. Table 11 presents the testing results for the differences in the shadow price between private and public banks. It shows that there is no signiﬁcant difference in the entire period of 1999–2012. However, the same tests attain at least the 10% signiﬁcance level in the ﬁrst three sub-periods. One is led to conclude that the “credit card and cash card crisis” did exert a signiﬁcant impact on shadow prices.

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Public

13

Private

Fig. 6. Shadow price by ownership.

Table 10 Estimates of the shadow price and its components by ownership. Period

Shadow price

P2

Public banks Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004k2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.0064 0.0671 0.1594 0.4954 0.1857

0.0808 0.0487 0.0424 0.0275 0.0503

Private banks Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.0003 0.1535 0.3330 0.3201 0.2096

0.0908 0.0695 0.0592 0.0420 0.0645

Table 11 Tests for the differences in shadow prices between public and private banks. Period

t-test

Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

1.73* [0.09] −3.10*** [2.57E − 03] -3.73*** [2.73E − 04] 1.09 [0.28] −0.50 [0.62]

Note: Figures in the brackets stand for p-value. Denotes signiﬁcance at the 10% level. Denotes signiﬁcance at the 5% level. *** Denotes signiﬁcance at the 1% level. * *

/∂b ∂D T 1 /∂y ∂D T 2

T /∂y2 ∂D

y2

T /∂b1 ∂D

b1

−0.0846 −1.3087 −4.3895 −16.5751 −5.7365

0.0006 −0.0002 0.0007 0.0002 0.0004

704,773 708,782 810,042 1,164,943 852,722

0.0001 0.0019 0.0042 0.0114 0.0045

41,503 34,383 15,587 8547 24,343

−0.0040 −2.4896 −5.9382 −8.2584 −4.4207

−0.0004 −0.0011 −0.0015 −0.0024 −0.0014

133,021 146,167 207,304 263,178 192,863

0.0000 0.0027 0.0092 0.0188 0.0083

9936 9706 5043 1925 6263

5.4.2. The effect of organizational structure on the shadow price Fig. 7 displays that the average shadow prices of banks belonging to non-FHC are higher than those of banks belonging to FHC. Table 12 exhibits that the average shadow price of non-FHC banks is equal to 0.2183 that is higher than 0.1647 for FHC banks. This outcome is similar to Ke et al. (2011), who explore the relationship between proﬁt efﬁciency and shadow prices of NPLs for Taiwan’s banking sector spanning 1999 to 2007. Their estimates of the average shadow prices of non-FHC and FHC banks are 0.223 and 0.119, respectively. After the enforcement of the Financial Holding Act in 2001, ﬁnancial institutions have been allowed to operate their business in the ﬁelds of banking, insurance, and securities. The member bank of a ﬁnancial holding company is able to create greater synergy through the efﬁcient mobilization of abundant internal resources

Table 12 Estimates of the shadow price and its components by organizational structure. /∂b ∂D T 1 /∂y ∂D T 2

T /∂y2 ∂D

y2

T /∂b1 ∂D

b1

0.0884 0.0665 0.0554 0.0438 0.0667

−0.0251 −2.5528 −7.1226 −12.1747 −4.8904

−0.0002 −0.0012 −0.0014 −0.0026 −0.0012

277,199 253,407 248,213 212,310 251,670

3.92E − 05 0.0031 0.0102 0.0211 0.0077

17,776 18,683 7367 2216 11,921

0.0824 0.0582 0.0538 0.0316 0.0458

0 −1.2817 −2.7380 −7.3605 −4.3728

−0.0004 0.0001 −0.0001 −0.0008 −0.0003

358,537 388,062 565,511 827,069 639,353

0 0.0010 0.0039 0.0116 0.0065

28,211 9937 8467 5142 7723

Period

Shadow price

P2

Non-FHC banks Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004k2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.0019 0.1519 0.3689 0.4566 0.2183

FHC banks Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0 0.0803 0.1456 0.2261 0.1647

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Non-FHC

FHC

Fig. 7. Shadow price by organizational structure.

Table 13 Tests for the differences in shadow prices between non-FHC and FHC banks. Period

t-test

Pre-FFR period (1999–2001) FFR period (2002–2003) Post-FFR period I (2004–2007) Post-FFR period II (2008–2012) Whole period (1999–2012)

0.18 [0.86] 2.63** [0.01] 5.52*** [1.45E − 07] 1.69* [0.09] 1.15 [0.25]

Note: Figures in the brackets stand for p-value. * Denotes signiﬁcance at the 10% level. ** Denotes signiﬁcance at the 5% level. *** Denotes signiﬁcance at the 1% level.

and can diversify its array of ﬁnancial products. A lower value of the average shadow price for FHC banks implies that these banks can lower their operating costs. Moreover, FHC banks can easily diversify their ﬁnancial products and enjoy scale economies in order to reduce production costs and improve operating performance. We next carry out the t-test for the differences in the shadow prices between the two types of banks. Table 13 reports the results. Although their average shadow prices are found to be close to each other in the entire sample period, they are signiﬁcantly different in the latter three sub-periods at least at the 10% level. 6. Conclusion This research investigates the impact of FFR policy on the operating efﬁciency of banks in Taiwan during the period 1999–2012 using the stochastic directional technology distance function. Compared to the conventional distance function, DDF simultaneously allows for the expansion of the desirables and the contraction of the undesirables. Following Koutsomanoli-Filippaki et al. (2009a), and differing from them, we include undesirable outputs in DDF to depict a bank’s true production activities. We estimate the quadratic form of DDF, which includes undesirable output, under the framework of Battese and Coelli (1992, 1995), respectively. We also provide the estimation results without considering undesirable output from DDF, for a comparison. To examine whether the policy does improve the technical efﬁciency of banks in Taiwan, we consequently divide the sample period into four sub-periods: preFFR period (1999–2001), FFR period (2002–2003), post-FFR period I (2004–2007), and post-FFR period II (2008–2012). We attain several interesting ﬁndings. First, the model speciﬁcation considering an undesirable output can portray a bank’s frontier better, whereas neglecting an undesirable output might induce an overestimation of the technical inefﬁciency. We ﬁnd that the banks

have a lower technical inefﬁciency on average with Models I and II compared to the other models, implying that the exclusion of economic bad outputs from DDF tends to overestimate inefﬁciency scores. In addition, the average inefﬁciency measure of Model I is less than that of Model II, implying that the omission of environmental variables is apt to exaggerate managerial inefﬁciency. The foregoing reﬂects the importance of including both undesirables and environment variables in the DDF. Second, the results of the current study have implications for the design of public policy by providing evidence to policymakers of FFR’s effectiveness. Prior to 2002, banks’ technical inefﬁciency exhibits a gradual upward trend, followed by a downward trend during the FFR period. These results suggest that the improved efﬁciency in the FFR period is possibly due to enhanced banking and beneﬁts obtained from compliance with FFR. After the FFR period, the inefﬁciency scores deteriorate sharply, especially during the “credit card and cash card crisis” in 2006 and “the subprime mortgage crisis” in 2008. Third, the results in this article also report differences in the efﬁciency performance of banks with different ownership and organizational structures. We examine the difference of technical efﬁciency between public banks and private banks. Results show that public banks are more efﬁcient than private banks, because public banks in Taiwan are older and have stronger relationships with business. Banks belonging to an FHC may operate more efﬁciently than those belonging to a non-FHC, since the former belongs to a large conglomerate. Finally, we also estimate the shadow price of NPLs from DDF. We classify the sample banks on the basis of ownership and members of a ﬁnancial holding company in order to relate these features to average shadow prices. The empirical results demonstrate that the average shadow prices of private banks are more stable and higher than those of public banks. The average shadow prices of non-FHC banks are higher than those of FHC banks. In sum, private and nonFHC banks tend to have higher shadow prices, whereas public and FHC banks are related to lower shadow prices, except in 2008 when the U.S. subprime crisis happened. The results herein suggest three avenues for future research. First, we can further explore productivity performance of Taiwan’s banking industry. Second, we can aim to gain further insights into the operating efﬁciencies of FHC and non-FHC banks using the metafrontier approach under the framework of DDF. Third, while we choose to study the efﬁciency effects of FFR, future research can also examine the effects of such regulatory changes on accounting, i.e., IFRS, as well as mergers and acquisitions.

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Appendix A. Distance functions and shadow prices The DDF

−x3 = ˛0 +

= ˛0 +

N

an xn +

n=1

+

N N 1

2

˛nn xn xn +

n=1 n =1

M N

+

mn ym xn +

n=1 m=1

M M 1

2

ni bi xn +

+

n=1

I M

I I 1

2

N−1 N−1

i bi 1 2

+

I I

ii bi bi

i=1 i =1

+

I N−1

n=1

m=1

ˇm (ym + x3 ) +

(A1)

I

+

M M

ˇmm (ym + x3 )(ym + x3 )

m=1 m =1

i i (bi − x3 )(bi − x3 ) +

M N−1

n=1

ni (bi − x3 )(xn − x3 ) +

1 ı2 t 2 + 2

m=1 N−1 n t(xn

− x3 ) +

mn (ym + x3 )(xn − x3 )

m=1

I M

n=1

i tbi + v.

1 2

˛nn (xn − x3 )(xn − x3 ) +

mi bi ym + ı1 t 2

i=1

i (bi − x3 )

I=1

i=1

+ı1 t 2 +

I

m=1

i =1

i=1

I

m tym +

M

n =1

n=1

m=1 i=1

M

n txn

I

1 2

+

I=1

ˇmm ym ym +

n=1 i=1

1 + ı2 t 2 + 2

ˇm ym +

m=1

m=1 m =1

I N

N

M

˛n (xn − x3 ) +

n=1

To empirically estimate the DDF, a quadratic DDF is commonly parameterized as follow: → D T (x, y, b; gx , gy , gb , t, )

N−1

mi (bi − x3 )(ym + x3 )

i=1

M

m t(ym + x3 )

m=1

(A5)

i t(bi − x3 ) + v − u.

i=1

Here, = (˛, ˇ, , , , , ı, , , ) is a vector of unknown parameters to be estimated and v is an error term. It is important to note that some theoretical restrictions have to be imposed on Eq. (A1). First of all, the symmetry conditions on the second-order terms require: (i) ˛nn = ˛n n , n = / n (ii) ˇmm = ˇm m , m = / m (iii)ii = i i , i = /

(A2)

−

N

˛n +

n=1

(ii) −

N

M

We deﬁne the proﬁt function as:

mn +

−

ii −

n n=1

+

ˇmm −

in +

M

n=1

m=1 I

m −

→

(x − DT (x, y, b; gx , gy , gb )gx , y + DT (x, y, b; gx , gy , gb )gy ,

n.

→

b − DT (x, y, b; gx , gy , gb )gb ) im = 0,for all

m.

(A3)

i=1

M m=1

→

in = 0, for all

I

im = 0, for all

is feasible, we have: → R(w, p, q) − (py − qb − wx) ≥ DT (x, y, b; gx , gy , gb ). wgx + pgy + qgb

i.

i = 0,

→

DT (x, y, b; gx , gy , gb ) = inf p,q

The translation property is described as follows: →

DT (x − ˇgx , y + ˇgy , b − ˇgb ; gx , gy , gb ) = DT (x, y, b; gx , gy , gb ) − ˇ, ˇ ≥ 0.

(A7)

If T is a closed, non-empty convex set, then the DDF can be obtained from the proﬁt function as (Färe & Grosskopf, 2005):

i=1

→

(A6)

where w is the vector of input prices, p is the vector of desirable output prices, and q is the vector of undesirable output prices. Since R(w, p, q) ≥ py − qb − wx for all feasible (x, y, b) ∈ T and

i = −1,

I

R(w, p, q) = max{py − wx − qb : (x, y, b) ∈ T },

i=1

m =1 N

i =1 N

(v)

mn −

m=1 M

n=1 I

(iv) −

I i=1

n =1 N

(iii) −

ˇm −

m=1 M

˛nn +

The shadow price of undesirable outputs

i .

Second, we impose the following conditions to meet the translation property of DDF:

(i)

Here, u is a one-sided error, which reﬂects the technical inefﬁciency of a bank and is assumed to be independent of v, and the composite error is deﬁned as ε = v − u. Note that other inputs, or outputs, or undesirable outputs can be chosen to be equal to ˇ.

(A4)

R(w, p, q) − (py − qb − wx) . wgx + pgy + qgb

(A8)

Assuming Eq. (A8) is differentiable, we apply the envelop theorem to yield the shadow prices. Suppose that the mth desirable output price and the nth input price are known (or equal to the shadow price). The shadow pricing formulae then take the form: →

Eq. (A4) says that if we translate the input, desirable output, and undesirable output vector (x, y, b) into (x − ˇgx , y + ˇgy , b − ˇgb ), then the value of DDF is reduced by the scalar ˇ. We have to impose the symmetric and translation properties into Eq. (A1) to yield the estimable regression equation. After set-

pm = −

ting ˇ = x3 and deﬁning DT (x, y, b; gx , gy , gb , t, ) = u ≥ 0, Eq. (A1) can be written as:

qi =

∂DT (x, y, b; gx , gy , gb ) × (wgx + pgy + qgb ), ∀m. ∂ym →

∂DT (x, y, b; gx , gy , gb ) × (wgx + pgy + qgb ), ∀n. wn = ∂xn

(A9)

→

→

∂DT (x, y, b; gx , gy , gb ) × (wgx + pgy + qgb ), ∀i. ∂bi

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Here, we assume wgx + pgy + qgb = / 0. Taking the ratio of qi to pm and qi to wn and rearranging terms, the shadow prices of bad outputs are computed either by: →

qi = pm ×

∂DT (x, y, b; gx , gy , gb )/∂bi

,∀

→

i and m.

(A10)

∂DT (x, y, b; gx , gy , gb )/∂ym →

qi = wn ×

→

J

aj = 1,

j

J

ajk =

, ∀ i and n.

∂DT (x, y, b; gx , gy , gb )/xn

j

The input distance function The standard translog input distance function with M outputs and J inputs is formulated as:

1n D = a0 +

J

aj 1n(xj ) +

j=1

1 2

+

M M

m=1

j=1

bm 1n(ym ) +

m=1

bml 1n(ym )1n(yl ) +

l=1

J

+

M

J M

−ln x3 = a0 +

j

jt = 0, ∀k, m.

J−1

aj ln(xj /x3 ) +

M

cjm 1n(xj )1n ym + j0 t +

(A12)

1 1 ajk ln(xj /x3 )ln(xk /x3 ) + bml ln ym ln yl 2 2

J−1 M

1 j00 t 2 2

bm lnym

m=1 M

+

M

m=1 l=1

j=1 k=1

k=1

cjm ln(xj /x3 )ln ym + j0 t +

1 j00 t 2 2

j=1 m=1

m=1

J−1

mt t1n(ym ) + V

J j

j=1

+

ajk 1n(xj )1n(xk )

M

jt t1n(xj ) +

cjm =

J−1 J−1

J J

j=1

j=1

1 2

J

In addition, symmetry restrictions require that ajk = akj , ∀j = / k / m. and blm = bml , ∀l = After imposing the restriction of linear homogeneity in inputs by normalizing the inputs and D by an input, say x3 , and letting 1n D = U (Färe & Primont, 1995; Karagiannis et al., 2004; Kumbhakar & Wang, 2007), Eq. (A11) becomes:

or

∂DT (x, y, b; gx , gy , gb )/∂bi

has to be linearly homogeneous in inputs, which requires Eq. (A11) to satisfy:

(A11)

m=1

where (a, b, c, j, , ) are unknown parameters and V ∼iid N (0, V2 ) denotes the error term. Readers are suggested to refer to Färe and Primont (1995) for a detailed discussion on the properties of the input and the output distance functions. An input distance function

+

jt t ln(xj /x3 ) +

j=2

M

mt t lnym + V − U.

(A13)

m=1

Appendix B.

Please cite this article in press as: Huang, T. -H., & Chung, M.-T. Do undesirables matter on the examination of banking efﬁciency using stochastic directional distance functions. The Quarterly Review of Economics and Finance (2016), http://dx.doi.org/10.1016/j.qref.2016.09.007

G Model

ARTICLE IN PRESS

QUAECO-983; No. of Pages 18

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17

Table B1 Parameter estimates of the stochastic DDF without undesirables. Variables

Model III

Model IV

Coefﬁcients

t-ratio

Coefﬁcients

t-ratio

Intercept x1 x2 x3 x12 x22 x32 x1 x2 x1 x3 x2 x3

˛0 ˛1 ˛2 ˛3 ˛11 ˛22 ˛33 ˛12 ˛13 ˛23

−72.739 −0.004*** 0.002 – 0.004*** −3.3E − 04 – −0.299*** – –

−0.640 −4.632 0.213 – 4.249 −0.379 – −14.673 – –

220.832*** −0.004*** 0.002 – 0.004*** −2.8E − 04 – −0.262*** – –

2.814 −5.391 0.149 – 4.969 −0.382 – −14.162 – –

Desirable outputs

y1 y2 y3 y12 y22 y32 y1 y2 y1 y3 y2 y3

ˇ1 ˇ2 ˇ3 ˇ11 ˇ22 ˇ33 ˇ12 ˇ13 ˇ23

1.3E − 08*** 1.2E − 09 2.6E − 07 1.5E − 08** 2.0E − 08*** −4.7E − 08 1.8E − 08*** −2.0E − 07*** 1.8E − 05***

3.868 0.032 0.483 2.264 5.041 −0.629 5.517 −2.646 8.491

6.8E − 09*** 2.7E − 08 1.5E − 08 1.8E − 08*** 2.0E − 08*** −2.0E − 07*** 9.9E − 09*** −2.9E − 07*** 1.1E − 05***

2.625 0.911 0.033 3.220 5.795 −3.262 3.840 −4.377 5.626

Undesirable outputs

b1 b21

1 11

– –

– –

– –

– –

Cross-products

y1 x1 y1 x2 y1 x3 y2 x1 y2 x2 y2 x3 y3 x1 y3 x2 y3 x3 b1 x1 b1 x2 b1 x3 b1 y1 b1 y2 b1 y3

11 12 13 21 22 23 31 32 33 11 12 13 11 12 13

−1.9E − 08*** 4.1E − 08 – −1.5E − 08*** 2.3E − 08 – 1.7E − 07** −2.4E − 06** – – – – – – –

−4.665 1.376 – −4.704 0.683 – 2.196 −2.001 – – – – – – –

−1.8E − 08*** 3.3E − 08 – −7.6E − 09*** −2.6E − 08 – 3.1E − 07*** −2.7E − 06*** – – – – – – –

−5.329 1.476 – −3.127 −0.977 – 4.503 −2.396 – – – – – – –

Technical change

t t2 tx1 tx2 tx3 ty1 ty2 ty3 tb1

ı1 ı2

1 2 3 1

10.105 0.987 3.2E − 04*** −0.004*** – −2.2E − 05 −1.7E − 04 −0.016*** –

0.444 0.277 3.178 −3.706 – −0.231 −1.625 −6.310 –

−55.632*** 7.869*** 1.0E − 04 −3.0E − 04 – −4.7E − 05 −5.6E − 05 −0.010*** –

−3.469 3.624 1.200 −0.280 – −0.650 −0.615 −4.477 –

Constant IC PD DB ROE HHI

z0 z1 z2 z3 z4 z5

−61.826 380.274 −2.444 0.160 −15.778 1.153

−0.606 0.620 −1.570 0.993 −1.427 0.758

2

190,004.260*** 0.244*

27,193.692 1.943

200,000.650*** 0.574*** 0.024***

172,373.770 22.162 2.573

Inputs

Zs

Other ML parameters

1 2 3

Number of observations Log-likelihood function * ** ***

589 −4379.504

589 −4256.692

Denotes signiﬁcance at the 10% level. Denotes signiﬁcance at the 5% level. Denotes signiﬁcance at the 1% level.

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Please cite this article in press as: Huang, T. -H., & Chung, M.-T. Do undesirables matter on the examination of banking efﬁciency using stochastic directional distance functions. The Quarterly Review of Economics and Finance (2016), http://dx.doi.org/10.1016/j.qref.2016.09.007

Do undesirables matter on the examination of banking efficiency using stochastic directional distance functions

Do undesirables matter on the examination of banking efficiency using stochastic directional distance functions

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