AN INTRODUCTION TO EFFICIENCY AND PRODUCTIVITY ANALYSIS
AN INTRODUCTION TO EFFICIENCY AND PRODUCTIVITY ANALYSIS by Tim Coelli D. S. Prasada Rao George E. Batlese ~. " Springer Science+Business Media, LLC
ISBN 978-0-7923-8062-7 DOI 10.1007/978-1-4615-5493-6 ISBN 978-1-4615-5493-6 (ebook) Library of Congress Cataloging-in-Publication Data A C.I.P. Catalogue record for this book is available from the Library of Congress. Copyright 1998 by Springer Science+Business Media New York Origina1ly published by Kluwer Academic Publishers in 1998 AII rights reserved. N o part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, record ing, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. Printed on acid-free pa per.
To Michelle, Visala and Marilyn
TABLE OF CONTENTS List of Figures List of Tables Preface page xi xiii xv 1. INTRODUCTION 1 1.1 Introduction 1 1.2 Some Informal Definitions 2 1.3 Overview of Methods 6 1.4 Outline of Chapters 7 1.5 What is Your Economics Background? 9 2. REVIEW OF PRODUCTION ECONOMICS 11 2.1 Introduction 11 2.2 Production Functions 12 2.3 Price Information and Cost Minimisation and Profit Maximisation 22 2.4 Econometric Estimation of Production Functions 34 2.5 Conclusions 37 3. ADDITIONAL TOPICS IN PRODUCTION ECONOMICS 39 3.1 Introduction 39 3.2 Duality in Production 39 3.3 Econometric Estimation of Cost and Profit Functions 53 3.4 Multi-output Production and Distance Functions 59 3.5 Conclusions 66 4. INDEX NUMBERS AND PRODUCTIVITY MEASUREMENT 69 4.1 Introduction 69 4.2 Conceptual Framework and Notation 70 4.3 Formulae for Price Index Numbers 72 4.4 Quantity Index Numbers 74 4.5 Properties ofindex Numbers: The Test Approach 79 4.6 A Simple Numerical Example 81 4.7 Transitivity in Multilateral Comparisons 84 4.8 TFP Measurement Using Index Numbers 87 4.9 Empirical Application: Australian National Railways 93 4.10 Conclusions 97 5. ECONOMIC THEORY AND INDEX NUMBERS 99 5.1 Introduction 99
viii CONTENTS 5.2 Decomposition ofa Simple TFP Index 100 5.3 The Economic-Theoretic Approach: Some Preliminaries 103 5.4 Output Price Indices 105 5.5 Input Price Indices 110 5.6 Output Quantity Indices 113 5.7 Input Quantity Indices 117 5.8 Productivity Indices 120 5.9 Malmquist Productivity Index: Some Additional Issues 126 5.10 Conclusions 130 6. EFFICIENCY MEASUREMENT USING DATA ENVELOPMENT ANALYSIS (DEA) 133 6.1 Introduction 133 6.2 Efficiency Measurement Concepts 134 6.3 The Constant Returns to Scale (CRS) DEA Model 140 6.4 The Variable Returns to Scale (VRS) Model and Scale Efficiencies 150 6.5 Input and Output Orientations 158 6.6 Conclusions 160 7. ADDITIONAL TOPICS ON DATA ENVELOPMENT ANALYSIS 161 7.1 Introduction 161 7.2 Price Information and Allocative Efficiency 161 7.3 Adjusting for Environment 166 7.4 Non-Discretionary Variables 171 7.5 Input Congestion 172 7.6 Treatment of Slacks 175 7.7 Empirical Application: Australian Universities 176 7.8 Conclusions 180 8. EFFICIENCY MEASUREMENT USING STOCHASTIC FRONTIERS 183 8.1 Introduction 183 8.2 The Stochastic Frontier Production Function 185 8.3 Maximum-Likelihood Estimation 187 8.4 Estimation of Mean Technical Efficiency 189 8.5 Prediction of Firm-level Technical Efficiencies 190 8.6 Tests of Hypotheses 190 8.7 A Simple Numerical Example 192 8.8 Conclusions 198 9. ADDITIONAL TOPICS ON STOCHASTIC FRONTIERS 199 9.1 Introduction 199 9.2 Truncated-Normal Distribution 199 9.3 Alternative Functional Forms 201 9.4 Panel Data Models 202 9.5 Time-varying Inefficiency Model 204 9.6 Modeling Inefficiency Effects 207
CONTENTS ix 9.7 Duality and Modeling of Allocative Efficiencies 9.8 Empirical Application: Wheat Fanning in South Africa 9.9 Conclusions 10. PRODUCTIVITY MEASUREMENT USING EFFICIENCY MEASUREMENT METHODS 10.1 Introduction 10.2 The Malmquist TFP Index 10.3 Two Estimation Methods 10.4 Empirical Application: Australian Electricity Generation 10.5 Conclusions 11. CONCLUSIONS 11.1 Summary of Methods 11.2 Relative Merits of the Methods: Some Comments 11.3 Some Final Points Appendix: Computer Software References Author Index Subject Index 209 212 218 221 221 222 226 234 241 243 243 245 247 251 259 269 273
FIGURES 1.1 Production Frontiers and Technical Efficiency page 4 1.2 Productivity, Technical Efficiency and Scale Economies 5 1.3 Technical Change Between Two Periods 6 2.1 TP, AP and MP Curves and Three Stages of Production 15 2.2 A Long-Run Production Function Represented by a Family of Short-Run Production Functions 16 2.3 An Isoquant 17 2.4 An Isoquant Reflecting Input Congestion 18 2.5 Elasticities of Substitution and Isoquant Shapes 20 2.6 TVC, TFC and SRTC Curves 24 2.7 Long Run Total Cost Curve 25 2.8 LRAC, LRTC and LRMC Curves 26 2.9 Isoquant and Isocost Line 28 2.10 LR Profit Curve 30 2.11 Equating MR and LRMC 30 3.1 Technical Change and the Isoquant 58 3.2 Production Possibility Curve 60 3.3 The Production Possibility Curve and Revenue Maximisation 61 3.4 Technical Change and the Production Possibility Curve 61 3.5 Output Distance Function and Production Possibility Set 64 3.6 Input Distance Function and Input Requirement Set 66 4.1 Indices of Output, Input and TFP for Australian National Railways 96 5.1 Revenue Maximisation 105 5.2 Output Price Index 106 5.3 Input Price Index III 5.4 Output Distance Function 115 5.5 Input Quantity Index 118 6.1 Technical and Allocative Efficiencies 135 6.2 Piece-wise Linear Convex Unit Isoquant 136 6.3 Input- and Output-Orientated Technical Efficiency Measures and Returns to Scale 137 6.4 Technical and Allocative Efficiencies from an Output Orientation 138 6.5 Efficiency Measurement and Input Slacks 143 6.6 CRS Input-Orientated DEA Example 145 6.7 Calculation of Scale Economies in DEA 152 6.8 VRS Input-Orientated DEA Example 153 6.9 Output-Orientated DEA 159 7.1 CRS Cost Efficiency DEA Example 164 7.2 Efficiency Measurement and Input Disposability (Congestion) 174
xii FIGURES 8.1 The Stochastic Frontier Production Function 186 9.1 Truncated Normal Distributions 200 9.2 Time-varying Inefficiency Effects in the Battese and Coelli (1992) Model 206 10.1 Malmquist Productivity Indices 225 10.2 VRS Input-Orientated DEA Example 229 10.3 Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - Stochastic Frontier Results 238 10.4 Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - DEA Results 240 10.5 Cumulative TFP Indices - DEA and Stochastic Frontier Results 241
TABLES 2.1 SHAZAM Instructions for Production Function Estimation page 36 3.1 SHAZAM Instructions for SUR Estimation of a Translog Cost Function 56 4.1 Data for Billy's Bus Company 82 4.2a SHAZAM Instructions for Output Price and Quantity Indices 83 4.2b SHAZAM Output for Output Price and Quantity Indices 84 4.3a Listing of Data File, EXl.DTA 89 4.3b Listing ofinstruction File, EXl.INS 90 4.3c Listing of Output File, EXl.OUT 90 4.4a Listing of Instruction File, EX2.INS 92 4.4b Listing of Output File, EX2.0UT 92 4.5 Output Data for the Australian National Railways Example 94 4.6 Non-capital Input Data for the Australian National Railways Example 94 4.7 Capital Input Data for the Australian National Railways Example 95 4.8 Indices of Output, Input and TFP for Australian National Railways 96 6.1 Example Data for CRS DEA Example 143 6.2 CRS Input-Orientated DEA Results 145 6.3a Listing of Data File, EO I.DT A 146 6.3b Listing of Instruction File, EO I.1N~ 147 6.3c Listing of Output File, EO 1.0UT 147 6.4 Example Data for VRS DEA 153 6.5 VRS Input-Orientated DEA Results 154 6.6a Listing of Data File, EG2.DTA 154 6.6b Listing of Instruction File, E02.INS 155 6.6c Listing of Output File, E02.0UT 155 7.1 CRS Cost Efficiency DEA Results 164 7.2a Listing of Data File, EG3.DT A 165 7.2b Listing ofinstruction File, EG3.INS 165 7.2c Listing of Output File, EG3.0UT 165 7.3 DEA Results for the Australian Universities Study 179 8.1 Data on Telecommunications Providers in 21 Countries in 1990 193 8.2a Listing of Data File, EXAl.DTA 194 8.2b Listing ofinstruction File, EXAl.INS 195 8.2c Listing of Output File, EXAl.OUT 195 9.1 FRONTIER Instruction File for Estimation of the Translog Stochastic Frontier Model for Wheat Farmers in South Africa 215 9.2: Output from FRONTIER for Estimation of the Translog Stochastic Frontier Production Function for Wheat Farmers in South Africa 216
xiv 9.3 FRONTIER Instruction File for Estimation of the Cobb-Douglas Frontier Model for Wheat Fanners in South Africa 218 10.1 Example Data for Malmquist DEA 228 1O.2a Listing of Data File, EG4.DTA 229 10.2b Listing of Instruction File, EG4.INS 230 1O.2c Listing of Output File, EG4.0UT 231 10.3 Maximum-Likelihood Estimates of the Stochastic Frontier Model 237 10.4 Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - Stochastic Frontier Results 238 10.5 Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - DEA Results 239 11.1 Summary of the Properties of the Four Principal Methods 243
PREFACE This book is designed to be a "first port of call" for people wishing to study efficiency and productivity analysis. The book provides an accessible introduction to the four principal methods involved, namely, least-squares econometric production models, index numbers, data envelopment analysis (DEA) and stochastic frontiers. For each method, we provide a detailed introduction to the basic method, give a simple numerical example to illustrate the concepts and then discuss some of the more important extensions to the basic methods and indicate some references for further reading. We also describe a number of detailed empirical applications using real data to illustrate these methods. The book may be used as a textbook or as a reference text. As a textbook it could be used in an advanced-undergraduate or graduate-level course. Two early chapters are devoted to a review of production economics. These chapters could be skimmed quickly in a course for graduate economics majors, but they should prove very useful to undergraduate students and those doing a major in another field, such as business management, health studies, etc. There have been several excellent books written on performance measurement in recent years, such as Piire, Grosskopf and Lovell (1985, 1994), Fried, Lovell and Schmidt (1993), Chames et al (1995) and Piire, Grosskopf and Russell (1997). The present book is not designed to compete with these books, but to provide a lowerlevel bridge to the material contained within them, and many other books and journal articles written on this topic. We believe this book contains three features unique to books in this field. 1. It is an introductory text. 2. It contains detailed discussion and comparison of all of the four principal methods. 3. It provides detailed advice on computer programs which can be used to calculate the various measures. This involves a number of presentations of computer instructions and output listings for the SHAZAM, TFPIP, DEAP and FRONTIER computer programs. The book has evolved from a set of notes for short courses which were given by the authors to a number of Government agencies in Australia during 1995 and 1996. Particular mention should be made of the NSW Treasury where the first of these
xvi PREFACE short courses was presented. We thank John Pierce from NSW Treasury for proposing the idea for a short course on this topic and for the encouragement he has given staff of the Centre for Efficiency and Productivity Analysis (CEPA). We are grateful to the many people from: NSW Treasury, Bureau of Industry Economics, Industry Commission, Victorian Treasury, Queensland Treasury, the Australian Bureau of Statistics and a number of other staff from NSW Government agencies who attended these courses and provided valuable feedback and suggestions. We are also particularly indebted to Bert Balk, Rolf Fiire, Knox Lovell and Chris O'Donnell for making valuable comments on various drafts of this manuscript. Tim Coelli D.S. Prasada Rao George E. Battese Centre for Efficiency and Productivity Analysis, University of New England, Armidale, N.S.W., Australia.