Knowledge Diffusion Processes: Theoretical and Empirical Considerations Inauguraldissertation zur Erlangung des Doktorgrades der Wirtschaftswissenschaftlichen Fakult¨at der Universit¨atAugsburg vorgelegt von Diplom-Volkswirt Univ. Torben Alexander Klarl Augsburg, im Juni 2009 Erstgutachter: Prof. Dr. Horst Hanusch Zweitgutachter: Prof. Dr. Alfred Maußner Vorsitzender der m¨undlichen Pr¨ufung: Prof. Dr. Fritz Rahmeyer Tag der m¨undlichen Pr¨ufung: 23. Dezember 2009 F¨urmeine Eltern und Unterst¨utzer Contents 1 Knowledge in economics 1 1.1 Basic considerations . .2 1.2 Knowledge diffusion, knowledge transfer and network effects . .3 1.3 Knowledge diffusion and learning, firm size and market structure . .5 1.4 Knowledge diffusion, scale effects and spatial proximity . .7 1.5 Knowledge diffusion and spatial econometrics . 11 1.6 Motivation for further research . 16 2 Knowledge diffusion and the role of knowledge transfer: a stochastic ap- proach 22 2.1 Motivation . 22 2.2 The Bass diffusion model . 24 2.3 Deterministic knowledge diffusion model . 28 2.3.1 Setup . 28 2.3.2 Solution . 30 2.3.3 Stability . 32 2.4 Stochastic knowledge diffusion model . 36 2.4.1 Setup . 36 2.4.2 Euler-Maruyama approximation . 38 2.5 Simulation . 40 2.5.1 Simulation of deterministic knowledge diffusion model . 40 2.5.2 Simulation of stochastic knowledge diffusion model . 42 2.6 Econometric Annotations . 46 2.7 Conclusion . 47 i Contents 3 The impact of learning and knowledge diffusion on industrial dynamics 49 3.1 Introduction . 49 3.2 The basic model . 52 3.2.1 Setup . 52 3.2.1.1 Market share evolution . 55 3.2.1.2 Technological progress and market selection . 57 3.2.1.3 Summary . 60 3.2.2 Dynamic behaviour of the basic model . 61 3.2.3 Stability analysis of the basic model . 63 3.2.4 Simulation study of the basic model . 68 3.3 Extension of the basic model: Learning and Knowledge Diffusion . 70 3.3.1 Integration of knowledge spillovers . 71 3.3.2 Integration of learning aspects . 72 3.3.3 Simulation study of the extended model . 76 3.4 Summary . 79 3.5 Appendix . 81 3.5.1 Appendix 1 . 81 3.5.2 Appendix 2 . 83 3.5.3 Appendix 3 . 83 3.5.4 Appendix 4 . 83 3.5.5 Appendix 5 . 87 3.5.6 Appendix 6 . 92 3.5.7 Appendix 7 . 96 4 The spatial dimension of knowledge diffusion 100 4.1 Introduction . 100 4.2 Theoretical model . 107 4.2.1 Setup . 108 4.2.2 Cellular Automaton . 113 4.2.3 Model simulation . 116 ii Contents 4.2.4 Simulation results . 117 4.2.4.1 First order spatial influence . 118 4.2.4.2 Second order spatial influence . 119 4.2.5 Conclusion . 121 4.3 Empirical model . 123 4.3.1 Motivation . 123 4.3.2 Spatial weight . 125 4.3.3 Higher order spatial influence specification . 126 4.3.4 Data and variables . 128 4.3.5 A first hint for spatial knowledge diffusion: a descriptive view . 135 4.4 Spatial model estimation . 141 4.4.1 Initial model estimation . 146 4.4.2 Expansion of the initial model . 151 4.4.3 Interpretation of obtained results . 164 4.5 Spatial filtering . 165 4.5.1 Concept of the filtering approach . 165 4.5.2 Eigenvector computation . 167 4.5.3 Spatial filtering estimation . 167 4.5.4 Interpretation of simulation results . 170 4.6 Policy implications . 173 4.7 Conclusion . 175 4.8 Appendix . 177 4.8.1 Appendix 1 . 177 4.8.2 Appendix 2 . 180 4.8.3 Appendix 3 . 181 4.8.4 Appendix 4 . 182 iii Contents 4.8.5 Appendix 5 . 182 4.8.5.1 Autocorrelation estimates . 182 4.8.5.2 Raftery-Lewis diagnostics . 182 4.8.5.3 Geweke diagnostics . 183 4.8.5.4 Geweke-χ2 test . 183 4.8.6 Appendix 6 . 184 5 Conclusions 189 5.1 Summary . 189 5.2 Prospects for future research . 195 iv List of Tables 2.1 Stability analysis of obtained equilibria from system 2.11 (I) . 34 2.2 Stability analysis of obtained equilibria from system 2.11 (II) . 34 2.3 Parameter values for system 2.11 . 41 3.1 Learning curve parameter setting . 77 3.2 Returns to scale scenarios for basic model simulation . 83 3.3 Parameter setting for basic model simulation . 83 4.1 Parameter setting . 117 4.2 List of German NUTS-2 regions . 130 4.3 Table of descriptive statistics (I) of variables used for the analysis . 136 4.4 Table of descriptive statistics (II) of variables used for the analysis . 137 4.5 Variables scatter plot of correlation coefficients . 137 4.6 Results of OLS estimation for German NUTS-2 regions . 150 3 pos 4.7 MC a posteriori model probabilities pu for variants of model (4)[SEM(1)]159 4.8 Estimation results for German NUTS-2 regions . 161 4.9 Spatial filtering of exogenous variables X . 168 4.10 Spatial filtering of labour productivity y . 169 4.11 Comparison of selected models . 182 4.12 MCMC-convergence summary for model (4,1) . 185 4.13 MCMC-convergence summary for model (4,2) . 186 4.14 MCMC-convergence summary for model (4,3) . 187 4.15 MCMC-convergence summary for model (4,4) . 188 v List of Figures 2.1 Phase plot of model 2.11 (I) . 34 2.2 Phase plot of model 2.11 (II) . 42 2.3 Graphical representation of simulated model 2.11 with q12 = 0:07 . 43 2.4 Graphical representation of simulated model 2.12 with q12 = 0:07 . 44 2.5 Graphical representation of simulated model 2.12 with q12 = 0:00 . 45 2.6 Graphical representation of simulated model 2.11 with q12 = 0:99 . 46 3.1 One-dimensional sigmoid learning curve . 73 i 3.2 P [φt = 1] expressed by ιi and t ...................... 74 i 3.3 P [φt = 1] expressed by χi and t ...................... 75 3.4 Some realizations of the stochastic sigmoid learning curve . 75 3.5 CRS impulse responses for the basic model . 84 3.6 IRS impulse responses for the basic model . 85 3.7 DRS impulse responses for the basic model . 86 3.8 DRS impulse responses for the extended model . 88 3.9 DRS impulse responses for the extended model . 89 3.10 DRS impulse responses for the extended model . 90 3.11 DRS impulse responses for the extended model . 91 3.12 IRS impulse responses for the extended model . 93 3.13 IRS impulse responses for the extended model . 94 3.14 IRS impulse responses for the extended model . 95 3.15 CRS impulse responses for the extended model . 97 3.16 CRS impulse responses for the extended model . 98 3.17 CRS impulse responses for the extended model . 99 4.1 Representation of (vN) and (M) neighbourship relations with (r = 1) . 114 vi List of Figures Y 4.2 Evolution of Gini-coefficient and spatial correlation of AL for DRS and r =1..................................... 118 Y 4.3 Evolution of Gini-coefficient and spatial correlation of AL for CRS and r =1..................................... 119 Y 4.4 Evolution of Gini-coefficient and spatial correlation of AL for IRS and r =1..................................... 119 Y 4.5 Evolution of Gini-coefficient and spatial correlation of AL for DRS and r =2..................................... 120 Y 4.6 Evolution of Gini-coefficient and spatial correlation of AL for CRS and r =2..................................... 120 Y 4.7 Evolution of Gini-coefficient and spatial correlation of AL for IRS and r =2..................................... 121 4.8 Spatial distribution of V (I) . 138 4.9 Spatial distribution of V (II) . 139 4.10 Scatter plot of variables used in the analysis . 140 4.11 Computation of Moran`s I with corresponding p-values for dependent and independent variable for r =1 .................... 142 4.12 Computation of.