Non-linear mean reversion of real exchange rates and purchasing power parity: some evidence from Turkey

Abstract

Evidence was found of non-linear mean reversion in Turkey's real exchange rates. This suggests that a more complete examination of the empirical validity of PPP requires a joint examination of the non-linearity and non-stationarity of the real exchange rate.

Acknowledgement

The authors wish to thank Bruce E. Hansen for his software programs and the editor of this journal for his helpful comments. Any remaining errors are their own.

Notes

Agénor et al. (1997) point out that in Turkey's case the sharp depreciation of the lira in the 1980s and the 1990s played a big role in precipitating high inflation.

Sarno and Taylor (2002) provide a critical review of the literature on real exchange rates and PPP, in particular the role of non-linearities in real exchange rate adjustment toward equilibrium.

ESTAR stands for exponential smooth transition autoregressive.

The Caner and Hansen model is a variant of the threshold autoregressive (TAR) model pioneered by Tong (1978).

Theoretical models of non-linear real exchange rates are generally based on transaction costs in international arbitrage that create a band of no arbitrage for the real exchange rate. For a review, see Sarno and Taylor (2002) and Taylor (2003).

Estimates of PPP exchange rates are important for some practical purposes, including measuring nominal exchange rate misalignment and determining exchange rate parities. Such practical implications of PPP take on added significance for Turkey, a developing country with a history of macroeconomic instability that is currently making a concerted effort to eventually join the European Union (EU) and, by extension, the single-currency euro zone.

For a comprehensive discussion of the model, please refer to Caner and Hansen (2001).

The two-sided Wald statistic is also considered, but as Caner and Hansen (2001) note, it may have lower power against the one-sided Wald statistic because the alternative hypotheses are one sided. Nevertheless, the test results of the one-sided Wald statistic are almost identical to the two-sided Wald statistic.

According to Andrews (1993), this division provides the optimal trade-off between various relevant factors.

Please refer to Caner and Hansen (2001) for a fuller description of W_T .

Please refer to the notes on Table 1. For a fuller description of R _{1 T} , t ₁ and t ₂, please refer to Caner and Hansen (2001).

We plot but do not report Turkey's real exchange rates classified according to regime 1 and regime 2. The diagram shows that regime 1 or the stationary regime coincides with the high-inflation episodes documented by Agénor et al. (1997). Details about the estimated division of the data into the two threshold regimes are available from the authors on request.