Do real exchange rates contain a unit root? Evidence from Turkish data

Abstract

This study explores whether the long-run purchasing power parity (PPP) hypothesis holds for selected real exchange rates from Turkish economy during the period 1982M1–2003M12. In addition to conventional unit root tests, five different unit root test procedures have been applied including efficient point-optimal tests, extended M tests and GLS-detrended variants of DF tests, to four monthly real exchange rate series defined in terms of both producer and consumer price indices. The countries analysed are the USA, the UK, Germany and Italy which are major trade partners of Turkey. Mixed evidence is found for the long-run PPP hypothesis when real exchange rate is defined in terms of German DM and Italian Lira. However, the empirical analysis reveals that the PPP hypothesis holds strongly in the long-run for the UK£ and US$ based real exchange rates series using either PPI or CPI. In corroboration with other studies in the literature, the bias correlated half-life estimates suggest relatively faster speeds of adjustment supporting the view that the deviations from the PPP rate dissipate rather quickly for relatively high inflation countries.

Acknowledgements

The author would like to thank Nuri Yildirim, Ensar Yilmaz and an anonymous referee for helpful comments on previous versions of this paper.

Notes

There are at least two contradicting views on the behaviour of real exchange rates in a floating system. The behaviour of real exchange rates may reflect the sluggish price adjustment or the impact of real shocks such as changes in economic fundamentals. Overshooting models of exchange rates predict that fluctuations in real exchange rates are caused by nominal shocks such as an unanticipated increase in money supply which would cause the exchange rates to overshoot its long run value due to price stickiness in the short run (Dornbusch, 1976). Equilibrium approach, on the other hand, asserts that short run to medium run movements in real exchange rates are due to real shocks rather than monetary shocks (Stockman, 1987).

For reviews on the performance of the Turkish economy during this period see Cizre-Sakallioglu and Yeldan (2000) and Ertugrul and Selcuk (2001).

This section is not intended to cover the vast empirical literature on PPP. For more complete reviews of the literature see Rogoff (1996), Sarno and Taylor (2002) and Taylor (2003).

Low power means that there is a high probability of accepting wrong null hypothesis of nonstationarity. It would be likely to reject the nonstationary null when the data is in fact stationary. The low power or high Type-II error problem can potentially arise when series under study span a short time period or when they contain structural breaks.

Ng and Perron, contrary to Engel's results found no negative moving average part in either level or first differences of real exchange rates, hence the size distortion is not an issue for the data set they studied. For the empirical situations where the size issue constitutes a problem they suggested using a modified information criteria to choose the appropriate lag length for correcting serial correlation.

It is shown in Hamilton (1994, chap. 17) that under the null hypothesis of unit root

needs to be multiplied by T rather than (T ^1/2) to obtain a useful asymptotic distribution. The unit root coefficient converges at a faster rate than a coefficient with ρ<1 (which converges at (T ^1/2).

The exchange rate data and CPI for Turkey can be obtained from the electronic data delivery system of Turkish Central Bank at: http://www.tcmb.gov.tr

The first month of 1982 was chosen as the base observation and all series were converted accordingly to have uniformity in the data set.

An underspecified trend model, where the true model contains both a constant and a time trend but the econometrician incorrectly uses the constant-only model, leads to inconsistent tests, while an over-specified model leads to reduced power (Stock, 1994, p. 2783).

Correlograms are not included to save space but available upon request.

Also, the sampling distribution of the ADF test statistic becomes a function of the initial truncation of the sample. Hence, the procedure of Caporale et al. (2003) may not be completely appropriate here since the Dickey and Fuller critical values cannot be used. However, the purpose here is to see the behaviour of the test statistic over time not to draw statistical inference. The author thanks an anonymous referee for pointing this out.

Half-life of a shock is defined as the time it takes for an half of an initial shock to dissipate and commonly calculated as

, where

is the OLS estimate of the AR(1) parameter. This half-life estimate is only appropriate for an AR(1) process – if the model includes higher autocorrelation terms to account for serial correlation it gives an approximate value for the speed of adjustment (See Murray and Papell (2002) and Murray and Papell (2004) for a discussion of the calculation of half-lives and its implication for the PPP puzzle).

Motivated by the fact that the OLS estimator

is biased downward in small samples, Mark (2001, p. 44) suggests using Kendall's correction which is defined as

, where T is the sample size.

Cheung and Lai (2000) report half-lives of about 1–3 years and statistical significant negative correlation between persistence and high inflation using a data set of 94 developing countries.