What is the shape of real exchange rate nonlinearity?

Abstract

Evidence that real exchange rate dynamics can be described using models which exhibit nonlinear mean reversion has been mounting over the past decade. This article attempts to better understand the shape of real exchange rate nonlinearity through the use of the Smooth Transition Autoregressive (STAR) model and the newly proposed skewed generalized error transition function. The advantage of this transition function it that it nests popularly used transition functions through simple parameter constraints. This allows the use of nested model selection tests. It is shown that more flexible transition functions are preferred in many cases over the commonly used exponential transition function. The results suggest that most of the real exchange rates studied in this article are better described by discrete threshold models rather than STAR models.

Keywords:

• purchasing power parity
• nonlinear mean reversion
• real exchange rates

JEL Classification::

• F31
• C22

Notes

¹ The plotted transition functions were normalized to take on values between one and zero.

² The regression in Equation 12 is based upon the true regression model in Equation 11, where the transition function has been replaced by a fourth-order Taylor approximation. This will allow the selection of the delay parameter to be based on a flexible nonlinear model.

³ The Double Logistic STAR (D-LSTAR) model is the same as the MR-LSTAR model of Bec et al. (2010) discussed in the previous section.

⁴ The sum of squared error values displayed in Figs 11–17 are obtained from a three-dimensional grid search over γ, α, φ. Given the inability to present a three-dimensional graph, the SEE values are plotted for only γ and α. This means that each sum of the squared error value potentially has a different value of φ associated with it. Given that γ and α drive the STAR versus TAR differences and φ is associated with only asymmetry, we chose to graph γ and α.