−0.4
−0.2 0.0 0.2 0.4
Autocorrelation
C 0 10 20 30 40 50
Time Lag
−0.4
−0.2 0.0 0.2 0.4
D
Figure 7: Autocorrelation spectrum of growth rates at the the macro-level in the multi-sector model for different interconnectedness structures between sectors. (A) fully independent sectors, (B) complete network (i.e. all sec-tors have direct influence on all other secsec-tors), (C) Yule-process generated network, (D) 1-d grid (ring) network structure.
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0.00 0.05 0.10 0.15 0.20 0.25
0.00 0.05 0.10 0.15 0.20 0.25 0.00
0.00 0.05 0.10 0.15 0.20 0.25 Frequency (1/Periods)
0.00 0.05 0.10 0.15 0.20 0.25 Frequency (1/Periods)
Figure 8: Frequency spectrum of growth rates at the the macro-level in the multi-sector model for different interconnectedness structures between sec-tors. (A) fully independent sectors, (B) complete network (i.e. all sectors have direct influence on all other sectors), (C) Yule-process generated net-work, (D) 1-d grid (ring) network structure.
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waves at the aggregated level result from intersectoral synchronization of structural change (i.e. technology type switching), figure 6 illustrates the reason behind the weak cyclicity in the isolated and fully connected network cases (panels A and B) and the cases with much stronger cycle or wave patterns (the clustered networks shown in panels C and D): From figure 6 it is apparent that there is no or little cross-sectoral alignment of dominant technology types as a result of the network effects in the cases without non-trivial network structures (panels A and B), as would be expected. The alignment is strong in the hierarchical case (panel C), and moderate but persistent alignment in the non-hierarchical (grid) case (panel D). The role of the dominant technology type changes multiple times across the period of study of 300 iterations. This would be interpreted as technology system changes in the framework provided by Freeman and Perez Freeman and Perez (1988) as indicated above.
Since the intersectoral interaction was restricted to the network effect in the present study, few further changes from the cross sectoral effects are to be expected for cases which do not result in cross-sectoral alignment of the dominant technology types (though growth rates may change slightly) since only this enables cross-sectoral benefits from the network externality. This is exactly what is found in the figures 5, 7, and 8. The complete network case (B) averages the growth rates out while the autocorrelation spectrum remains relatively unchanged and the frequency spectrum shows that there is no indication of low frequency signals any more compared to all the other cases (including, interestingly the isolated sector case). The quasi-cycles observed in the isolated sector case stem from rare radical innovations occur-ring (with equal likelihood) in every one of the sectors, but with the (though unstructured and very limited) cross-sectoral effects in case B, this signal seems to be completely drowned. With the Yule-process generated network (hierarchical) and grid network cases (panels C and D) this is different: For the grid network (panel D), a very dominant 20-period cycle emerges as is apparent from the autocorrelation spectrum (figure 7) and also visible in the frequency spectrum (0.05) next to a much fainter signal of the order of 12 periods (0.08). In the - most realistic - hierarchical case (panel C), the au-tocorrelation spectrum does not offer strong evidence of cycles (a hint at a rather irregular pattern), but in the frequency spectrum, a number of long-term signals appear, the most prominent being of the order of 10 periods (0.1) and 50 periods (0.02) (but 15, 20, 25 periods also having strong signals).
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0 50 100150200250300350400 10 0
20 30 40 50 60 70
-nated by Technology Type
A 40 10 20 30 50 60 70 0 0 50 100150200250300350400 B
0 50 100150200250300350400 Time
10 0 20 30 40 50 60 70
Number of Sectors Domi-
Domi-C 0 50 100150200250300350400
Time 10 0
20 30 40 50 60 70
D
Figure 9: Number of sectors dominated by the same technology type in an interconnected multisector model (Yule-process generated network) for dif-ferent research research success functions: (A) incremental innovation max-imum progress factor α = 0.005, radical innovation maximum success rate β = 0.1, public research γ = 0.05, (B) α = 0.005, β = 0.1, γ = 0, (C) α = 0.005, β = 0, γ = 0, (D) α= 0, β = 0.1,γ = 0.
27
0 200 400 600 800100012001400 10 0
20 30 40 50 60 70
-nated by Technology Type
A 40 10 20 30 50 60 70 0 0 200 400 600 800100012001400 B
0 200 400 600 800100012001400 Time
10 0 20 30 40 50 60 70
Number of Sectors Domi-
Domi-C 0 200 400 600 800100012001400
Time 10 0
20 30 40 50 60 70 D
Figure 10: Number of sectors dominated by the same technology type in an interconnected multisector model (Yule-process generated network) for dif-ferent research research success functions: (A) incremental innovation max-imum progress factor α = 0.001, radical innovation maximum success rate β = 0.1, public research γ = 0.05, (B) α = 0.001, β = 0.1, γ = 0, (C) α = 0.001, β = 0, γ = 0, (D) α= 0, β = 0.1,γ = 0.
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Brief note on incremental innovations, radical innovations, and open technologies in the model. The technology change mechanism as introduced in section 3 follows the literature and has a number of different effects. The exact values are chosen to (1) allow a prominent enough network effect, such that intersectoral alignment of the dominant technology is possi-ble (as explained above, this is also observed in the real world and no further cross-sectoral alignment effects could realistically be expected without this) and (2) to keep the number of plants in existence from exploding beyond what the available computation capacity could manage. As is seen in figure 9, for the chosen values, the intersectoral alignment pattern breaks down if the mentioned effects (open technologies / public research, incremental inno-vations, radical innovation) is removed. This, however, is because sector-level incremental research then becomes the dominant force (with public research removed, progress is much slower as every agent has to rely solely on her own research even for cumulative effects); if incremental innovation is weakened, to rincr =U nif orm(0,0.001) (figure 10), the effect persist across all regimes (with and without open technologies, with or without radical and incremen-tal innovations), though it is much slower now. (Note that the time scale is 1400 iterations here compared to 300 and 400 in the simulations above.)
5 Conclusion
Solow famously exclaimed in the early 1990s that computers could be seen
”everywhere except in the productivity statistics” (quoted in Brynjolfsson (1993)). In 2008, empirical studies have already taken a starkly different view Jalava and Pohjola (2008) and today it becomes apparent that the entire industry structure is dependent on information and communication technologies in various ways. This dependence came in multiple ways; first electronics, then computer networks and real time control in manufacturing and trading, finally mobile devices and most recently affordable and widely available distributed computing enabling even small firms and individuals to work with ”big data”. The changes came in waves; they relied heavily on network externalities and lock-in effects, and they did have an impact on growth and productivity (as discussed in the introduction). It is therefore entirely opportune to take up the challenge to investigate the interrelations of network externalities and economic growth, also in the context of business cycles which may be - as it is argued in the present paper - effects of the
29
waves of successive small technological ”revolutions”, technological changes that can not happen gradually as a result of network externalities and lock-ins.
Consider again the introductory examples of the electrification of the manufacturing industry16: they were introduced in different regions and countries at different times, but when they were, they had a pronounced impact on all aspects of the economic system. Across virtually all sectors, the system quickly became dominated by products and standards based on the new technology.
The current paper presented an alternative agent-based mechanism ca-pable of reconstructing and explaining realistic patterns of cycles (or waves) in economic growth. Building on other models of evolutionary economics Nelson and Winter (1974, 1982); Silverberg et al (1988); Freeman and Perez (1988), the model is based on micro- (enterprise-) level processes but ex-tends to a sectoral and an aggregated macroeconomic level. To accomplish this the central element is technological change with network externalities which are relevant for one sector but are influenced by the situation on other sectors. For interconnections between sectors, different network structures were considered.
Most importantly, micro-founded models for growth cycles have to take care that sector level cycles do not average out at the aggregated level. For the present approach using network effects it is generally plausible why this cycle pattern may by synchronized and interdependent between sectors and why therefore the growth cycle pattern may be retained on the macro level.
Strong effects were found for both Yule-process generated networks (hi-erarchical) and grid networks (non-hi(hi-erarchical). While the non-hierarchical network amplified one circular pattern, the Yule-process generated (hierarchi-cal) network yielded a more diverse pattern of growth waves with nevertheless strong (overlaying) signals for different period lengths.
Compared to real interdependence networks between industry standards, and thus likely also between sectors, the hierarchical network is more real-istic. Base technologies such as communication systems, but also measure-ment standards (say, 3/8-inch screws) are widely accepted. In many other industries, firms need to comply with those systems and standards or face increased costs for house manufacturing and maintaining of their own in-compatible systems. This descends through a highly branched system of
16And, slightly less pronouncedly, also the spread of ICT systems.
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base technologies, say electricity and computer processor architectures, de-rived technologies, say personal computers, operating systems or periphery devices, but also supply sectors, raw material mining, and refinement, and specialized sub-branches, say software for specific chemical production plants, as well as meta-technologies, say social networks. Firms in all of these sectors and technologies will have to comply and will be able to benefit from network effects from compliance with the standards to some extent where the number of standards that need to be taken into account relates to the specialization.
The non-hierarchical grid network would, at best, if at all, apply to relatively undifferentiated regionally organized low-technology intensive sectors.
Network externalities were not extensively studied in economic theory until recent decades, being neglected though they may constitute one of the most important and most prevalent effects in economic systems. The inclusion of this effect in the current model helps to explain growth cycles (or rather, growth waves); it may also be able to explain many more unsolved problems in contemporary economics if taken into consideration with proper models.
Acknowledgements
The author is grateful to 3 anonymous reviewers for many helpful comments and suggestions. All remaining errors are my own.
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