1040 The Econometrics of Exchange Rates
22.3.2 Uncovered interest parity (UIP)
In the absence of frictions an agent should be indifferent between holding domestic
or foreign assets of identical type. The return from the foreign asset over a given
holding period is its return plus or minus the return from exchange rate changes
over the holding period. The latter component is risky so that risk averse agents
will require a risk premium. Employing interest rates as the asset’s return, the UIP
condition is given by:
it−i∗t=Etst+n−st+rpt, (22.32)
whereEtst+nis the expectation at timetof the exchange rate innperiods time,
the time to maturity of the interest rates, conditional on all information available
at timet. The uncovered parity condition in conjunction with the covered parity
condition imply that:
ft=Etst+n+rpt, (22.33)
and assuming rational expectations we obtain:
st+n=ft−rpt+ (^) t+n, (22.34)
where (^) t+nis the rational expectations forecast error, which can follow up to an
n−1 order moving average error process (see Hansen and Hodrick, 1980). Early
tests of the properties of the forward rate were based on testing the hypothesis that
β=1 in the following OLS regression:
st+n=α+βft+ut. (22.35)
The estimates ofβwere typically close to unity. However, the early research, nat-
urally, was unaware that ifstandftare integrated variables, so that (22.35) is a
cointegration regression, thet-ratio is not asymptotically standard normal.
A number of different estimation techniques have been employed to estimate
(22.35) which remedy this deficiency. For example, Haiet al.(1997) estimate
αandβwith the dynamic OLS (DOLS) and dynamic generalized least squares
(DGLS) cointegration vector estimators of Stock and Watson (1993). Moore and
Copeland (1995) employ the fully modified maximum likelihood procedure
(FM-OLS) of Phillips and Hansen (1990), which treats equation errors in a gen-
eral semi-parametric way to estimateαandβ. Phillipset al.(1996), building
on Phillips (1995), estimate the coefficients employing the fully modified least
absolute deviations (FM-LAD) estimator.^39
A comparison by Phillips of the FM-LAD estimates ofαandβwith those obtained
from FM-OLS and OLS on interwar data suggests it can make a major difference to
the magnitude and significance of the estimated coefficients. The properties of the
FM-LAD estimator appear to us to make it a prime candidate for use in many areas
of finance, e.g., the relationship between asset prices and fundamentals and tests
of bubbles (see section 22.5). It appears to us a neglected contribution.
Overall, the estimates ofβdo not appear to differ significantly from unity.^40
The estimates ofαdo appear to differ from zero but this, of course, could be the
influence of a stationary, non-zero mean risk-premium. However, an estimate of