# A dynamic exchange rate model with heterogeneous agents

## 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.

## References

- Anufriev M (2013) Heterogeneous Beliefs in an asset pricing model with endogenous fundamentals. MimeoGoogle Scholar
- Brock W, Hommes C (1997) A rational route to randomness. Econometrica 65:1059–1095CrossRefGoogle Scholar
- Brock W A, Hommes C H (1998) Heterogeneous beliefs and routes to chaos in a simple asset pricing model. J Econ Dyn Control 22:1235–74CrossRefGoogle Scholar
- Day R, Huang W (1990) Bulls, bears and market sheep. J Econ Behav Organ 14:299–329CrossRefGoogle Scholar
- De Arcangelis G, Gandolfo G (1997) Nonlinear phenomena in economics: the exchange rate. Nonlinear Anal Theory Appl 30:1043–1049CrossRefGoogle Scholar
- De Grauwe P, Rovira P K (2012) Animal Spirits in the foreign exchange market. J Econ Dyn Control 36:1176–1192CrossRefGoogle Scholar
- Federici D, Gandolfo G (2012) The Euro/Dollar exchange rate: Chaotic or non-chaotic? A continuous time model with heterogeneous beliefs. J Econ Dyn Control 36:670–681CrossRefGoogle Scholar
- Gandolfo G (1986) Economia Internazionale, vol II, Ed. UTET, TorinoGoogle Scholar
- Hommes C H (2006) Heterogeneous agent models in economics and finance. In: Tesfatsion L, Judd K L (eds) Handbook of computational economics, volume 2: agent-based computational economics. Elsevier, pp 1109–1186Google Scholar
- Kirman A (1998) On the transitory nature of gurus. MimeoGoogle Scholar
- Laursen S, Metzler L (1950) Flexible exchange rate and the theory of employment. Rev Econ Stat 32: 281–99CrossRefGoogle Scholar
- LeBaron B (2006) Agent-based computational finance. In: Tesfatsion L, Judd K L (eds) Handbook of computational economics, volume 2: agent-based computational economics. Elsevier, pp 1187–1233Google Scholar
- Lengnick M, Wohltmann H W (2013) Agent-based financial markets and new keynesian macroeconomics - a synthesis. J Econ Interac Coord 8:1–32Google Scholar
- Naimzada A K, Ricchiuti G (2008) Heterogeneous Fundamentalists and Imitative Processes. Appl Math Comput 199:171–180Google Scholar
- Naimzada A K, Ricchiuti G (2009) Dynamic Effects of Increasing Heterogeneity in Financial Markets. Chaos, Solitons & Fractals 41:1764–1772CrossRefGoogle Scholar
- Naimzada A K, Pireddu M (2014) Dynamic Behavior of Product and Stock Markets with a Varying Degree of Interaction. Econ Model 41:191–197CrossRefGoogle Scholar
- Proaño C R (2011) Exchange Rate Determination, Macroeconomic Dynamics and Stability under Heterogenous Behavioural FX expectations. J Econ Behav Organ 77:177–188CrossRefGoogle Scholar
- Rovira P K (2010) Uncertainty about fundamentals and herding behavior in the FOREX market. Physica A 389:1215–1222CrossRefGoogle Scholar
- Westerhoff F (2009) Exchange rate dynamics: a nonlinear survey. In: Rosser Jr, J B (ed) Handbook of Research on Complexity. Edward Elgar, Cheltenham, pp 287–325Google Scholar
- Westerhoff F (2012) Interactions between the real economy and the stock market: A simple agent-based approach. Discrete Dynamics in Nature and SocietyGoogle Scholar