12.1 The Uncovered Interest Parity

Exchange market participants constantly shift funds around the globe such that yields of international assets with similar risk should be equalized. However, sometimes we do observe substantial differences in interest rates across different countries. To get a more complete picture we have to take exchange rates into account. This is done by the theory of uncovered interest parity (UIP). A typical macroeconomic textbook model of the UIP (e.g. Burda and Wyplosz; 1993) has the following form: Let us denote the domestic interest rate as $ i$, the foreign interest rate as $ i^*$ and the nominal exchange rate as $ S$. At time $ t$ we can write the UIP as

$\displaystyle (1+i)_t = (1+i^*)_t \frac{E(S_{t+1})}{S_t}.$ (12.1)

Simply speaking, the foreign interest income expressed in the domestic currency should equal the domestic interest rate. From this relationship we obtain the approximation:

$\displaystyle i_t \simeq i^*_t + E(s_{t+1}) -s_t,$ (12.2)

where $ s_t$ denotes the logarithm of $ S_t$, i.e. $ s_t=\log S_t$.

Following MacDonald and Nagayasu (1999) we modify equation (12.2). First, we use real exchange rates and real interest rates. Second, since it is not clear whether the UIP holds for short or long term interest rates, we include a short and a long term interest rate. The panel dataset contains observations $ i=1, \ldots, N$ countries and at $ t=1, \ldots, T_i$ time periods. Therefore, the log exchange rate of country $ i$ at time $ t$ is written as $ s_{it}$. Since we are interested in the change of the exchange rate we calculate first differences as $ \Delta s_{it} = s_{it}
-s_{i,t-1}$. Then $ \Delta s_{it}$ is interpreted as the growth rate of the exchange rate. It is impossible to include the expected exchange rate growth in the empirical analysis because it is unobservable. Instead we use the observable growth rate denoted as $ \Delta s_{it}$ as a proxy for the expectations formed at time $ t$. In doing so we assume economic agents have static expectations, i. e.  $ \mathrm{E}(\Delta s_{it+1})= \Delta s_{it}$ . Although this assumption can be problematic too, we proceed in order to make empirical analysis feasible.

Furthermore, let $ (r_l - r^*_l)_{it}$ be the long-term interest rate differential, where $ r_l$ and $ r^*_l$ denote the domestic and foreign long-term rates respectively. Finally, we use $ (r_s -
r^*_s)_{it}$ to denote the short-term interest differential. At best, economic theory predicts that UIP holds in the long-run (see Burda and Wyplosz (1993)). We test this assumption by including short and long-term interest rate differentials in the estimated equation. If the UIP holds in the long-run, we expect $ \beta_1$ to be positive and close to unity and $ \beta_2=0$.

Now, we can estimate an equation of the following form:

$\displaystyle \Delta s_{it} = \beta_0+ \beta_1 (r_l - r^*_l)_{it-1} + \beta_2 (r_s -r_s^*)_{it}$ (12.3)

where the interest rate differentials have different time indices to avoid problems with multicollinearity between the two regressors.