Efthymios G. Pavlidis, Ivan Paya and David A. Peel 1071
whereiandi∗are the domestic and foreign nominal interest rates,pandp∗are logs of
the domestic and foreign price level, andyis the log of the real exchange rate. We note
immediately that empirical work that examines the relationship between real interest
rates and excludes the real exchange rate will, in general, be misspecified unless the real
exchange rate follows an RW as suggested by Roll (1979). However, this does not appear
to be either theoretically or empirically justified (see Taylor and Sarno (2004); Minford
and Peel (2007), and the references suggesting real exchange rates are nonlinear mean
reverting processes above).
The empirical studies on the relationship between real interest rates and real exchange
rates are problematic and inconsistent. For example, a number of studies have examined
the relationship in a cointegration framework, though there are no theoretical grounds for
expecting the real exchange rate to be cointegrated with the real interest rate differential,
as noted by Baxter (1994).
The implications of nonlinear real exchange rate adjustment have also not been inte-
grated into the empirical literature. As discussed above, temporal aggregation of the
“monthly” process changes the form of the ESTAR process (Paya and Peel, 2006b). In
particular, the number of autoregressive terms increases. One procedure, if the correct
DGP is an ESTAR process, is to derive multi-period forecasts from it using Monte Carlo
methods. These forecast changes should be employed as regressors in empirical work.
Our exercise shows why, in empirical studies, the reported results and their implications
are likely to change as the horizon of expectations and the temporal nature of the data
changes. These implications appear worthy of investigation in further work.
- Bertola and Svensson (1993) consider imperfect credibility, Miller and Weller (1991) con-
sider price-stickiness. Baueret al.(2007) develop a non-rational model based on chartists
and fundamentalists.
- Chung and Tauchen (2001), using the efficient method of moments proposed by Gallant
and Tauchen (1996, 2000), allow for intermarginal intervention. They report evidence
that this model parsimoniously describes the dynamics of the French franc/Deutsche Mark
exchange rate from January 1987 until July 1993. We note that they employ weekly data,
and further tests with daily data appear warranted.
- Lundbergh and Teräsvirta (2006) point out that the asymmetry parameter is essential to
ensure that movements of the exchange rate are restricted by the bounds. The parameter
restrictionsγ>0,θ>0 are identifying restrictions, andμ<1 identifies an implicit
bound. Non-symmetry around the lower or upper bound – explicit or implicit – can be
allowed for by different values ofγ,θ.
- The STARTZ model can capture the dynamics of behavior implied by many theoretical
target zone models. When the exchange rate is near the centre of the band, such thatGl
andGuare close to zero, then the exchange rate will depend on its own lags,φ′xt. Given
previous research we would anticipate that the exchange rate would appear to be a unit
root process in this vicinity. As the exchange rate approaches the edges of the bands, so
thatGlandGuare close to unity, then the exchange rate process will be described by
white noise like behavior aroundμslorμsu. Also, as the deviation from the central parity
increases, so thatGlandGuapproach unity, there is smooth transition from the standard
GARCH model represented byη′wttowards a constantδ>0 that is expected to be close
to zero. The assumption thatδis non-zero means there is a positive probability that the
exchange rate could leave the band even though no realignment takes place. This feature
implies that a credible zone can be one in which occasional breaches occur.
- Following Mark (1995), the money demand income elasticity is set equal to one.
- The mathematical form of the bubble is the same as that obtained in the stock market. If
the exchange model exhibited sticky prices the process followed by the speculative bubble
would be different although the features are qualitatively the same. For example, with a
simple sticky-price adjustment of the formpt−pt− 1 =θ(st−pt− 1 ),θ∈[0, 1], the bubble
