Searching for nonlinearities in real exchange rates

Abstract

A recent innovation in modelling exchange rates has been the use of nonlinear techniques such as threshold autoregressive models and its smooth transition variants. This article investigates the Smooth Transition Autoregressive (STAR) modelling strategy in an application to real exchange rates. The key findings are as follows. First, using the methodology advocated by Teräsvirta (1994), we find evidence of nonlinear dynamics for several of the spot dollar real exchange rates using monthly data on five of the G7 countries. However, once estimated, we find that the STAR specification is appropriate for only one of the three exchange rate series indicated to be an Exponential Smooth Transition Autoregressive (ESTAR) process. Moreover, using simulations, we show that the underlying methodology used to detect nonlinearities in the data exhibit substantial size biases, which we attribute to influential observations. We find, upon investigating alternative nonlinear specifications, that the open-loop Threshold Autoregressive (TAR) process is a more appropriate specification than the ESTAR process for the dollar–sterling and dollar–lira real exchange rates.

Acknowledgements

We would like to thank James Morley, Ming Chien Lo, Ivan Paya, Mark Taylor and an anonymous referee for constructive discussions as well as very helpful comments and suggestions that we believe improved this article. Any errors that remain in the article are purely our own.

Notes

¹ For unit-root test pertaining to bilateral and effective real exchange rates see Roll (1979), Adler and Lehman (1983), Darby (1983), Edison (1985), Meese and Rogoff (1988), Enders (1988) and Mark (1990). For cointegration tests pertaining to bilateral and effective real exchange rates see Enders (1988), Taylor (1988), Mark (1990) and Patel (1990).

² We implement Teräsvirta's (1994) approach in this article in a comparable way to the papers implementing the ESTAR framework mentioned in this section. Details can be found in Section IV.

³ We wish to point out at this juncture that we leave choice of the transition function to use as the outcome of the STAR estimation methodology, rather than imposing the ESTAR transition function ourselves. More details follow regarding the choice in the next section.

⁴ According to the 2005 IMF Direction of Trade Statistics, Canada, Japan and the UK make up three of the US's top four trading partners.

⁵ Details for the reasoning behind the decision rule are outlined in Teräsvirta (1994).

⁶ In estimating the model through nonlinear least squares, we follow a suggestion by Teräsvirta (1994) and normalize the exponent of the transition function by the sample variance of y. This then provides γ = 1 as an appropriate starting value for the gamma parameter in the nonlinear least squares procedure.

⁷ Estimation results are not reported here.

⁸ The purpose of this section is not so much to provide an exhaustive search. Rather, the purpose is to show that real exchange rates can be modelled using other nonlinear specifications.

⁹ For a discussion about this period see Eichengreen (2007, 2008).

¹⁰ The effect of inflation the lira is also discussed in Sarantis and Piard (2004). These authors use a Markov regime switching framework, to show how inflation influences the likelihood of moving between a credible and a low credible state associated with maintaining the ERM currency pegs for the Belgium, French and Italian real exchange rates.

¹¹ The latter test yields a significant F-statistic of F = 8.30 in August 1992.