Exchange Rate Economics: Theories and Evidence

308 Target zone models
Table 12.1 FIML estimation results 1890/02–1908/12 a
Variable Coefficient Std error T-statistic
1. Mean reversion, β 1 −0.260 0.122 −2.132
Size of devaluation
2. Devaluation size, β 2 0.581 0.020 29.741
Probability of devaluation, γ
3. Constant −4.380 0.439 −9.972
4. Money 1.609 1.600 0.969
5. Income 0.060 0.459 0.131
6. Real exchange rate 3.356 0.529 6.345
7. Cotton exports −0.038 0.024 −1.586
8. S and P index −1.557 0.341 −4.571
9. Gold reserves 0.009 0.057 0.166
10. Sherman dummy 0.163 0.039 4.234
11. Silver debate dummy 0.686 0.147 4.652
12. Trend 0.004 0.001 4.389
Risk premium
13. Variance in mean, δ 1.218 0.312 3.907
14. Variance constant, v 1 0.048 0.016 2.915
15. ARCH, v 2 1.196 0.507 2.362
16. Asymmetric ARCH, v 3 −0.907 0.406 −2.232
17. GARCH, v 4 0.331 0.151 2.188
Notes
a The general form of the model is
i t − it
∗ =[(prob. of deval.)(size of deval.) + (1 − prob. of deval.)(mean reversion)
+ risk premium]/k,
mean reversion = β 1 x t ,
size of deval. = β 2 ,
prob of deval. = (γ z t ),
risk premium = δh t ,
h t = v 1 + v 2 εt−1 2 + v 3(εt−1 2 |ε t−1 < 0) + v 4 h t−1 .
Source: Hallwood,MacDonald and Marsh (2000).
since there are no bands the expected change in the exchange rate is zero and
of course there can be no monetary independence. At the other extreme with
freely floating exchange rates there may be some,quite considerable,monetary
independence to the extent that a non-zero expected change in the exchange rate,
E t s t+k ,term enters the UIP condition:
i t = i ∗ t + E t s t+k . (12.38)
The recognition that all historical fixed exchange rate regimes (with the exception of
currency board – not regime) have had exchange rate bands means that in principal