1026 The Econometrics of Exchange Rates
22.1 Introduction
The purpose of this chapter is to provide a selective overview of the econometric
methods employed in the modeling of exchange rates. Given space constraints, we
can only give very brief outlines of the underlying economic theory, which is well
covered in, e.g., Taylor (1995), Obstfeld and Rogoff (1996), and Sarno and Taylor
(2002).
Whilst always an important focus of applied work, econometric developments,
in conjunction with new high-quality datasets and the move to generalized floating
exchange rates in 1973, have generated a vast number of empirical papers in the
last couple of decades. Perhaps the major change in emphasis over this period has
been the application of nonlinear rather than linear methods. These nonlinear
models are based on theoretical models that embody factors such as transactions
costs, limits to arbitrage and heterogeneity of expectations of market participants
(see, e.g., Dumas, 1992; De Grauweet al., 1993; Shleifer and Vishny, 1997).
An essential building block of many macroeconomic models is that purchasing
power parity (PPP) holds in the long run. PPP states that the nominal exchange
rate between two currencies should be equal to the ratio of aggregate price levels
between the two countries, so that a unit of currency of one country will have the
same purchasing power in a foreign country. The first empirical studies employing
unit root tests in the late 1980s were consistent in their failure to reject the unit
root hypothesis for major real exchange rates (e.g., Taylor, 1988; Mark, 1990). Sub-
sequent research employing longer time series datasets or panel methods suggested
that the early non-rejections of the unit root hypothesis was due to low power of
the corresponding test (Lothian and Taylor, 1996). However, the implied speeds of
adjustment of the real exchange rate in these studies was implausibly slow, typically
with half-life in the range of three to five years. Rogoff (1996, p. 647) summarized
this position as follows, “How can one reconcile the enormous short-term volatil-
ity of real exchange rates with the extremely slow rate at which shocks appear to
damp out?”
Perhaps the most important explanation of the Rogoff puzzle is that real
exchange rates can be described by a nonlinear data-generating process (DGP)
that exhibits a region of unit root or near unit root behavior near the equilib-
rium real exchange rate. Nonlinear models that capture this type of behavior are
the threshold autoregressive model of Tong (1983), and the exponential smooth
transition autoregressive model of Ozaki (1978). Econometric testing requires
appropriate tests for nonlinearity, where the null can be a stationary linear pro-
cess or a non-stationary linear process. In addition, the error process can exhibit
heteroskedasticity due to changes in regime (e.g., fixed to floating, or different
monetary regimes), as well as time-varying volatility. Consequently, the tests have
to allow for this feature and critical values have been obtained by either Monte
Carlo or bootstrap methods. Because many other empirical tests of aspects of
exchange rate behavior employ these tests, we initially consider the econometric
tests of PPP in section 22.2.