Benchmarking with DEA, SFA, and R (eBook)
XVI, 352 Seiten
Springer New York (Verlag)
978-1-4419-7961-2 (ISBN)
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.
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 competitionauthorities.
Preface 8
Subject 8
Audience and style 8
Acknowledgements 9
Contents 10
Acronyms and Symbols 16
Chapter 1 Introduction to Benchmarking 18
1.1 Why benchmark 18
1.1.1 Learning 19
Practical application: Danish Waterworks 20
1.1.2 Coordination 20
Practical application: Reallocation of agricultural production 21
1.1.3 Motivation 22
Practical application: Regulation of Electricity Networks in Europe 22
1.2 Ideal evaluations 23
1.3 Key Performance Indicators and Ratios 25
1.4 Technology and efficiency 28
1.5 Many inputs and outputs 30
1.6 From effectiveness to efficiency 32
1.7 Frontier models 34
1.7.1 A simple taxonomy 34
1.7.2 Pros and cons 35
1.8 Software 37
1.9 Summary 37
1.10 Bibliographic notes 38
Chapter 2 Efficiency Measures 40
2.1 Introduction 40
2.2 Setting 40
2.3 Efficient production 41
2.4 Farrell efficiency 43
Numerical example 44
2.4.1 Non-discretionary inputs and outputs 46
2.4.2 Using Farrell to rank firms 46
2.4.3 Farrell and Shephard distance functions 47
2.5 Directional efficiency measures 48
Practical application: Benchmarking in waterworks 51
2.6 Efficiency measures with prices 52
2.6.1 Cost and input allocative efficiency 53
Numerical example 55
2.6.2 Revenue and output allocative efficiency 56
2.6.3 Profit efficiency 58
2.7 Dynamic efficiency 58
Numerical example 61
Practical application: Regulation of electricity networks 62
2.8 Structural and network efficiency 62
Practical application: Merger control in health care 63
Numerical example 64
2.9 Choice between efficiency measures 65
2.10 Summary 67
2.11 Bibliographic notes 67
2.12 Appendix: More advanced material on efficiency measures 68
2.12.1 The rationale of efficiency 69
2.12.2 Axiomatic characterization of efficiency measures 70
Chapter 3 Production Models and Technology 73
3.1 Introduction 73
3.2 Setting 73
3.3 The technology set 75
Practical application: Bulls 76
3.4 Free disposability of input and output 76
Practical application: Credit unions 79
Practical application: Universities 79
3.5 Convexity 80
3.6 Free disposal and convex 84
Numerical example 85
3.7 Scaling and additivity 86
Practical application:Waterworks 89
3.8 Alternative descriptions of the technology 90
3.9 Summary 93
3.10 Bibliographic notes 94
3.11 Appendix: Distance functions and duality 94
Chapter 4 Data Envelopment Analysis DEA 97
4.1 Introduction 97
4.2 Setting 98
4.3 Minimal extrapolation 98
Numerical example 100
Practical application: Regulatory models 100
4.4 DEA technologies 101
Practical application: DSO regulation 105
4.5 DEA programs 106
Practical application: DSO league tables 108
4.6 Peer units 109
4.6.1 Numerical example in R 111
Practical application:Waterworks 110
4.7 DEA as activity analysis 114
Practical application: Quasi-activities in regulation 115
4.8 Scale and allocative efficiency 115
4.8.1 Scale efficiency in DEA 115
Numerical example in R 117
4.8.2 Allocative efficiency in DEA 118
Numerical example in R 119
4.9 Summary 120
4.10 Bibliographic notes 121
4.11 Appendix: More technical material on DEA models 122
4.11.1 Why the T . / sets work 122
4.11.2 Linear programming 123
4.11.3 DEA “cost” and production functions 125
The single input “cost” function 125
The single-output production function 128
Chapter 5 Additional Topics in DEA 130
5.1 Introduction 130
5.2 Super-efficiency 130
Numerical example in R 133
5.3 Non-discretionary variables 133
Practical application: Fishery 135
5.4 Directional efficiency measures 136
Practical application: Bank branches 138
5.5 Improving both inputs and outputs 139
Numerical example in R 141
5.6 Slack considerations 142
Numerical example in R 144
5.7 Measurement units, values and missing prices 146
5.8 Dual programs 147
5.9 Maximin formulations 152
5.10 Partial value information 153
Numerical example in R 155
5.10.1 Establishing relevant value restrictions 157
Practical application: Regulation 157
5.10.2 Applications of value restrictions 158
5.11 Summary 160
5.12 Bibliographic notes 161
5.13 Appendix: Outliers 162
5.13.1 Types of outliers 162
5.13.2 Identifying outliers 163
5.13.3 Data cloud method 164
5.13.4 Finding outliers in R 166
Chapter 6 Statistical Analysis in DEA 169
6.1 Introduction 169
6.2 Asymptotic tests 170
6.2.1 Test for group differences 171
Numerical example in R: Milk producers 173
6.2.2 Test of model assumptions 174
Numerical example in R: Milk producers 176
Practical application: DSO regulation 178
6.3 The bootstrap method 179
Numerical example in R 181
6.3.1 Confidence interval 183
6.4 Bootstrapping in DEA 184
6.4.1 Naive bootstrap 185
6.4.2 Smoothing 186
6.4.3 Bias and bias correction 187
6.5 Algorithm to bootstrap DEA 187
6.5.1 Confidence intervals 190
6.6 Numerical example in R 190
6.7 Interpretation of the bootstrap results 193
6.7.1 One input, one output 194
6.7.2 Two inputs 195
6.8 Statistical tests using bootstrapping 197
6.9 Summary 199
6.10 Bibliographic notes 200
6.11 Appendix: Second stage analysis 201
6.11.1 Ordinary linear regressions OLS 202
6.11.2 Tobit regression 203
Output efficiency and tobit 205
6.11.3 Numerical example in R 206
6.11.4 Problems with the two-step method 210
Chapter 7 Stochastic Frontier Analysis SFA 211
7.1 Introduction 211
7.2 Parametric approaches 212
7.3 Ordinary regression models 214
7.4 Deterministic frontier models 215
Numerical example in R 216
7.5 Stochastic frontier models 218
7.5.1 Normal and half–normal distributions 220
7.6 Maximum likelihood estimation 221
7.6.1 Justification for the method 222
7.6.2 Numerical methods 223
7.7 The likelihood function 224
7.8 Actual estimation 226
Numerical example in R 226
7.9 Efficiency variance 228
Practical application:Milk producers 229
7.9.1 Comparing OLS and SFA 230
7.10 Firm-specific efficiency 231
7.10.1 Firm-specific efficiency in the additive model 235
7.11 Comparing DEA, SFA, and COLS efficiencies 237
7.12 Summary 241
7.13 Bibliographic notes 243
7.14 Appendix: Derivation of the log likelihood function 244
Chapter 8 Additional Topics in SFA 246
8.1 Introduction 246
8.2 Stochastic distance function models 246
Numerical example in R: Single-output milk producers 248
Numerical example in R: Multi-output pig producers 249
8.2.1 Estimating an output distance function 251
8.3 Functional forms 252
8.3.1 Approximation of functions 252
8.3.2 Homogeneous functions 254
8.3.3 The translog distance function 256
8.4 Stochastic cost function 257
Numerical example in R: Pig producers 260
8.5 Statistical inference 261
8.5.1 Variance of parameters 262
8.5.2 Hypothesis testing using the t-test 263
8.5.3 General likelihood ratio tests 264
8.5.4 Is the variation in efficiency significant? 265
8.6 Test for constant returns to scale 266
Numerical example in R: Milk producers 267
8.6.1 Rewrite the model: t-test 267
8.6.2 Linear hypothesis 268
8.6.3 Likelihood ratio test 269
8.7 Other distributions of technical efficiency 270
Truncated normal 270
Exponential 271
Gamma 271
What is the difference? 272
8.8 Biased estimates 273
8.9 Summary 275
8.10 Bibliographic notes 275
Chapter 9 Merger Analysis 276
9.1 Introduction 276
9.2 Horizontal mergers 277
9.2.1 Integration gains 278
9.2.2 Disintegration gains 281
9.3 Learning, harmony and size effects 282
9.3.1 Organizational restructuring 285
Low learning measure LE 285
Low harmony measure HA 286
Low size measure SI 286
9.3.2 Rationale of the harmony measure 286
9.3.3 Decomposition with a cost function 287
9.4 Implementations in DEA and SFA 288
9.4.1 Numerical example in R 290
9.4.2 Mergers in a parametric model 293
9.4.3 Technical complication 294
9.4.4 Methodological complication 295
9.5 Practical application: Merger control in Dutch hospital industry 295
9.6 Practical application: Mergers of Norwegian DSOs 304
9.7 Controllability, transferability, and ex post efficiency 304
9.8 Summary 308
Chapter 10 Regulation and Contracting 311
10.1 Introduction 311
10.2 Classical regulatory packages 311
10.2.1 Cost-recovery regimes 312
10.2.2 Fixed price regimes (price-cap, revenue cap, CPI-X) 313
10.2.3 Yardstick regimes 315
10.2.4 Franchise auctions 317
10.2.5 Applications 317
10.3 Practical application: DSO regulation in Germany 318
10.3.1 Towards a modern benchmark based regulation 318
10.3.2 Revenue cap formula 319
10.3.3 Benchmarking requirements 320
10.3.4 Model development process 322
10.3.5 Model choice 323
10.3.6 Final model 325
10.4 DEA based incentive schemes 326
10.4.1 Interests and decisions 327
10.4.2 Super-efficiency in incentive schemes 328
10.4.3 Incentives with individual noise 329
10.4.4 Incentives with adverse selection 330
10.4.5 Dynamic incentives 332
10.4.6 Bidding incentives 332
10.4.7 Practical application: DSO regulation in Norway 333
10.5 Summary 335
10.6 Bibliographic notes 335
Appendix A Getting Started with R: A Quick Introduction 337
A.1 Introduction 337
A.2 Getting and installing R 337
A.3 An introductory R session 338
A.3.1 Packages 343
A.3.2 Scripts 344
A.3.3 Files in R 344
A.4 Changing the appearance of graphs 345
A.5 Reading data into R 345
A.5.1 Reading data from Excel 346
A.6 Benchmarking methods 346
A.7 A first R script for benchmarking 346
A.8 Other packages for benchmarking in R 348
FEAR 348
frontier 349
A.9 Bibliographic notes 350
References 351
Index 358
| Erscheint lt. Verlag | 19.11.2010 |
|---|---|
| Reihe/Serie | International Series in Operations Research & Management Science |
| Zusatzinfo | XVI, 352 p. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Studium ► 1. Studienabschnitt (Vorklinik) ► Biochemie / Molekularbiologie |
| Technik ► Bauwesen | |
| Technik ► Maschinenbau | |
| Wirtschaft ► Allgemeines / Lexika | |
| Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation | |
| Wirtschaft ► Betriebswirtschaft / Management ► Unternehmensführung / Management | |
| Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie | |
| Schlagworte | Data envelopment analysis • DEA • Econometrics • Operations Research • Production and Operations Management • Productivity |
| ISBN-10 | 1-4419-7961-1 / 1441979611 |
| ISBN-13 | 978-1-4419-7961-2 / 9781441979612 |
| Haben Sie eine Frage zum Produkt? |
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