Page 171 - DECO503_INTERNATIONAL_TRADE_AND_FINANCE_ENGLISH

Unit 14 : Exchange Rate : Meaning and Components

Notes
2
σ
cov P ,E S +1 − S t )) is negative and larger in magnitude than (ES + − S t )) . The complementary
( t
( t
( t1
estimate of β > 1 then implies that cov P ,E S +1 − S t )) is smaller in absolute magnitude than
( t
( t
1
σ 2 ( ) t 2 ( ) t 2 ( (ES + t1 − S t )) .
P , and thus that σ
P is larger than σ
ES
t
+
The non-zero covariance between P and ( t1 − S ) t prevents us from using the regression
P and (ES
coefficients to estimate the levels of σ 2 ( ) t σ 2 ( t1 − S t )) . With (5) and (6), however, we can
+
estimate the difference between the two variances as a proportion of σ 2 ( t ) t .
F – S
σ 2 ( ) σ−P 2 ( (E S − S ))
β – β = t + t 1 t . ... (10)
1
2
σ 2 ( t ) t
F – S
The differences between the estimates of β and β in table 2 range from 1.58 (Japan) to 4.16 (Belgium).
2
1
Except for Japan, all the differences between the estimated coefficients are greater than 2.0. Thus, the
P
point estimates are that the difference between the variance of the premium, t , and the variance of
ES
+
t
t
the expected change in the spot rate, ( t1 − S ) t , in F – S is typically more than twice the variance
of F – S . Moreover, since β and β sum to 1.0, the estimates of the regression coefficients are
2
1
t
t
perfectly negatively correlated, and the standard error of their difference is twice their common
standard error. Only the estimates of β – β for Japan, Switzerland, and West Germany are less
2
1
than two standard errors from zero, and all are more than 1.5 standard errors from zero. Thus, we
P is reliably greater than σ
can conclude that σ 2 ( ) t 2 ( (ES + t1 − S t )) .
F – S
ES
P
In short, negative covariation between t and ( t1 − S ) t attenuates the variability of t t , and
+
obscures the interpretation of the regression slope coefficients in (3) and (4). Nevertheless the regression
slope coefficients provide the interesting information that both the premium, P , and the expected
t
P is large relative to
ES
t
t
+
change in the spot rate, ( t1 − S ) t , in F – S , vary through time, and σ 2 ( ) t
σ 2 ( (ES + t1 − S t )) .
ES
t
+
A good story for negative covariation between P and ( t1 − S ) t is difficult to tell. For example, in
the PPP model for the exchange rate underlying (9), the dollar is expected to appreciate relative to a
ES
+
foreign currency, that is, ( t1 − S ) t is negative, when the expected inflation rate in the U.S. is
lower than in the foreign country. (Remember that the exchange rates are all expressed as dollars per
unit of foreign currency.) A negative cov P ,E S +1 − S t )) then implies a higher purchasing power
( t
( t
risk premium in the expected real returns on dollar denominated bonds relative to foreign currency
bonds when the anticipated U.S. inflation rate is low relative to the anticipated foreign inflation rate.
We return to economic interpretations of the negative covariance between the P and E (S t + 1 – S )
t
t
components of F – S after exploring some purely statistical possibilities.
t t
SUR estimates
The apparent negative covariation between P and E (S – S ) may be sampling error. All the slope
t t + 1 t
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