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Deterministic randomness in a model of finance and growth

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Abstract

Following the literature on growth, cycles and financial development, this paper develops an economic growth model in which the source of endogenous business cycles relates to the allocation of credit between productive investment and consumption. An important role is given to consumer sentiment, because this determines the demand of households for credit; in particular, optimistic beliefs about the economy’s macro performance divert financial resources from investment in favor of consumption. The dynamic analysis indicates that Neimark–Sacker and flip bifurcations eventually separate stable and unstable manifolds and, as a result, a region of nonlinear motion is generated: cycles of various periodicities and chaotic motion characterize the behavior of the long run time paths of accumulated wealth, output and consumption.

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Notes

  1. For a survey on nonlinear dynamics in macroeconomics see Gomes (2006).

  2. This value is obtained by solving Det(J) = 1 in order to μ.

  3. The use of the expression ‘a better intertemporal allocation of resources’ suggests the need to clarify what one interprets as a benchmark efficient allocation of resources. This is the one that would be observed if no financial constraints whatsoever existed.

  4. Condition \(\sigma \le \frac{1}{4}\times \frac{\left( {1-\rho \times \theta } \right)^2}{\theta }\) implies node stability; \(\frac{1}{4}\times \frac{\left( {1-\rho \times \theta } \right)^2}{\theta }<\sigma <1\) refers to a stable focus.

  5. Stable node and stable focus cases continue to be distinguished by the same conditions as previously.

  6. All the figures concerning global dynamics presented in this paper are drawn using IDMC software (interactive Dynamical Model Calculator). This is a free software program available at www.dss.uniud.it/nonlinear, and copyrighted by Marji Lines and Alfredo Medio.

  7. Remind that variable \(\widetilde {w}_t \) is the difference between the wealth variable (detrended) and the steady state level of wealth (also detrended). Thus, no problem arises from the value of this variable being negative at almost all the observations. This simply means that the level of wealth remains below the steady state level most of the time. This is a logical result given the assumption of m = 1 (if the level of wealth attains the referred steady state level, all credit would be channelled to consumption).

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Acknowledgements

Financial support from the Fundação Ciência e Tecnologia, Lisbon, is gratefully acknowledged, under the contract no. POCTI/ECO/48628/2002, partially funded by the European Regional Development Fund (ERDF). I would like to thank as well the helpful comments made by two anonymous referees. The usual disclaimer applies.

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  1. Escola Superior de Comunicação Social [Instituto Politécnico de Lisboa], Campus de Benfica do IPL, 1549-014, Lisbon, Portugal

    Orlando Gomes

  2. Unidade de Investigação em Desenvolvimento Empresarial—Economics Research Center [UNIDE/ISCTE-ERC], Lisbon, Portugal

    Orlando Gomes

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Gomes, O. Deterministic randomness in a model of finance and growth. J Evol Econ 20, 95–114 (2010). https://doi.org/10.1007/s00191-009-0132-1

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