Geweke-χ 2 test

Geweke’s-χ² test is based on the intuition that sufficiently large draws have been taken, estimation based on the draws should rather identical, provided the Markov chain has reached an equilibrium state. This test is a simple comparison of the means for each

split of the draws. In this work, the χ² test, based on the null hypothesis of equality of the means of splits is carried out for each tapered case.

It should be mentioned that the diagnostic tools introduced here are not foolproof and sometimes MCMC diagnostic tools lead to misleading decisions.⁹²

4.8.6 Appendix 6

For appendix 6, please refer to the following pages.

92Refer for this topic to (Koop, 2003), p. 66.

Dependentvariabley:lnY L

1.AWEPC VariableLag1Lag5Lag10Lag50—— λ10.8000.4140.205-0.035—— σ0.4100.022-0.0290.009—— 2.RLDEPC VariableThinBurninNNminI-statistic— λ1 11847369375.054— σ11847369375.054— 3.GDEPC VariableMeanStd.deviationNSE(iid)RNE(iid)—— λ10.5611340.1872920.0019221.000000—— σ0.0032830.0012140.0000121.000000—— VariableNSE4%RNE4%NSE8%RNE8%NSE15%RNE15% λ10.0074010.0671060.0077820.0609690.0088090.047582 σ0.0000140.7671260.0000140.8301730.0000130.904161 4.GCSTEPC λ1NSEMeanp-Value——— i.i.d.0.5698990.0022640.000000——— 4%taper0.5650110.0082530.057527——— 8%taper0.5629320.0083230.055775——— 15%taper0.5657650.0084270.065577——— σNSEMeanp-Value——— i.i.d.0.0032700.0000150.378822——— 4%taper0.0032670.0000210.592235——— 8%taper0.0032670.0000180.536563——— 15%taper0.0032660.0000170.530511———  Note:”AWEPC”standsfor”Autocorrelationwithineachparameterchain”.”RLDEPC”standsfor”Raftery-LewisDiagnosticsforeachparameterchain”. ”GDEPC”standsfor”GewekeDiagnosticsforeachparameterchain”.”GCSTEPC”standsfor”Geweke-χ2 -Testforeachparameterchain”.”RNE”stands for”RelativeNumericalEfficiency”,”NSE”standsfor”NumericalStandardError”. Table4.12:MCMC-convergencesummaryformodel(4,1)

Dependentvariabley:lnY L

1.AWEPC VariableLag1Lag5Lag10Lag50—— λ10.7340.2450.0760.039—— σ0.4570.034-0.0020.035—— 2.RLDEPC VariableThinBurninNNminI-statistic— λ1 11950479371.0005.386 σ11950479371.0005.386 3.GDEPC VariableMeanStd.deviationNSE(iid)RNE(iid)—— λ10.5555950.1830090.0018781.000000—— σ0.0032660.0012410.0000131.000000—— VariableNSE4%RNE4%NSE8%RNE8%NSE15%RNE15% λ10.0065910.811550.0064160.0856460.0055190.115728 σ0.0000180.5286290.0000150.6828270.0000140.856455 4.GCSTEPC λ1NSEMeanp-Value——— i.i.d.0.5591350.0022210.000089——— 4%taper0.5603350.0063560.152210——— 8%taper0.5616100.0066830.162430——— 15%taper0.5607640.0067560.173295——— σNSEMeanp-Value——— i.i.d.0.0032550.0000150.380291——— 4%taper0.0032570.0000220.582485——— 8%taper0.0032590.0000190.572221——— 15%taper0.0032590.0000180.547883———  Note:”AWEPC”standsfor”Autocorrelationwithineachparameterchain”.”RLDEPC”standsfor”Raftery-LewisDiagnosticsforeachparameterchain”. ”GDEPC”standsfor”GewekeDiagnosticsforeachparameterchain”.”GCSTEPC”standsfor”Geweke-χ2 -Testforeachparameterchain”.”RNE”stands for”RelativeNumericalEfficiency”,”NSE”standsfor”NumericalStandardError”. Table4.13:MCMC-convergencesummaryformodel(4,2)

Dependentvariabley:lnY L

1.AWEPC VariableLag1Lag5Lag10Lag50—— λ10.000-0.0030.015-0.005—— σ0.146-0.0060.000-0.002—— 2.RLDEPC VariableThinBurninNNminI-statistic— λ1 129749371.039— σ129749371.039— 3.GDEPC VariableMeanStd.deviationNSE(iid)RNE(iid)—— λ10.1566840.1932350.0019831.000000—— σ0.0083860.0021390.0000221.000000—— VariableNSE4%RNE4%NSE8%RNE8%NSE15%RNE15% λ10.0020510.9343740.0019261.0590810.0018641.131157 σ0.0000240.8643180.0000230.9248050.0000230.941651 4.GCSTEPC λ1NSEMeanp-Value——— i.i.d.0.1592540.0023750.694409——— 4%taper0.1594020.0024740.689738——— 8%taper0.1595000.0023920.672743——— 15%taper0.1595530.0022360.648753——— σNSEMeanp-Value——— i.i.d.0.0083870.0000260.285231——— 4%taper0.0083800.0000310.325237——— 8%taper0.0083810.0000310.329946——— 15%taper0.0083800.0000300.303602———  Note:”AWEPC”standsfor”Autocorrelationwithineachparameterchain”.”RLDEPC”standsfor”Raftery-LewisDiagnosticsforeachparameterchain”. ”GDEPC”standsfor”GewekeDiagnosticsforeachparameterchain”.”GCSTEPC”standsfor”Geweke-χ2 -Testforeachparameterchain”.”RNE”stands for”RelativeNumericalEfficiency”,”NSE”standsfor”NumericalStandardError”. Table4.14:MCMC-convergencesummaryformodel(4,3)

Dependentvariabley:lnY L

1.AWEPC VariableLag1Lag5Lag10Lag50—— λ10.6770.1600.025-0.003—— σ0.4400.0320.004-0.006—— 2.RLDEPC VariableThinBurninNNminI-statistic— λ1 11540239374.293— σ21540239374.293— 3.GDEPC VariableMeanStd.deviationNSE(iid)RNE(iid)—— λ10.5414360.1896260.0006011.000000—— σ0.0032680.0012360.0000041.000000—— VariableNSE4%RNE4%NSE8%RNE8%NSE15%RNE15% λ10.0014220.1786160.0014330.1760050.0013120.210008 σ0.0000070.2964030.0000070.3050180.0000070.285996 4.GCSTEPC λ1NSEMeanp-Value——— i.i.d.0.5416330.0007220.013795——— 4%taper0.5415600.0017430.299201——— 8%taper0.5415980.0017890.316022——— 15%taper0.5417190.0016970.306570——— σNSEMeanp-Value——— i.i.d.0.0032670.0000050.018101——— 4%taper0.0032690.0000090.173843——— 8%taper0.0032730.0000080.135064——— 15%taper0.0032750.0000070.077024———  Note:”AWEPC”standsfor”Autocorrelationwithineachparameterchain”.”RLDEPC”standsfor”Raftery-LewisDiagnosticsforeachparameterchain”. ”GDEPC”standsfor”GewekeDiagnosticsforeachparameterchain”.”GCSTEPC”standsfor”Geweke-χ2 -Testforeachparameterchain”.”RNE”stands for”RelativeNumericalEfficiency”,”NSE”standsfor”NumericalStandardError”. Table4.15:MCMC-convergencesummaryformodel(4,4)

The aim of this chapter is to draw some major conclusions from the previous chapters of this thesis. The first section gives a summary of the contents of the thesis. Particularly, it focuses on the results obtained. The second section provides an overview of possible revenues for further research.

5.1 Summary

In the introductory chapter it has been laid out, that knowledge as an input factor of production exhibits a strong influence on economic development. The increasing knowledge intensity in the globalised economy needs to focus on the determinants of the ”knowledge based society”. Two major determinants on which the ”knowledge based society” and its economic analogon the ”knowledge based economy” rely, are the creation and the diffusion of knowledge. The main motivation for this thesis stems exactly from the importance of knowledge and ”knowledge diffusion” for the ”knowl-edge based economy” and finally for the modern economic theory and empirics. As mentioned in the first chapter of this thesis, knowledge diffusion topics are not only con-sidered as a cornerstone of modern growth literature and of new economic geography but is also important for microeconomic related fields, such as dynamic applications of industrial organization. As mentioned in the introduction, the economic field of

”knowledge diffusion” literature is widespread and many applications which cover the topic ”knowledge diffusion” can be found in literature which are on the one hand, mi-croeconomic based but on the other hand knowledge diffusion is also a relevant topic in macroeconomics, especially in (regional) growth theory. As a consequence, only some recent topics of ”knowledge diffusion” literature have been outlined in this thesis. As mentioned in the introduction of this thesis, particularly knowledge diffusion in the context of dynamic industrial organization and knowledge diffusion in the context of new economic geography are currently discussed in the relevant literature but also gen-erates revenues for further research. That defines the field where the contributions of this thesis set in.

The first two chapters after the introduction are direct applications from dynamic

in-dustrial organization. The first chapter deals with the question how knowledge transfer affects knowledge diffusion, whereas the second chapter tackles the relationship between firm size, innovation, market structure and learning.

Knowledge transfer and knowledge diffusion are two sides of one medal. Knowledge transfer is defined as the pure exchange process of knowledge between sender to receiver.

Particularly, knowledge networks can be considered as the ideal environment in which sender and receiver of knowledge come together. But as mentioned in this chapter, knowledge transfer is not a sufficient condition for knowledge diffusion. Knowledge diffusion is completed if transferred knowledge can be understood and used by the receiver. Thus, it is worth to integrate both aspects, knowledge transfer and knowledge diffusion in a comprehensive knowledge framework of industrial organization. The so called (Bass, 1969) model which is referred to in this chapter stems originally from product diffusion literature and is very popular in applied diffusion research and some disciplines of business administration such as marketing. The idea of the (Bass, 1969) model is pretty simple. The before mentioned contribution assumes, that two groups of adopters, so called innovators and imitators have to decide when they should adopt a certain technology or product. The adoption decision is influenced by external and internal factors, such as marketing effort and communication between these groups.

But this model has some limitations. One major drawback of this model is that (Bass, 1969) does not replicate the behaviour of these subgroups of adopters in a notational form. In the recent years several extensions of the (Bass, 1969) model have been proposed. But these models are all less suitable to cover the aspect of knowledge diffusion and knowledge transfer. Therefore the aim of this chapter was to setup a model which first, integrates innovators and imitators as well as their specific adoption decision of new knowledge. Thereby, so called network effects have been acknowledged.

According to the network structure, knowledge transfer is easier or more difficult. If a dense network structure is available, ”knowledge transfer” is easier and thus the imitator should adopt faster. On contrary, if networks do not exist, knowledge transfer is excluded and thus adoption takes place later. The latter scenario often leads to the so called ”chasm” pattern between early and late adoptions, which is extensively discussed in diffusion related literature. In consequence, network effects should also have an influence on the shape of the adoption curve, which is in the latter case not necessarily unimodal but bimodal for the entire market. The point is, that the introduced model treats the ”chasm” pattern as endogenous, not as a given exogenous number. The literature is still silent on this topic and only a few micro based paper take these network effects into account. Additionally, the model was extended towards a stochastic knowledge diffusion model to capture the idea that uncertainty of adoption is a function of time, which means at the beginning and at the end of the diffusion