Innovation Diffusion Models

List of Figures xi

List of Tables xvii

About the Author xxi

Preface xxiii

Acknowledgments xxv

Acronyms xxvii

About the Companion Website xxix

Introduction xxxi

1 Theory of Innovation Diffusion 1

1.1 Basic Concepts and Definitions 1

1.1.1 Innovation 1

1.1.2 Innovation Diffusion 3

1.1.3 Innovation Diffusion Models 3

References 7

2 Innovation Diffusion as an Empirical Generalization: The Bass Model 9

2.1 Introduction 9

2.2 Bass Model: Theory 10

2.2.1 Closed-Form Solution 12

2.3 Model Estimation 14

2.3.1 Goodness of Fit 15

2.4 The Bass Model: Case Studies 15

2.4.1 Model Fit 16

2.4.2 Apple iPhone 16

2.4.3 RIM Blackberry 19

2.4.4 Wind Energy Consumption in Denmark 20

2.5 Recap 23

References 24

3 Innovation Diffusion with Structured Shocks: The Generalized Bass Model 27

3.1 Introduction 27

3.2 Generalized Bass Model: Theory 28

3.2.1 Closed-Form Solution 28

3.2.2 Structured Shocks 29

3.2.2.1 Exponential Shock 29

3.2.2.2 Rectangular Shock 30

3.2.2.3 More Complex Shocks 32

3.3 Generalized Bass Model: Case Studies 32

3.3.1 Model Fit 32

3.3.2 Apple iPhone 33

3.3.3 Apple Mac 34

3.4 Recap 39

References 40

4 Innovation Diffusion with a Dynamic Market Potential: The GGM 43

4.1 Introduction 43

4.2 Dynamic Market Potential: Theory 44

4.2.1 Closed-Form Solution 45

4.3 GGM 45

4.3.1 Specification of m(t) in the GGM 46

4.3.2 Communication and Adoption in the GGM 48

4.4 Generalizations of the GGM 50

4.4.1 GGM with Structured Shocks 50

4.4.2 GGM with Deterministic Seasonality 50

4.5 A Dynamic Market Potential Model with Network Externalities 51

4.6 GGM: Case Studies 53

4.6.1 Model Fit 53

4.6.2 Apple iPhone 54

4.6.3 Apple iPod 56

4.6.4 Samsung Smartphones 59

4.7 Recap 60

References 61

5 Dealing with Autocorrelation and Seasonality in Innovation Diffusion 63

5.1 Introduction 63

5.2 ARMAX Refinement: Theory 64

5.2.1 ARMAX Models 65

5.3 ARMAX Refinement: Case Studies 66

5.3.1 Netflix Subscriptions 66

5.3.2 Apple iPod 69

5.4 Recap 70

References 71

6 Innovation Diffusion in Competition 73

6.1 Introduction 73

6.2 UCRCD Model: Theory 74

6.2.1 More General Models in Competition 77

6.2.1.1 Lotka-Volterra with Churn Model, LVch 78

6.2.1.2 Competition Dynamic Market Potential 79

6.2.1.3 Competition Between Three Products, UCTT 80

6.3 UCRCD Model: Case Studies 83

6.3.1 Model Fit 83

6.3.2 Denmark 84

6.3.3 Australia 85

6.4 Recap 87

References 88

7 Estimation Methods for Innovation Diffusion Models 91

7.1 Introduction 91

7.2 Nonlinear Least Squares 91

7.2.1 Gauss-Newton Method 92

7.2.2 Levenberg-Marquardt Method 93

7.3 Confidence Intervals and Hypothesis Testing 93

7.3.1 Exact Inference 93

7.3.2 Asymptotic Inference and Linear Approximations 94

7.3.2.1 Prediction Intervals 96

References 96

8 Case Studies 97

8.1 Introduction 97

8.2 Sales of Smartphones 97

8.2.1 Recap 106

8.3 Music Industry in the US 107

8.3.1 Recap 117

8.4 Revenues of a Company 117

8.4.1 Recap 125

8.5 The Life Cycle of Tablets 126

8.5.1 Recap 130

8.6 Energy Transition in Germany 131

8.6.1 Coal 132

8.6.2 Gas 135

8.6.3 Nuclear 138

8.6.4 Renewables 141

8.6.5 Nuclear and Renewables 144

8.6.6 Coal, Nuclear, and Renewables 146

8.6.7 Recap 150

8.7 Growth of Video Conferencing 150

8.7.1 Share Price 151

8.7.2 Google Searches 154

8.7.3 Recap 157

8.8 Diffusion of a Scientific Paper 157

8.8.1 Recap 162

8.9 Diffusion of Internet Usage 163

8.9.1 Recap 170

References 170

9 Modeling a Diffusion Process 173

9.1 Statistical Modeling 173

9.2 To Explain or to Predict 174

9.2.1 To Explain 174

9.2.2 To Predict 175

9.3 Conclusion 176

References 176

References 177

Index 183