# A dynamic exchange rate model with heterogeneous agents

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## Abstract

In this paper, we analyze a heterogeneous agent model in which the fundamental exchange rate is endogenously determined by the real markets. The exchange rate market and the real markets are linked through the balance of payments. We have analytically found that there exists at least a steady state in which the exchange rate is equal to its fundamental value and incomes of both countries are equal to the autonomous components times the multiplier (as in the Income-Expenditure model). This steady state can be unique and unstable when all agents act as contrarians, while when agents act as fundamentalists it is unique but its stability depends on the reactivity of actors of the market. Finally, we show that the (in)stability of the economic system depends on both the reactivity of the markets and that of different types of agents involved. Employing well-know functional forms, we show that the model can replicate some of the statistical features of the true time series of the exchange rate.

## Keywords

Complex dynamics Heterogeneous agents models Financial markets## JEL Classification

C62 D84 E12 E32 G02## Notes

### Acknowledgements

We really thank an anonymous referee and the Editor, Uwe Cantner, for suggestions that improved the paper. We also wish to thank Marco Dardi and Frank Westerhoff who discussed with us an early version of the paper, the participants in the workshops held in Scuola Normale di Pisa in December 2013 and in Univerisità Milano-Bicocca in February 2014, and the participants in the conference Computing in Economics and Finance (CEF 2014) held in Oslo in June 2014.

## Compliance with Ethical Standards

**Conflict of interests**

The authors declare that they have no conflict of interest.

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