Three essays on bank technology, cost structure, and performance

Three essays on bank technology, cost structure, and performance

THREE ESSASYS ON BANK TECHNOLOGY, COST STRUCTURE,

DISSERTATION

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics

in the Graduate School of Binghamton University

State University of New York

2007

UMI Number: 3266486

3266486 2007

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Accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics

in the Graduate School of Binghamton University State University of New York

2007

Feb 28, 2007 Chairman, Subal C Kumbhakar, Department of Economics, Binghamton University Christopher L Hanes, Department of Economics, Binghamton University Daniel J Henderson, Department of Economics, Binghamton University Jian Zhou, School of Management, Binghamton University

ABSTRACT

This dissertation addresses the issues around the technology and cost structure in commercial banking industries in both industrialized economy (US) and transitional economy (China) In addition, internal and external factors that affect bank performance,

in terms of technical change, technical efficiency and total factor productivity, are examined to provide policy and business implications to regulatory authorities and banking managers

The first paper investigates the existence of strategic group and heterogeneous technology in the US banking industry Two stages of analyses are conducted First, cluster analysis is carried out to segment the US commercial banks into seven distinct strategic groups in terms of their product mix and allocation of inputs The membership shifts across strategic groups during the sample period (1991-2000) are traced to explore the response of banks to the changes of market conditions and regulatory environments Second, based on the segmentation by cluster analysis, we further investigate the production technology and cost structures for each strategic group in the US commercial banking industry A system of cost function and derived share equations are used to estimate the technology for each group The distributions of returns to scale and technical change for each strategic group are also examined The results provide the evidence of the presence of distinct strategic groups and heterogeneous technologies in the US banking industry We find returns to scale and technical change vary substantially across strategic

groups Based on our findings, we conclude that the traditional application of a single homogeneous technology to the entire industry is likely to misrepresent the US banking industry

The second paper examines how and why the de novo banks in the US banking industry distinguish from their peer established banks Using a selected sample data of 2001-2005, we find that a typical de novo bank has higher capital equity ratio, higher concentration in real estate loans, higher cost of deposits and labor, and higher average quality of loans as well In terms of profitability (ROA), our observation on the de novo banks in recent years is consist with previous studies on the de novo banks active in the 1980s: negative earnings in first two or three years followed by substantial improvement

in their profitability, though still lagging behind a typical established bank at least in their first eight years of operation In order to link profitability with production process, we introduce a cost metafrontier model that enables us to compare technologies across different groups of banks by using measures of technology gap and global technical (cost) efficiency Empirically, we find that improving cost efficiency leads higher profitability for the de novo banks In contrast, this effect is absent for the established banks Scale economy exhibits its most advantageous effects on the smallest new banks by improving their technology, cost efficiency and thus profitability, while these advantages of scale diminish with the increase in size and finally they disappear when bank size reaches certain level

In the third paper, focus is shifted from industrialized economy (US) to transitional economy, China, where markets and institutional structures are different from those of

developed countries We employ an input distance function approach to analyze the impact of banking deregulations/reforms in China since early 1990s on the efficiency and the total factor productivity (TFP) change in Chinese banking industry We find that the joint-equity banks are more efficient than the wholly state-owned banks (WSOBs) Furthermore, both the WSOBs and the joint-equity banks are found to be operating slightly below their optimal size, suggesting potential advantages of expansion of their businesses Overall, TFP growth in Chinese banking industry was 4.4% per annum for the sample period 1993-2002 Joint-equity banks experienced much higher growth in TFP

(5.5% per annum) compared to the WSOBs (1.4% per annum)

To Quan and Julie

ACKNOLEGEMENTS

I am greatly indebted to Subal C Kumbhakar, my dissertation advisor, for his thoughtful guidance, critical comments, and constant encouragement Throughout my tenure as a Ph.d student, Subal has been a teacher, a mentor, and a friend Thanks to Subal, I have enjoyed learning econometrics and research skills from scientific writing to structural way of thinking He gave me his hearty support during the time when I was on the job market

Additional thanks go to other members of my dissertation Committee I am very grateful to Christopher L Hanes and Daniel J Henderson for their intuitive questions and invaluable comments on my dissertation I thank Jian Zhou, who joined my dissertation committee as an outside examiner, for his tireless reading and commenting I would also like to thank Neha Khanna, Clifford Kern and staffs in the Economics Department at Binghamton University for many helps and considerations along the way in the years back in Binghamton

My mother-in-law, JieZhi Hu came to the States and took care of my daughter during

my hectic days of preparing my dissertation Without her help, I couldn’t have gone so far with family obligations I greatly appreciate all she has done I am deeply indebted to my parents for their unconditional love and support during all these years when I am away from them

Julie, my daughter, is my angel and brings endless joys and laughs to my life

Without her, I couldn’t have been so energetic and kept pushing myself beyond what I thought I was capable of Last but not least, I cannot express the level of gratitude and love that I have for my husband, Quan Zhou He witnessed and shared every difficult and happy moments of my research His encouragement, support and help are so appreciated that my feelings are beyond any words to describe.

TABLE OF CONTENTS

Page

ABSTRACT IV ACKNOLEGEMENTS VIII LIST OF TABLES XII LIST OF FIGURES XIII

INTRODUCTION 1

CHAPTER 1 8

STRATEGIC GROUPS AND HETEROGENEOUS TECHNOLOGIES: AN APPLICATION TO THE US BANKING INDUSTRY 8

1.1 INTRODUCTION 8

1.2 CLUSTER ANALYSIS AND STRATEGIC GROUPS 11

1.2.1 C LUSTERING V ARIABLES 15

1.2.2 N UMBER OF C LUSTERS 16

1.3 COST ANALYSIS 17

1.3.1 M ETHODOLOGY 17

1.3.2 V ARIABLES 22

1.4 RESULTS AND FINDINGS 26

1.4.1 D IFFERENCES ACROSS C LUSTERS AND I DENTIFICATION OF S TRATEGIES 26

1.4.2 M EMBERSHIP S HIFT OF S TRATEGIC G ROUPS 28

1.4.3 B ANK S IZE D ISTRIBUTIONS OF S TRATEGIC G ROUPS 30

1.4.4 C OST STRUCTURE , R ETURNS TO S CALE AND T ECHNICAL C HANGE 31

1.4.5 C OMPARISON OF RTS AND TC ACROSS S TRATEGIC G ROUPS WITHIN B ANK S IZE G ROUP 34

1.5 SUMMARY AND CONCLUSIONS 36

CHAPTER 2 54

THE PERFORMANCE OF DE NOVO COMMERCIAL BANKS:

A COST METAFRONTIER APPROACH 54

2.1 INTRODUCTION 54

2.2 LITERATURE REVIEW 58

2.2.1 B ALANCE S HEET C OMPOSITION OF D E N OVO B ANKS 59

2.2.2 E VOLUTION OF P ERFORMANCE IN THE L IFE C IRCLE OF D E N OVO B ANKS 59

2.2.3 D ETERMINANTS OF P ERFORMANCE 61

2.3 METHODOLOGY 64

2.4 DATA 73

2.5 MODEL SPECIFICATION AND ESTIMATION 76

2.5.1 M ODEL S PECIFICATION 76

2.5.2 V ARIABLES 78

2.5.3 E STIMATION AND T ESTS 80

2.6 RESULTS 83

2.6.1 S IZE , A GE AND P ROFITABILITY 83

2.6.1.1 Size and Profitability 83

2.6.1.2 Age, Profitability and Convergence 84

2.6.2 E STIMATION R ESULTS OF C OST M ETAFRONTIER M ODEL 85

2.6.2.1 Test Results for Heterogeneous Technologies 85

2.6.2.2 Effects of Z Variables on the Cost Frontier 86

2.6.2.3 Technology Gap and Technical Efficiency Relative to Metafrontier 89

2.6.3 R ELATIONSHIP BETWEEN P ROFITABILITY AND C OST E FFICIENCY 90

2.7 SUMMARY AND CONCLUSION 96

CHAPTER 3 110

ECONOMIC REFORMS, EFFICIENCY, AND PRODUCTIVITY IN CHINESE BANKING 110

3.1 INTRODUCTION 110

3.2 INSTITUTIONAL AND REGULATORY CHANGES IN THE CHINESE BANKING INDUSTRY 114

3.3 METHODOLOGY 118

3.4 DATA 125

3.5 EMPIRICAL RESULTS 130

3.5.1 R ETURNS TO S CALE (RTS) 131

3.5.2 T ECHNICAL E FFICIENCY 131

3.5.3 E FFECT OF E XOGENOUS F ACTORS ( THE Z S ) ON T ECHNICAL E FFICIENCY 132

3.5.4 P RODUCTIVITY G ROWTH 135

3.6 SUMMARY AND CONCLUSIONS 136

BIBLIOGRAPHY 149

LIST OF TABLES

Table 1 1: Definitions of the Variables 38

Table 1 2: Descriptive Statistics of Variables in Cost Function for Selected Years 40

Table 1 3: Means of Selected Variables for Different Clusters 41

Table 1 4: Total Assets, RTS and Technical Change by Strategic Groups 42

Table 1 5: RTS of Bank Size Groups across Strategic Groups 43

Table 1 6: Technical Change of Size Groups across Strategic Groups 44

Table 1 7: Stochastic Dominance Tests of RTS and Technical Change 45

Table 2 1: Definitions of the Variables 99

Table 2 2: Descriptive Statistics of Relevant Variables 101

Table 2 3: Effects of Z variables on Cost Functions 102

Table 2 4: Summary of Technical Efficiency and Technology Gap Ratio 103

Table 2 5: Estimation Results of Regression of ROA 104

Table 3 1: Descriptive Statistics of Key Variables 138

Table 3 2: Estimation Result of the Input Distance Function 139

Table 3 3: Efficiency, RTS, Δ TFP and TFP Index by Ownership 140

LIST OF FIGURES

Figure 1 1: Share of Non-interest Income, 1984-2004 46

Figure 1 2: Membership of Different Strategic Groups, 1991-2000 47

Figure 1 3: Percent of Total Assets for Different Strategic Groups, 1991-2000 48

Figure 1 4: Average Bank Size for Different Strategic Groups, 1991-2000 49

Figure 1 5: Distribution of Total Assets (Logs) For Different Strategic Groups 50

Figure 1 6: Kernel Density of Returns to Scale by Strategy Group 51

Figure 1 7: Empirical CDFs of Returns to Scale by Strategy Group 52

Figure 1 8: Empirical CDFs of Technical Change by Strategy Group 53

Figure 2 1: Trends of De Novo Banks and Total Commercial Banks 105

Figure 2 2: Metafrontier Cost Function Model – Simple Case 106

Figure 2 3: Bank Size and Profitability (ROA) 107

Figure 2 4: Age and ROA 108

Figure 2 5: Comparison of Profitability: De Novo Bank Vs Established Bank 109

Figure 3 1: An Input Distance Function with Two Inputs 141

Figure 3 2: Asset Distribution of Banking Institution (end of 2000) 142

Figure 3 3: Labor Productivity of Chinese Banks (1993-2002) 143

Figure 3 4: Returns to Scale of WSOBs and Joint-Equity Banks (1993-2002) 144

Figure 3 5: Technical Efficiency of WSOBs and Joint-Equity Banks (1993-2002) 145

Figure 3 6: Dynamics of Total Factor Productivity Change (1993-2002) 146 Figure 3 7: Dynamics of Components of TFP Change (1993-2002) 147 Figure 3 8: Dynamics of Total Factor Productivity Index (1993-2002) 148

of banking industries across many countries in the world (See Berger and Humphrey (1997) for an international survey of banking studies of production, efficiency and performance)

This dissertation consists of three independent but related studies on the US commercial banking industry, the de novo banks in the US and the banking industry in China, respectively All of the three chapters address the topics around technology, cost structures, and performance of commercial banks with different emphasis in each chapter Being the most profound banking system in the world, the US banking industry has always been the focus of banking studies (for example, Hunter & Timme (1986), Bauer, Berger & Humpherey (1993), Berger and Mester (2003), among many others) The past decade was a fascinating time for the US banking industry, which features trend of consolidation and expansion of interstate banking, renewed energy for changes after the dismal days of the early part of the 1990s, the laid-out of legislative ground work for Gramm-Leach-Bliley, the ever intense competition in the broader financial services arena, etc To complement the existing literature, the first chapter in this dissertation addresses the issues of technology, cost structure and performance of the US commercial banking industry from 1991 to 2000

Instead of following the traditional cost function approach that assumes single technology for all the firms in the industry, the first paper hypothesizes the existence of heterogeneous technologies in the US commercial banking industry The hypothesis arises from the observation that the US banks have been creating their own niches by adopting different business strategies in order to retain their competitive advantages in the market

This study takes two steps First, it carries out a cluster analysis that is purely data based without any assumption on why clusters exist As the result of cluster analysis, the US banks are segmented into different strategic groups Within each strategic group, banks share similar characteristics of major attributes, like product specialization, cost shares, etc, while across strategic groups, banks are dissimilar to each other by the attributes Then, in the second step, a system of cost function and derived share equations are introduced to estimate the underlying production technology for each strategic group The returns of scales (RTS) and technical change (TC) for each bank are derived from the parameter estimates of the cost function system The substantial variations of RTS and TC across strategic groups provide the evidence of heterogeneous production technologies and cost structures within the US banking industry As a result, in order to reduce estimation biases and accurately measure the production technology (or/and cost structure)

of the US banking industry, it is necessary to treat different strategic groups separately Otherwise, misleading conclusions are very likely to be drawn, based on the analysis by pooling all banks together This is the major conclusion and contribution of the first paper Concurrent to the overall trend of diminishing banks in the US, there was a rejuvenated wave of new banks (de novo banks) since the middle of 1990s What makes the bankers of these de novo banks decide to enter the market while others are retreating?

By common sense, a new bank is usually more financially fragile and has higher chances

to fail than an established bank, even though they are in similar scale The questions arising from the common sense are: in what aspects these de novo banks distinguish themselves from the established banks and what enables them to compete again the

established banks? The second paper in the dissertation attempts to answer the above questions by examining the characteristics of the de novo banks in the US that were established since early 1990s

There are a handful of studies on the de novo banks (for example, Hunter and Srinivasan (1990), DeYound and Hasan (1998), Seelig and Critchfield (2003), etc) The major focuses of these studies are on the balance compositions of de novo banks, the entry and exit of de novo banks, the evolution of performance in the life circle of de novo banks, and the determinants of their performance The second chapter in the dissertation complements the existing literature in two aspects First, almost all prior studies dealt with the de novo banks that were established in the 1980s, and their performance during the 1990s was investigated in those studies The study in the second chapter explores the performance and its determinants of the de novo banks that were established after 1993 and are active in recent five years (2001-2005) A study on the most recent data should apparently be better suited than those on historical data for providing reliable inference on the policy implications in the current economic and banking industrial environments Second, the study employs a cost metafrontier model, which is relatively new and has only been applied in a few recent empirical studies The cost metafrontier approach provides a tool to assess technological gaps and technical efficiencies across different production technologies, which is an unattainable task by the traditional cost function approach

Specifically, following the standard approach in the existing literature, the second chapter starts with the examination of the de novo banks’ assets structure, funding mix,

capital levels, asset quality, credit risk, profitability (ROA), etc Next, the study assumes again the existence of heterogeneous technologies in the de novo banks in the US, and then employs a cost metafrontier model and estimates a cost function for each of the five groups of the de novo banks Furthermore, for comparison purpose, a population of established banks with similar scale as the de novo banks is included in the study Cost structures and cost efficiencies across the groups of de novo banks and between subpopulations of the de novo banks and the established banks are examined and compared Last, one step further, the study links cost efficiency and profitability with controls on other factors, attempting to identify whether cost factor or revenue factor is the driving force for profitability Overall, the approaches employed in the study provide

a thorough examination on the de novo banks and help capture the variations of performance caused by embedded heterogeneous technologies across different groups in the de novo banks and between the de novo banks and the established banks

Transitional economies distinguish themselves from developed economies in a number of ways, which makes them deserve special attention of research Since 1980s, many studies have shown increasing interests on the banking industries in the transitional economies, including former Soviet republics, east European countries, China, India, etc China’ central government has launched a series of financial reforms since 1980s, aiming

to tackle the problems caused by its dysfunctional banking sector The issues with Chinese banking industry have attracted a great deal of interests from academic and governmental/organizational research institutions However, the studies on Chinese banking industry are limited and insufficient, mainly due to the difficulty of obtaining

reliable data Most of the existing studies are case studies with emphasis on the comparison of financial ratios The third chapter contributes to the Chinese banking studies by focusing on the assessment of effectiveness of the reforms using a regress-based input distance function The study uses the data of 14 major domestic banks from 1993 to 2002 During this period of time, the banking sector reforms were strengthened and the domestic banks had experienced gradual transformation in many aspects, which were supposed to aid in improving the performance and enhancing the competitive capacity of these domestic banks The objective of the study is to answer the questions whether the reforms achieved the goals that were originally set at the start, and how the performance of these domestic banks was affected by various internal and external factors

An input distance function approach is employed in the study Distance functions have the advantage of accommodating multiple inputs and multiple outputs, which is quite common in the banking industry Furthermore, they provide cost implications without requiring price information for estimation, which is particularly important when assumptions about competitive markets are unlikely to be met or when price information

is not available or accurate Based on these two major advantages, an input distance function approach is well suited for the study in Chinese banking in the dissertation The third chapter first investigates the effects of possible forces on technical efficiency of the domestic banks in China, including ownership type, capital adequacy ratio, bank size and environmental factors Second, it examines the dynamic pattern of total factor productivity changes of these domestic banks by decomposing them into scale effects,

technical change, technical efficiency change and change induced by bank characteristics and environmental forces Through the examination, the third chapter provides a comprehensive assessment of the performance of Chinese domestic banks, and the internal and external factors that affect their performance

All in all, the dissertation enriches the body of literature of banking studies on production and performance with some new perspectives The results from these three studies strengthen the findings from prior studies and offer new insights to understanding production technologies and cost structures of banking industry in both developed economy and transitional economy This more in-depth understanding of technologies and cost structures further helps assess the performance of the banking industries in a more accurate way and provide more relevant policy implications

CHAPTER 1

STRATEGIC GROUPS AND HETEROGENEOUS TECHNOLOGIES:

1.1 INTRODUCTION

Deregulation and technological innovations since the 1980s have provided great opportunities for many banks in the US to create their own niche in the ever increasing competitive environment If one takes a cursory look at the operations of banks today, one will observe that banks tend to exhibit less resemblance to each other and follow widely divergent business strategies Some banks specialize in a particular area of products and services, while others follow a strategy of diversification by participating in a wide range

of activities Banks also differ in terms of their funding sources Some utilize core deposits as their main source while others rely more on federal purchased funds Therefore, traditional partitioning of the banking industry into wholesale and retailing appears to be too broad to represent the existing diverse strategies in the US banking industry

The theory of strategic groups proposes the possibility of existence of multiple

strategic groups within the same industry The concept of strategic groups was first introduced in the work of Hunt (1972), Caves and Porter (1977), and Porter (1980), and it was used to explain the observed heterogeneity of firm’s conduct and performance within industries In this literature, strategy groups are commonly classified by a set of strategic variables (or several strategic dimensions) that affect the decision making of a firm Firms

in the same group have similar values of those strategic variables, and tend to react in a similar way to the changes in market conditions Porter (1980) pointed out that one cannot determine a priori whether all firms in the same industry will adopt the same strategy or each firm will choose a unique strategy Therefore, the issue of existence and identification of meaningful strategic groups, if there are any, is left to empirical studies.Strategy is usually manifested in several dimensions simultaneously In the banking industry, these dimensions include product mix, funding sources, customer focus, size, geographical scope, etc Grouping banks by only one predetermined variable, as usually done in past studies (for example, Grifell and Lovell (1997), Wheelock and Wilson (2001), and Berger et al (1987), ignores other key components of a business strategy, which might result in false classifications and wrong conclusions Cluster analysis can be used

as a sorting mechanism to classify banks into various strategy groups Cluster analysis allows one to conduct multi-dimensional analysis by utilizing an array of relevant information that might reflect the business strategy a bank adopts, and it requires minimum assumptions with regard to statistical inference One implication of cluster analysis is that members in a given cluster tend to be similar to each other in some sense, and members in different clusters tend to be dissimilar In the context of our study of the

US banking industry, banks in the same group are assumed to be adopting similar business strategies while banks in different groups are adopting different strategies

To address the significance of strategic groups on issues related to estimating production technology, one has to estimate either production or cost functions However, most studies of production or cost functions rely on the assumption of a single technology

in the industry, ignoring the existence of diverse strategic choices within the industry The aim of our study is to offer reconciliation between the strategy studies and the production/cost function studies By conducting a two-stage analysis, our study provides

a thorough examination of both business strategies and technologies in the US banking industry At the first stage, we carry out a cluster analysis on a large sample of the US banks to identify various business strategies based on banks’ product mix and allocation

of inputs The shifts of membership among different strategic groups over time are traced

to investigate the banks’ response to changes of market conditions and regulatory environments Moreover, we look into the total assets distributions across different strategic groups to check the validation of bank size as a proxy for strategy

At the second stage, we further explore the relationship between business strategy and production technology The underlying production technology, represented by a cost function, is estimated for each strategic group, and heterogeneity of cost functions is tested econometrically Furthermore, returns to scale (RTS) and shifts in the underlying technology (technical change) of each group are evaluated in order to investigate the difference in the performance of banks under different business strategies Specifically, a system of translog cost function and derived share equations is used for estimation

purposes, and this flexible system of equations allows for variable RTS and non-neutral technical change Statistical tests for the equality of distributions of RTS and technical change (TC) for each pair of strategic groups are performed using nonparametric Kolmogorov-Smirnov tests In additional, we also performed stochastic dominance tests between each pairs of RTS distributions and TC distributions to examine whether economy scale (technical change) of one strategic group is statistically better than another over a range of RTS (technical change) Another feature of our study is that we control for asset quality and risk exposure of earning assets in the cost analysis, which is often ignored in other studies Ignoring them from the analysis is likely to confound improvements of assets quality and risk exposure over time as improvements in technology

The rest of the paper is organized as follows First, cluster analysis is performed and comparison of characteristics of banks across clusters is made to identify various business strategies adopted by the US banks Next, an empirical model of cost function is outlined, followed by discussion of variables and data Empirical results of both cluster and cost analysis are summarized in section 4 Meanwhile, the validity of bank size as a grouping criterion is also assessed in section 4 Section 5 concludes the paper

1.2 CLUSTER ANALYSIS AND STRATEGIC GROUPS

Deregulation and technological innovations in the 1980s contributed, to a large extent,

to the strategic diversity in the US banking industry Although the inclusion of multiple

outputs in the production analysis helps to characterize the nature of the banking industry better, the accommodation of different strategies and the associated heterogeneity in production technologies are perhaps far more important In order to accurately capture the strategic choices that banks make, selection of a scientific approach of grouping becomes

a critical issue The traditional method of segmenting banking industry into groups by using a single, predetermined variable, like bank size, ignores other important features of the strategy that a bank adopts In contrast, the multivariate cluster technique allows an array of potential relevant variables to be included in strategic choices Clair (1987), Kolari and Zardkoohi (1987), Amel and Rhoades (1988, 1992), Brown and Glennon (2000) and Tortosa (2002) are among the few studies that employed multivariate clustering technique in segmenting banking industry into different strategic groups These studies defined strategies in terms of banks’ product mix and funding sources Items from balance sheets and off-balance-sheets (OBS) were used as strategic variables in their clustering procedures

Some studies have provided empirical evidence of multiple strategic groups in financial services industry, for example, Hayes et al (1983) on investment banking industry, Curry and Rose (1997) on thrift institutions, and Amel and Rhoades (1988, 1992)

on commercial banking industry However, there is no consensus among these studies on the definition of “strategy” and hence on the criterion which is used to classify strategic groups As a result, various strategic variables and grouping methods have been used in the literature Some of the studies carried out single dimensional classification methods: bank size, location, ownership type, sources of income, etc For example, Grifell and

Lovell (1997) divided a sample of Spanish banks into private and savings banks, and Wheelock and Wilson (2001) grouped the US commercial banks in terms of total assets which is a proxy for size Bank size is by far the most popular variable used to classify banks (see Wheelock and Wilson (2001), Berger et al (1987), among others) However, there is no theoretical reason (other than the fact that it is quite simple and intuitive) supporting the belief that banks of equal size should opt for the same business strategy, conduct the same types of activities and adopt the same product technology In addition, the asset limits to define bank groups are usually arbitrarily determined As a result, the number of groups2 in these studies varies, and the concepts of “small”, “medium” and

“large” sized banks are not consistently defined This makes comparison of results across studies difficult

Cluster analysis is ideal for grouping data It sorts objects of similar characteristics into respective groups without requiring any explanation as to why they exist Several types of clusters are possible, including disjoining clusters, hierarchical clusters and overlapping clusters For the purpose of cost analysis in the next section, a clearly defined segmentation of disjoint clusters is needed Disjoint clusters are mutually exclusive, which means each observation belongs to one particular cluster Fastclus procedure in SAS3 is used to find disjoint clusters of observations We adopt the k-means clustering algorithm (Hartigan (1975)) in our clustering procedure As a result, means of all variables across clusters are distinct, banks within a cluster exhibit similarity in terms of

2 For example, ten groups in Wheelock and Wilson (2001) for entire banking industry; seven groups in Hunter and Timme (1995) for large banks with more than 1 billion of total assets; only two groups (“large” and “small”) in Humphrey and Pulley (1997)

their product mix and use of inputs, and banks in different clusters tend to be dissimilar

We take several issues into account in our clustering procedure used in this paper First, clusters are based on an array of financial variables that are believed to be related to the unobserved business strategy It is the data rather than some arbitrary a priori classification criterion that defines various strategies that might exist Second, the number

of clusters is not decided arbitrarily, but determined by the descriptive approach of canonical variables4 Third, since clusters are formed so that a minimum distance among clusters is achieved, large scaled variables tend to have large weights and thus have greater effect on the variance across clusters In order to avoid scale biases of any particular variable, all clustering variables are standardized before we carry out the cluster analysis

The significance of strategic groups in estimating an underlying production process can be examined by estimating either production or cost functions Since late 1960s the production function and its dual cost function approaches have been well employed in the empirical studies using microeconomic data (for example, Diewert (1974), Christensen and Greene (1976), Brown, Caves and Christensen (1979), Caves and Christensen and Swanson (1981), among others) Both the production function and its dual cost function represent an underlying technology Production technology, according to Frisch (1965), is

a pure technical process of transformation of certain goods and/or services (as inputs) to other goods and services (outputs), directed by human beings Thus, business strategy

4 Canonical variables are obtained through canonical discriminant analysis in SAS “Given two or more groups of observations with measurements on several quantitative variables, canonical discriminant analysis derives a linear combination of the variables that has the highest possible multiple correlation with the

determines the choice of inputs and product mix which in turn determines the production technology of a firm In other words, production technology is closely related to business strategy Consequently, it is reasonable to assume that homogenous production technology is adopted within a strategic group and heterogeneous production technologies exist across strategic groups However, the conventional production/cost function approach relies on the assumption of a single homogeneous production technology for all firms

of total assets) aggregated from balance sheets5 are selected for cluster analysis These include: five outputs (individual loans, real estate loans, business loans, federal funds sold

5 These items include individual loans, real estate loans, business loans, federal funds sold and securities purchased under agreements to resell, fixed assets, securities and all other assets from asset side, borrowed funds, interest bearing deposits, equity and all other liability from liability side These variables are directly aggregated from the balance sheet, and the ratios of those assets or equity and liabilities to the total assets are then constructed Since those ratios from asset side add up to one, the variable “all other assets” is dropped in order to avoid multicollinearity problem Similarly, ratio of equity and all other liability is

and securities purchased under agreements to resell, and securities), two funding inputs (borrowed funds and interest bearing deposits) and one quasi-fixed input (fixed assets and premises) Beyond the balance sheet, average number of full time equivalent employees is also included in the list of clustering variables In addition, non-interest income (as a percentage of total operating income) is also included in our cluster analysis Our rationale for incorporating the latter variable is that in recent years, many of the US banks have earned substantial amount of non-interest income from off-balance sheet activities, like letter of credits, securities brokerage and underwriting, and mutual funds sale In

2004, the share of non-interest income accounted for 43% of the total net operating income, up from 25% in 1984 This is shown in Figure 1.16 Thus if we exclude this non-interest income variable from our cluster analysis, strategic shift towards non-traditional activities would have been concealed

1.2.2 Number of Clusters

Theoretically, the optimal number of population clusters differs across the types of cluster analyses (Hartigan 1985; Bock 1985).7 There are two conflicting concerns when determining the appropriate number of strategic groups On one hand, it might not be meaningful if there are too many clusters, as differences across clusters tend to be trivial

6 Data source is from aggregate data from historical statistics on banking, provided by FDIC (www.fdic.gov)

7 Empirically, the number of strategic groups used in the past banking studies based on cluster techniques varies across studies For example, Amel and Rhoades (1988) concluded that six clusters exist in 16 selected US banking markets in 1978, 1981 and 1984, while Kolari and Zardloohi (1987) identified four groups with distinct product mix by analyzing 600 banks in the Functional Cost Analysis program in the U.S during the 1979-1983 period More recently, Brown and Glennon (2000) concluded that there were six

and identification of strategies becomes difficult On the other hand, if too few clusters are determined, some different strategies might be mixed into one cluster and thus “true” heterogeneous technologies might be erroneously treated as homogeneous In order to avoid having too few or too many groups, we took several measures At first, a preliminary analysis specifies a large number of clusters, and initial seeds (means of clustering variables) of preliminary clusters are obtained8 Next, extreme outliers are identified as those observations in a cluster that has low frequency (less than five observations) In order to avoid the distortion of outliers on the cluster centers, those outliers are excluded from the main clusters and only the remaining observations are tossed in the cluster analysis again with a smaller number of clusters specified In each round of the procedure, descriptive plots of canonical variables are used to diagnose whether the appropriate number of clusters is achieved so that difference across clusters is discernable and also meaningful Last, after the number of cluster is determined and the cluster means are calculated, the outliers that were previously excluded from main cluster analysis are then re-assigned to the nearest clusters By this treatment, we reduce the potential distortional effects of outliers on the formation of clusters

1.3 COST ANALYSIS

1.3.1 Methodology

8 Several numbers were used in the experiments, including 20, 25, 30, 50 and so on After the elimination

of clusters with low frequency and repetition of the process, it turned out that the similar numbers of clusters were always obtained

Conventional cost function estimation is based on the assumption of homogeneous production technology for all firms However, as we have shown in the previous section, firms within same industry adopt different strategies and technologies Therefore, we hypothesize that the assumption of a single technology for all firms might not hold in our case, and it is more appropriate to estimate the underlying technologies separately for each strategic group, instead of estimating a homogeneous technology for the whole industry

Technology is either directly represented by a production function, or indirectly by a cost function Since outputs in service industries are exogenous to the firms (demand determined) and cannot be stored, a cost function approach is more appropriate and is widely used in banking studies Furthermore, the cost function approach has an advantage over a production function approach in handling multiple outputs (Kumbhakar and Lovell (2000)) We use a system of cost function and the derived input cost share equations The advantage of using a cost system instead of the cost function alone is that the system approach uses more information via the share equations without adding any extra parameters Thus, the system approach gives more degrees of freedom and the estimated parameters are more efficient

For estimation purposes, we assume the following flexible translog function form for cost function with M outputs (y), N input prices (w), Q environmental variables (z) and time (t):

equations (2)) are total cost and input cost shares, while the exogenous variables are input

prices, output quantities, and environmental variables that control for quality of assets,

risk exposure, etc Since our data covers ten years from 1991 to 2000, time is

incorporated in the cost function (and in the share equations as well) to capture exogenous

technical changes that might have taken place during the period

According to the properties of cost function9, some restrictions are to be imposed on

the parameters in the cost system (1) First, a cost function is homogeneous of degree one

in input prices, which imposes the following restrictions ∑

n n

β = 1, ∑

k nk

where C and it* w are normalized by nit* w , and thus 1it C it* =(C it/w1it)andw nit* =(w nit/w1it)

By dropping the first input share equation we avoid the singularity problem associated with the fact that the sum of cost shares is unity

Second, we impose the symmetry restrictions by imposing the following restrictions

on the parameters

mj

α = αjm for all m, j and βnk= βknfor all n, k (5)

Classical error terms are added to the equations in (3) and (4) and the system is jointly estimated by using iterative seemingly unrelated regression procedure which is equivalent to the full information maximum likelihood method All parameters that are associated with the input pricew1can be recovered from

∑

−

=

n n

2 ( ( 1))

g

I SSE −∑I SSE χ −

(6) where ln r and ln u ln ug

g

L L =∑ L are the values of the likelihood functions for the

restricted (single technology) and unrestricted (seven different technologies, one for each cluster) models; K is the number of parameters in each group; I is the number of total observations in the sample; g is the number of groups, SSE is the weighted (by the r

inverse of the estimated variance covariance matrix of the error vector in the cost system) sum of squared residuals from the restricted model, and SSE is weighted the sum of g

squared residuals from cluster g

In a translog cost function the parameters themselves are usually not of prime interest The estimated parameters are used to compute measures such as returns to scale and technical change, which are of interest to policy makers and firm managers RTS is a standard and popular measure of scale efficiency in production, and it tells us whether a firm is operating at its minimum efficient scale (defined by unitary RTS) In the context

of a single output, increasing returns to scale implies falling average cost with the expansion of output as long as the input prices remain unchanged Similarly, decreasing returns to scale means the average cost curve rises as output increases, and constant returns to scale means that with expansion/contraction of output average cost remains unchanged, ceteris paribus The measure of RTS is reciprocal to scale economies that can

be empirically obtained from a cost function by differentiating the total cost function with respect to all the bank outputs For the translog cost function, the RTS is:

*

* ln

In the context of a cost function, technical change is viewed as a shift in the cost function and is often called the dual rate of technical change, which is not identical to the primal rate of technical change obtained from the production function10 The dual rate of technical change is defined as the rate of cost diminution If there is technical progress (regress) the cost function ( , , )c w y t will be non-increasing (non-decreasing) in t Thus, the expression for the dual rate of technical change (TC) derived from the translog cost function is:

* *

ln ( , , , )( , , , )

transaction approach failed to carefully analyze both the technical and economic aspects

of production of financial firms According to them, banks function as an intermediary between depositors and investors In doing so banks use deposits along with capital and labor as inputs and produce various types of earning assets which are treated as outputs The dollar values of earning assets are outputs of a bank

Since the 1980s, fee-based income from innovative activities has increased substantially, up from 25% of the total net operating income in 1984 to 43% in 2004 (Figure 1.1) These innovative activities are usually not reflected in balance sheets Therefore, ignoring these nontraditional activities and only focusing on the balance sheet activities will result in omission of output(s) and hence misrepresentation of the underlying technology To avoid this problem we include off-balance-sheet (OBS) assets

as another important output However, it is difficult to accurately measure the aggregate OBS assets since there are many OBS products from derivatives to loan commitments In addition, each OBS product has its own attributes and characteristics, and serves different needs and purposes Three major alternative methods are used in the existing literature to measure the aggregate OBS assets, viz., credit equivalent measure11, revenue equivalent measure12 and asset equivalent measure For the purpose of this paper, the third approach

is adopted so that the OBS assets are measured in terms of stock value of assets, which is

11

First, the face value or nominal amount of OBS items are converted to credit equivalent amount by using credit conversion factors set out by Basel Committee’s guidelines for risk-based capital standards Then, those OBS items are classified into four categories of risk weights (0%, 20%, 50% and 100%) Risk-weighted credit equivalent measure (RWCEM) of OBS is constructed as average of credit equivalent amounts of OBS items weighted by risk factors assigned to them Since this measure is based on the risk characters of those OBS activities, some OBS items in the category of 0% risk weight are excluded from the measure As a result, the amount of OBS activities is understated

12

Some use non-interest income as a proxy for the quantity of OBS activities It is simple and convenient, but it overstates the amount of OBS activities since non-interest income also come from service charges on deposits/loans transactions In addition, this measure is not comparable to the other outputs that are

consistent with other balance sheet assets The asset equivalent measure was proposed by Boyd and Gertleo (1994) and used in Siems and Clark (1997, 2002) Assuming equal rates of return on both balance sheet assets and OBS assets, the non-interest income associated with off-balance-sheet assets is capitalized to construct an asset equivalent

measure of all OBS assets using formula: asset equivalent of OBS = A0*Adj NII_

I− −E LLP ,

where A is the total earning assets on the balance sheet, 0 Adj _ NII is non-interest income associated with off-balance-sheet assets, I is the total interest and dividend income, E is the total interest expenditure and LLP is the loan loss provision This approach not only gives a consistent measure of OBS assets, but also takes the revenue-generating capacity of those OBS activities into account

Four inputs are used in this study, namely, labor, fixed assets, borrowed funds and interest-bearing deposits Price of labor is the average annual wage per full time equivalent employee Prices of fixed assets, borrowed funds and interest-bearing deposits are calculated from the flow of expenses on these inputs divided by the corresponding stocks values, and they are measured as interests per dollar of fixed assets/borrowed funds/interest-bearing deposits

Earning assets from both balance sheets and off-balance-sheet are considered as outputs in this study, including individual loans, real estate loans, business loans, federal funds sold and securities purchased under agreement of resale, securities and asset equivalent measure of off-balance-sheet assets The quantities of those outputs are measured as their dollar values

Besides input prices and output quantities, quality and risk exposure of assets affect

bank costs as well Three types of proxies of control variables are included in the cost function - risk of insolvency, quality of loans and credit risk of loans Ratio of equity to total asset is usually used to measure risk of insolvency, or market-based risk A lower ratio of equity means that the banks are more likely to go into bankruptcy when it is in trouble and facing default This is because these banks need to borrow more to finance their funding needs, which means more interests will be paid for their deposits and borrowed funds thereby increasing their cost Therefore, we expect a negative sign on the coefficient of risk of insolvency variable in the cost function Quality of loans is measured by the ratio of non-performing loans (NPL) to total loans and lease financing receivables We expect that the higher the ratio, the higher the cost because banks need more sources to monitor those NPL and to negotiate with borrowers in order to reduce the potential loan loss as much as possible Credit risk of loans is proxied by the ratio of allowance and reserve to total loans and lease financing receivables Allowance and reserve to total loans and lease is the accumulated stock value established and maintained against claims on domestic and foreign borrowers experiencing difficulties in servicing their debts according contracts The higher the ratio, the better is the cushion to absorb the loss if the borrowers default their loans

Our sample data is taken from the quarterly Reports of Condition and Income from

1991 to 2000 The data covers most of commercial banks in the US during this time period This gives us a sample of 82,398 banks All the variables that are used in both cluster analysis and cost analysis are calculated from the disaggregate data that is directly reported by the banks in the Call Reports The detailed construction of the relevant