E ciency analysis: A multi-output nonparametric approach

Eciency analysis:

A multi-output nonparametric approach

Barnabé Walheer

Thèse présentée en vue de l'obtention du titre de

Docteur en Sciences Economiques et de Gestion

Université Libre de Bruxelles

Solvay Brussels School Economics & Management

European Center for Advanced Research in Economics and Statistics

Belgium

Under the supervision of

Laurens Cherchye (University of Leuven)

Bram De Rock (Université Libre de Bruxelles)

Jury members

Thomas Demuynck (Université Libre de Bruxelles)

Antonio Estache (Université Libre de Bruxelles)

Contents

Acknowledgments 1

Introduction 2

1 Nonparametric eciency analysis 7

1.1 Input-oriented technical eciency and cost eciency . . . 8

1.1.1 Dene the technology . . . 8

1.1.2 Input-oriented technical eciency . . . 10

1.1.3 Cost eciency . . . 13

1.1.4 Duality between technical and cost eciencies . . . 16

1.2 Directional distance function and prot eciency . . . 17

1.2.1 Dene the technology . . . 17

1.2.2 Directional distance function . . . 19

1.2.3 Prot eciency . . . 21

1.2.4 Duality between directional distance function and prot eciency . . . 23

1.3 Returns-to-scale . . . 24

1.4 Discussion . . . 27

2 Growth and Convergence of the OECD countries 28 2.1 Introduction . . . 29

2.2 Methodology . . . 32

2.2.1 Multi-sector production-frontier approach . . . 32

2.2.2 Quadripartite decomposition of labor productivity growth . . . 36

2.3 Application . . . 38

2.3.1 Data . . . 38

2.3.2 Results . . . 39

2.4 Conclusion . . . 44

3 Multi-output eciency with good and bad outputs 49 3.1 Introduction . . . 50

3.1.1 Multi-output eciency and bad outputs . . . 50

CONTENTS ii

3.2 Methodology . . . 54

3.2.1 Preliminaries . . . 54

3.2.2 Eciency measurement . . . 56

3.2.3 Output objectives . . . 59

3.3 An application to US electric utilities . . . 60

3.3.1 Set-up . . . 61

3.3.2 Data and results . . . 63

3.4 Conclusion . . . 66

4 Eciency and technical changes 68 4.1 Introduction . . . 69

4.2 Methodology . . . 72

4.2.1 Preliminaries . . . 72

4.2.2 Eciency measurement . . . 73

4.2.3 Malmquist productivity index . . . 76

4.3 Application . . . 80

4.4 Conclusion . . . 84

4.5 Appendix . . . 86

5 Multi-output prot eciency 87 5.1 Introduction . . . 88

5.2 Preliminaries . . . 90

5.3 Multi-output prot eciency . . . 92

5.4 Shadow prices and duality . . . 95

5.5 Empirical application . . . 100

5.6 Conclusion . . . 105

List of Figures

1.1 Input set and Input isoquant . . . 8

1.2 Monotone, nested and convex input set . . . 9

1.3 technical eciency in the input set . . . 13

1.4 Cost eciency . . . 14

1.5 Production possibility set . . . 18

1.6 Input eciency . . . 20

1.7 Output eciency . . . 20

2.1 Multi-sector setting of country j in period t . . . 33

2.2 Output-capital graph . . . 44

2.3 Distribution of output per worker in 1995 and 2008 . . . 45

2.4 Output growth against initial output level . . . 45

2.5 Role of the quadripartite decomposition in the divergence of the two groups . . . 45

3.1 Sub-joint inputs in production . . . 62

3.2 Ecient rms (percentage) with varying output objectives; four scenarios . . . 66

5.1 Production process - 2 outputs/1 allocated input . . . 99

List of Tables

2.1 Relative shares of output, labor and output/labor (%) . . . 39

2.2 Eciency scores in 1995 and 2008 . . . 40

2.3 Quadripartite decomposition . . . 41

2.4 Median for the quadripartite decomposition . . . 42

2.5 Quadripartite decomposition: median per group . . . 43

2.6 Eciency scores in 1995 and 2008 with all sectors . . . 47

2.7 Quadripartite decomposition with all sectors . . . 47

2.8 Quadripartite decomposition for the worst case scenario: median per group . . . 48

3.1 Descriptive statistics for our 573 plants . . . 63

3.2 Eciency scores without output objectives . . . 64

3.3 Alternative output objective scenarios . . . 64

3.4 Scenario 2 - bad output weights . . . 65

4.1 Descriptive statistics for the 277 plants in 2009 . . . 82

4.2 Descriptive statistics for the 277 plants in 2012 . . . 82

4.3 MPI and decomposition results . . . 83

4.4 MPI and decomposition for selected plants . . . 84

5.1 Data and input allocation for the three DMUs . . . 98

5.2 Eciency scores for the three DMUs . . . 100

5.3 Multi-output prot eciencies without price restrictions . . . 102

5.4 Multi-output prot eciencies with price restrictions . . . 103

5.5 Output-specic prot eciencies . . . 104

5.6 Share of the total production per output (sample average) . . . 104

5.7 Output-specic prot eciencies for selected DMUs . . . 105

5.8 Output-specic prot ineciencies for the input reduction direction . . . 106