Stochastic Frontier Analysis

This book develops econometric techniques for the estimation of production, cost and profit frontiers, and for the estimation of the technical and economic efficiency with which producers approach these frontiers. Since these frontiers envelop rather than intersect the data, and since the authors continue to maintain the traditional econometric belief in the presence of external forces contributing to random statistical noise, the work is titled Stochastic Frontier Analysis. Hb ISBN (2000): 0-521-48184-8

Subal C. Kumbhakar is Associate Professor of Economics at the University of Texas, Austin C. A. Knox Lovell holds the C. Heman and Mary Virginia Terry Chair in the Department of Economics in the Terry College of Business, University of Georgia, and is Professor in the School of Economics at the University of New South Wales

Preface

ix

1 Introduction

1

(14)

1.1 The Objectives of the Book

1

(3)

1.2 A Brief History of Thought

4

(7)

1.2.1 Intellectual Antecedents of Stochastic Frontier Analysis

5

(3)

1.2.2 The Origins of Stochastic Frontier Analysis

8

(1)

1.2.3 Developments in Stochastic Frontier Analysis since 1977

9

(2)

1.3 The Organization of the Book

11

(4)

2 Analytical Foundations

15

(48)

2.1 Introduction

15

(3)

2.2 Production Technology

18

(24)

2.2.1 Representing Technology with Sets

18

(7)

2.2.2 Production Frontiers

25

(3)

2.2.3 Distance Functions

28

(4)

2.2.4 Cost, Revenue, and Profit Frontiers

32

(8)

2.2.5 Variable Cost Frontiers and Variable Profit Frontiers

40

(2)

2.3 Technical Efficiency

42

(8)

2.3.1 Definitions and Measures of Technical Efficiency

42

(4)

2.3.2 Single-Output Production Frontiers and the Measurement of Technical Efficiency

46

(2)

2.3.3 Multiple-Output Distance Functions and the Measurement of Technical Efficiency

48

(2)

2.4 Economic Efficiency

50

(11)

2.4.1 Cost Frontiers and Cost Efficiency

51

(3)

2.4.2 Revenue Frontiers and Revenue Efficiency

54

(3)

2.4.3 Profit Frontiers and Profit Efficiency

57

(3)

2.4.4 Variable Cost Efficiency and Variable Profit Efficiency

60

(1)

2.5 A Guide to the Literature

61

(2)

3 The Estimation of Technical Efficiency

63

(68)

3.1 Introduction

63

(1)

3.2 Cross-Sectional Production Frontier Models

64

(31)

3.2.1 Deterministic Production Frontiers

66

(6)

3.2.2 Stochastic Production Frontiers

72

(21)

3.2.3 Stochastic Distance Functions

93

(2)

3.3 Panel Data Production Frontier Models

95

(20)

3.3.1 Time-Invariant Technical Efficiency

97

(11)

3.3.2 Time-Varying Technical Efficiency

108

(7)

3.4 Stochastic Production Frontier Models with Heteroskedasticity

115

(15)

3.4.1 Heteroskedastic Cross-Sectional Models

116

(6)

3.4.2 Heteroskedastic Panel Data Models with Time-Invariant Technical Efficiency

122

(4)

3.4.3 Heteroskedastic Panel Data Models with Time-Varying Technical Efficiency

126

(4)

3.5 A Guide to the Literature

130

(1)

4 The Estimation and Decomposition of Cost Efficiency

131

(53)

4.1 Introduction

131

(5)

4.2 Cross-Sectional Cost Frontier Models

136

(30)

4.2.1 Single-Equation Cost Frontier Models

136

(10)

4.2.1.1 The Single-Output Cobb Douglas Cost Frontier

138

(5)

4.2.1.2 The Multiple-Output Translog Cost Frontier

143

(1)

4.2.1.3 The Single-Output Translog Variable Cost Frontier

144

(2)

4.2.2 Simultaneous-Equation Cost Frontier Models

146

(12)

4.2.2.1 Single-Output Cobb-Douglas Cost Systems

147

(7)

4.2.2.2 The Multiple-Output Translog Cost System

154

(4)

4.2.3 Decomposing Cost Inefficiency

158

(8)

4.3 Panel Data Cost Frontier Models

166

(9)

4.3.1 Single-Equation Cost Frontier Models

167

(3)

4.3.2 Simultaneous-Equation Cost Frontier Models

170

(5)

4.4 Two Additional Approaches to the Estimation of Cost Efficiency

175

(7)

4.4.1 Thick Frontier Analysis

176

(3)

4.4.2 A Distribution-Free Approach

179

(3)

4.5 A Guide to the Literature

182

(2)

5 The Estimation and Decomposition of Profit Efficiency

184

(32)

5.1 Introduction

184

(2)

5.2 Single-Output Models

186

(19)

5.2.1 The Primal Production Frontier Approach

186

(6)

5.2.2 The Dual Variable Profit Frontier Approach

192

(13)

5.3 Multiple-Output Models

205

(7)

5.3.1 The Primal Distance Function

205

(4)

5.3.2 The Dual Variable Profit Frontier Approach

209

(3)

5.4 Alternative Profit Frontiers

212

(2)

5.5 A Guide to the Literature

214

(2)

6 The Shadow Price Approach to the Estimation and Decomposition of Economic Efficiency

216

(45)

6.1 Introduction

216

(2)

6.2 Cross-Sectional Models

218

(36)

6.2.1 Estimating and Decomposing Cost Inefficiency

221

(18)

6.2.2 Estimating and Decomposing Profit Inefficiency

239

(15)

6.3 Panel Data Models

254

(5)

6.3.1 Estimating and Decomposing Cost Inefficiency

255

(3)

6.3.2 Estimating and Decomposing Profit Inefficiency

258

(1)

6.4 A Guide to the Literature

259

(2)

7 Incorporating Exogenous Influences on Efficiency

261

(18)

7.1 Introduction

261

(1)

7.2 Early Approaches to the Incorporation of Exogenous Influences

262

(4)

7.3 Recent Approaches to the Incorporation of Exogenous Influences

266

(11)

7.4 A Guide to the Literature

277

(2)

8 The Estimation of Efficiency Change and Productivity Change

279

(32)

8.1 Introduction

279

(2)

8.2 The Primal (Production Frontier) Approach

281

(6)

8.2.1 The Analytical Framework

282

(3)

8.2.2 Estimation and Decomposition

285

(2)

8.3 A Dual (Cost Frontier) Approach

287

(12)

8.3.1 The Analytical Framework

288

(6)

8.3.2 Estimation and Decomposition

294

(2)

8.3.3 An Extension to Multiple Outputs

296

(3)

8.4 A Dual (Profit Frontier) Approach

299

(8)

8.4.1 The Analytical Framework

299

(3)

8.4.2 Estimation and Decomposition

302

(4)

8.4.3 An Extension to Multiple Outputs

306

(1)

8.5 A Guide to the Literature

307

(4)

References

311

(18)

Author Index

329

(3)

Subject Index

332

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Stochastic Frontier Analysis

Summary

Author Biography

Table of Contents

Supplemental Materials