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ADVANCED ROBUST AND NONPARAMETRIC METHODS IN EFFICIENCY ANALYSIS METHODOLOGY AND APPLICATIONS

Studies in Productivity and Efficiency

Series Editors:

Rolf Färe

Shawna Grosskopf

Oregon State University

R. Robert Russell

University of California, Riverside

Books in the series:

Fox, Kevin J.:

Efficiency in the Public Sector

Ball, V. Eldon and Norton, George W.:

Agricultural Productivity:

Measurement and Sources of Growth

Färe, Rolf and Grosskopf, Shawna:

New Directions:

Efficiency and Productivity

Daraio, C. and Simar, L.:

Advanced Robust and Nonparametric Methods in Efficiency Analysis:

Methodology and Applications

by

Cinzia Daraio

Institute of Informatics and Telematics (CNR), Pisa

and

Department of Electrical Systems and Automation,

School of Engineering, University of Pisa

Léopold Simar

Institute of Statistics

Université Catholique de Lovain, Louvain la Neuve, Belgium

Springer

1. INTRODUCTION 1

1.1 What this work is about 1

1.2 Improving the nonparametric approach in frontier analysis 4

1.3 An outline of the work 8

Part I Methodology

2. THE MEASUREMENT OF EFFICIENCY 13

2.1 Productivity and Efficiency 13

2.2 A short history of thought 16

2.3 The economic model 19

2.4 A taxonomy of efficient frontier models 25

2.5 The nonparametric frontier approach 30

2.5.1 Data Envelopment Analysis (DEA) 31

2.5.2 Free Disposal Hull (FDH) 33

2.6 Recent developments in nonparametric efficiency analysis 39

3. STATISTICAL INFERENCE IN NONPARAMETRIC

FRONTIER ESTIMATION 43

3.1 Statistical foundation 43

3.2 Introducing stochastic noise in the model 45

viii

3.3 Asymptotic results 47

3.3.1 Consistency 47

3.3.2 Sampling distributions 49

3.4 Bootstrap techniques and applications 50

3.4.1 Bootstrap in frontier models 52

3.4.2 Correcting the bias 54

3.4.3 Bootstrap confidence intervals 55

3.4.4 Is the bootstrap consistent? 56

3.4.5 Applications of the bootstrap 63

3.4.6 Bootstrapping FDH estimators 64

4. NONPARAMETRIC ROBUST ESTIMATORS:

PARTIAL FRONTIERS 65

4.1 A re-formulation based on the probability of being dominated 66

4.2 Order-m frontiers and efficiency scores 68

4.3 Order-α quantile-type frontiers 72

4.4 Properties of partial frontier estimators 77

4.4.1 Statistical properties 77

4.4.2 Robust estimators of the full frontier 77

4.4.3 Advantages of using partial frontiers 78

4.4.4 Detection of outliers 79

4.5 Summary of the results for the output oriented case 81

4.6 Parametric approximations of robust nonparametric frontiers 85

4.6.1 Two stage methods 87

4.6.2 The bootstrap algorithms 89

4.7 Multivariate parametric approximations 90

4.7.1 Generalized Cobb-Douglas parametric model 91

4.7.2 Translog parametric model 93

5. CONDITIONAL MEASURES OF EFFICIENCY 95

5.1 Explaining efficiency in the literature 96

5.2 Introducing external-environmental variables 100

5.2.1 Conditional full frontier measures 100

5.2.2 Conditional order-m measures 101

5.2.3 Conditional order-α measures 103

5.2.4 Summary for the output oriented case 105

5.3 Bandwidth selection 108

5.3.1 Univariate case 109

5.3.2 Multivariate case 110

Contents

Contents ix

5.4 An econometric methodology 113

5.4.1 Global effect of Z on the production process 113

5.4.2 A decomposition of conditional efficiency 119

5.5 Simulated illustrations 121

5.5.1 Univariate Z 122

5.5.2 Multivariate Z 124

Part II Applications

6. ECONOMIES OF SCALE, SCOPE AND EXPERIENCE

135

6.1 Introduction 135

6.2 Data description 139

6.2.1 Definition of outputs and inputs 142

6.2.2 An exploratory investigation 145

6.2.3 Aggregation of inputs and outputs 148

6.3 Testing returns to scale and bootstrapping efficiency scores 151

6.4 Economies of scale 157

6.5 Economies of scope 160

6.6 Economies of experience 163

6.7 Conclusions 164

7. AGE, SCALE AND CONCENTRATION EFFECTS

167

7.1 Introduction 167

7.2 Data description 176

7.3 Scale and concentration effects 178

7.4 Age effects on CNR scientific productivity 181

7.5 Robust parametric approximation of multioutput

distance function 186

7.6 Conclusions 191

8. EXPLORINGTHEEFFECTSOFMANAGERTENURE,FUND

AGE AND THEIR INTERACTION 193

8.1 Introduction 193

8.2 Data description 196

8.3 Impact of mutual fund manager tenure on performance 199

8.4 Interaction between manager tenure and fund age 208

IN THE ITALIAN MOTOR-VEHICLE SECTOR

IN A PUBLIC RESEARCH SYSTEM

8.5 Conclusions 216

9. CONCLUSIONS 217

References 221

Topic Index 243

Author Index 245