Causes of nonlinearities in low-order models of the real exchange rate

This paper investigates the extent to which modern DSGE models, which feature local currency pricing, home bias, nontraded goods, and incomplete markets, can generate nonlinear real exchange rate dynamics that are consistent with those found in the time series literature using data from the current floating period. Our key findings are as follows. First, if the true model can be appropriately characterized as a set of linear equations, then linearity tests that utilize univariate autoregressions of the real exchange rate suffer from an omitted variables problem, which leads them to overestimate the true incidence of nonlinearity. Consequently, studies that fail to control for this problem may spuriously find evidence of nonlinearities in the data, despite the fact that the data generating process may be linear. Second, we propose a strategy that can largely eliminate this distortion. Finally, we find that DSGE models solved using higher order approximations are capable of generating true structural nonlinearities in real exchange rates both asymptotically and in short samples.