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Tiêu đề Incomplete Contracts and Corporate Governance: Theory and Evidence - Case Studies on Chinese Banking and U.S. Franchising
Tác giả Chen Shaoling
Người hướng dẫn Susheng Wang
Trường học Hong Kong University of Science and Technology
Chuyên ngành Economics
Thể loại thesis
Năm xuất bản 2008
Thành phố Hong Kong
Định dạng
Số trang 256
Dung lượng 5,23 MB

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List of Figures Figure 2.1 The Effect of Market Share on Choice of Control Structures.... 29 Figure 2.3 The Effect of Internal Control Ability on Choice of Control Structure .... Chart

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Incomplete Contracts and Corporate Governance:

Theory and Evidence

Case Studies on Chinese Banking and U.S Franchising

by

CHEN Shaoling

A Thesis Submitted to The Hong Kong University of Science and Technology

in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

in the Department of Economics, School of Business and Management

August 2007, Hong Kong

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3306803

3306803

2008

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Acknowledgements

I am deeply grateful to my supervisor, Susheng WANG, who has been a warm, generous, and highly intelligent mentor over time and has supervised more than just the product itself Professor WANG took an active concern with the development of this thesis, annotating it with many excellent suggestions, and extending my intellectual horizons in terms of method and purpose My appreciation to Professor WANG for his practical advice and continuing encouragement throughout my entire graduate education is immeasurable

An unparalleled gratitude must be extended to all members of my thesis committee, Professors Jiahua CHE, Xinyu HUA, Sudipto DASGUPTA, and Steven WEI (Hong Kong Polytechnic University) for reading such a lengthy thesis, and for providing many helpful discussions of the topic, which brought this thesis to fruition

I would like to thank all of my instructors, in particular Professors Songnian CHEN,

In CHOI, Leonard K CHENG, Danyang XIE, Jaehyon NAHM, as well as Professor Stephen Y CHIU (University of Hong Kong) for introducing me to the rewarding and challenging world of economic research in HKUST Without the time and energy they contributed to my academic career, this thesis could not have been made

My warmest appreciation goes to my fellow students for their generosity, insight and friendship I cannot list all from whom I obtained invaluable information and ideas, but I would like to mention Jun WU, Jin ZHANG, Lin GENG and Ping SHU for seeing me through to the end, for being my biggest supporter, and for surrounding

me with positive energy and love

And most of all, this thesis is dedicated to my parents, to whom I owe everything, for enriching my life with tireless commitment, support and confidence; and to my husband, Haisheng YANG, for creating an atmosphere of love in which hard work became easy

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Table of Contents

Title Page i

Authorization Page ii

Signature Page iii

Acknowledgements iv

Table of Contents v

List of Tables vii

List of Figures viii

List of Charts x

Acronyms… xi

Abstract… … xi

Chapter 1 Introduction 1

Chapter 2 What Drives Recent Changes in the Control Structure of Chinese Banks 5

2.1 Introduction 5

2.1.1 One Reaction to Four Facts 5

2.1.2 Literature Review 10

2.1.3 My Contributions 11

2.2 Model 12

2.2.1 Decentralized Hierarchy 15

2.2.2 Centralized Hierarchy 17

2.2.3 Specifications and Solutions 20

2.3 Main Conclusions 24

2.3.1 Opening Up of Banking Market 24

2.3.2 Reform of Going Public 27

2.3.3 Increasing Serious Financial Frauds 30

2.3.4 Persistent High Ratio of NPLs 32

2.3.5 Major Determinant: A Comparison among Four Facts 36

2.4 Minor Results 40

2.4.1 Choice of Control Structure 40

2.4.2 Job Satisfaction 45

2.4.3 Payment System 49

2.4.4 Testable Hypotheses 52

2.5 Concluding Remarks 53

Chapter 3 Dynamic Behaviors of Franchise Chains From a Combined Perspective of Resource Scarcity and Agency Theory 55

3.1 Introduction 55

3.1.1 What’s franchising? 56

3.1.2 Literature Review 58

3.1.3 Contributions and Structure 63

3.2 The Two-Period Dynamic Model 65

3.2.1 Second-period Choice 69

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3.2.2 First-period Choice 74

3.3 General Properties 76

3.3.1 A Summary 77

3.3.2 Benchmark 82

3.4 Main Results 90

3.4.1 Choice of Governance Structure: Franchising vs Integration 92

3.4.2 Dynamic Franchise Contract 100

3.5 Minor Results 108

3.5.1 Pricing 108

3.5.2 Franchisee’s Effort 110

3.5.3 Franchisor’s Effort 116

3.6 Empirical Implications 118

3.6.1 Proxies for Chain-specific Attributes 118

3.6.2 Proxies for Decision Variables 121

3.6.3 Concluding Testable Hypotheses 122

3.5 Concluding Remarks and Possible Extensions 126

Chapter 4 An Empirical Analysis on Strategic Interactions among Franchise Chains A Spatial Econometric Approach 129

4.1 Introduction 129

4.2 Theoretical Background 135

4.2.1 Sources of Interactions 135

4.2.2 Theoretical Models for Strategic Interactions 137

4.2.3 Strategic Interactions among Franchise Chains 139

4.3 The Reduced-form Model of Spatial Strategy 143

4.3.1 The Spatial Econometric Models 143

4.3.2 Specification of the Spatial Weights Matrix 146

4.3.3 Estimation Methodologies 149

4.4 Data and Variables 152

4.4.1 Data Collection and Sample Descriptions 152

4.4.2 Measurement of Variables and Descriptive Statistics 159

4.5 Results and Discussions 161

4.5.1 Preliminary Specification Tests 161

4.5.2 Regression Results and Robustness Tests 164

4.5.3 Discussions 167

4.6 Conclusions and Comments 171

Appendix A Proofs of Propositions, Corollaries and Results 174

Appendix B Steps in Chinese Banking Reform (1994~2006) 194

Appendix C Requirements Proposed by CBRC on Corporate Governance for the Ownership Restructuring Reforms of the SOBs 197

Appendix D Game Tree of the Two-period Dynamic Model 198

Appendix E Numerical Results of the Parametric Effects on Franchise chains 199

Reference… 226

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List of Tables

Table 3.1 Concluding Testable Hypotheses 123

Table 3.2 Results of an Empirical Test for Our Theoretical Conclusions 124

Table 3.3 Explanatory Power of Three Models 125

Table 4.1 Industry Overview I: Units 154

Table 4.2 Industry Overview II: Monetary Contract Terms 155

Table 4.3 Descriptive Statistics for Dependent and Independent Variables 161

Table 4.4 Statistics of Specification Tests for Spatial Effects 162

Table 4.5 White’s Test for Heteroscedasticity 163

Table 4.6 MLE Results for the Spatial Regressions of All Three Variables 165

Table 4.7 Robustness Tests for Spatial Effects 166

Table 4.8 Robustness Tests for Non-spatial Effects 166

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List of Figures

Figure 2.1 The Effect of Market Share on Choice of Control Structures 26

Figure 2.2 The Effect of Bureaucracy on Choice of Control Structure 29

Figure 2.3 The Effect of Internal Control Ability on Choice of Control Structure 31

Figure 2.4 The Effect of External Uncertainty on Choice of Control Structure 34

Figure 2.5 The Effect of Loan Expansion Productivity on Choice of Control Structure 42

Figure 2.6 The Effect of Risk Control Productivity on Choice of Control Structure 43

Figure 2.7 The Effect of Risk Aversion on Choice of Control Structure 43

Figure 2.8 Effects on Choice of Control Structure: Risk-adjusted Profitability 45

Figure 2.9 The Effect of Internal Control Ability on Job Satisfaction 46

Figure 2.10 The Effect of External Uncertainty on Job Satisfaction 47

Figure 2.11 The Effect of Market Share on Job Satisfaction 47

Figure 2.12 The Effect of Bureaucracy on Job Satisfaction 48

Figure 2.13 The Effect of Local Productivity on Job Satisfaction 49

Figure 2.14 The Effect of Risk Aversion on Job Satisfaction 49

Figure 3.1 Effects of Branding Value on Choice of Governance Structure: Scenario 1 87

Figure 3.2 Effects of Branding Value on Choice of Governance Structure: Scenario 2 88

Figure 3.3 Effects of Branding Value on Choice of Governance Structure: Scenario 3 88

Figure 3.4 Effects of Branding Value on Choice of Governance Structure: Scenario 4 89

Figure 3.5 Initiating Franchising: Relative Importance of Franchisee’s Resources 93

Figure 3.6 Initiating Franchising: High Branding Value 94

Figure 3.7 Initiating Franchising: Low Financial Constraints on Business Starting-up 95

Figure 3.8 Contract Renewal: Complementary Team Work 96

Figure 3.9 Contract Renewal: Quick Response to Local Market 97

Figure 3.10 Contract Renewal: High Marginal Productivity 97

Figure 3.11 Contract Renewal: High Discounting Rate of Future Value 98

Figure 3.12 Contract Renewal: Strong Bargaining Power of Franchisor 98

Figure 3.13 Contract Renewal: Huge Breakdown Loss 99

Figure 3.14 Royalty Rate: Relative Importance of Franchisee’s Resources 105

Figure 3.15 Royalty Rate: Complementary Team Work 106

Figure 3.16 Royalty Rate: Marginal Productivity 106

Figure 3.17 Pricing: Demand Elasticity 109

Figure 3.18 Pricing: Marginal Productivity 109

Figure 3.19 Franchisee’s Effort: Marginal Contribution of Franchisee’s Resources 111

Figure 3.20 Franchisee’s Effort: Marginal Contribution of Franchisor’s Resources 112

Figure 3.21 Franchisee’s Effort: Branding Value 112

Figure 3.22 Franchisee’s Effort: Marginal Cost of Franchisee’s Resources 113

Figure 3.23 Franchisee’s Effort: Marginal Cost of Franchisor’s Resources 113

Figure 3.24 Franchisee’s Effort: Complementary Team Work 114

Figure 3.25 Franchisee’s Effort: Demand Elasticity 114

Figure 3.26 Franchisee’s Effort: Breakdown Loss 115

Figure 3.27 Franchisee’s Effort: Franchisor’s Bargaining Power 115

Figure 3.28 Franchisor’s Effort: Demand Elasticity 118

Figure E.1 Governance Structure: Relative Importance of Franchisee’s Resources 199

Figure E.2 Governance Structure: Branding Value 200

Figure E.3 Governance Structure: Financial Constraints 200

Figure E.4 Governance Structure: Complementary Team Work 200

Figure E.5 Governance Structure: Demand Elasticity 200

Figure E.6 Governance Structure: Marginal Productivity 201

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Figure E.7 Governance Structure: Discount Rate 201

Figure E.8 Governance Structure: Breakdown Loss 201

Figure E.9: Governance Structure: Franchisor’s Bargaining Power 201

Figure E.10 Royalty Rate: Relative Importance of Franchisee’s Resources 202

Figure E.11 Royalty Rate: Branding Value 203

Figure E.12 Royalty Rate: Financial Constraints 203

Figure E.13 Royalty Rate: Complementary Team Work 203

Figure E.14 Royalty Rate: Demand Elasticity 203

Figure E.15 Royalty Rate: Marginal Productivity 204

Figure E.16 Royalty Rate: Discount Rate 204

Figure E.17 Royalty Rate: Breakdown Loss 204

Figure E.18 Royalty Rate: Franchisor’s Bargaining Power 204

Figure E.19 Franchise Fee: Relative Importance of Franchisee’s Resources 205

Figure E.20 Franchise Fee: Branding Value 206

Figure E.21 Franchise Fee: Financial Constraints 206

Figure E.22 Franchise Fee: Complementary Team Work 206

Figure E.23 Franchise Fee: Demand Elasticity 206

Figure E.24 Franchise Fee: Marginal Productivity 207

Figure E.25 Franchise Fee: Discount Rate 207

Figure E.26 Franchise Fee: Breakdown Loss 207

Figure E.27 Franchise Fee: Franchisor’s Bargaining Power 207

Figure E.28 Pricing: Importance of Franchisee’s Resources 208

Figure E.29 Pricing: Importance of Franchisor’s Resources 209

Figure E.30 Pricing: Branding Value 210

Figure E.31 Pricing: Financial Constraints 210

Figure E.32 Pricing: Complementary Team Work 211

Figure E.33 Pricing: Demand Elasticity 211

Figure E.34 Pricing: Marginal Productivity 212

Figure E.35 Pricing: Discount Rate 212

Figure E.36 Pricing: Breakdown Loss 213

Figure E.37 Pricing: Franchisor’s Bargaining Power 213

Figure E.38 Franchisee’s Effort: Importance of Franchisee’s Resources 214

Figure E.39 Franchisee’s Effort: Importance of Franchisor’s Resources 215

Figure E.40 Franchisee’s Effort: Branding Value 216

Figure E.41 Franchisee’s Effort: Financial Constraints 216

Figure E.42 Franchisee’s Effort: Complementary Team Work 217

Figure E.43 Franchisee’s Effort: Demand Elasticity 217

Figure E.44 Franchisee’s Effort: Marginal Productivity 218

Figure E.45 Franchisee’s Effort: Discount Rate 218

Figure E.46 Franchisee’s Effort: Breakdown Loss 219

Figure E.47 Franchisee’s Effort: Franchisor’s Bargaining Power 219

Figure E.48 Franchisor’s Effort: Importance of Franchisee’s Resources 220

Figure E.49 Franchisor’s Effort: Importance of Franchisor’s Resources 221

Figure E.50 Franchisor’s Effort: Branding Value 222

Figure E.51 Franchisor’s Effort: Financial Constraints 222

Figure E.52 Franchisor’s Effort: Complementary Team Work 223

Figure E.53 Franchisor’s Effort: Demand Elasticity 223

Figure E.54 Franchisor’s Effort: Marginal Productivity 224

Figure E.55 Franchisor’s Effort: Discount Rate 224

Figure E.56 Franchisor’s Effort: Breakdown Loss 225

Figure E.57 Franchisor’s Effort: Franchisor’s Bargaining Power 225

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List of Charts

Chart 2.1 Publicly Disclosed Financial Frauds in Chinese Banks (1987~2005) 8

Chart 2.2 Reported NPLs in Chinese SOBs 9

Chart 2.3 Market Share on Assets by Type of Institutions (1993~2005) 27

Chart 2.4 Beginning Years for Centralization and Going Public of the SOBs 29

Chart 2.5 Frequency of Financial Frauds—Internal Misconduct vs External Finagler 32

Chart 2.6 Composition of Capital Source in Chinese NFI Sector a at End-2005 35

Chart 2.7 Structure of China’s Financial Sector at Q3-2006 (% of Total Assets) 35

Chart 2.8 Amount and Ratio of NPLs in each SOB (2000~2006) 36

Chart 2.9 Distribution of Financial Frauds among the SOBs (1987~2005) 38

Chart 2.10 Selected Performance Indicators of Each SOB 39

Chart 3.1 Percentage Change in Number of Chains (2003~2005) 55

Chart 3.2 Percentage Change in Franchised Units (2003~2005) 55

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Acronyms

PBC: People’s Bank of China

SOBs: State-owned banks

Big Four: Big four state-owned banks

BOC: Bank of China

CCB: China Construction Bank

ICBC: Industrial and Commercial Bank of China

ABC: Agriculture Bank of China

JSCBs: Joint share commercial banks

CCBs: City commercial banks

NBFIs: Non-bank financial institutions

CBRC: China Banking Regulatory Commission

NFI Sector: Non-financial-institutional sector

AMCs: Asset management companies

NPLs: Non-performing loans

SOEs: State-owned enterprises

WTO: World Trade Organization

RST: Resource Scarcity Theory

AT: Agency Theory

IFA: International Franchise Association

IFAEF: International Franchise Association Educational Foundation USDOC: United States Department of Commerce

BID: Branding-inherent Demand

SAR: Spatial Autoregressive

SMA: Spatial Moving Average

Bond: Bond’s Franchise Guide

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Incomplete Contracts and Corporate Governance:

Theory and Evidence

Case Studies on Chinese Banking and U.S Franchising

by CHEN Shaoling

Department of Economics School of Business and Management The Hong Kong University of Science and Technology

Abstract

This thesis applies the incomplete contract approach to studying the corporate governance in two cases: Chinese banking and U.S franchising, both of which are issues of great significance from either academic or industrial perspective, but researches on them are still far from enough

First, a wave of centralizing control rights has been widely observed in Chinese banking recently Based on a two-state incomplete contract model, we show that it’s actually a reaction to the following four facts—the opening up of the banking market, the reform of going public, the increasing serious financial frauds and the persistent high ratio of non-performing loans—which happen almost at the same time

Second, the mixed governance structure as well as the uniform and time-invariant linear contract in franchising also confuses many economists This thesis establishes

a two-period double-sided moral hazard model to study the dynamic decision making

on governance structure and contracting of a franchise chain Our results suggest that both resource scarcity theory and agency theory work but carry different weights in

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different stages along the whole life Moreover, the accumulation of branding value brings helps remove the diversification of contracting across outlets as well as phases

in the long run

Following this logic, we conduct an empirical analysis on the strategic interactions among franchise chains Using data of 351 U.S franchise chains from 43 sectors in

2005, we find significant evidence for spatial effects among franchise chains Specifically, the coexistence of the complementary strategy in governance structure and the substituting strategy in contracting is consistent with the observed competition behavior and duopoly industrial structure in franchising

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Chapter 1 Introduction

Corporate governance is now a topic of considerable interest to a large and expanding cross-section of the community, which, until fairly recently, was not a topic that attracted enough attention from both academic and industrial applications However, recent events, such as the Enron scandal and other corporate governance failures, have put it on the front pages of our main newspapers Although none of us welcomes this kind of painful result, it has highlighted the important role that corporate governance plays in a modern economy and the consequences of getting it wrong And it has also strengthened the incentives for directors and policy-makers alike to reassess the structures needed to produce high quality corporate governance

CORPORATE GOVERNANCE deals with the ways in which suppliers of finance to corporations assure themselves of getting a return on their investment (Shleifer & Vishny, 1997) How can financiers be sure that they get anything but a worthless piece of paper back from the manager after the initial funding has been secured, especially when new information accrues and circumstances that are not clearly conceptualized at onset arise? To answer it, we should draw most of our attention to the examination of the decision making processes during which parties may have dissonant preferences, which obviously could be understood straightforwardly from an agency’s perspective

The agency problem is an essential element of corporate governance, which has been raised by Coase (1937) and more recently developed by Jensen and Meckling (1976), Fama and Jensen (1983a, b), Williamson (1985), and Tirole (2006) The essence of the agency problem is the separation of finance and management, or—in more standard terminology—of ownership and control The former stemmed

from financing the firm is linked with income rights, and so with formal control rights; while the latter authorizes the real control rights to managers by attaching

them to the physical possession of assets due to their proprietary information

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Whether or not, control rights always stand in the core of all issues The firm therefore needs a governance structure that will solve the parties’ agency problem through selecting a design of decision making processes, in particular a special class

of decision making processes—allocation of control rights While in reality, most of these decision making processes are fulfilled through a series of contracts

In recent years, the contract theory has become one of the most active fields

of research in contemporary microeconomics Specifically, rather than the traditional theory of complete contracts which is closely related to the theory of implementation

or mechanism design, the incomplete contracts approach pioneered by Grossman and Hart (1986) and Hart and Moore (1990) as another branch can be more helpful to answer questions proposed above The advantage is, most future contingencies are hard to describe and foresee ex ante, and as a result, complete contracts are technologically infeasible and decisions on allocating residual control rights—i.e., the rights to make decisions under circumstances not fully foreseen by the contract—should be made in ex ante contracting The works by Agnion and Bolton (1992), Hart (1995), and Hart and Moore (1998) are such examples applying the incomplete contracts approach to explaining the efficiency of different allocations of control rights However, this incomplete contracts approach is still often criticized by some researchers either because the situation in practice is much more complicated than those simple allocation frameworks addressed in current models based on this approach (Shleifer & Vishny, 1997), or because a clear definition of incomplete contracts has not been agreed upon yet One popular view is that incomplete contract theorists restrict the class of contracts they consider to an ad hoc subset of complete contracts which are renegotiable (Huberman & Kahn, 1988; Aghion, Dawatripont & Rey, 1994; Chung, 1991; Rogerson, 1992; Hermalin & Katz, 1991 & 1993; Che & Hausch, 1999) The problem of this is the difficulty in designing an implemented renegotiation game without ineffective threat ex ante (Rubinstein & Wolinsky, 1992; Tirole, 1999) Besides that, the incomplete contracts approach from this perspective

is basically same as the traditional complete contracts approach, which causes it to be further inapplicable for the purpose of our study While the label “incomplete

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contracts” used in this thesis most refers to the class of models initiated by Grossman and Hart (1986), which are mainly concerned about the optimal allocation of asset ownership1 as well as the control rights derived from it rather than about the specific way—renegotiation process for example—to achieve it In fact, we stress an efficient design ex ante in the contract about allocations of both formal control rights and real control rights on spot assets

Two cases are studied here: Chinese banking and U.S franchising Partly due

to the Asian financial crisis, the corporate governance in this area’s financial sector has received most attention in recent years (Oman, 2001; Goswami, 2001; Lin, 2001; Malherbe & Segal, 2001; Classens & Fan, 2002; Arun & Turner, 2004) And given the overwhelming role banks play in the financial system in China and the widespread as well as dramatic banking reforms implemented in this nation, the corporate governance in Chinese banking should also have no doubt to be one issue

of the greatest essence However, relative to that in firms, the corporate governance

in banks has quite been ignored by researchers, especially by economic theorists Even outside emerging markets, this issue has not been discussed in the literature until recently (Macey & O’Hara, 2001) Our study provides some creative insights into recent changes in the corporate governance of Chinese banks which would shed light on further productive works in this field Specifically, based on a two-state incomplete contract model, we analyze the allocation of control rights along the hierarchy of a bank under uncertainty The results indicate that such changes in the control structure of Chinese banks are closely related to current fluctuations of their own transformations and external competition environment

The same incomplete contract approach is also applied to studying the corporate governance in U.S franchising, which as one typical governance structure mixing the features of both contracts and corporate organizations has rarely been taken into account since the prosperity during the period from late 1980s to mid 1990s, either in theoretical models or in empirical works relative to its outstanding growth day by day However, arguments about the mixed governance structure of

1 Therefore, sometimes studies on this branch are also called as “the property (or ownership) rights approach”

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franchise chains from the two mainstream theories—Resource Scarcity Theory (RST) and Agency Theory (AT)—have never stopped ever since In addition, the uniform and time-invariant linear rule of revenue sharing in franchise contracts has still not been well explained, especially from a dynamic perspective Based on a two-period double-sided moral hazard model with branding value as a capital stock of the greatest importance, the thesis studies the dynamic decisions on governance structure and contracting made by a franchise chain, which suggest that both RST and AT matter in choosing governance structure but carry different weights in different stages along the whole life Moreover, the establishment of branding value brings bargaining power to the franchisee in a long-run relationship which helps remove the diversification of contracts across outlets as well as phases

Finally, we close the study with an empirical analysis on strategic interactions among franchise chains Although such an issue, sometimes also referred to as

“reaction functions” among independent firms, seems to be passionately discussed in traditional economic theories but remains untouched in empirical studies probably due to lack of feasible econometric technologies, it becomes hot today by reason of the rapid growth of spatial econometrics since 1990s Using data of 351 U.S franchise chains from 43 sectors in 2005, we estimate a series of strategic interactions on their governance structures and contract terms in this thesis Significant evidence for spatial effects among franchise chains is found However, the reaction strategies are different between governance structure and contracting behavior It provides a reasonable interpretation to the observed puzzle that even outlets offering same products or service but with different brands are usually open side by side, the coexistence of a few of man-sized chains and a large number of median-sized chains could still be a stable equilibrium

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Chapter 2 What Drives Recent Changes in the Control Structure

of Chinese Banks?

2.1 Introduction

In the last over two decades, China has been through a “gradualist” but very impressive reform in its banking system, especially in the state-owned banks (SOBs), which replaced the monobank system with a multilayered system that separates commercial lending, policy lending and central banking functions from one another

as well as transformed the SOBs from specialized state banks into state dominated share holding companies Such an institutional shake-up is being boosted step by step through three main transformations: a) banking restructuring, containing the disposal

of non-performing loans (NPLs), recapitalization and rebuilding the ownership structure as well as the corporate governance structure; b) reduction of government interference, containing quantity and price liberalization as well as opening up to the foreign competition and c) improved regulation and supervision Among them, the first transformation always attracts most attention in both industrial and academic fields probably because it’s the only one combining the self choice of the banks into the authority’s activity, and the focus of our article is exactly one major self choice—choice of control structure to achieve better corporate governance Although

it sounds less familiar relative to other transformations, it has been playing a non-negligible role during the whole banking reform

2.1.1 One Reaction to Four Facts

As shown in Appendix B, the transformation of control structure has been the focus of the banking reform in China since 1994 as every change along this transformation was always coupled with one significant step taken in other parts of the banking reform However, our study concentrates on the recent wave of centralizing control rights since 2001, which could be characterized as follows:

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—In 2001, the Industrial and Commercial Bank of China (ICBC) as pilot

began to try out the so-called oblate management in part of its municipal branches,

which strengthened the direct control rights of its provincial branches on all affiliates instead of extending the decision chain vertically In more detail, the municipal branch in the capital city of each province was downgraded as a district branch and all district branches, some of which used to be subordinated to the municipal branch, are now subject to the provincial branch directly

—In 2004, a large number of Chinese banks, represented by the Banks of China (BOC) and the China Construction Bank (CCB), further collected some control rights—mainly on credit extending—from the municipal branches to their provincial branches or even their headquarters in order to push the oblate and vertical management throughout the whole hierarchy For example, in the big four SOBs (Big Four), except for the examining and approval right on re-extended loans which is still controlled by the municipal branch and that on loans with mortgages or collaterals in amount of less than 100,000 Yuan which is assigned to the county branch, such a decision making right on other kinds of loans especially those with large amounts or extended to major customers was centralized up to the provincial branch or even a higher level in the hierarchy Managers at the lower level are only responsible for recommending these good-sized projects but have no rights to determine which one and how much should be financed2 In addition, with the withdraw of many county affiliates, the decision making right on fixed loans—especially those financing projects in steel, electroanalysis aluminum, real estate, automobile and other over-invested sectors—was also centralized to the provincial branch; that on liquidity loans is still controlled by the municipal branch but greatly constrained3 Besides those, an even more centralized tendency was found in the BOC In four of its municipal branches in Shanghai, the examine and approval right on retail loans was transferred to the provincial branch as well4 More commonly, such a wave of

2 Choice of Periodicity and Long-run Consistency: Credit Centralization and Policy Implications, 2006/08/12,

http://www.studa.net/jinrong/060812/0804531.html

3 Global Investment Web, 2005/08/11, http://www.investf.com/construction/8-11/16153270931.html

4 Jiangsu Banking Association, 2006/03/17, http://www.jsbank.org/mag/detail.php?info_id=499

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centralization is not the specific phenomenon attributed to the Big Four In 2006, the Bank of Communications announced to push a transformation changing its control structure from a “divisional bank” towards a “flow bank” in the next three years, which would centralize control rights of all municipal branches on their chief appointments, operation decisions and expense allocations to the headquarter5

Following these significant changes in the control structure of Chinese banks recently, question here is what are the driving forces underlying Our study suggests that such a wave of centralization behaves like a reaction to the following four facts which happened almost during the same period: the opening up of the banking market, the reform of going public, increasing serious financial frauds and the persistent high ratio of non-performing loans (NPLs)

Firstly, the Chinese banking market was agreed to be fully opened up to foreign affiliates by the end of 2006, as one major assignment of China’s accession to the World Trade Organization (WTO) in late 2001 However, during the period towards this final objective, besides extending as more as possible branches throughout the whole nation step by step, many foreign financial institutions have engaged in competing for holding shares in Chinese banks (see more details in Appendix B) as well as other non-bank financial institutions (NBFIs), such as the insurance company, the fund management company and so forth

Secondly, all SOBs have been through or are planning to carry out a transformation of going public, most of which were actually driven by the state in order to improve efficiency and governance Recently, the pace of such a transformation of the ownership structure was significantly speeded by the following measurements: a) recapitalizing injection of $45 billions into the BOC and the CCB

in end of 2003 which was extended to ICBC in 2005 with an amount of about $15 billions6; b) establishments of the BOC Limited and the CCB Corporation in 2004 as well as the ICBC Limited in 2005 All above ultimately led to the oversea listing of the CCB in late 2005 followed by the IPOs of both the BOC and the ICBC in the

5 21 st Century Business Herald, November 3 rd , 2006

6 Hang Seng Economic Monthly, 2007

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next year

Thirdly, many serious financial frauds have been observed in Chinese banks since 2000 which reached a peak around 2003 no matter measured with the frequency or with the loss (see Chart 2.1) Technologically, such financial frauds are

referred to as operational risk events in line with the new Basel I accord More

specifically, as pointed out by Ren’s survey in 2006, among all financial frauds publicly disclosed since 2000, over 17 cases have a loss of more than 100,000 Yuan and with a total amount of over 8.7 billion fund involved Also, in 2004 there were

354 cases taking place in the five largest national banks including the four state-owned banks and the Bank of Communications with an increase of 69% in the total loss of that of the last year

80000 Frequency (#)

Loss (million Yuan)

Source: Author’s own calculations based on samples provided by Zhang (2004) & Sheng (2005)

Chart 2.1 Publicly Disclosed Financial Frauds in Chinese Banks (1987~2005)

Lastly, the NPLs of the SOBs which resulted in serious credit risk was so huge that accounted for 2,175 billions Yuan, or about 40% of total loans, before 2000, and still had a two-digit ratio higher than 15% by the end of 2004 (See Chart 2.2) Although more than 80% of NPLs in the Big Four were caused by the government intervention, the support of the SOEs, the low standard of legal system and the close

or merge of some industries including military industries7 and so should not be paid for by financial institutions themselves, it had really put a significant negative

7 Ba, 2004

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pressure on the performance of the SOBs, which left no schedule for them to wait for the rescue from the government especially when competitions from foreign banks have been so close

Source: Cui, 2006; Xiao, 2006; Annual reports by CBRC

a García-Herrero et al., 2006

Chart 2.2 Reported NPLs in Chinese SOBs

The basic reason for Chinese banks’ reaction in centralizing control rights to above facts is to improve their self-control ability on risks through establishing a healthier governance structure We argue from the following three aspects Firstly, this tendency to centralization is widespread in almost all commercial banks including the joint share commercial banks (JSCBs) and other NBFIs rather than the SOBs only, implying that it’s more like a self-enforcing decision less regardless of ownership structure Secondly, during the whole process of this transition, the biggest trouble is always the risk control, represented by the credit risk and the operational risk, which becomes most urgent in the latest wave of banking reform It’s mainly because the approval of the new Basel accord in 2004 placed emphasis on the risk control again by proposing further requirements for the capital adequacy to the three main risks—credit risk, operational risk and market risk—individually in the banking sector Finally, such an upward movement of the control rights along the

Amount of NPLs

% of Total Loans

% of NPLs in Eastern Europe Banks a

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hierarchy is more consistent with the new requirements8 of the corporate governance proposed by the CBRC Actually, as mentioned by Ba in 2004, the latest institution restructuring reform aims to rebuild a healthy banking sector subject to good corporate governance rather than write off NPLs simply

2.1.2 Literature Review

As a whole, the latest trend to a centralized control structure in Chinese banks has distinguished itself from other changes happened before as a transformation towards efficient corporate governance, requiring the focus of researches to lean towards the problems related to incentives and risk-sharing contained in the transformations, with the centralization of control structure as a typical example However current researches on this field are still far behind consideration, especially from the view of corporate governance

In specific, except for a few domestic articles which mentioned it with just general comments (Wang & Gao, 2002; Luo, Wang & Fang, 2002; Liu, 2004) as well

as an outline in the year book of each bank, the work by Ren (2006) is one contributing study which proposed an oblate managerial structure characterized by

“Strong Headquarter—Weak Branch” as an efficient alternative to enhance the control of operational risk, which is indeed a detailed practice of the centralized control structure Another useful work is the empirical study conducted by Cheng and Fu (2006) which tested the correlation between such a centralized control structure and the performance of commercial banks, concluding that no significant impacts of the control structure were found on the performance However, their study used a sample of 100 commercial banks in Europe, U.S and Asia9, which ignored the special features of Chinese banks as well as the restructuring reform in them and so caused a bias in their conclusions inevitably Moreover, since this change in the control structure as a guideline to the bank’s operation was usually found in the bank’s operation manual rather than public media, even fewer studies are available in foreign literature

8 See Appendix C

9 More specifically, the sample assigns only a weight of 1/3 to Asian banks

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Actually, for quite a long time, literature on Chinese banks’ reform usually pay most attention to the state’s active operations in dealing with its historical and social costs that have been paid by the SOBs for the transition, such as huge amount

of NPLs, extremely insufficient capital, lending behavior with obvious features of planning economy, and so on (Bai & Wang, 1998; Naughton, 1998; Bonin, 1999; Nanto & Sinha, 2002; Barth, Koepp & Zhou, 2004; Harmid, 2005; Podpiera, 2006),

as well as an assessment of these operations (García-Herrero, Gavilá & Santabárbara, 2006; García-Herrero & Santabárbara, 2004) and their impacts (Fung, Ho & Zhu, 2000; Park & Sehrt, 2001; Fu & Heffernan, 2005) Even though some people have noticed the importance of corporate governance in China’s banking reform (Leung, Liu, Shen, Taback & Wang, 2002; Hamid, 2005), they just described roughly some movements in building healthy corporate governance implemented by either the government or banks, such as deregulation of the financial sector, dilution of state shares, creation of the board of directors, introduction of foreign investors and so forth; while both the theoretical and empirical studies based on an analysis about its microeconomic foundation still remain untouched

2.1.3 My Contributions

One methodology useful for our analytical framework is the incomplete contract approach which emphasizes the allocation of income rights and control rights when there exists something uncertain which could not be contracted ex ante

In the field of hierarchy theory, this methodology is often observed in analyzing the government behavior within a hierarchy containing either central government and local governments (Mishra & Anant, 2004), or government and its legal agent (Grajzl

& Murrell, 2007); but rarely found in examining the self choice of a profit-maximizing agent, especially of a bank in a transitional financial system, since

it was proposed by Hart and Holmström in 1987 Nevertheless, the increasing uncertainty in the environment surrounding Chinese banks suggests that the incomplete contract approach incorporated in our model as an initial try in this field would probably be one appropriate tool to provide a microeconomic foundation for recent changes in Chinese banks’ control structures

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Most importantly, this article comes up with some conclusions consistent with the four significantly observed facts—the opening up of Chinese banking market, reform of going public, increasing serious financial frauds and persistent high ratio of NPLs—simultaneously found during the latest banking reform It suggest that our model really does well in explaining the economic rationale underlying current behaviors of Chinese banks, especially of the SOBs, which used

to be denoted as a “black box” and still remains undisclosed in existing literature

Moreover, several testable hypotheses further describing the tendency to a centralized control structure are proposed based on preliminary works, which could

be clarified by further empirical studies and so sheds additional light on the extent to which Chinese financial sector has been liberalized

The whole paper is organized as follows The second section addresses the basic theoretical framework of a two-state principal-agent model, using the incomplete contract approach to describe the allocation of risk control rights between the higher level manager and the lower level manager to deal with the ex post uncertainty After that, main results concentrating on the choice of control structures are discussed based on specific functions in the third section Following them, other minor but by no means non-important results are also examined in the next section

We close this article with some concluding remarks and possible extensions

2.2 Model

Consider a situation in which the principal of a bank decides to allocate some control rights from a lower level manager to a higher level manager, or vice versa, where contracting control rights ex ante is the typical feature of an incomplete contract when someone should be authorized to make ex post decisions Specifically,

we focus on the re-allocation of control rights on the average risk level of outlets and leave control rights on the output level to the local manager as before In reality,

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promoting the output level is usually assigned as the major task of the lower level manager of the local outlet while controlling the average risk level of outlets by carefully choosing project portfolios as the core of banking management is often re-allocated to different levels along the hierarchy The trade-off is affected by the balancing between agency incentives and risk control If the lower level local manager has the risk control rights, she has better incentives to work, but might introduce more risks to the principal; if the risk control rights are in the hands of a relatively higher level manager, the principal can better improve her welfare, but the local manager’s incentive tends to be low Whether or not to endow more authorities

to the local manager depends on different cases

For simplicity, we use a two-state model to describe the uncertainty which generates the source of risks in the hierarchy The output of the project portfolio of the outlet is a lottery in the form of:

{x a p b( ), ( );0,1−p b( )}

where x i and ( )( ) p i are the revenue function of the project portfolio10 and the probability function respectively, both of which are concave and strictly increasing functions The probability function ( )p b implies the average probability that the

project would not default which in some sense could also be interpreted as the success probability of the project If the project succeeds, ( )x a is the overall

revenue received by the bank; and if the project fails, nothing would be paid and the bank would be compensated by the collateral, the value of which exactly covers investment costs and prevents the bank from negative loss For example, suppose the project refers to the loan extended to a company, ( )x a would be the total receipts

from the loan minus the principal as well as its cost, that is, the difference between the loan interest receipts and the deposit interest payments, if the company succeeds with probability ( )p b However, if the company fails with probability 1p b( ) and

so defaults, the bank would liquidate the collateral which covers the principal as well

10 It would be called as “the project” in below

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as the deposit interest payments and then leaves zero profit to the bank

In an uncertain environment, the goal of the manager to maximize the expected revenue could be divided into two sub-tasks: extending more loans and controlling risk at a lower level Since in general, these two sub-tasks are negatively correlated, the problem of the manager becomes which sub-task should be put more

weights on Suppose a and b measure the efforts that the manager contributes to the two sub-tasks respectively In particular, a referring to the work of increasing the

amount of loans is neither assignable nor observable, and has to be supplied by the

agent However, b refers to the work of identifying good projects either through

trying hard to gather more information about projects or through improving the ability to make professional loan decisions by training or self-education, which is assignable and supplied either by the agent or by the principal Note that we suppose the average risk is controllable by the manager through diversification of the project portfolio but still noncontractable Besides the care about risks, another important

factor of the question who should decide b is the cost Since the principal is distant

from the local market, it costs more for her to achieve the same quality in decision

making Therefore, if we let the agent’s cost of supplying a be a, the agent’s cost of supply b be ( ) c b , and the principal’s cost of supplying b be ( ) C b , we should have

C bc b Apparently, both cost functions are increasing and convex

Moreover, we suppose the higher level manager11 to represent the principal directly and let the lower level manager of the local outlet12 be the agent Both of them are risk averse but the principal would be relatively more risk averse than the local agent due to the special feature of Chinese banks Let ( )v i be the principal’s

utility function and ( )u i be the agent’s utility function with (0) u =v(0) 0=

Finally, suppose the contract determined by the principal and offered to the agent is ( )s x for only the revenue ( ) x i is contractable As in a two-state situation,

11 Or the manager of a provincial branch, for example

12 Or the manager of a municipal branch, for example

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the principal’s strategy should be to reward the agent properly in a good state13 and

to punish the agent as much as possible in a bad state, with the limited liability condition ( ) 0s x ≥ , we should have (0) 0s = which is the maximum punishment that the principal could impose Now, let’s examine optimal strategies of the principal and the agent separately when control rights on risks are assigned to the agent or to the principal In reality, the former case is also called a “decentralized hierarchy” and the latter case is called a “centralized hierarchy”

2.2.1 Decentralized Hierarchy

The control structure in a decentralized hierarchy could be simply described

as follows:

In this case, the principal needs to provide incentives to the agent to choose

proper a and b, which should be balanced to fit with the principal’s objective for both

high return and low risk Then the agent’s expected utility function is

a

EU = p b u s x a − −a c b (2.1) and the principal’s expected utility function is

p

EU = p b v x as x a (2.2) The IC and IR conditions are

13 Too good a reward might cause overinvestment

Principal: s(x)

Agent: a & b

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controls b, the solution may not be efficient Given (a,b), we can easily define a contract s(x), say a linear contract, to satisfy conditions (2.3) and (2.4) Hence, there

exists an optimal linear contract in a decentralized hierarchy For example, ( )

s x = +F rx , where F and r stand for the fixed payment and revenue-sharing parameter respectively If the contract is linear, the SOC for a is satisfied Moreover,

given a convex ( )p b and a convex ( ) c b , the SOC for b is also satisfied Thus, the

SOCs would be omitted from the discussions below for we will have optimal linear contracts in all cases

2.2.1.1 The First-best Solution

The principal’s first-best problem is

and the optimal contract can be a linear contract s x l**( )=F l**+r x l** with a pair of

(F r l**, l**) which satisfies following conditions

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** **

s =F

2.2.1.2 The Second-best Solution

The principal’s second-best problem is

(a b from the following problem l*, l*)

1 ,

The control structure in a centralized hierarchy is similarly described as:

In this case, the principal does not need to provide an incentive to the agent to

choose a proper b; instead, she needs an incentive for herself to commit to a proper b

Principal: s(x) & b

Agent: a

Trang 32

assume that the two parties choose a and b separately in a Nash equilibrium Hence,

the agent’s expected utility is

a

EU = p b u s x aa (2.8) and the principal’s expected utility is

p

EU = p b v x as x aC b (2.9) The IC and IR conditions are

Similar to the decentralized hierarchy, condition (2.13) should be satisfied

whatever the contract is It implies that when the principal controls b, the solution may also not be efficient Given (a,b), we can easily define a contract s(x), say a

linear contract, to satisfy (2.10) and (2.11) Hence, there is an optimal linear contract

in a centralized hierarchy as well

2.2.2.1 The First-best Solution

The principal’s first-best problem in the case of higher control is

and the optimal contract can be a linear contract s x**h ( )=F h**+r x h** with a pair of

(F r h**, h**) which satisfies following conditions

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2.2.2.2 The Second-best Solution

The principal’s second-best problem is

Then the problem can be solved in two steps First, the principal chooses (a b h*, *h)

from the following problem

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Second, the principal designs a linear contract s i to satisfy the two IC h*( )conditions However, without specific assumptions of the agent’s utility function, we could not derive clear solutions to the optimal linear contract A general case and further results about the second-best contract in both hierarchies would be discussed

in the next section

2.2.3 Specifications and Solutions

It is hard to say which control structure, the lower control structure in a decentralized hierarchy described by problem (2.7) or the higher control structure in

a centralized hierarchy described by problem (2.14), is more efficient Hence, we need to choose some simple functions in order to find the explicit solutions for comparison Let

be affected by the bank’s market share; ρ ∈(0,1) measures the productivity of the

loan expansion effort a; B>0 describes the difficulty of one bank in controlling risks which could inversely be measured with the internal control ability of each bank14; 1β ≥ 15 is an inverse index of the productivity of the risk control effort b;

1

γ ≥ implies inefficiency of the principal in identifying good projects relative to the local agent which could be measured with the distance no matter geographically or politically in most cases and so commonly be considered as an index of bureaucratic inefficiencies; (0,1)ε∈ represents the success probability influenced negatively by the uncontrollable risk resulted from the external uncertainty16 which is assumed to

be chosen as constant ex ante by the nature and so uniform to all banks; α∈(0,1) is the constant relative risk aversion of the principal Specifically, following points need to be clarified first

14 Or we can use 1/B to represent the internal control ability

15 Similarly, we can use 1/ β to represent the productivity of risk control

16 In fact, the failure probability 1 − exactly measures the degree of external uncertainty ε

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a) The agent’s utility function ( )u x should be concave in general However,

we find that the relative risk aversion of the two parties is enough for our study Hence, for simplification without loss of generality, we could let the less risky party

be risk neutral On the other hand, the fact that the local manager is risk neutral could also be found in the real world In fact, managers of municipal branches are frequently inter-replaced by each other recently in Chinese banking The average tenure of their positions is only 2~3 years or even shorter if something unexpected happens The high mobility of internal manager market causes local managers to tend

to be risk neutral because they would be engaged in the production-booming work, the advantages of which could be enjoyed during the incumbency while the disadvantages of which, say possible loss due to high risks, would be born by their successors Another important reason is the specific feature of credits which helps the manager produce output at present but bear costs of default in the future Such a separation between revenue and risk coupled with the short tenure in position strengthens the local manager’s short-sighted behaviour pursuing high return but high risk projects Lastly, the career promotion system for local managers at present might be an additional cause Because of increasing competition, a large number of Chinese banks tend to link the career promotion of most local managers to their productions of both deposits and loans whereas give few weights to the risk quality

of their productions That also explains why the local managers are more likely to be risk neutral Actually, even a risk averse agent is taken into account with a concave

b) The probability function ( )p b could be concave in normal However, this

may not be necessary as the convexity of cost functions is symmetric to the concavity of ( ).p b A more concave ( ) p b is equivalent to a more convex cost

functions Cautiously, a concave probability function p b( )=bθε θ, <1 is

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examined numerically in following analysis and few deviations from current results are found

c) The success probability ε affected by external uncertainty could be random rather than constant However, if we treat it as the risk state that all banks are facing status quo, it would be quite stable as well as be traced or estimated precisely Hence, it’s not unreasonable to assume ε to be constant ex ante which measures all

uncontrollable risks Intuitively, if b reflects the controllable risk, say the portfolio

risk of a local branch, which is usually viewed as unsystematic risks and could be

eliminated through active portfolio diversification; and B describes the

uncontrollable but adjustable risk17, say the internal risk situation of an individual bank subject to its internal control ability, which as partly systematic risks might possibly be abated through an increase in costs; ε would be an index of systematic risks which are determined by external macroeconomic environment and could not

be removed with efforts

Given above specific function forms, we can find closed-form solutions for all cases, which are listed below

Proposition 2.1 Under lower control in a decentralized hierarchy, the FB solution is

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The SB solution is always inefficient Specifically, we have a l∗∗ <a l and

b∗∗>b

Since in a decentralized hierarchy, both a and b are controlled by the local

manager and so could be considered as substitutes, proper incentives should be provided to the local manager for each effort Therefore, the introduction of the agency problem will lead to the underinvestment at the aggregate effort level However, since the local manager prefers loan expansion effort to risk control effort either due to the positive correlation to her payments, or the lower cost, or the exclusiveness of the former activity, she would replace some of her input into the risk control effort with more input into the loan expansion effort, resulting in an overinvestment in loan expansion effort under lower control Notice that, in this case, the principal’s risk aversion does not affect the balancing within the pair (a b *l, l*)

Similarly, we have the following proposition in the case of centralization

Proposition 2.2 Under higher control in a centralized hierarchy, the FB solution

is

1 1 1

1 1 1

1 1

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who share the join revenue of their team production, proper incentives are separately provided to each party implying that investments in loan expansion and risk control are now complementary In this case, the risk aversion of the principal increases the requirement for risk premium which weakens the incentives to both parties and so results in the underinvestment in both activities

2.3 Main Conclusions

Our main results concentrate on the choice of different control structures, decentralization or centralization, which could be interpreted mainly by effects of the

following four crucial parameters: the internal control ability 1/B and the external

uncertainty 1−ε, the market share A and the bureaucratic inefficiency γ More importantly, we show in this section that these parametric effects are consistent with the four facts mentioned above, indicating that our model really supports previous arguments for Chinese banks responding to these facts with a centralized control structure

2.3.1 Opening Up of Banking Market

The most direct result due to the opening up of the Chinese banking market is the shrinkage of market shares for each domestic bank, which in our model is

described by the parameter A; and based on solutions derived from the two

propositions previously, we have

∂ ∂ ∂ ∂ It implies that all efforts are

increasing in A, or the market share Moreover, both efforts are more responsive

to changes in the market share under lower control than under higher control, i.e e l > e h

The proof is quite straightforward Take partial derivatives on the SB

solutions w.r.t A respectively, we have

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in running business among more competitors also induces the manager at either level

to pay most attention to pulling through troubles rather than improving the risk quality as the latter task usually requires higher expenses including the opportunity cost resulted from losing projects with high but risky returns Additionally, a small market share as an index of an unsuccessful or inexperienced bank would probably leave a poor pool of loan applications to the bank which further weakens the bank’s productivity of risk control efforts Therefore, the incentive to work harder in selecting low-risk projects also declines Furthermore, since the local manager is always more sensitive to make prompt decisions responding to market fluctuations while the higher level manager has advantages of making overall decisions in a longer sight, both efforts will be more frustrated by the shrinkage of market shares under lower control It implies that the efficiency loss in a decentralized control structure will be greater than that in a centralized control structure, and so

Conclusion 2.1 Centralizing control rights is more efficient when the market share A drops due to the Chinese banking market’s opening up

∂ >

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conclusion is easily obtained, which is also supported by numerical solutions18 based

on the following set of initial values of parameters in our model,

Figure 2.1 indicates that the social gain under higher control would be larger than that under lower control when the market share is small because of increasing competition from foreign banks as a result of the opening up of the domestic banking market In this case, a centralized control structure will help prevent the efficiency loss resulted from the individualism of local managers with discouraged incentives to both efforts as well as maintain the profitability and competitiveness in the long run

Figure 2.1 The Effect of Market Share on Choice of Control Structures

In reality, such a trend of declining market share was observed after 2000 in most Chinese banks, especially in the four SOBs and other policy-related financial institutions; while the market share of foreign banks began to increase in 2002 (see Chart 2.3) Both of them took place almost at the same time that the wave of centralizing control rights was observed for the first time around 2001 Moreover, the market share of the SOBs was observed to further shrink in 2004 probably because

of the dramatically increasing competition from the JSCBs, for the dominating ones

of which their ownership have been or announced to be jointly held by several big

18 All results are obtained by using MathCAD 13

19 The values of parameters have been screened to ensure that p b( )∈ [0,1] is satisfied

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