The R&D stochastic component within the ‘sailing-ship effect’

ABSTRACT

In this work, we apply a stochastic component to a previously proposed deterministic model which expounds the ‘sailing-ship effect’ – that is, the reaction of an existing technology to the appearance of a new, potentially better, technology. The evolution of the technical performance – e.g. data transmission capacity – is studied taking into account the noise engendered by the presence of a random variable that mimics the uncertainty of R&D productivity. Both a Gaussian and a Cauchy–Lorentz distribution are considered. Performances’ evolution is studied by running simulations of a nonlinear functional map which is capable of showing the sailing-ship effect in the two possible variants, i.e. either the old or the new technology prevails in terms of performance. A noteworthy counterintuitive result for the Gaussian case is that noise may actually be beneficial to performance improvement.

KEYWORDS:

• Sailing-ship effect
• stochastic processes
• technological competition
• R&D
• simulations

JEL Classification:

• O31
• O32
• C63

Acknowledgements

An earlier version of this work was presented at the DySES (Dynamics of Socio-Economic Systems) Paris conference, 9–12 October 2018. Comments by the participants, and in particular by Didier Sornette and Massimo Squillante, are gratefully acknowledged. The authors also wish to thank the Referees whose criticisms have undoubtedly helped to improve this paper. Any remaining errors are our own responsibility.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Incidentally, this ‘law’ seems to comply with the hypotheses of the original model: R&D expenditure, in fact, is also accelerating to keep the law going, and now that we are close to the physical upper limit – single atom chips – R&D figures are accelerating even more. Furthermore, Aghion and Howitt’s model of growth through creative destruction also contains a deterministic component (Aghion and Howitt 1992, 324).

2 The Poisson distribution is today widely adopted (see, e.g. Santos-Arteaga et al. 2017), and this reinforces our Gaussian point; see also Scherer (1967).

3 In general, when the sum of distributions of the same type generates the same type of distribution, a distribution is said to be ‘stable’, and both Gaussian and Lévy distributions are stable in this sense (Sato 2001).

4 See especially pp. 367–371.

5 This does not aim to be a review of the literature, and we want to draw attention to the richness of approaches which can be found in the literature itself, from analyses concerned with welfare (Arrow 1962; Reynolds and Isaac 1992) or with the private and social returns to R&D (Nelson 1959). For broad analyses and reviews, see also Griliches (1984), Stephan (1996) and Hall, Mairesse, and Mohnen (2010).

6 For full explanation, see De Liso and Filatrella (2008, 596–598 and 608–609).

7 The Cauchy–Lorentz distribution takes the form: $f\left(x\right)={\displaystyle \frac{1}{\pi }\frac{\eta }{x^2+{\eta }^2}}$; an infinite variance distribution exhibits a finite probability of observing very large fluctuations.

8 We are grateful to one of the Referees for drawing our attention to these aspects – which were not considered in the De Liso and Filatrella (2008 and 2011) works.