Estimating Output-Specific Efficiencies
The present book is the offspring of my Habilitation, which is the key to academic tenure in Austria. Legal requirements demand that a Ha bilitation be published and so only seeing it in print marks the real end of this biographical landmark project. Fro
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Applied Optimization Volume 64 Series Editors:
Panos M. Pardalos University of Florida, U.S.A.
Donald Hearn University of Florida, U.S.A.
The titles published in this series are listed at the end of this volume.
Estimating Output-Specific Efficiencies by
Dieter Gstach Vienna University of Economics, Austria
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-1-4613-4883-2 ISBN 978-1-4615-0007-0 (eBook) DOI 10.1007/978-1-4615-0007-0
Printed on acid-free paper
AII Rights Reserved
© 2002 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 2002 Softcover reprint ofthe hardcover lst edition 2002 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner
For Aurelia with love and gratitude
Contents
xi
Preface Acknowledgments
Part I
xiii
Motivating the concept 3
l. INTRODUCTION
1
Outline of the book
12
2
Related literature
17
3
Motivation
27
4
Geometrical illustration
30
5
Interpreting the difference
34
Part II
Operationalizing the concept
2. TECHNOLOGY ESTIMATION
41
1
Statistical structures underlying DEA
42
2
Output-ratios to characterize technology
44
3
DEA bias correction
54
vii
viii
ESTIMATING OUTPUT-SPECIFIC EFFICIENCIES
4
Estimator consistency
3. RELATION TO RADIAL MEASURES
60 63
1
Ouput-specific vs. radial efficiencies
64
2
An example that works
68
3
So why not use simple regression analysis ?
71
4
A counterexample
72
4. MARKOV CHAIN MONTE CARLO ANALYSIS
77
1
The Metropolis-Hastings algorithm
79
2
Single-component updates
80
3
Sampling from conjugate distributions
81
5. DATA GENERATING PROCESS
83
1
Target output ratios
83
2
Output specific efficiencies
84
3
Distribution of output vectors
86
6. IDENTIFICATION
89
1
The basic tradeoff in an expectational perspective
90
2
The role of domain observations
92
3
Likelihood surface
98
1- POSTERIOR DISTRIBUTIONS
109
1
The prior assumptions
109
2
Sampling
110
3
Scale Invariance
115
Contents
IX
Part III Evaluating the concept 8. ESTIMATOR PERFORMANCE
127
1
Sample generation
127
2
Case of DEA-estimated frontier
132
3
Case of known frontier
141
Part IV Putting the concept to work
9. AN APPLICATION
153
1
A brief review of related literature
154
2
Estimating technology
157
3
The statistical model
158
4
Constructing the Markov chains
163
5
Data
167
6
Results
172
7
Conclusions from the application
183
10. CONCLUDING REMARKS
187
1
Summary
187
2
Routes for future research
194
References
197
Preface
The present book is the offspring of my Habilitation, which is the key to academic tenure in Austria. Legal requirements demand that a Habilitation be published and so only seeing it in
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