AN INTRODUCTION TO EFFICIENCY AND PRODUCTIVITY ANALYSIS

Transcription

1 AN INTRODUCTION TO EFFICIENCY AND PRODUCTIVITY ANALYSIS

2 AN INTRODUCTION TO EFFICIENCY AND PRODUCTIVITY ANALYSIS by Tim Coelli D. S. Prasada Rao George E. Batlese ~. " Springer Science+Business Media, LLC

3 ISBN DOI / ISBN (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.

4 To Michelle, Visala and Marilyn

5 TABLE OF CONTENTS List of Figures List of Tables Preface page xi xiii xv 1. INTRODUCTION Introduction Some Informal Definitions Overview of Methods Outline of Chapters What is Your Economics Background? 9 2. REVIEW OF PRODUCTION ECONOMICS Introduction Production Functions Price Information and Cost Minimisation and Profit Maximisation Econometric Estimation of Production Functions Conclusions ADDITIONAL TOPICS IN PRODUCTION ECONOMICS Introduction Duality in Production Econometric Estimation of Cost and Profit Functions Multi-output Production and Distance Functions Conclusions INDEX NUMBERS AND PRODUCTIVITY MEASUREMENT Introduction Conceptual Framework and Notation Formulae for Price Index Numbers Quantity Index Numbers Properties ofindex Numbers: The Test Approach A Simple Numerical Example Transitivity in Multilateral Comparisons TFP Measurement Using Index Numbers Empirical Application: Australian National Railways Conclusions ECONOMIC THEORY AND INDEX NUMBERS Introduction 99

6 viii CONTENTS 5.2 Decomposition ofa Simple TFP Index The Economic-Theoretic Approach: Some Preliminaries Output Price Indices Input Price Indices Output Quantity Indices Input Quantity Indices Productivity Indices Malmquist Productivity Index: Some Additional Issues Conclusions EFFICIENCY MEASUREMENT USING DATA ENVELOPMENT ANALYSIS (DEA) Introduction Efficiency Measurement Concepts The Constant Returns to Scale (CRS) DEA Model The Variable Returns to Scale (VRS) Model and Scale Efficiencies Input and Output Orientations Conclusions ADDITIONAL TOPICS ON DATA ENVELOPMENT ANALYSIS Introduction Price Information and Allocative Efficiency Adjusting for Environment Non-Discretionary Variables Input Congestion Treatment of Slacks Empirical Application: Australian Universities Conclusions EFFICIENCY MEASUREMENT USING STOCHASTIC FRONTIERS Introduction The Stochastic Frontier Production Function Maximum-Likelihood Estimation Estimation of Mean Technical Efficiency Prediction of Firm-level Technical Efficiencies Tests of Hypotheses A Simple Numerical Example Conclusions ADDITIONAL TOPICS ON STOCHASTIC FRONTIERS Introduction Truncated-Normal Distribution Alternative Functional Forms Panel Data Models Time-varying Inefficiency Model Modeling Inefficiency Effects 207

7 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

8 FIGURES 1.1 Production Frontiers and Technical Efficiency page Productivity, Technical Efficiency and Scale Economies Technical Change Between Two Periods TP, AP and MP Curves and Three Stages of Production A Long-Run Production Function Represented by a Family of Short-Run Production Functions An Isoquant An Isoquant Reflecting Input Congestion Elasticities of Substitution and Isoquant Shapes TVC, TFC and SRTC Curves Long Run Total Cost Curve LRAC, LRTC and LRMC Curves Isoquant and Isocost Line LR Profit Curve Equating MR and LRMC Technical Change and the Isoquant Production Possibility Curve The Production Possibility Curve and Revenue Maximisation Technical Change and the Production Possibility Curve Output Distance Function and Production Possibility Set Input Distance Function and Input Requirement Set Indices of Output, Input and TFP for Australian National Railways Revenue Maximisation Output Price Index Input Price Index III 5.4 Output Distance Function Input Quantity Index Technical and Allocative Efficiencies Piece-wise Linear Convex Unit Isoquant Input- and Output-Orientated Technical Efficiency Measures and Returns to Scale Technical and Allocative Efficiencies from an Output Orientation Efficiency Measurement and Input Slacks CRS Input-Orientated DEA Example Calculation of Scale Economies in DEA VRS Input-Orientated DEA Example Output-Orientated DEA CRS Cost Efficiency DEA Example Efficiency Measurement and Input Disposability (Congestion) 174

9 xii FIGURES 8.1 The Stochastic Frontier Production Function Truncated Normal Distributions Time-varying Inefficiency Effects in the Battese and Coelli (1992) Model Malmquist Productivity Indices VRS Input-Orientated DEA Example Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - Stochastic Frontier Results Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - DEA Results Cumulative TFP Indices - DEA and Stochastic Frontier Results 241

10 TABLES 2.1 SHAZAM Instructions for Production Function Estimation page SHAZAM Instructions for SUR Estimation of a Translog Cost Function Data for Billy's Bus Company a SHAZAM Instructions for Output Price and Quantity Indices b SHAZAM Output for Output Price and Quantity Indices a Listing of Data File, EXl.DTA b Listing ofinstruction File, EXl.INS c Listing of Output File, EXl.OUT a Listing of Instruction File, EX2.INS b Listing of Output File, EX2.0UT Output Data for the Australian National Railways Example Non-capital Input Data for the Australian National Railways Example Capital Input Data for the Australian National Railways Example Indices of Output, Input and TFP for Australian National Railways Example Data for CRS DEA Example CRS Input-Orientated DEA Results a Listing of Data File, EO I.DT A b Listing of Instruction File, EO I.1N~ c Listing of Output File, EO 1.0UT Example Data for VRS DEA VRS Input-Orientated DEA Results a Listing of Data File, EG2.DTA b Listing of Instruction File, E02.INS c Listing of Output File, E02.0UT CRS Cost Efficiency DEA Results a Listing of Data File, EG3.DT A b Listing ofinstruction File, EG3.INS c Listing of Output File, EG3.0UT DEA Results for the Australian Universities Study Data on Telecommunications Providers in 21 Countries in a Listing of Data File, EXAl.DTA b Listing ofinstruction File, EXAl.INS c Listing of Output File, EXAl.OUT FRONTIER Instruction File for Estimation of the Translog Stochastic Frontier Model for Wheat Farmers in South Africa : Output from FRONTIER for Estimation of the Translog Stochastic Frontier Production Function for Wheat Farmers in South Africa 216

11 xiv 9.3 FRONTIER Instruction File for Estimation of the Cobb-Douglas Frontier Model for Wheat Fanners in South Africa Example Data for Malmquist DEA 228 1O.2a Listing of Data File, EG4.DTA b Listing of Instruction File, EG4.INS 230 1O.2c Listing of Output File, EG4.0UT Maximum-Likelihood Estimates of the Stochastic Frontier Model Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - Stochastic Frontier Results Cumulative Indices of Technical Efficiency Change, Technical Change and TFP Change - DEA Results Summary of the Properties of the Four Principal Methods 243

12 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 Particular mention should be made of the NSW Treasury where the first of these

13 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.