Wealth-sensitive positional competition as a source of dynamic complexity in OLG models

This paper examines the interactions between economic activity and consumption externalities in an overlapping generations model. Existence of multiple steady states
is studied from a global point of view, and possible mechanisms producing cycles and chaotic behavior are analyzed. Wealth-sensitive positionality is found to be able to generate persistent endogenous fluctuations, whereas wealth-neutral positionality doesn’t. Under wealth-sensitive positionality, the economy may moreover experience complex dynamics, with sensitivity to initial conditions, leading to poverty traps even when starting from relatively large endowments of capital assets.

Article by Ahmad Naimzadaa, Pierluigi Sacco , Mauro Sodini
Published in Nonlinear Analysis: Real World Applications (2012)

From the Conclusions (excerpt)
(…) What really makes a difference is the possibility that positional competition becomes wealth-sensitive, and in particular that it is increasing in the level of wealth. In this instance, depending on the structural parameters and on the strength of positional competition itself, we can observe a variety of complex dynamic behaviors. In most cases, the more pronounced the wealth-sensitive component of positionality, the more complex the dynamics becomes, although there is a (somewhat extreme) case where wealth-sensitive positionality may act as a stabilizer. The most subtle and delicate implication of the model is that wealth-sensitive positionality goes much further than simply causing the economy to deviate from the steady state. It makes possible, and sometimes even likely, that the economy falls into a long run poverty trap, and this even starting from relatively safe conditions where initial levels of the capital endowment are high. Moreover, this final outcome may be very difficult to predict even during the actual transition toward the poverty trap.
A simple lesson coming from this model is, therefore, that it might be unwise trying to stimulate the economy’s level of activity by pushing on the consumers’ positional motivations, as it is commonly done, for instance, in mass media commercials. Although this may, at the moment, cause a rise in consumption expenditure, this may also, in a more long-run oriented perspective, subtly erode the sustainability of the economy in terms of the preservation of its productive stock, and this is all the more dangerous the more the economy progresses along the affluence scale and the more, consequently, positional competition is fueled by the increase in the level of wealth. Our analysis suggests that there may be other channels to stimulate the economy’s level of activity, that are socially more sustainable, and that the undermining effects of strong (wealth-sensitive) positionality might be subtle and deceivingly difficult to evaluate in the immediate, to manifest their destabilizing effects only when it is too late. (…).

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