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

Abstract

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 ‡oating period. Our key …ndings are as follows. First, if the solution to the DSGE model is approximated to the …rst order, then linearity tests that utilize univariate autoregressions of the real exchange rate su¤er 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 …nd 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 …nd 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.JEL Classi…cation: C15 C32 F41 F47

Outliers and persistence in threshold autoregressive processes

“…For example, Bai (1998) shows that attempting to detect structural breaks in highly persistent linear processes often leads to spurious rejections of the null hypothesis of linearity. In a similar vein, Ahmad, Lo, and Mykhaylova (2013) demonstrate the presence of size distortions within the context of new open economy macroeconomic models, where the null of linearity is rejected too frequently in favor of nonlinear specifications.…”

Nonlinearities in the real exchange rates: new evidence from developed and developing countries

“…We now examine the correspondence between the data generating process (DGP) of the simulated RER series and the speci…cations (1) and (2). The simulated data comes from an n-th order Taylor expansion around the steady state of the theoretical DSGE model described in ALM.…”

“…1 However, since these models are rarely built on an explicit theoretical framework, their predictions need to be interpreted with great care. In fact, Ahmad, Lo, and Mykhaylova (2013), ALM hereafter, demonstrate that the ability of empirical tests to detect nonlinearities in real exchange rates (RERs) hinges critically on the underlying data generating process. Within a theoretical framework, the authors show that linearity tests-which express the real exchange rate as a univariate function of its own lags-su¤er from misspeci…cation in some cases, which consequently leads them to overestimate the incidence of nonlinearity in the RER series.…”

“…These papers are among many which have found that the data on real exchange rates can be parsimoniously characterized as smooth transition autoregressive (STAR) process, or one of its variants. 2 However, these studies lack rigorous theoretical foundations that could help to explain the existence of nonlinearities in RER behavior. Consequently, the tests of real exchange rate dynamics are based on ad-hoc univariate data generating processes, and their result can potentially be misleading due to misspeci…cation problems.…”

“…test switch to being linear under the modi…cation proposed byAhmad, Lo, and Mykhaylova (2013), where exogenous variables are added to the test. Second, we employ the Monte Carlo approach to study the relationship between test performance and the underlying RER (linear) data generating process.…”