Model-free evaluation of directional predictability in foreign exchange markets, страница 7

where r_t and r_t^Ł denote the domestic and foreign risk-free interest rates, respectively. Under the UIP condition, the interest rate market will lead the currency market as money flows from one country to another: higher (lower) domestic interest rates would increase expectations of a US dollar appreciation (depreciation) with an inflow (outflow) of foreign capital. While theoretically apparent, there has been little solid empirical evidence to support the above claim. A detailed analysis of the causes of its empirical failure is beyond our scope here; we simply note that the existence of a risk premium, the Peso problem, and expectational errors is known to account for the violation of UIP (see Froot and Thaler, 1990; Hodrick, 1987; Lewis, 1995; for a survey). Other explanations include transaction costs (e.g., Frenkel and Levich, 1975, 1977), capital control such as monetary policies (Chinn and Meredith, 2004; Faust and Rogers, 2003), market intervention (Mark and Moh, 2003), delayed overshooting (Eichenbaum and Evans, 1995), and misleading statistical inference problems (e.g., Baillie and Bollerslev, 2000; Maynard and Phillips, 2001; Bekaert and Hodrick, 2001).

Recent works have been more favorable for the validity of the UIP condition: Alexius (2001), Bekaert and Hodrick (2001), and Chinn and Meredith (2004) argue that UIP remains valid at long horizons, while Chaboud and Wright (2005) show that the UIP condition cannot be rejected by high-frequency intra-daily data. In a similar vein, Mark (1995) shows that the forecastability of exchange rates associated with monetary fundamentals is more pronounced in longer horizons. Further, Kilian and Taylor (2001) demonstrate that, using a (mean-reverting) nonlinear smooth transition autoregressive (STAR) model, exchange rates are forecastable over long horizons but not in short horizons.^[9] Besides the horizon-specific findings, Huisman et al. (1998), and Flood and Rose (2002) also pointed out that UIP holds better during volatile periods whereas Bansal and Dahlquist (2000) and Bekaert et al. (2002) showed that the validity of UIP is more related to currencies (rather than horizons).

These inherent weaknesses in the empirical validity of the UIP condition led us to look for an alternative linkage; we instead focus our attention on the relationship between the direction of foreign exchange rates and interest rate differentials, which yet remains to be investigated thoroughly. Let I^ID_t1 denote an information set at time t  1 available in the interest rate market, which contains lagged interest rate differentials,ID_t, where ID_t.

Accordingly, our next question is whether interest rate differentials ID_t can be used to predict the direction of foreign exchange rate changes:

                                                                 ₀ :E[Z_tc[Z_tc] a.s.                                                            4

Apparently, this hypothesis is more sensible to postulate the link between interest rates and exchange rates, because it does not require a one-to-one relationship between interest rate differentials and expected foreign exchange rate changes in the UIP condition (3). Indeed, recent studies suggest that interest rate differentials are associated with the direction of future foreign exchange rates. Furman and Stiglitz (1998) and Flood and Rose (2002) argue that, despite the violation of UIP (i.e., a discrepancy between expectations of appreciation/depreciation and interest rate differentials), higher domestic interest rates relative to foreign interest rates at least tend to appreciate the domestic currency during a crisis period.