1048 The Econometrics of Exchange Rates
various parameter values. The simulated moments estimator is found by minimiz-
ing the following loss function given weak regularity conditions and a symmetric
weighting matrixWz:
L={Hz(k)−HN[y(β)]}′
Wz{Hz(k)−HN[y(β)]}, (22.59)whereHz(k)=( 1 /Z)
∑Z
z= 1 h(kz),Hn[y(β)]=(^1 /N)∑N
j= 1 h[yj(β)]are the sample
moments of, respectively, the observed data forZobservations(kz,z=1, 2,...,Z);
and the simulated data forNobservations of the Krugman model conditional
on a vector of parametersβ,(yj(β),j=1, 2,...,N). Taylor and Iannizzotto note
that Hansen (1982) shows that:
Wz∗=(
1 +
1
n)− 1
−^1 ,is an optimal choice for the weighting matrix in that it yields the smallest asymp-
totic covariance matrix for the estimator.=
∑∞
i=−∞Rx(i), whereRx(i)is theith
autocovariance matrix of the population moments of the observed process, and
n=N/Zis the ratio of the length of the simulated series to the length of the
observed series. GivenWz∗, the MSM estimator converges in distribution to the
normal:
√
Z(̂βzN−β 0 )→DN⎛
⎝0,[
B′(
1 +
1
n)− 1
−^1 B]− 1 ⎞
⎠asZ,N→∞,whereB ≡ E[∂h(yj(β))/∂β]. The moment restrictions are tested by Taylor and
Iannizzotto by exploiting a result of Hansen (1982) that the minimized value
of the loss function converges asymptotically to aχ^2 distribution given the null
hypothesis of no errors in specification:
Z{Hz(k)−HN[y(β̂zN)]}′
W∗z{Hz(k)−HN[y(β̂zN)]}→Dχ^2 (&−k),where&is the number of moment conditions andkthe number of parameters
being estimated. Taylor and Iannizzotto’s papers improve on previous literature in
a number of respects. First, they employ daily data, making appropriate allowance
for holidays and weekends, so that the frequency is more consistent with the under-
lying theoretical model. Second, they use data only from periods when the target
zone wasa prioricredible – again trying to map the data to the underlying theo-
retical assumptions of the model. They report statistically significant parameters
of plausible magnitudes and the inability to reject the model using specification
tests. However, the degree of nonlinearity implied by their parameter estimates is
very small, so that the estimated honeymoon effect is small. Another interesting
finding, though perhaps not too surprising given their results on the magnitude of
the honeymoon effect, is that standard unit root tests have low power against data
generated from a credible target zone. They found, in fact, that the chances of non-
rejection of the unit root hypothesis may exceed 90% even when the exchange rate
conforms to a fully credible Krugman target zone.^54