Review of Quantitative Finance and Accounting, 20: 385413, 2003c 2003 Kluwer Academic Publishers. Manufactured in The Netherlands.

Banking Mergers: The Impact of FinancialLiberalization on the Taiwanese Banking IndustryPEIYI YUDepartment of Banking and Finance, National Chi Nan University, TaiwanE-mail: peiyi yu@yahoo.com

BAC VAN LUULandesbank Baden-Wurttemberg, 4121 Bond Markets, Am Hauptbahnhof 2, 70191 Stuttgart, GermanyE-mail: vanluu@yahoo.de

Abstract. The objective of this paper is to examine the nature of the Taiwanese banking sector and to analyzethe impact of financial liberalization on the Taiwanese banking industry. We present empirical evidence to showthat the recent wave of bank mergers observed in other countries is also suitable for Taiwan. Based on empiricalresults for overall economies of scale and expansion path subadditivity, Taiwanese banks should obtain the benefitof scale economies by merging with other banks rather than expanding by opening more branches. Furthermore,we show that the Relative Market Power hypothesiswhich postulates that greater market shares lead to higherprofitabilityfinds empirical support in Taiwanese banking data after financial reforms were enacted.

Key words: scale economies, scope economies, cost efficiency, merger

JEL Classification: C33, G21, G14, L11

Introduction

In the 1980s, technological advances in communication and information systems, progres-sive elimination of official barriers to capital flows, and intensification of competition in anincreasingly deregulated environment were identified as three major forces to shape the newlandscape for global financial markets. As a matter of fact, these forces have either directlyor indirectly accelerated the process of financial liberalization in Taiwan.1 Moreover, likemany of the governments in Southeast Asia, Taiwan foresaw that after joining the WorldTrade Organisation (WTO), the opening of the market and foreign competition could dec-imate local banks unless it first reformed its financial markets internally. Thus, Taiwansaggressive banking deregulation program was launched in the early 1990s. For instance, theTaiwanese government allowed sixteen private commercial banks to be established since1991 and domestic banks were granted permission to conduct stock brokering, trading, andinvestment banking activities through subsidiaries.2

In this paper, we examine whether the recent wave of bank mergers observed in othercountries is suitable for Taiwan by evaluating the competitve forces that impact on theTaiwanese banking sector. These competitive issues are discussed from three different

Corresponding author.

386 YU AND LUU

perspectives: scale and scope economies, cost efficiency and the tests of market-power andefficient-structure hypotheses. Overall economies of scale (OES) are important for bankmanagers and regulators. For example, if overall scale diseconomies are found to exist, thenpolicies that encourage mergers or expansion of branch numbers should be reconsidered. Inthis paper, we choose expansion path subadditivity as a more appropriate method than thetraditional scope economy measure for examining the cost structure of banking markets.If expansion path subadditivity, a concept proposed by Berger, Hanweck and Humphrey(1987), is found to exist, a combination of output is produced more cost-efficiently by alarge bank than any combination of smaller ones. Breaking up large banks may thus leadto higher costs for consumers. Moreover, from the existence of OES and expansion pathsubadditivity it can be inferred that Taiwanese banks should choose to merge with otherbanks rather than to expand their network by opening more branches, if they want to obtainthe benefit from scale economies. Finally, we investigate whether the market-power (MP)and efficient-structure (ES) hypothesis offer explanations of the observed variation in bankprofitability. We apply a model3 similar to Bergers (1995) to study the extent to whichthe ES and MP hypotheses can explain the Taiwanese banking market, and still add directmeasures of both X-efficiency and scale efficiency to the empirical analysis.4 Based onthese studies, we may be able to judge whether the Taiwanese banking industry shouldbe restructured through consolidation in the next stage or not. Recently, some authorshave followed the research agenda suggested by the seminal contribution of Berger (1995).Altunbas et al. (2001) and Carbo, Gardener and Williams (2002) estimate scale economies,X-inefficiencies and technical change for European banks between 1989 and 1997. Bothstudies yield similar results and find that X-efficiency, i.e. differences in technological andmanagerial efficiency, accounts for most of the variation in bank profitability while scaleeffects are quantitatively less important. Punt and van Rooij (1999) arrive at a very similarconclusion attaching higher weight to X-efficiency than other factors in explaining return onequity of banks. These results stand in contrast to the inconclusive study of Berger (1995)himself, who states that for the US banking sector it does not appear that any of the ES orMP hypotheses are of great importance in explaining bank profits. The unique situation ofthe Taiwanese financial system, with its rapid pace of change and reform, provides an idealenvironment for studying the impact of regulatory reform on scale and scope economies aswell as the profit-structure relationship.

The remaining sections of this paper are structured as follows. Section 2 outlines thefunctional form and measurement methodologies adopted in this study. Section 3 discussesthe data sources and shows the impact of the 1990s financial liberalization on the differentcompetitive issues of the Taiwanese banking industry. In Section 4 we will compare andsummarize our findings and give suggestions for the future industrial organization of theTaiwanese banking sector.

Specifications of models

The earlier banking literature only considers one measure of bank output5 and uses simplestatistical models resembling ratio-based analyses to examine scale economies in the bank-ing industry. Although accounting ratios in banking are typically used to obtain a partial

BANKING MERGERS 387

measure of banking productivity, these measures are problematic.6 Benston et al. (1982)were the first to use the conventional translog cost function system to estimate economiesof scale in banking7 and evaluate the bank output by the production approach. The con-ventional translog cost function system enables the cost structure of banks to be modelledwith maximum flexibility and each of the outputs can be considered explicitly. However,one limitation to the use of the translog cost function is that the translog cost functionform is potentially subject to misspecification (McAllister and McManus, 1993). Since thetranslog cost function is developed as a local approximation to the underlying cost func-tion, the Fourier approximation and the Kernel regression technique can overcome thesedeficiencies to provide a global approximation by restricting the sample to homogeneousbanks. However, the Fourier approximation and the Kernel regression technique require alarge sample to obtain accurate results and in particular, the Fourier approximation is moresuitable for large banks8 (McAllister and McManus, 1993; Mitchell and Onvural, 1996).Since our sample of Taiwanese banks is small and very few of the institutions are large insize, the translog cost function seems the most appropriate to study the Taiwanese bankingsystem. Moreover, the ordinary translog functional form cannot be modified to define zerooutputs since all of the outputs enter in logarithmic form. Therefore, we replace the originaltranslog cost function by the Box-Coxs (1964) transformation, which is called the hybridtranslog cost function.9

Methodology: The hybrid translog cost function system

In this study, bank multi-outputs are measured by the intermediation approach and themodified model from Molyneux, Altunbas and Gardener (1997) is used to examine scaleeconomies and scope economies. In our view, the nature of banks is more accurately de-scribed as intermediators of financial services rather than producers of loan and depositaccount services, a view taken by the production approach. The latter usually defines banksoutput as the number of deposit or loan accounts or the number of transactions performed onthese accounts. Benston, Hanweck and Humphrey (1982) and Pulley and Humphrey (1993)are among the contributions in the production approach literature. Kolari and Zardkoohi(1987) argue that the intermediation approach has crucial advantages over the productionapproach. In their view, banks compete via nominal amounts, not the number of accounts.Furthermore, dollar amounts constitute a common denominator for the many kinds of ser-vices banks provide. Therefore, the intermediation approach seems to be more appropriatein a competitive, asset-side driven banking market. We in fact assume that domestic banksin Taiwan operate in a competitive environment and all of banks aim to minimize costs withprofit-maximising behavior.

The hybrid transformation methodology evaluates a translog functional form where thelogarithms of outputs are replaced by the Box-Cox (1964) transformation. The Box-Coxhybrid transformation can be written as follows:

Q(Qi ) =(Qi 1)

for other than zero, and (1)

Q(Qi ) = ln Qi for equal to zero (2)

388 YU AND LUU

Greene (1997) pointed out that if a minimum of the sum of squares in the translog costfunction is found, by repeating this procedure for different values of (from 1 to +1),the optimal value of can be found. After determining the optimal value of , the modelbecomes linear again and the maximum likely estimators of all the parameters are obtained.By using the Box-Cox transformation, the hybrid translog cost function used in this studyhas the form:

ln TC = 0 +2

i=1i Qi +

3i=1

i ln pi + b ln B

+ 12

(2

i=1

2j=1

i j Qi Qj +3

i=1

3j=1

i j ln pi ln p j + bb ln B ln B)

+3

i=1

2j=1

i j ln pi Qj +2

i=1bi ln BQi +

3i=1

bi ln B ln pi + (3)

Where:

ln TC: The natural logarithm of the total costs for interest costs, labor cost and capital costQi : A vector of outputs with the Box-Cox transformation (Q1 = total loans, Q2 =

government bonds, total securities and the other investments)ln pi : The natural logarithm of i th input prices (pi = interest rate, p2 = wage rate and p3 =

capital price)ln B: The natural logarithm of the number of branches

, , , , , and are coefficients to be estimated.

According to Shephards Lemma10 (Christensen, Jorgenson and Lau, 1973), the deriveddemand for an input can be inferred by partially differentiating the cost function withrespect to the input price, pi . Thus, three cost share equations can be generated from thehybrid translog cost function (3) as follows:

3i=1

Si =3

i=1i +

3i=1

3j=1

i j ln p j +3

i=1

2j=1

Qj +3

i=1bi ln B + ui (4)

Since the duality theorem requires the cost function to be linearly homogeneous in inputprices, the following restrictions have to be imposed on the parameters of the hybrid translogcost function (3):

3i=1

i = 13

i=1ri j = 0 for all j

(5)3

i=1i j = 0

3i=1

bi = 0 for all j

BANKING MERGERS 389

Also the second order parameters of the hybrid translog cost function (3) must satisfy thesymmetry condition.

i j = j i i j = j i for all i j (6)

The hybrid translog cost function (3) is estimated jointly with the cost share Eq. (4) usingthe seemingly unrelated regression estimation (SURE) technique. Since the input cost shareequations will sum to unity, one cost share equation should be omitted from the estimatedsystem of equations to avoid the problem of a singular contemporary covariance matrix ofdisturbances11 (Berndt, Hall and Hansman, 1974).

Scale and scope economies

Overall economies of scale

The concept of scale economies is based on the shape of the average cost curve. For instance,economies of scale are present up to the level where the long-run marginal cost (LMC) curvelies below the long-run average cost (LAC) curve. If diseconomies of scale exist, the LMClies above the LAC curve. By following Molyneux, Altunbas and Gardener (1997) andNoulas, Miller and Ray (1990), we estimate OES for each bank by evaluating Eq. (7) toexamine how changes in scale affect total cost.

OES =2

i=1

ln TC Q (7)

It is only appropriate to use Eq. (7) to estimate OES if other regressors included in the hybridtranslog cost function remain unchanged as outputs vary. If OES < 1, there are increasingreturns to scale, i.e. economies of scale exist. If OES = 1, constant returns to scale exist.If OES > 1, there are decreasing returns to scale. The existence of scale economies meansthat the average cost of producing a product, in the long run, decreases as more of the outputis produced.

Expansion cost subadditivity

Previous studies argue that (Molyneux, Altunbas and Gardener, 1997; Noulas, Miller andRay, 1993; Berger, Hunter and Timme, 1993) expansion path subadditivity is a more appro-priate method than traditional scope economy measures for examining the cost structure ofbanking markets. The reason is that cost subadditivity can measure the relative efficiencyof large and small firms and consider both scale and scope economies simultaneously.

By following Berger, Hanweck and Humphreys (1987) definition, expansion path sub-additivity is explained as whether a bank of a given size can produce a combination ofoutputs more effectively than two smaller banks which produce the same combination of

390 YU AND LUU

outputs. Expansion path subadditivity can be measured as follows:

EPSUB(Q A) = T C(QB) + T C(QC ) T C(Q)A

T C(Q A) (8)

whereTwo kinds of output: Q1 and Q2.Two smaller banks: bank B and bank C , and one large bank: bank A. EPSUB(Q A) means

that cost changes resulting from breaking large bank A into two smaller bank B and bankC . If the value of the expansion path subadditivity is positive, breaking up a large bankinto smaller ones cannot bring about lower costs. Negative values indicate the oppositesituation. Moreover, the overall economies of scope is a special case of the expansion pathsubadditivity. If economies of scope exist,

TC(Q A1 , 0) + T C(0, Q A2 ) T C(Q A) > 0 (9)

Although Eq. (9) is a special case of Eq. (8), Eq. (8) shows whether cost effective multi-product firms should be larger or smaller. Equation (9) explains whether the firms shouldspecialize in production.

Cost efficiency

Leibenstein (1966, 1980) defines that inefficiency comprises allocative inefficiency and X-inefficiency12 and also argue that there are important distinctions in the economictheoriesunderlying X-efficiency and technical efficiency.13

Efficiency measurement techniques

For banking cost studies, the difficulty in measuring efficiency is the problem of disen-tangling relative cost efficiency differences from short-term differences due to luck ormeasurement error that temporarily give banks relatively high or low costs. In the bankingliterature, numerous methods have been used to solve this problem with different distri-butional assumptions. In this case, we choose a version of the distribution-free approach(DFA) described in Berger (1993), variants of which have also been applied to banking databy Berger et al. (1993) and Berger and Humphrey (1992a). Rather than imposing prede-termined distributions on the relative cost inefficiencies and random error, DFA identifiesone from the other methods using the basic assumption that relative cost inefficiency dif-ferences across banks should persist over time, while random errors should be ephemeraland average out over time.14

Equation (10) is estimated for each of the n periods by using a translog cost functionwhich we defined in the previous cases of scale and scope economies, and ln x + ln v willbe treated as a composite error term. The cost equations for each of the n periods of a panel

BANKING MERGERS 391

data set can be specified as:

ln OCit = ln Ct (Yit , wi t ) + ln xi + ln i t (10)

where:

OC is operating costsC(Y, w) is a cost function with output quantity and input price vectorsln x represents relative cost inefficiency,ln v is a mean-zero random error, andt indexes time.

All the components in Eq. (10) vary over time except for the efficiency factor xi , whichis constant for bank i . For example, bank is efficiency for 1988 will be calculated usingthe average of each banks cost function residual over 198587 and 198991. The currentresidual is excluded from the computation of current relative cost inefficiency given thatcurrent costs are used to compute current profits. Furthermore, the ln xi t are transformedinto a normalised relative cost efficiency measure as follows:

X EFFit = exp(ln xmint ln xi t

) (11)where:

ln xmint indicates the minimum ln xi t for all i for that t .It may be seen that this is an estimate of xmin/xi , the ratio of estimated costs for the most

efficient bank in the sample to the predicted costs for bank i for any given vectors of outputsand input prices. This corresponds with the conventional notion of efficiency as the ratioof the minimum resources needed for production to the resources actually used, and rangesover [0, 1].

Tests of market-power and efficient-structure hypotheses

The purpose of this part is to distinguish the market-power and efficient-structure hypothesesas they apply to the Taiwanese banking market. These hypotheses stress different factors inexplaining the performance, i.e. the profitability of banks. From the banking regulators pointof view, there is a fundamental trade-off between maintaining strong competition on the onehand and promoting the exploitation of scale economies and financial sector stability on theother. Both goals may often directly contradict one another and studying and quantifying theforces that shape the performance of financial institutions may enable policymakers to decidewhich of the two goals they should pursue in a given market structure. In brief, four majorhypotheses have emerged in the banking literature to explain the profit-structure relationship.The market-power (MP) hypotheses comprise the structure-conduct-performance (SCP) andrelative-market-power (RMP) and the efficient-structure (ES) hypotheses include ESX (X-efficiency version of the efficient-structure hypothesis) and ESS (scale efficiency versionof the efficient-structure hypothesis). The SCP hypothesis states that banks set prices that

392 YU AND LUU

are less favourable to consumers in more concentrated markets because of competitiveimperfections. The RMP hypothesis suggests that only banks with large market shares andwell-differentiated products can exercise market power in pricing these products and earnsupernormal profits (Shepherd, 1982). Although both hypotheses appear very similar, theyhave fundamentally different implications in terms of consumer welfare. While consumersare unambiguously worse off when SCP hypothesis holds, the case is less clear-cut with theRMP hypothesis. Under the latter and if SCP is rejected at the same time, banks are thoughtto have gained their market share by providing well-differentiated or novel products. UnderESX, banks with superior management or production technologies have lower costs andhence can earn higher profits. Moreover, since these more efficient banks are also assumedto gain large market shares that may result in high concentration, the positive profit-structurerelationship is spurious in this case (Peltzman, 1977). Finally, under ESS, all banks haveequally good management and technology, but some banks simply produce at more efficientscales than others. This hypothesis also yields a positive profit-structure relationship as aspurious outcome since these banks are assumed to have large market shares that may resultin high levels of concentration (Lambson, 1987).

We apply a model similar to Bergers (1995) and employ direct measures of both X-efficiency and scale efficiency to the empirical analysis.

ROE = f1(CONC, MS, Relative cost efficiency, SEFFE, MGTH,Dummy variables) + (12)

CONC = f2(Relative cost efficiency, SEFFE, MGTH, Dummy variables) + (13)MS = f3(Relative cost efficiency, SEFFE, MGTH, Dummy variables) + (14)

Table 1 summarizes the definitions for all variables in this model of profit-structurerelationship.

Table 1. Definitions for all variables in the model of profit-structure relationship

Symbol Definitions

ROA Ratio of net before-tax income to assets.ROE Ratio of net before-tax income to equity.CONC Herfindahl index of concentration of deposit marketMS Bank is share of total market deposit.Relative Cost Relative cost efficiency: ratio of the smallest (n 1)-year average residual ofEfficiency all banks to the banks (n 1)-year average residual (current years data

excluded). The smallest and largest 1 percent are set equal to the 1st and 99thpercentiles, respectively.

S-EFF Scale efficiency can be obtained from the previous case of scale economies.S-EFFe Scale economy efficiency: equals S-EFF if bank is below efficient scale; equals

1 otherwise.S-EFFd Scale diseconomies efficiency; equals S-EFF if bank is above efficient scale;

equals 1 otherwise.MGTH Real growth of deposits in banks markets.Dummies Dummies for (n 1) different bank groups.Source: This table is made by author.

BANKING MERGERS 393

The major Eq. (12) is shown to be a valid reduced form for all of the hypotheses and anyor all of them may be found to be consistent with the data. A positive profit-concentrationrelationship occurs because concentration (CONC) affects price and price affects profit. Onthe other hand, under the RMP hypothesis, market share (MS) becomes the key exogenousvariable since banks with large market shares have well-differentiated products and are ableto exercise market power in pricing these products. Furthermore, if only RMP holds, CONCwill have a zero coefficient because CONC is only spuriously related to profit through itscorrelation with MS.

By contrast, if ES hypotheses are accepted, the coefficients of the appropriate efficiencyvariables will be positive and the coefficients of all the other key variables are either relativelysmall or zero. An important limitation of the reduced-form profit equation in (12) is that ittests only one of the three necessary conditions of the ES hypotheses. More precisely, inorder to explain the profit-structure relationship spuriously, two more conditions (Eq. (13)and Eq. (14)) should be met since both profits and the market structure variables mustbe positively related to efficiency. For instance, one of the conditions required is that inEq. (14), i.e. that more efficient firms have greater market shares. This requirement can beexplained by the fact that more efficient banks obtain greater market share through pricecompetition or through acquisition of less efficient banks.

Estimation and results

Since our sample is small in size, we use pooled time-series and cross-section data to es-timate the hybrid translog cost function system. This approach is different from that ofprevious studies, which use a single year to investigate economies of scale. Although thepositive serial correlation and heteroscedasticity will still exist, using panel data enablesus to investigate the relationships between temporal changes and across-sectional differ-ence. We employ the seemingly unrelated regression estimation (SURE) technique, whichis particularly useful with large panel data sets (Avery, 1977) to estimate several equa-tions simultaneously. In this specific error components model, the regression errors in eachequation are assumed to be composed of three independent componentsone componentassociated with time, another with cross-sectional units, and a third with each observation.15

u jnt = jn + j t + jnt (15)

The model developed above makes the assumptions that both within and between equationerror covariances are composed of independent individual, time period, and observationcomponents and the covariances of all three components are non-zero.

In this study, the hybrid translog cost function system comprises the hybrid translog costfunction (3), the two cost share Eq. (4), two restrictions (5) and the symmetry condition (6).Moreover, since the Taiwanese banking industry was heavily regulated until the beginningof the 1990s, a pre- and post-analysis of the changes and an assessment of their impacton the banking sector is conducted. For instance, as part of this regulation, entry into theindustry has been restricted.

394 YU AND LUU

The data resources and definitions of variables

The data resources

In this study, the major data resources were banks balance sheets and income statementsobtained from the Central Bank of China (CBC).16 The data on branch numbers for Tai-wanese banks were also gathered from the Central Bank of China (CBC).17 Other relevantinformation which was not available in the Central Bank of China (CBC) was obtainedfrom the following sources. Personnel expense was obtained from the Bureau of Mone-tary Affairs.18 The general index of consumer price in the Taiwan area in each year wasavailable from Directorate-General of Budget, Accounting and Statistics, Executive Yuan,Republic of China.19 The number of total employees for each bank was obtained from theinternational bank database BankScope. Given the chosen intermediation approach, we usetwo categories of outputs, three kinds of input variables and one control variable in ourfollowing models. All variables in this study are measured in NT million dollars. Data fromincome statements are gathered from 1st of January to 31st of December for each year. Datafrom balance sheets and the other official reports are obtained on 31st of December for eachyear. Finally, each variable should be deflated by the general index of consumer price inTaiwan for each year to correct for price inflation. All variables in this paper are defined inAppendix 1.

The sample period of study

Since financial deregulation in the early 1990s offers the potential for a pre- and post-analysis of the changes, we separate the whole sample period into two shorter periods:19851991 and 19931997. 1992 is omitted because the reforms were enacted during thisyear and some of new established banks did not have data for the whole year. The em-pirical analysis ends in 1997, as another shift in the banking sector regime took placeafterwards. After 1997, Taiwan started privatizing some of the large government-ownedbanks. Since the latter were subject to numerous restrictions in their operations, such aslimitations on the number of senior management, restrictive pay and bonus stipulations andthe inability to fire poor performers, they were perceived as slumbering giants. TaipeiBankstarted privatizing in 1997 and finished its stock offering in July 1997. Until October 2002,five more formerly government-owned20 banks completed their privatization. Thus weconsider the steps taken by the government to float the large public banks to constitutea substantial change in the external environment and restrict the post-reform analysis tothe period before 1997. Moreover, the question of whether to pool the data or not natu-rally arises with panel data. In our case, we partition each period data into two subsam-ples to carry out Chows breakpoint test. All the tests for poolability are summarized inTable 2.

Table 2 shows that Chows breakpoint test does not reject poolability across time pe-riods, under the null hypothesis: H0 = t = for t = 1, . . . , T . It can be conc-luded that parameters in our model are constant, and stable in the estimatedrelationship.

BANKING MERGERS 395

Table 2. Chows breakpoint test performed for poolability

Sample Period Test Statistics Critical Value Decision

19851991 1.95 F0.01(21, 105) = 2.03 Not rejected19931997 1.90 F0.01(21, 143) = 1.99 Not rejected

The constitution of the sample in this study

Before 1991, the Taiwanese government imposed many restrictions on the Taiwanese bank-ing market and there were only twenty-four domestic banks in the market. From 1991 to1992, the Taiwanese government started to relax some financial restrictions imposed on thebanking market, and sixteen new banks were established during these two years. The sampleis extended to include 38 domestic banks in the period between 1993 and 1997. Foreignbanks are excluded in our sample, although one main rationale of allowing competitionfrom foreign institutions is the expected gain in the operation efficiency and service qualityin the local financial market.21 However, statistics on the market share of foreign banks indifferent areas of the banking business indicate that derivatives trading, foreign exchangetrading and guarantee constitute main business of foreign banks.22 In 1994, Taiwan sig-nificantly revised the Guidelines for the Reviewing of Foreign Banks Applications for theEstablishment of Branch and Representative Offices in accordance with the GATT. Thoserevisions aimed at according foreign banks national treatment to compete on an equal foot-ing with local banks. They did not remove all restrictions on foreign banks, however, so thatthe latter were not allowed to acquire more than 50% of local banks until 1999. Because ofthe different business focus of foreign banks and the diverging restrictions on expansion bymergers, we drop them from the sample.

Furthermore, based on bank asset size and business similarity, we can divide the wholesample of domestic banks into four different small subgroups: Government-owned banks(GOB), local banks (LB), old-private banks (OPB) and new-private banks (NPB). GOBsare subject to government control in their day-today operations and have average assets ofaround 25 billion US-$, while the three other groups are much smaller with average assetsof roughly 5 billion US-$. OPBs and LBs were established before financial reform, wherethe latter faced geographical restrictions regarding their branch network. Those restrictionswere abolished by the financial reform in 1991, which also enabled NBPs to be established.In this paper, the empirical results of scale and scope economies will be compared betweenthese four groups. These four groups of banks are listed in Appendix 2.

OES and expansion path subadditivity

Estimation of the hybrid translog cost function system

We show all coefficients derived from the hybrid translog cost function system and thetwo cost share equations from (3) to (6) in the following Table 3. In brief, our empiricalresults in Table 3 are similar to the findings of the banking studies reviewed earlier (Mester,

396 YU AND LUU

Table 3. Empirical results of the hybrid translog cost function system

19851991 19931997Coefficient = 0.1 = 0.5

Constant 3.0675 6.1665(0.3383) (0.1915)

Q1 0.2197 0.0048(0.0786) (0.0005)

Q2 0.0150 0.0031(0.0555) (0.0009)

ln p1 0.1906 0.4790(0.0619) (0.0403)

ln p2 1.2106 0.2180(0.1112) (0.0270)

ln B 0.3961 0.7037(0.1960) (0.1699)

Q1 Q1 0.0308 2.70E-07(0.0123) (5.97E-07)

Q1 Q2 0.0209 6.63E-07(0.0084) (8.70E-07)

Q2 Q2 0.0156 4.75E-07(0.0082) (2.16E-06)

ln p1 ln p2 0.0616 0.0204(0.0047) (0.0036)

ln p1 ln p3 0.0645 0.0363(0.0086) (0.0069)

ln p2 ln p3 0.0037 0.0181(0.0056) (0.0030)

ln B ln B 0.0227 0.1054(0.1842) (0.0817)

ln p1 Q1 0.0603 7.87E-05.0054) (2.83E-05)

ln p2 Q1 0.0137 2.46E-05(0.0024) (1.02E-05)

ln p1 Q2 0.0324 0.0001(0.0048) (6.45E-05)

ln p2 Q2 0.0096 4.33E-05(0.0016) (2.56E-05)

ln B Q1 0.0536 0.0007(0.0306) (0.0002)

ln B Q2 0.0488 0.0008(0.0067) (0.0003)

ln B ln p1 0.0238 0.1444(0.0147) (0.0064)

ln B ln p2 0.2502 0.0683(0.0353) (0.0075)

Adjusted R squared of the 0.9968 0.9992hybrid translog cost function

Approximate standard error in parentheses.Significantly different from zero at 10% level.Significantly different from zero at 5% level.Significantly different from zero at 1% level.

BANKING MERGERS 397

1987; Molyneux, Altunbas and Gardener, 1997) since all the coefficients of input prices arestatistically significant. There are two factors of input, capital and labor, whose prices aredenoted by P1 and P2 respectively and two kinds of output, total loans and investments, Q1and Q2. Moreover, we also consider the number of branches B as one factor impacting ontotal cost. The coefficients on the output variables and input factors are significant, exceptfor total investments before financial liberalization. Post-reform, however, investments alsobecome highly significant in determining total costs, which indicates that banks increasinglyengaged in securities dealing, brokerage, underwriting, as well as investment management.We also find that before the financial reform, labor has the most influential role in determin-ing total cost, hence we argue that banks did not have an incentive or the ability (e.g. if thegovernment imposes restrictions on laying off employees) to control labor cost efficiently.This result is similar to the finding obtained for the Italian banking system (Molyneux,Altunbas and Gardener, 1997). The results subsequent to the financial reform suggest thatthe cost of interest input becomes more important than the other two kinds of inputs. Thecoefficients of interest cost and labor cost are both significant, but the magnitude of theinterest cost has increased. Finally, the number of branches B are significant in explainingtotal cost pre- and post-reform alike. The remaining variables are merely cross-products ofthe main factors.

Empirical results of OES

We summarize the empirical results of OES for the Taiwanese banking industry in Ta-ble 4. The average value of OES obtained from the hybrid translog cost function system isaround 0.3470. This means that Taiwanese banks were able to obtain the benefit from OESbefore financial reform. This value is similar to the result for Spain whose value of OESis nearly equal to 0.3695 (Molyneux, Altunbas and Gardener, 1997). Evidence from theEuropean banking sector using Fourier flexible functional form and stochastic cost frontiermethodologies indicate that scale economies range between 7 to 10%, while X-efficiencymeasures appeared to be much larger at about 22% (Carbo, Gardener and Williams, 2002;Altunbas et al., 2001). From Table 4, we also find that after 1992, OES still exist in the

Table 4. Empirical results of OES for the Taiwanese banking industry from1985 to 1997

Model I of the Hybrid Conventional TranslogTranslog Cost Function System Cost Function System

19851991 0.3470 0.5629(0.0420) (0.0855)

19931997 0.0030 0.7017(0.0011) (0.0568)

Approximate standard error in parentheses.Significantly different from one at 10% level.Significantly different from one at 5% level.Significantly different from one at 1% level.

398 YU AND LUU

Taiwanese banking market. However the value of OES had gone down dramatically nearlyto 0.0030. Since the average value of OES is extremely small comparing with the resultsobtained from the previous conventional translog cost function studies, it might be usefulto reestimate the OES by using the conventional translog cost function system. Moreover,we show these results estimated by using the conventional translog cost function system inTable 4. The values of OES obtained from the conventional translog cost function systemare much bigger than the results estimated by the hybrid translog cost function system, buttheir values are still smaller than one and indicate that OES exist in the Taiwanese bankingmarket. For the pre-analysis, the average value of OES is 0.5629, although the value isincreased to 0.7017 after financial reform.

Based on Table 4, we argue that the specification of the hybrid translog cost function andtwo-stage estimation procedure sometimes may be causing problems for the OES estimates.Comparing the results before and after financial reform, both types of cost functions indicatethat economies of scale still exist post financial liberalization. However, the estimates forOES based on the hybrid translog cost function are very low with a value of 0.003, implyingthat total cost would increase only by 0.003% if output were raised by 1%. The potentialbenefits from increasing overall scale hence are unusually large. This is particularly odd asinflation-adjusted average assets of domestic banks actually increased by 30% in 19931997compared to 19851991. A previous study on European banking markets by Molyneux,Altunbas and Gardener (1997) using hybrid translog cost functions reports values for OESranging from 0.37 to 0.74. Our results for the conventional translog cost functionfall withina similar range before and after financial reform and thus seem to be a more reasonablemeasure of true scale economies. The two stage estimation method used for deriving thehybrid translog cost function may be less robust to structural breaks such as the financialreforms enacted in Taiwan in 1992 and the subsequent establishment of new banks.

According to the empirical results of OES, we discover that OES actually exist in Tai-wanese banking industry. However, there are two ways for banks to obtain the benefit ofscale economies as follows:

1. Taiwanese banks can achieve OES by increasing branch numbers or2. Taiwanese bank can increase their size by mergers.

To find out which way can benefit the Taiwanese banking sector, we examine the presenceof expansion path subadditivity in the following part.

Empirical results of expansion path subadditivity

We can use Eq. (8) to estimate expansion path subadditivity and divide all representativebanks into two smaller bank groups by taking the mean value of outputs. In our case, we usethe average output prices for the whole group to divide the whole sample into two subsam-ples. The empirical results of expansion path subadditivity are given in the following Table 5.

From Table 4, our estimated values of expansion path subadditivity are always positive.This result suggests that the Taiwanese banking market exhibits expansion path subadditivityand breaking up large banks into smaller ones can lead to higher costs. From the point of

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Table 5. Expansion path subadditivity from 1985 to 1997 (%)

Model I

1985 1.23121986 1.23561987 1.23711988 1.23651989 1.25481990 1.27941991 1.3093The financial environment of Taiwanese banking market was

dramatically changed around 19921993 1.59231994 1.59011995 1.58801996 1.58391997 1.5803

view of cost efficiency and scale, it may be concluded that it is better to have fewer banksin the Taiwanese banking market. This strong conclusion has to be balanced against thepotential drawbacks of reduced competition or increased need for government regulationwhen banks become larger. Compared with other previous studies, Noulas, Miller andRay (1993) also find positive values of expansion path subadditivity for medium-sized USbanks and Molyneux, Altunbas and Gardener (1997) find that the France, Germany and Italybanking markets are natural monopolies and have a tendency for banks to become large.Finally, based on the empirical results of expansion path subadditivity and OES obtained,we can infer that Taiwanese banks should choose to merge with other banks rather than toexpand their network by opening more branches to obtain the benefit from OES.

Cost efficiency

In our case, relative cost efficiency will include allocative cost efficiency and X-efficiency. Inthis part, the theoretical models are applied to the same data set as in the cases of scale andscope economies. However, in this part, the entire data set is reconsidered for five groups: thegovernment-owned specialised banks (GOSB), the government-owned commercial banks(GOCB), local banks (LB), old-private banks (OPB) and new-private banks (NPB).

Average cost efficiency

We obtain relative cost efficiency by estimating the previous hybrid translog cost functionsystem with a common effect. The table below summarizes the results of relative costefficiency for different Taiwanese bank groups.

From Table 6, we observe that after financial reform, different bank groups have a similarrelative cost efficiency. However, the range of relative cost efficiencies is very wide forindividual banks, even those within the same group (please refer Appendix 3. For example,the most efficient bank, YP belongs to the most inefficient group of new private banks.

400 YU AND LUU

Table 6. Empirical results of relative cost efficiency for different Taiwanese bank groups

19861991 (before financial reform) 19941997 (after financial reform)& Model I & Model I

The government-owned 0.7416 0.7441specialised banks (GOSB) (0.0384) (0.0459)

The government-owned 0.8205 0.7971commercial banks (GOCB) (0.1097) (0.0883)

Local banks (LB) 0.7468 0.7892(0.0476) (0.0653)

Old-private banks (OPB) 0.7680 0.7983(0.0267) (0.0575)

New-private banks (NPB) 0.7176(0.1069)

Source: Calculated from the data which are collected by the Central Bank of China (CBC).

From Table 7, we observe that for some banks, the explicit repeal of regulations mayresult in an increase in allocative efficiency, while a general increase in the level of competi-tion permitted increases in technical efficiency. However, we also find that for some banks,the results obtained after financial reform are reversed. Furthermore, the rankings of banksaccording to their relative cost efficiency are changed dramatically and their rankings do notdepend on which bank group they belong to. This stands in contrast to recent results fromChen and Yeh (1999), who employ a Data Envelopment Analysis to evaluate the relativeefficiency of the Taiwanese banking sector. They find that publicly-owned banks predom-inantly manage their resources less efficiently than private banks. Among the inefficientbanks they identified, technical inefficiency is said to be the main source of inefficiencyrather than scale factors. From Appendix 3 it can be seen that both the most efficient bankand the most inefficiency bank are in the NPB (new private bank) group. This result maybe explained by the different management strategies which banks choose to implement tocounter the increasing competitive pressure, such as entering new markets or the creationof innovative products.

The results of tests of market-power and efficient-structure hypotheses

Firstly, the panel data indicates that the sample of banks is homogeneous so that the degreeof pooling is valid (Please refer to Appendix 4). Then, we describe empirical results of thebasis model and investigate the market-power (MP) and efficient-structure (ES) hypothesesas alternative explanations of the observed variation in bank profitability.

Empirical results before financial reform

In Table 8, the coefficient of concentration (CONC) in the major Eq. (12) is negativeand statistically significant at the 1% critical level. This means that there is a negativeprofit-concentration relationship in the Taiwanese banking industry, which contradicts thestructural-conduct-performance (SCP) hypothesis. Since the market share (MS) coefficientin Eq. (12) is positive, but not significant, the relative market power (RMP) hypothesis

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Table 7. Rank of asset and relative cost efficiency for each bank from 19861997

19861991 19941997

Relative Rank of Relative Rank ofRank Cost Relative Cost Rank of Cost Cost Relative

Asset of Asset Efficiency Efficiency Asset Asset Efficiency Efficiency

A 223735.8 9 0.7039 19 380119.0 12 0.7579 19B 208569.6 10 0.7404 15 404278.5 9 0.6928 29C 698042.2 2 0.8378 4 1486397.0 1 0.7586 18D 241936.8 8 1 1 428851.5 8 0.7624 16E 501024.8 5 0.7807 9 1090496.0 3 0.7815 13F 797036.8 1 0.6307 21 1462416.0 2 0.6286 35G 503190.0 4 0.8069 5 815007.3 4 0.8724 5H 542943.0 3 0.7745 12 806957.5 5 0.8400 10I 493078.2 6 0.8430 3 763248.5 6 0.8418 9J 124909.8 12 0.7549 13 346554.5 13 0.8782 3K 174470.8 11 0.7807 10 388858.8 11 0.8019 11L 51660.6 17 0.7983 7 190100.0 17 0.7560 17M 62733.8 16 0.7381 16 180944.3 18 0.7530 22N 344359.6 7 0.8504 2 701428.8 7 0.8759 4O 79542.2 13 0.7803 11 227947.5 14 0.7680 15P 64510.0 14 0.7833 8 206337.8 16 0.7972 12Q 62944.2 15 0.7186 18 219412.0 15 0.7405 23R 29589.2 18 0.7507 14 123779.3 20 0.7105 27S 26687.8 19 0.7336 17 99786.3 33 0.7549 21T 8027.2 20 0.6612 20 35913.5 38 0.8709 6U 4088.6 21 0.7999 6 42995.5 37 0.8822 2YA 109731.3 25 0.7083 28YB 105654.3 27 0.8448 8YC 107387.5 26 0.7138 26YD 105589.0 28 0.7768 14YE 88994.3 35 0.8542 7YF 91435.8 34 0.7556 20YG 114039.8 23 0.7375 24YH 114068.0 22 0.6696 31YI 115746.0 21 0.6127 36YJ 104275.8 29 0.6591 33YK 102162.0 32 0.6468 34YL 124227.0 19 0.6708 30YM 110794.5 24 0.7239 25YN 103121.3 30 0.6671 32YO 102876.5 31 0.5955 37YP 82849.3 36 0.9970 1YQ 396985.5 10 0.5661 38Source: Calculated from the data which are collected by the Central Bank of China (CBC).

does not explain the profit-structure relationship well, although efficiency variables arecontrolled for in the equation. We also observe that the coefficient of the relative costefficiency (Efficiency) is positive (insignificant) in the major Eq. (12), but not positivelyrelated to market share in the market share Eq. (14). Hence the ESX hypothesis cannot

402 YU AND LUU

Table 8. The sample banks with the period of 19861991 are estimated by the FGLS procedures

Variable ROE (Eq. (12)) CONC (Eq. (13)) MS (Eq. (14))

Constant 0.9495 0.0806 0.3142(0.4850) (0.0216) (0.0654)

Concentration rate (CONC) 5.0050(1.3871)

Market share (MS) 1.3975(0.8716)

Relative cost efficiency (Efficiency) 0.3409 0.0490 0.0025(0.2578) (0.0125) (0.0452)

Scale economy efficiency (SEFFE) 0.4412 0.0097 0.0593(0.2018) (0.0123) (0.0272)

Scale diseconomy efficiency (SEFFD) 0.3391 0.0223 0.2318(0.2614) (0.0113) (0.0352)

Real growth of deposit market (MGTH) 0.0551 0.0351 0.0423(0.1889) (0.0054) (0.0179)

Adjusted R-squared 0.2438 0.1557 0.9100Approximate standard error in parentheses.Significantly different from zero at 10% level.Significantly different from zero at 5% level.Significantly different from zero at 1% level.

significantly contribute to the explanation of the profit-structure relationship. It seems thatsuperior management techniques or technological differences between banks do not playan important role in explaining differences in profitability.

Turning to the scale efficiency results, since the scale efficiency coefficient (SEFFE) isnegative and significant at 5% critical level in the major Eq. (12), we may conclude thatthe ESS hypothesis contradicts the profit-structure relationship of the Taiwanese bankingmarket before financial reform. This may happen when banks try to have higher profits by ex-ploiting economies of scale. At the same time, the benefit is depreciated by the invisible cost,such as a change in management strategies or a change in relative cost efficiency following amerger.

Empirical results after financial reform

From the empirical results in Table 9, the market share (MS) coefficient in the majorEq. (12) is positive and significant at the 1% critical level. This suggests that the relativemarket power (RMP) hypothesis can explain part of the profit-structure relationship ofthe Taiwanese banking market, while efficiency variables are controlled for. According tothe relative market power hypothesis (RMP), Taiwanese banks should obtain relative largemarket share by producing well-differentiated products in order to attract more consumersif they want to earn supernormal profit.

In order to explain the profit-structure relationship spuriously, both profits and the marketstructure variables (concentration and market share) must be positively related to efficiency.However, in the major Eq. (12), the coefficient of the relative cost efficiency (Efficiency) isnegative (significant at 5% critical level) and not positively related to market share in the

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Table 9. The sample banks with the period of 19931997 are estimated by the FGLS procedures

Variable ROE (eq. (12)) CONC (eq. (13)) MS (eq. (14))

Constant 0.3382 0.0242 0.1431(0.0744) (0.0016) (0.0248)

Concentration rate (CONC) 1.2954(2.4342)

Market share (MS) 1.1115(0.2809)

Relative cost efficiency (Efficiency) 0.1305 0.0022 0.0607(0.0591) (0.0011) (0.0164)

Scale economy efficiency (SEFFE) 0.3086 0.0055 0.0790(0.0969) (0.0019) (0.0283)

Real growth of deposit market (MGTH) 1.1094 0.2740 0.1553(0.5429) (0.0049) (0.0754)

Adjusted R-squared 0.5348 0.9603 0.6508Approximate standard error in parentheses.Significantly different from zero at 10% level.Significantly different from zero at 5% level.Significantly different from zero at 1% level.

market share Eq. (14). We conclude that the ESX hypothesis cannot determine part of theprofit-structure relationship.

On the other hand, the scale efficiency coefficient (SEFFE) is negative and significant atthe 1% critical level in the major Eq. (14). We may conclude that ESS hypothesis finds nosupport in the Taiwanese banking market after financial reform. Moreover, the coefficientof the real growth of deposit market (MGTH) is positively related to ROE and significantat 5% critical level in the major Eq. (12). This means that the real growth rate of thedeposit market can bring about a positive effect on the profitability of Taiwanese banks.The results of our analysis of the market structureprofit relationship are summarized inTable 10. It is striking that none of the four alternative explanations offers a superior approachto explaining profitability in the Taiwanese banking sector before financial reforms wereenacted. This is very similar to conclusions drawn by Berger (1995) for the US bankingindustry using essentially the same empirical model. The latter author finds that the RMPand ESX are weakly supported by single year cross-section analyses for the period between19801989. However, as the median R2 of the regressions are below 10%, he concludesthat it is impossible to distinguish whether the profit structure relationship reflected superior

Table 10. Summary of results on market structureProfit relationship

19861991 19931997

Market powerStructural conduct performance (SCP) Rejected RejectedRelative market power (RMP) Insignificant Accepted

Efficient structureX-Efficiency (ESX) Rejected RejectedScale efficiency (ESS) Rejected Rejected

404 YU AND LUU

management (as according to the ESX hypothesis) or greater market power (as postulatedby the RMP theory). For the period after financial reform, however, our own results forTaiwan are more clear-cut. While the SCP, ESX and ESS are still rejected even after theliberalization of financial markets, the hitherto insignificant coefficient of market sharebecomes significantly positive, offering firm support to the RMP thesis. The liberalization offinancial markets seems to have favoured banks with well differentiated products, enablingthem to gain a high market share. Those banks have been able to exploit their market power tobecome more profitable than their smaller competitors. Unlike the SCP hypothesis, however,the acceptance of the RMP hypothesis is not a strong argument against banks becomingbigger. Consumer welfare may even benefit from banks pursuing product innovation anddifferentiation actively. Under the RMP hypothesis, market power is not derived from a highdegree of concentration, as the rejection of SCP shows, but from the provision of productsmore tailored to the needs of customers, as suggested by the higher market share of thesebanks.

Conclusion

In the early 1990s, when the Taiwanese government wanted to enhance local banks com-petitiveness, financial markets were liberalized and the government allowed sixteen privatecommercial banks to be established. To address the impact of financial liberalization on theTaiwanese banking industry, we investigate the profit-structure relationship, relative costefficiency, and examine whether the current wave of mergers observed elsewhere might besuitable for Taiwanese banking. For all sample banks and the whole Taiwanese bankingindustry, the values of OES are statistically significant at the 1% level and smaller than one.The implications of the results are that, if Taiwanese banks want to benefit further from OES,they should produce more output. Moreover, since our positive values of expansion pathsubadditivity indicate that breaking up large banks into smaller ones can lead to higher costs,the Taiwanese banking market is characterized by expansion path subadditivity. The latteralso implies that, if Taiwanese banks want to obtain the benefit from OES, they shouldchoose to merge with other banks rather than to expand their network by opening morebranches. The results for expansion path subadditivity suggest that, from a cost perspective,the Taiwanese banking industry would be better off with fewer banks.

Turning to the cost efficiency results, we observe that after financial reform, differentbank groups have similar relative cost efficiency, but their rankings do not depend on whichbank group they belong to. However, for some banks, comparing with the pre-analysis,the results obtained after financial reform are reversed and the rankings of relative costefficiency are changed dramatically.

Finally, we study four alternative explanations of the observed profitability of banks usinga reduced-form model suggested by Berger (1995). Before financial reform, none of the fourhypotheses has significant explanantory power for variations in profitability. After financialreform, however, it is striking that the strength of empirical support for the RMP hypothesisincreased. Although the SCP and RMP hypotheses are related in the sense that they linkmarket power with profitability, there is a fine but crucial difference between them. Whilemarket power in the RMP hypothesis is said to stem from innovative and well-differentiated

BANKING MERGERS 405

products (hence the attribute relative), the SCP hypothesis states that high concentrationitself is the source of market power. If SCP was accepted and the three other hypothesesrejected for Taiwan, it would have substantially weakened the normative case for furtherconsolidation. It would mean that banks already use their oligopolistic power to chargeunfavourable prices to consumers, while other sources of higher profitability, such as scale,technical efficiency or high relative market share are ruled out. The insignificance of RMPbefore financial reform and acceptance thereafter suggests that government regulations inplace before 1992 weakened the positive correlation of market share and profitability. IfTaiwanese banks want to achieve higher profits in the liberalized environment, they shouldaim at developing highly differentiated products to increase their market share. Since SCP isin fact rejected in our study, they cannot rely on oligopolistic pricing power to enhance theirprofitability. This also suggests that banks strive for higher market shares is not necessarilydetrimental to consumer welfare. The rejection of ESS and ESX implies that neither scalefactors nor technical or managerial efficiency played a significant role in determining bankprofitability. Our analysis of scale economies and expansion path subadditivity indicatesthat overall efficiency gains may be reaped through a trend towards bigger and fewer banks.It should be pointed out, however, that consolidation should proceed cautiously so as notupset the balance between efficiency considerations on the one hand and the interests ofTaiwanese bank customers on the other. After emerging from years of protected regulation,Taiwans efforts to fully liberalize its financial sector will, in our view, provide importantlessons for China and South East Asia.

Appendix 1: Definition of variables

Definition of input variables

Since we assume that Taiwanese domestic banks are in a competitive market, we can con-sider input prices as exogenous variables.

1. p1, the average price of interest rate: p1is the average interest cost per dollar of interest-bearing total deposits and total borrowed funds.

Interest cost = p1 Rwhere: R = (total deposits23) + (borrowed funds)

But if banks hold government deposits, they do not have to pay interest expense. Accord-ing to this reason, government deposits must be eliminated from total deposits, then wecan get more accurate interest cost.

The average price of interest rate can be calculated by the equation below:

p1 = interest cost(total deposits + borrowed funds)2. p2, the average price of labor:

p2 = personnel expense for yearAverage employee number per branch branch number

406 YU AND LUU

Subsequently, it is difficult to differentiate between labor expense and capital expense, be-cause these two specific items are included in the big item:the selling and administrativeexpense.24 We can not gather more details for labor expense and capital expense. To over-come this difficulty, in this study labor expense and capital expense are measured in thefollowing way:

Personnel expense include wage, overtime pay, reward, pensions, bonus and so on. Weuse the personnel expense from Financial Statistics Abstract published by Bureau ofMonetary Affairs from 1994 to 1997. By observing that ratios of personnel expense dividedby selling and administrative expenses are almost constant by years, we can calculate theaverage ratio for each bank by the available data. Since we use the average ratio timesselling and administrative expenses, the personnel expense for each bank in every year canbe inferred. Finally, according to the equation, the average price of labor can be obtained.3. p3, the average price of capital: The average price of capital is calculated by the followingequation:

p3 = summing the capital expensenet fixed assets

= summing the capital expense(fixed assets accumulated depreciation)Many studies on the structure of costs in banking define capital equipment as the sum ofconcepts like rent, depreciation, furniture and equipment (Mester, 1987; Murray and White,1983). In this study, we assume capital expenses include four specific items:

(1) the depreciation for fixed assets and all equipment(2) rental expense(3) the expenses for maintenance and repair(4) insurance cost

Because of the same difficulty, we can not obtain the capital expense directly from balancesheets and income statements. The data we only can obtain are selling and administrativeexpenses. By using the relationship described below,

Capital expense = (selling and administrative expenses personnel expense)

The capital expense can be inferred for each bank in every year. Since selling and adminis-trative expenses includes not only personnel expense, capital expense but also the expensesfor water supply, electricity, and advertisement, the only disadvantage is capital expense isoverestimated slightly.

Definitions of two categories of outputs

The empirical approach to output definition in this study is supported theoreticallyby Molyneux, Altunbas and Gardeners (1997) model of scale and scope economies in

BANKING MERGERS 407

European banking markets. The definitions of outputs in this study are similar with thedefinition in Kolari and Zardkoohi (1987) and most other European studies.

In this study, we define two categories of outputs as total investments and total loans.

1. Q1, total loans: In our models, total loans comprise:

Q1 = (discounts) + (bills purchased net) + (overdrafts) + (short-term loan)+ (middle-long term loan) + (other loans) (reserve for loan loss)

2. Q2, total investments: Total investments include:

Q2 = investments in government bonds and securities+ other investments allowance for unrealized loss

Definitions of other variables

1. Total cost (TC): Total cost as the dependent variable comprises interest expense, laborexpense and capital expense. Their relationship can be explained as follows:

T C = p1 R + p2 L + p3 K= (interest cost) + (ive selling and administrative expenses)

where

p1 R : interest expensep2 L : labor expensep3 K : capital expense

2. ROE: The value of ROE is the ratio of net before-tax income to equity.3. CONC: We choose to measure the degree of concentration in the Taiwanese banking

industry by using banking deposits and the Herfindahl Index.4. MS: MS is defined as the banks share of deposits market.5. Relative cost efficiency: We define that Relative cost efficiency is comprised by X-

efficiency and allocation efficiency.In this study, we apply the distribution-free method to estimate Relative cost effi-ciency. It is the ratio of the smallest n-year average multiplicative cost function residualof banks to the banks n-year average residual (current years data excluded).

6. SEFFE, scale economy efficiency: We will use the value obtained from the estimationof OES. If a bank locates on the left hand side of the bottom of the average cost (AC)curve for the whole banking industry at that year, SEFFE will equal the value of OES;equal one otherwise.

7. SEFFD: On the other hand, if a bank locates on the right hand side of the bottom ofthe average cost (AC) curve for the whole banking industry at that year, SEFFD willequal the value of overall diseconomies of scale; equal one otherwise.

408 YU AND LUU

8. MGTH, market growth: MGTH is estimated by the real growth of the Taiwanese depositmarket.

10. sdroa, indicator of the portfolio risk: The portfolio risk is defined as the stand error ofthe ROA (return of asset). For example, sdroa for the kth period is obtained from thestandard error of ROA for k, k 1, and k 2 period.

Appendix 2: The constitution of sample

Table A.2.1. The constitution of sample

Group Bank Name

(1) Government-owned banks A Chiao Tung Bank Co., Ltd.B The Farmers Bank of ChinaC Bank of TaiwanD TAIPEIBANK CO., LTD.E Land Bank of TaiwanF Taiwan Cooperative BankG First Commercial BankH Hua Nan Commercial Bank, Ltd.I Chang Hwa Commercial Bank, Ltd.N Taiwan Business BankYQ Chinatrust Commercial Bank

(2) Local banks O Taipei Business BankP Taichung Business BankQ Hsinchu BankR Tainan Business BankS Kaoshang Business BankT Hwalain Business BankU Taidon Business Bank

(3) Old-private banks J The International Commercial Bank of ChinaK United World Chinese Commercial BankL The Shanghai Commercial & Savings Bank., Ltd.M Overseas Chinese Commercial Banking Corporation

(4) New-private banks YA Grand Commercial BankYB Dah An Commercial BankYC Union Bank of TaiwanYD The Chinese BankYE Far Eastern International BankYF Asia Pacific BankYG Bank SinoPaoYH E. Sun Commercial Bank., Ltd.YI Cosmos Bank, TaiwanYJ Pan Asia BankYK Chung Shing Commercial BankYL Taishin International BankYM Fubon Commercial BankYN Ta Chong Bank Ltd.YO BaoDao Commercial Bank Ltd.YP Entie Pacific Bank

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Appendix 3: The cost efficiency analyses of different groups

Table A.3.1. Relative cost efficiency for government- ownedspecialised banks (GOSB)

19851991 19931997

Bank A 0.7039 0.7579Bank B 0.7404 0.6928Bank E 0.7807 0.7815Average 0.7416

(0.0384)0.7441(0.0459)

Table A.3.2. Relative cost efficiency for Government-ownedcommercial banks (GOCB)

19851991 19931997

Bank C 0.8378 0.7586Bank D 1 0.7624Bank F 0.6307 0.6286Bank G 0.8069 0.8724Bank H 0.7745 0.8400Bank I 0.8430 0.8418Bank N 0.8504 0.8759Average 0.8205

(0.1097)0.7971(0.0883)

Table A.3.3. Relative cost efficiency for local banks (LB)

19851991 19941997

Bank O 0.7803 0.7680Bank P 0.7833 0.7972Bank Q 0.7186 0.7405Bank R 0.7507 0.7105Bank S 0.7336 0.7549Bank T 0.6612 0.8709Bank U 0.7999 0.8822Average 0.7468

(0.0476)0.7892(0.0653)

Table A.3.4. Relative cost efficiency for old privatebanks (OPB)

19851991 19931997

Bank J 0.7549 0.8782Bank K 0.7807 0.8019Bank L 0.7983 0.7560Bank M 0.7381 0.7530Average 0.7680

(0.0267)0.7983(0.0575)

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Table A.3.5. Relative cost efficiency fornew-private banks (NPB)

19931997

Bank YA 0.7083Bank YB 0.8448Bank YC 0.7138Bank YD 0.7768Bank YE 0.8542Bank YF 0.7556Bank YG 0.7375Bank YH 0.6696Bank YI 0.6127Bank YJ 0.6591Bank YK 0.6468Bank YL 0.6708Bank YM 0.7239Bank YN 0.6671Bank YO 0.5955Bank YP 0.9970Bank YQ 0.5661Average 0.7176

(0.1069)

Appendix 4: Describe statistics of all variables in the modelof profit-structure relationship

Table A.4.1. Describe statistics of all variables from 19861991

Relative CostEfficiency CONC MS ROA ROE MGTH

19861991 Data StatisticsMean 0.7747 0.0992 0.0476 0.0099 0.2046 0.2102Median 0.7704 0.0962 0.0192 0.0087 0.1951 0.2204Maximum 1.0000 0.1117 0.1886 0.0536 0.6427 0.2635Minimum 0.5990 0.0910 0.0006 0.007543 0.0586 0.0859Std. Dev. 0.0794 0.0082 0.0511 0.0077 0.1199 0.0573Skewness 0.6618 0.4695 1.0491 2.4364 0.8150 1.4319Kurtosis 4.3845 1.5248 2.8132 12.5403 4.4761 3.7444Jarque-Bera 22.4726 16.0553 23.2943 602.4961 25.3878 45.9684Probability 0.0000 0.0003 0.0000 0.0000 0.0000 0.0000Observations 126 126 126 126 126 126

Source: Calculated from the data which are collected by the Central Bank of China (CBC).

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Table A.4.2. Describe statistics of all variables from 19931997

Relative CostEfficiency CONC MS ROA ROE MGTH

19931997 Data StatisticsMean 0.7560 0.0616 0.0263 0.0082 0.1042 0.1171Median 0.7515 0.0600 0.0122 0.0081 0.0904 0.1086Maximum 1.0000 0.0710 0.1538 0.0161 0.2963 0.1494Minimum 0.4673 0.0534 0.0023 0.0083 0.1363 0.0935Std. Dev. 0.1100 0.0059 0.0306 0.0035 0.0663 0.0207Skewness25 0.1754 0.2598 1.8893 0.9410 0.2919 0.4536Kurtosis26 2.7971 2.0277 6.1676 6.8319 3.5418 1.6676Jarque-Bera27 1.2997 9.6215 192.4728 144.2873 5.0222 20.5702Probability28 0.5221 0.0081 0.0000 0.0000 0.08112 0.0000Observations 190 190 190 190 190 190

Source: Calculated from the data which are collected by the Central Bank of China (CBC).

Notes

1. Measure adopted by the Taiwanese government include: deregulation of interest rates and foreign exchangerates restrictions, liberalization of establishment of new banks and foreign entry, enlargement of the businessscope of financial institutions, and internationalisation of financial market operations.

2. In the past, stock brokering and investment banking had largely been domain of Taiwans two hundred andsix local stock brokering firms.

3. The same as Berger (1995), we apply the distribution-free method on the same banking data rather thanimposing predetermined distributions on the X-efficiencies and random error.

4. Although accounting ratios in banking are typically used to obtain a partial measure of banking productivity,these measures are problematic. For example, if we want to increase labor productivity by replacing peoplewith machines, then labor productivity will rise, but actually the cost of the machines is not included in themeasure.

5. Prior studies did not measure the total cost of banking operations. For example, demand deposits are separatedfrom commercial loans.

6. For example, if we want to increase labor productivity by replacing people with machines, then labor produc-tivity will rise, but actually the cost of the machines is not included in the measure.

7. The conventional translog cost function system was developed by Christen, Jorgenson and Lau (1973), as asecond-order Taylor expansion series in output quantities, input prices and control variables.

8. In the study of Mitchell and Onvural (1996), total assets of their sample banks range from $0.5 billion to $100billion.

9. This limitation can be avoided by using the hybrid translog cost function proposed by Caves, Christensenand Tretheway (1980). Subsequently, Kolari and Zardkoohi (1987), Mester (1990), Rodriguez, Alvarez andGomez (1993), and the others have employed the hybrid translog cost function.

10. The cost-minimising input vector is just given by the vector of derivatives of the cost function with respect tothe prices.

11. Zellners (1962) iterative SURE technique will only be practicable by dropping one of the cost share equations.12. People sometimes have the tendency to use the terms X-efficiency and technical efficiency interchangeably.

However, there are important distinctions in the economic theories underlying X-efficiency and technicalefficiency (Leibenstein, 1980, p.27). Leibenstein also suggests that X-inefficiency was often much larger thanallocative inefficiency.

13. The concept of T.E (Technical efficiency) suggests that the problem is a technical one and has to do with thetechniques of an input called management. Under X-efficiency, the basic problem is viewed as one that is

412 YU AND LUU

intrinsic to the nature of human organization, both rganization whithin the firm and organization outside ofthe firm (Leibenstein, 1977, p. 312).

14. Deyoung (1997) demonstrate the diagnostic test in DFA cost efficiency model that uses eleven years datafrom U.S. commercial banks. His results suggest that 6 years of data is adequate to be reasonably sure thatestimated X-efficiency contains only small amounts of random error and that using 8 or more years of datamay violate the central DFA assumption that banklevel inefficiency remains constant over time.

15. Comparing with the assumptions for a single equation model, this specific error components model only relaxthe assumption that the covariance of residuals between equations is zero.

16. Accounting data were available from important businesses of Taiwanese financial institutions from 1985 to1998 made by the Central Bank of China.

17. The data about branch number for Taiwanese domestic banks was gathered from Financial StatisticsMonthly Taiwan District the Republic of China from 1985 to 1998 published by Economic Research De-partment, the Central Bank of China.

18. Personnel expense was obtained from Financial Statistics Abstract from 1994 to 1998 published byBureau of Monetary Affairs.

19. Suitable construction cost index in Taiwan area was not available because before 1991. Based on thisreason, we choose general index of consumer price in Taiwan area to replace construction cost index.General index of consumer price in Taiwan area was available from Commodity-Price Statistics Monthlyin Taiwan Area of the Republic of China published by Directorate-General of Budget, Accounting andStatistics, Executive Yuan, Republic of China.

20. They are Chiao Tung Bank, The Farmers Bank of China, Taiwan Cooperative Bank, First Commercial Bank,Hua Nan Commercial Bank and Chang Hwa Commercial Bank.

21. Cf. Bureau of Monetary Affairs (2000)22. In analyzing the market share, foreign banks accounted for 3.4% of total bank deposits, 3.65% of total

bank loans, 30.09% of total foreign exchange trading , 28.57% of total guarantee business, and 89% of totalderivatives trading at the end of June 1998. See Bureau of Monetary Affairs (2002).

23. Total deposits include: (1) due to the Central Bank of China and other banks (2) checking deposits (3) demanddeposits (4) time deposits (5) saving deposits (6) foreign deposits (7) (government deposits)

24. According the income statements form the CBC, we just can obtain the big item, the selling and admistrativeexpense, which include two specific items, labor expense and capital expense.

25. Skewness is a measure of asymmetry of the distribution of the series around its mean. Positive skewnessmeans that the distribution has a long right tail and negative skewness implies that the distribution has a longleft tail.

26. Kurtosis measures the peakedness or flatness of the distribution of the series. The kurtosis of the normaldistribution is 3. If the kurtosis exceeds 3, the distribution is peaked relative to the normal; if the kurtosis isless than 3, the distribution is flat relative to the normal.

27. Jarque-Bera is a test statistic for testing whether the series is normally distributed. Under the null hypothesisof a normal distribution, the Jarque-Bera statistic is distributed as x2 with 2 degrees of freedom.

28. The reported probability is the probability that a Jarque-Bera statistic exceeds the observed value under thenullsmall probability value leads to the rejection of the null hypothesis of a normal distribution.

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