Will a currency appreciate or depreciate with a higher interest rate?
Uncovered Interest Parity (UIP) requires the expected depreciation of home currency to be equal to the home minus foreign interest rate differential (ID). However, empirical studies relying on the Fama regression have found that the estimated coefficient of ID (Fama’s beta) is likely to be significantly less than 1 or even negative while it should be +1 to be consistent with the UIP. In the literature, this phenomenon is known as the UIP puzzle or the forward discount bias.
As pointed out by Sarno and Taylor (p. 12 in The economics of exchange rates, 2002, Cambridge University Press), a negative beta violates UIP but it does not necessarily mean that home currency should appreciate because its effect may be dominated by a large and positive value of the intercept. Moreover, as well-summarized in Miller (Exchange Rate Economics: The Uncovered Interest Parity Puzzle and Other Anomalies, 2014, Edward Elgar Pub.), some more recent studies report positive estimates for Fama’s beta under certain conditions using various new approaches.
Given that appreciation and depreciation of home currency are both possible with a higher interest rate, one interesting question is what the odds are for each possibility. Are they equally likely, or depreciation is more likely as implied by UIP?
In order to answer these questions, focusing on the directions or signs of the exchange rate movements ignoring the sizes, I plan to use probit or logit type models rather than the Fama regression. In addition, to investigate the conditions under which appreciation or depreciation has a higher probability, linear probability models will be used in the context of TAR or STAR models where the relationships are piecewise linear but overall nonlinear. The main source of the monthly data, including the exchange rates and the nominal interest rates of emerging markets as well as the OECD member nations, will be the International Financial Statistics (IFS) of IMF. I believe that my approach will identify a relationship between the probability of depreciation and the interest rate differential which is more stable than the relationship between the log return and ID estimated by Fama regression.