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Multi-level multi-stage efficiency measurement: the case of innovation systems

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Abstract

Efficiency measurement has been receiving significant attention the last years especially after the recent economic crises and the need of efficient use of public money. Although single step efficiency measurement is usually applied, taking into account the internal structure of the system is expected to provide more meaningful and informative results. This could be done in two axes: decomposition of the process into sub-processes and hierarchical modeling among system components. In this framework we extend the Data Envelopment Analysis approach by examining efficiency through multi-level and multi-stage modeling. The proposed modeling approach (1) can give a better insight in sub-processes compared to single-stage ones and (2) can take into account functional/systemic characteristics (e.g., a Decision Making Unit operating as a part of a greater system). Through a ‘soft’ integration approach, not only different stages can be introduced but also hierarchies can be easily accommodated. Analysis of the efficiency of national/regional innovation systems is used as an illustrative example. The innovation process is modeled as a multi-stage process including knowledge production and knowledge commercialization and multi-level one, where regional innovation is achieved within a national innovation system.

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Author information

Authors and Affiliations

  1. The George Washington University, Washington, DC, 20052, USA

    Elias G. Carayannis

  2. Department of Economics, University of Ioannina, 45110, Ioannina, Greece

    Yorgos Goletsis

  3. School of Production Engineering and Management, Technical University of Crete, 73100, Chania, Greece

    Evangelos Grigoroudis

Authors
  1. Elias G. Carayannis
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  2. Yorgos Goletsis
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  3. Evangelos Grigoroudis
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Corresponding author

Correspondence to Elias G. Carayannis.

Appendix: Regional efficiency scores

Appendix: Regional efficiency scores

DMU

Regions

\( \theta_{0}^{*} \)

θ 10

θ 20

DMU

Regions

\( \theta_{0}^{*} \)

θ 10

θ 20

1

BE1

0.5603

0.5603

1.0000

52

ES51

0.6856

0.7486

0.9158

2

BE2

0.4685

0.5430

0.8628

53

ES52

0.3329

0.5673

0.5868

3

BE3

0.3586

0.3801

0.9434

54

ES53

0.3902

0.8549

0.4565

4

BG3

0.7658

0.7658

1.0000

55

ES61

0.3171

0.6612

0.4797

5

BG4

0.1992

0.5018

0.3970

56

ES62

0.2449

0.5941

0.4122

6

CZ01

0.6520

0.9317

0.6998

57

ES63

1.0000

1.0000

1.0000

7

CZ02

1.0000

1.0000

1.0000

58

ES64

0.4966

1.0000

0.4966

8

CZ03

0.8144

0.9711

0.8386

59

ES7

0.3791

0.6920

0.5479

9

CZ04

1.0000

1.0000

1.0000

60

FR1

0.7359

0.7359

1.0000

10

CZ05

0.9143

1.0000

0.9143

61

FR2

0.6125

0.6125

1.0000

11

CZ06

0.6476

0.7644

0.8472

62

FR3

0.5501

0.5584

0.9852

12

CZ07

0.6542

0.6555

0.9979

63

FR4

0.4451

0.6448

0.6903

13

CZ08

0.6129

0.8634

0.7098

64

FR5

0.3872

0.5122

0.7559

14

DK01

0.4257

0.4257

1.0000

65

FR6

0.3620

0.5258

0.6885

15

DK02

0.3226

0.4304

0.7496

66

FR7

0.4479

0.5215

0.8589

16

DK03

0.2986

0.4084

0.7312

67

FR8

0.4982

0.6560

0.7594

17

DK04

0.3183

0.3802

0.8372

68

FR9

0.5389

1.0000

0.5389

18

DK05

0.3071

0.4378

0.7016

69

ITC1

0.9258

1.0000

0.9258

19

DE1

1.0000

1.0000

1.0000

70

ITC2

0.8098

0.8098

1.0000

20

DE2

0.8925

0.8925

1.0000

71

ITC3

0.5081

0.7890

0.6440

21

DE3

0.8601

1.0000

0.8601

72

ITC4

1.0000

1.0000

1.0000

22

DE4

0.4540

0.5865

0.7740

73

ITD1

0.7238

0.7238

1.0000

23

DE5

0.7460

0.9562

0.7802

74

ITD4

0.7303

0.9014

0.8102

24

DE6

0.9239

1.0000

0.9239

75

ITD5

0.7688

0.9527

0.8070

25

DE7

0.8916

0.9377

0.9508

76

ITE1

0.4643

0.6555

0.7083

26

DE8

0.5229

0.6782

0.7709

77

ITE2

0.5773

1.0000

0.5773

27

DE9

0.7491

0.9095

0.8236

78

ITE3

0.5730

0.8961

0.6394

28

DEA

0.7252

0.8265

0.8774

79

ITE4

0.6276

0.9513

0.6597

29

DEB

0.8066

0.8263

0.9761

80

ITF1

0.4379

0.7405

0.5913

30

DEC

0.9910

0.9960

0.9950

81

ITF2

0.5080

1.0000

0.5080

31

DED

0.4986

0.8047

0.6196

82

ITF3

0.5563

0.9045

0.6151

32

DEE

0.4764

0.6923

0.6882

83

ITF4

0.5774

0.7363

0.7842

33

DEF

0.7346

0.8413

0.8731

84

ITF5

0.5660

0.7438

0.7609

34

DEG

0.5778

0.7942

0.7275

85

ITF6

0.4951

0.7707

0.6423

35

IE01

0.4064

0.4947

0.8216

86

ITG1

0.4034

0.7062

0.5713

36

IE02

0.4641

0.7053

0.6580

87

ITG2

0.5550

0.5990

0.9265

37

GR1

0.4010

0.7155

0.5605

88

HU1

0.3735

0.7917

0.4718

38

GR2

0.3883

0.6178

0.6286

89

HU21

0.6183

1.0000

0.6183

39

GR3

0.5810

1.0000

0.5810

90

HU22

0.4701

0.8604

0.5464

40

GR4

0.3985

0.8086

0.4928

91

HU23

0.2503

0.5591

0.4476

41

ES11

0.3075

0.6724

0.4573

92

HU31

0.3174

0.7412

0.4282

42

ES12

0.5474

1.0000

0.5474

93

HU32

0.2147

0.5853

0.3668

43

ES13

0.3537

0.5209

0.6791

94

HU33

0.2171

0.4734

0.4585

44

ES21

0.6830

1.0000

0.6830

95

NL11

0.2862

0.3550

0.8063

45

ES22

0.6128

0.7296

0.8399

96

NL12

0.3105

0.3248

0.9559

46

ES23

0.4628

0.8032

0.5763

97

NL13

0.3122

0.3175

0.9831

47

ES24

0.6049

0.8330

0.7261

98

NL21

0.2762

0.3034

0.9102

48

ES3

0.7960

1.0000

0.7960

99

NL22

0.3018

0.3226

0.9353

49

ES41

0.4349

0.8849

0.4915

100

NL23

0.4096

0.4470

0.9162

50

ES42

0.3413

0.6546

0.5213

101

NL31

0.4325

0.4827

0.8960

51

ES43

0.3373

1.0000

0.3373

102

NL32

0.4587

0.5096

0.9001

103

NL33

0.4693

0.5193

0.9037

145

SK03

0.4166

0.6949

0.5995

104

NL34

0.4731

0.4731

1.0000

146

SK04

0.4179

0.8124

0.5143

105

NL41

0.4708

0.4708

1.0000

147

FI13

0.3204

0.3913

0.8188

106

NL42

0.4149

0.4149

1.0000

148

FI18

0.5002

0.6091

0.8212

107

AT1

0.5110

0.5195

0.9836

149

FI19

0.5054

0.5520

0.9156

108

AT2

0.4584

0.4584

1.0000

150

FI1A

0.3301

0.3959

0.8337

109

AT3

0.4853

0.4853

1.0000

151

FI2

1.0000

1.0000

1.0000

110

PL11

0.1941

0.5064

0.3833

152

SE11

0.7861

0.9245

0.8503

111

PL12

0.2658

0.6983

0.3806

153

SE12

0.5032

0.5106

0.9857

112

PL21

0.2137

0.4415

0.4841

154

SE21

0.4501

0.5091

0.8841

113

PL22

0.2702

0.6322

0.4274

155

SE22

0.4241

0.4772

0.8886

114

PL31

0.2059

0.4579

0.4495

156

SE23

0.4793

0.5081

0.9434

115

PL32

0.2609

0.4406

0.5922

157

SE31

0.3063

0.3713

0.8248

116

PL33

0.6994

0.6994

1.0000

158

SE32

0.3731

0.4324

0.8629

117

PL34

0.2301

0.5771

0.3988

159

SE33

0.2627

0.3422

0.7678

118

PL41

0.2143

0.5324

0.4025

160

UKC

0.4096

0.4982

0.8223

119

PL42

0.3804

0.7589

0.5013

161

UKD

0.3649

0.5149

0.7088

120

PL43

0.2974

0.5875

0.5062

162

UKE

0.3701

0.4997

0.7407

121

PL51

0.2762

0.5894

0.4686

163

UKF

0.3871

0.4795

0.8073

122

PL52

0.4698

0.7901

0.5945

164

UKG

0.4433

0.5375

0.8249

123

PL61

0.2748

0.6352

0.4326

165

UKH

0.4525

0.5771

0.7841

124

PL62

0.2857

0.6759

0.4227

166

UKI

0.4315

0.7324

0.5891

125

PL63

0.2860

0.6495

0.4404

167

UKJ

0.6420

0.9137

0.7026

126

PT11

0.6292

0.7948

0.7916

168

UKK

0.3435

0.4496

0.7639

127

PT15

1.0000

1.0000

1.0000

169

UKL

0.3840

0.4960

0.7742

128

PT16

0.9027

0.9027

1.0000

170

UKM

0.3281

0.5092

0.6444

129

PT17

0.8477

1.0000

0.8477

171

UKN

0.2532

0.4671

0.5420

130

PT18

0.8050

0.8117

0.9917

172

CH01

0.4329

0.5345

0.8100

131

PT2

0.9069

1.0000

0.9069

173

CH02

0.4680

0.6494

0.7206

132

PT3

1.0000

1.0000

1.0000

174

CH03

0.6803

0.7293

0.9328

133

RO11

0.2990

0.8702

0.3436

175

CH04

0.9389

1.0000

0.9389

134

RO12

0.6278

1.0000

0.6278

176

CH05

0.4249

0.6059

0.7013

135

RO21

0.6481

1.0000

0.6481

177

CH06

0.4859

0.6610

0.7352

136

RO22

1.0000

1.0000

1.0000

178

CH07

0.4536

0.6083

0.7458

137

RO31

0.3562

1.0000

0.3562

179

NO01

0.8055

0.8055

1.0000

138

RO32

0.3505

1.0000

0.3505

180

NO02

0.3493

0.7590

0.4603

139

RO41

0.2872

1.0000

0.2872

181

NO03

0.4036

0.6412

0.6295

140

RO42

0.6236

1.0000

0.6236

182

NO04

0.7808

0.7808

1.0000

141

SI01

0.4260

0.5006

0.8511

183

NO05

0.4461

0.6257

0.7129

142

SI02

0.4439

0.5771

0.7692

184

NO06

0.3426

0.4990

0.6867

143

SK01

0.6351

0.9975

0.6367

185

NO07

0.2910

0.5963

0.4881

144

SK02

0.4567

0.7792

0.5861

     

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Carayannis, E.G., Goletsis, Y. & Grigoroudis, E. Multi-level multi-stage efficiency measurement: the case of innovation systems. Oper Res Int J 15, 253–274 (2015). https://doi.org/10.1007/s12351-015-0176-y

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