Learning Dynamics in a Nonlinear Stochastic Model of Exchange Rates

This paper considers a version of the Dornbusch model of exchange rate dynamics which allows a nonlinear domestic demand for foreign assets function and imperfect substitutability between domestic and foreign interest bearing assets. Expectations of exchange rate changes are modelled as adaptive with perfect foresight being obtained as a limiting case. For sufficiently rapid speed of adjustment of expectations the model is able to generate cyclical behaviour of the exchange rate and expectations of its change. In the perfect foresight limit the cycles become relaxation cycles. To this underlying model of the fundamentals a white noise "news" process is added. Agents are assumed to attempt to learn about the system dynamics and the link between such learning and exchange rate volatility is studied. Two learning scenarios are considered. In the first scenario economic agents are regarded as a uniformly well-informed group of sophisticated traders. In the second scenario a group of "naive" traders coexist with the sophisticated traders. We find that both learning scenarios lead to increased volatility. However this effect increases in proportion to the weight of the "naive" traders.