What do we know about real exchange rate nonlinearities?

Abstract

This research points to the serious problem of potentially misspecified alternative hypotheses when testing for unit roots in real exchange rates. We apply a popular unit root test against nonlinear ESTAR and develop a Markov Switching unit root test. The empirical power of these tests against correctly and misspecified non-linear alternatives is analyzed by means of a Monte Carlo study. The chosen parametrization is obtained by real-life exchange rates. The test against ESTAR has low power against all alternatives whereas the proposed unit root test against a Markov Switching autoregressive model performs clearly better. An empirical application of these tests suggests that real exchange rates may indeed be explained by Markov-Switching dynamics.

Weak identification in the ESTAR model and a new model

“…It is noteworthy that the plot in Figure 6 is not unique for this particular data set but a common finding in empirically estimated ESTAR models. Kruse et al. (2011) for example support these findings for other real exchange rates (see their Figure 1).…”

“…In these cases it is notoriously hard to distinguish between the two regimes and as a consequence the power decreases. However, the power is still high enough to deliver reliable test results and is in particular higher than found by Kruse et al (2011) for extant test. In the case (2003) and therefore yields more reliable results in empirical applications as indicated by Kruse (2009).…”

“…As empirical studies using smooth transition models such as ESTAR frequently find very small variances of the innovation term we examine the behaviour of the newly developed unit root test against TSTAR in such a framework. Studying this behaviour is critical since Kruse et al (2011) show via Monte Carlo simulation that under small error term variances the power of unit root tests developed for nonlinear models rapidly deteriorates. We report simulation results for small sample sizes of T ¼ 100 (Table 6) and T ¼ 500 (Table 7) and consider error term standard deviations of r e ¼ 0.1.…”

“…Applying especially unit root tests against ESTAR to real exchange rates very rarely brings a rejection of the null hypothesis of a unit root. Kruse et al . (2011) show in an extensive simulation study that unit root tests against ESTAR have power close to the nominal size of the test for parameter settings taken from real exchange rate data.…”

Enhancing the forecasting power of exchange rate models by introducing nonlinearity: Does it work?

“…Kempa and Riedel (2013) estimate a Markov switching model for the bilateral Canadian-U.S. dollar exchange rate and find that an active monetary policy stance may account for nonlinearity in the exchange ratefundamentals nexus and that nonlinearity confirms the notion that exchange rate movements cannot be explained exclusively in terms of any one particular exchange rate model. Kruse et al (2012) criticise the disproportionately large body of literature in which ESTAR models are used whilst neglecting competing nonlinear models, such as the Markov switching AR model. Diaz et al (2002) use an ARFIMA model and find that this model is not always able to capture all of the nonlinearity in the data.…”