Bogetoft / Otto Benchmarking with DEA, SFA, and R

1. Auflage 2010
ISBN: 978-1-4419-7961-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 157, 352 Seiten

Reihe: International Series in Operations Research & Management Science

This book covers recent advances in efficiency evaluations, most notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA) methods.  It introduces the underlying theories, shows how to make the relevant calculations and discusses applications. The aim is to make the reader aware of the pros and cons of the different methods and to show how to use these methods in both standard and non-standard cases.Several software packages have been developed to solve some of the most common DEA and SFA models. This book relies on R, a free, open source software environment for statistical computing and graphics. This enables the reader to solve not only standard problems, but also many other problem variants. Using R, one can focus on understanding the context and developing a good model. One is not restricted to predefined model variants and to a one-size-fits-all approach. To facilitate the use of R, the authors have developed an R package called Benchmarking, which implements the main methods within both DEA and SFA.The book uses mathematical formulations of models and assumptions, but it de-emphasizes the formal proofs - in part by placing them in appendices -- or by referring to the original sources. Moreover, the book emphasizes the usage of the theories and the interpretations of the mathematical formulations.  It includes a series of small examples, graphical illustrations, simple extensions and questions to think about. Also, it combines the formal models with less formal economic and organizational thinking. Last but not least it discusses some larger applications with significant practical impacts, including the design of benchmarking-based regulations of energy companies in different European countries, and the development of merger control programs for competition authorities.

Autoren/Hrsg.

Bogetoft, Peter

Otto, Lars

Inhaltsverzeichnis

1;Preface;8
1.1;Subject;8
1.2;Audience and style;8
1.3;Acknowledgements;9
2;Contents;10
3;Acronyms and Symbols;16
4;Chapter 1 Introduction to Benchmarking;18
4.1;1.1 Why benchmark;18
4.1.1;1.1.1 Learning;19
4.1.1.1;Practical application: Danish Waterworks;20
4.1.2;1.1.2 Coordination;20
4.1.2.1;Practical application: Reallocation of agricultural production;21
4.1.3;1.1.3 Motivation;22
4.1.3.1;Practical application: Regulation of Electricity Networks in Europe;22
4.2;1.2 Ideal evaluations;23
4.3;1.3 Key Performance Indicators and Ratios;25
4.4;1.4 Technology and efficiency;28
4.5;1.5 Many inputs and outputs;30
4.6;1.6 From effectiveness to efficiency;32
4.7;1.7 Frontier models;34
4.7.1;1.7.1 A simple taxonomy;34
4.7.2;1.7.2 Pros and cons;35
4.8;1.8 Software;37
4.9;1.9 Summary;37
4.10;1.10 Bibliographic notes;38
5;Chapter 2 Efficiency Measures;40
5.1;2.1 Introduction;40
5.2;2.2 Setting;40
5.3;2.3 Efficient production;41
5.4;2.4 Farrell efficiency;43
5.4.1;Numerical example;44
5.4.2;2.4.1 Non-discretionary inputs and outputs;46
5.4.3;2.4.2 Using Farrell to rank firms;46
5.4.4;2.4.3 Farrell and Shephard distance functions;47
5.5;2.5 Directional efficiency measures;48
5.5.1;Practical application: Benchmarking in waterworks;51
5.6;2.6 Efficiency measures with prices;52
5.6.1;2.6.1 Cost and input allocative efficiency;53
5.6.1.1;Numerical example;55
5.6.2;2.6.2 Revenue and output allocative efficiency;56
5.6.3;2.6.3 Profit efficiency;58
5.7;2.7 Dynamic efficiency;58
5.7.1;Numerical example;61
5.7.2;Practical application: Regulation of electricity networks;62
5.8;2.8 Structural and network efficiency;62
5.8.1;Practical application: Merger control in health care;63
5.8.2;Numerical example;64
5.9;2.9 Choice between efficiency measures;65
5.10;2.10 Summary;67
5.11;2.11 Bibliographic notes;67
5.12;2.12 Appendix: More advanced material on efficiency measures;68
5.12.1;2.12.1 The rationale of efficiency;69
5.12.2;2.12.2 Axiomatic characterization of efficiency measures;70
6;Chapter 3 Production Models and Technology;73
6.1;3.1 Introduction;73
6.2;3.2 Setting;73
6.3;3.3 The technology set;75
6.3.1;Practical application: Bulls;76
6.4;3.4 Free disposability of input and output;76
6.4.1;Practical application: Credit unions;79
6.4.2;Practical application: Universities;79
6.5;3.5 Convexity;80
6.6;3.6 Free disposal and convex;84
6.6.1;Numerical example;85
6.7;3.7 Scaling and additivity;86
6.7.1;Practical application:Waterworks;89
6.8;3.8 Alternative descriptions of the technology;90
6.9;3.9 Summary;93
6.10;3.10 Bibliographic notes;94
6.11;3.11 Appendix: Distance functions and duality;94
7;Chapter 4 Data Envelopment Analysis DEA;97
7.1;4.1 Introduction;97
7.2;4.2 Setting;98
7.3;4.3 Minimal extrapolation;98
7.3.1;Numerical example;100
7.3.2;Practical application: Regulatory models;100
7.4;4.4 DEA technologies;101
7.4.1;Practical application: DSO regulation;105
7.5;4.5 DEA programs;106
7.5.1;Practical application: DSO league tables;108
7.6;4.6 Peer units;109
7.6.1;4.6.1 Numerical example in R;111
7.6.2;Practical application:Waterworks;110
7.7;4.7 DEA as activity analysis;114
7.7.1;Practical application: Quasi-activities in regulation;115
7.8;4.8 Scale and allocative efficiency;115
7.8.1;4.8.1 Scale efficiency in DEA;115
7.8.1.1;Numerical example in R;117
7.8.2;4.8.2 Allocative efficiency in DEA;118
7.8.2.1;Numerical example in R;119
7.9;4.9 Summary;120
7.10;4.10 Bibliographic notes;121
7.11;4.11 Appendix: More technical material on DEA models;122
7.11.1;4.11.1 Why the T . / sets work;122
7.11.2;4.11.2 Linear programming;123
7.11.3;4.11.3 DEA “cost” and production functions;125
7.11.3.1;The single input “cost” function;125
7.11.3.2;The single-output production function;128
8;Chapter 5 Additional Topics in DEA;130
8.1;5.1 Introduction;130
8.2;5.2 Super-efficiency;130
8.2.1;Numerical example in R;133
8.3;5.3 Non-discretionary variables;133
8.3.1;Practical application: Fishery;135
8.4;5.4 Directional efficiency measures;136
8.4.1;Practical application: Bank branches;138
8.5;5.5 Improving both inputs and outputs;139
8.5.1;Numerical example in R;141
8.6;5.6 Slack considerations;142
8.6.1;Numerical example in R;144
8.7;5.7 Measurement units, values and missing prices;146
8.8;5.8 Dual programs;147
8.9;5.9 Maximin formulations;152
8.10;5.10 Partial value information;153
8.10.1;Numerical example in R;155
8.10.2;5.10.1 Establishing relevant value restrictions;157
8.10.2.1;Practical application: Regulation;157
8.10.3;5.10.2 Applications of value restrictions;158
8.11;5.11 Summary;160
8.12;5.12 Bibliographic notes;161
8.13;5.13 Appendix: Outliers;162
8.13.1;5.13.1 Types of outliers;162
8.13.2;5.13.2 Identifying outliers;163
8.13.3;5.13.3 Data cloud method;164
8.13.4;5.13.4 Finding outliers in R;166
9;Chapter 6 Statistical Analysis in DEA;169
9.1;6.1 Introduction;169
9.2;6.2 Asymptotic tests;170
9.2.1;6.2.1 Test for group differences;171
9.2.1.1;Numerical example in R: Milk producers;173
9.2.2;6.2.2 Test of model assumptions;174
9.2.2.1;Numerical example in R: Milk producers;176
9.2.2.2;Practical application: DSO regulation;178
9.3;6.3 The bootstrap method;179
9.3.1;Numerical example in R;181
9.3.2;6.3.1 Confidence interval;183
9.4;6.4 Bootstrapping in DEA;184
9.4.1;6.4.1 Naive bootstrap;185
9.4.2;6.4.2 Smoothing;186
9.4.3;6.4.3 Bias and bias correction;187
9.5;6.5 Algorithm to bootstrap DEA;187
9.5.1;6.5.1 Confidence intervals;190
9.6;6.6 Numerical example in R;190
9.7;6.7 Interpretation of the bootstrap results;193
9.7.1;6.7.1 One input, one output;194
9.7.2;6.7.2 Two inputs;195
9.8;6.8 Statistical tests using bootstrapping;197
9.9;6.9 Summary;199
9.10;6.10 Bibliographic notes;200
9.11;6.11 Appendix: Second stage analysis;201
9.11.1;6.11.1 Ordinary linear regressions OLS;202
9.11.2;6.11.2 Tobit regression;203
9.11.2.1;Output efficiency and tobit;205
9.11.3;6.11.3 Numerical example in R;206
9.11.4;6.11.4 Problems with the two-step method;210
10;Chapter 7 Stochastic Frontier Analysis SFA;211
10.1;7.1 Introduction;211
10.2;7.2 Parametric approaches;212
10.3;7.3 Ordinary regression models;214
10.4;7.4 Deterministic frontier models;215
10.4.1;Numerical example in R;216
10.5;7.5 Stochastic frontier models;218
10.5.1;7.5.1 Normal and half–normal distributions;220
10.6;7.6 Maximum likelihood estimation;221
10.6.1;7.6.1 Justification for the method;222
10.6.2;7.6.2 Numerical methods;223
10.7;7.7 The likelihood function;224
10.8;7.8 Actual estimation;226
10.8.1;Numerical example in R;226
10.9;7.9 Efficiency variance;228
10.9.1;Practical application:Milk producers;229
10.9.2;7.9.1 Comparing OLS and SFA;230
10.10;7.10 Firm-specific efficiency;231
10.10.1;7.10.1 Firm-specific efficiency in the additive model;235
10.11;7.11 Comparing DEA, SFA, and COLS efficiencies;237
10.12;7.12 Summary;241
10.13;7.13 Bibliographic notes;243
10.14;7.14 Appendix: Derivation of the log likelihood function;244
11;Chapter 8 Additional Topics in SFA;246
11.1;8.1 Introduction;246
11.2;8.2 Stochastic distance function models;246
11.2.1;Numerical example in R: Single-output milk producers;248
11.2.2;Numerical example in R: Multi-output pig producers;249
11.2.3;8.2.1 Estimating an output distance function;251
11.3;8.3 Functional forms;252
11.3.1;8.3.1 Approximation of functions;252
11.3.2;8.3.2 Homogeneous functions;254
11.3.3;8.3.3 The translog distance function;256
11.4;8.4 Stochastic cost function;257
11.4.1;Numerical example in R: Pig producers;260
11.5;8.5 Statistical inference;261
11.5.1;8.5.1 Variance of parameters;262
11.5.2;8.5.2 Hypothesis testing using the t-test;263
11.5.3;8.5.3 General likelihood ratio tests;264
11.5.4;8.5.4 Is the variation in efficiency significant?;265
11.6;8.6 Test for constant returns to scale;266
11.6.1;Numerical example in R: Milk producers;267
11.6.2;8.6.1 Rewrite the model: t-test;267
11.6.3;8.6.2 Linear hypothesis;268
11.6.4;8.6.3 Likelihood ratio test;269
11.7;8.7 Other distributions of technical efficiency;270
11.7.1;Truncated normal;270
11.7.2;Exponential;271
11.7.3;Gamma;271
11.7.4;What is the difference?;272
11.8;8.8 Biased estimates;273
11.9;8.9 Summary;275
11.10;8.10 Bibliographic notes;275
12;Chapter 9 Merger Analysis;276
12.1;9.1 Introduction;276
12.2;9.2 Horizontal mergers;277
12.2.1;9.2.1 Integration gains;278
12.2.2;9.2.2 Disintegration gains;281
12.3;9.3 Learning, harmony and size effects;282
12.3.1;9.3.1 Organizational restructuring;285
12.3.1.1;Low learning measure LE;285
12.3.1.2;Low harmony measure HA;286
12.3.1.3;Low size measure SI;286
12.3.2;9.3.2 Rationale of the harmony measure;286
12.3.3;9.3.3 Decomposition with a cost function;287
12.4;9.4 Implementations in DEA and SFA;288
12.4.1;9.4.1 Numerical example in R;290
12.4.2;9.4.2 Mergers in a parametric model;293
12.4.3;9.4.3 Technical complication;294
12.4.4;9.4.4 Methodological complication;295
12.5;9.5 Practical application: Merger control in Dutch hospital industry;295
12.6;9.6 Practical application: Mergers of Norwegian DSOs;304
12.7;9.7 Controllability, transferability, and ex post efficiency;304
12.8;9.8 Summary;308
13;Chapter 10 Regulation and Contracting;311
13.1;10.1 Introduction;311
13.2;10.2 Classical regulatory packages;311
13.2.1;10.2.1 Cost-recovery regimes;312
13.2.2;10.2.2 Fixed price regimes (price-cap, revenue cap, CPI-X);313
13.2.3;10.2.3 Yardstick regimes;315
13.2.4;10.2.4 Franchise auctions;317
13.2.5;10.2.5 Applications;317
13.3;10.3 Practical application: DSO regulation in Germany;318
13.3.1;10.3.1 Towards a modern benchmark based regulation;318
13.3.2;10.3.2 Revenue cap formula;319
13.3.3;10.3.3 Benchmarking requirements;320
13.3.4;10.3.4 Model development process;322
13.3.5;10.3.5 Model choice;323
13.3.6;10.3.6 Final model;325
13.4;10.4 DEA based incentive schemes;326
13.4.1;10.4.1 Interests and decisions;327
13.4.2;10.4.2 Super-efficiency in incentive schemes;328
13.4.3;10.4.3 Incentives with individual noise;329
13.4.4;10.4.4 Incentives with adverse selection;330
13.4.5;10.4.5 Dynamic incentives;332
13.4.6;10.4.6 Bidding incentives;332
13.4.7;10.4.7 Practical application: DSO regulation in Norway;333
13.5;10.5 Summary;335
13.6;10.6 Bibliographic notes;335
14;Appendix A Getting Started with R: A Quick Introduction;337
14.1;A.1 Introduction;337
14.2;A.2 Getting and installing R;337
14.3;A.3 An introductory R session;338
14.3.1;A.3.1 Packages;343
14.3.2;A.3.2 Scripts;344
14.3.3;A.3.3 Files in R;344
14.4;A.4 Changing the appearance of graphs;345
14.5;A.5 Reading data into R;345
14.5.1;A.5.1 Reading data from Excel;346
14.6;A.6 Benchmarking methods;346
14.7;A.7 A first R script for benchmarking;346
14.8;A.8 Other packages for benchmarking in R;348
14.8.1;FEAR;348
14.8.2;frontier;349
14.9;A.9 Bibliographic notes;350
15;References;351
16;Index;358