A Model of Procyclical Exchange Rate

Exchange rates in the standard macro-finance model with a representative agent are counter-cyclical. The reason is that exchange rates are equal to the ratio of marginal utilities of consumption of the representative investor in each country. This prediction is counterfactual: across a variety of countries, (real) exchange rates are, on average, positively correlated with output and consumption growth. We provide a model in which the cyclical behavior of exchange rates varies with the source of the economic shocks. A key feature of our model is incomplete markets, which introduces a wedge between aggregate consumption and the marginal utility of the average investor. We introduce a minimal deviation from the standard endowment economy model of exchange rate depreciation: in a boom, new trees are created, but they are randomly distributed to a small part of the population. As a result, the marginal utility of the average investor can rise, leading to an appreciation of the real exchange rate. Our calibrated model does a good job replicating key features of the data, specifically, the joint dynamics of exchange rates, stock returns, real output and consumption growth, and trade flows.