The official exchange rate of U.K. with respect to US dollar during last 40 years behaves more or less like other countries of EU and Asia because it shows volatility. If we use co-efficient of variation as the very simple measure of volatility , then we got the value of 22.16% which is too high. In the Fig-1, the volatility of the exchange rate is given.
Fig-1, Official exchange rate of UK per US dollar
In contrast to the behavior of the official exchange rate of UK per US dollar, the nature of the REER of UK during 1975-2009 is plotted below.
Fig-2, REER of UK
This REER (2005=100) is found as cyclical having co-efficient of variation is 9.6572% ie less volatile than the level series data. It is linearly estimated as,
REER = 80.8878+0.4293 T+U
(31.994)*(3.539)*
R2=0.275 , F= 12.53 (significant) and * = significant at 10% level.
On the other hand, the linear estimated equation of the level series of exchange rate is given below.
EX.RATE =0.38009+0.005913t +u
(16.69)*(7.759)*
R2=0.551 , F=60.21(sig) , where * = significant at 10% level.
The REER is positively skewed (value = 0.13007) but the level series is negatively skewed(value = -0.0843).
The long run trend of the curve is estimated in the linear form is shown in the figure-3, and the nature of the actual exchange rate curve is also shown and it is cyclically upward.
Fig-3 , Estimated series of exchange rate
The exchange rate shows auto-correlation and partial auto-correlation problems.In the Table-1,the correlogram of auto-correlation and partial auto-correlation are given along with the values of auto-correlation and partial auto-correlation along showing Q statistic and probabilities for significance.
Table-1
Correlogram of exchange rate series
| Sample: 1960 2010 | ||||||
| Included observations: 51 | ||||||
| Autocorrelation | Partial Correlation | | AC | PAC | Q-Stat | Prob |
| . |*******| | . |*******| | 1 | 0.892 | 0.892 | 43.055 | 0.000 |
| . |****** | | ***| . | | 2 | 0.730 | -0.327 | 72.446 | 0.000 |
| . |***** | | . |*. | | 3 | 0.593 | 0.112 | 92.250 | 0.000 |
| . |**** | | . |*. | | 4 | 0.512 | 0.133 | 107.35 | 0.000 |
| . |**** | | . | . | | 5 | 0.470 | 0.036 | 120.33 | 0.000 |
| . |**** | | . |*. | | 6 | 0.472 | 0.195 | 133.69 | 0.000 |
| . |**** | | . |*. | | 7 | 0.494 | 0.068 | 148.66 | 0.000 |
| . |**** | | .*| . | | 8 | 0.484 | -0.120 | 163.40 | 0.000 |
| . |*** | | .*| . | | 9 | 0.417 | -0.142 | 174.58 | 0.000 |
| . |** | | .*| . | | 10 | 0.311 | -0.104 | 180.95 | 0.000 |
| . |** | | . | . | | 11 | 0.216 | 0.018 | 184.11 | 0.000 |
| . |*. | | . | . | | 12 | 0.149 | -0.036 | 185.65 | 0.000 |
| . |*. | | .*| . | | 13 | 0.091 | -0.138 | 186.24 | 0.000 |
| . | . | | . | . | | 14 | 0.050 | -0.020 | 186.42 | 0.000 |
| . | . | | . | . | | 15 | 0.036 | 0.047 | 186.52 | 0.000 |
| . | . | | . | . | | 16 | 0.025 | -0.039 | 186.57 | 0.000 |
| . | . | | . | . | | 17 | -0.009 | -0.036 | 186.58 | 0.000 |
| .*| . | | **| . | | 18 | -0.088 | -0.196 | 187.21 | 0.000 |
| .*| . | | . | . | | 19 | -0.168 | 0.003 | 189.60 | 0.000 |
| **| . | | .*| . | | 20 | -0.250 | -0.149 | 195.06 | 0.000 |
| ***| . | | .*| . | | 21 | -0.329 | -0.111 | 204.79 | 0.000 |
| ***| . | | . |*. | | 22 | -0.367 | 0.114 | 217.34 | 0.000 |
| ***| . | | . |*. | | 23 | -0.338 | 0.124 | 228.38 | 0.000 |
| **| . | | . | . | | 24 | -0.276 | 0.044 | 235.99 | 0.000 |
The exchange rate of UK from 1960 to 2010 does not face unit root because from the unit root test we found the value of Augmented Dicky Fuller (ADF)which is -3.2857 and found significant at 10% level.
The estimated unit root test is,
X t-1 = 0.1006 – 0.2489 + 0.4794 ∆X t-1+u
(3.24)* (-3.2857)* (3.665)*
R2= 0.2969, ( moderately low), F= 6.334(insignificant), where * = significant at 10% level.
But, the exchange rate series has no common variance and therefore, the Auto Regressive Common homoscedasticity test appeared to be significant where Observed R2= 24.041(low but significant) ,F=44.456(sig) in which the estimated values are:
Constant 0.001929 (t= 1.41 , insignificant)
Residual 0.6932 (t= 6.66,significant)
Moreover, the series contains heteroskedasticity where the value of log likelihood ratio was found as 24.53(significant) from the Ramsey Reset Test.
So, we have to face numerous exchange rate policies for stabilization. The falling REER is the condition for net gain in terms of trade and positive current account balance. The stability of exchange rate with inflation targeting policy is crucial and to be adjusted with LIBOR and interest rate of EU for good behavior of exchange rate of the economy. Any interest rate differential is to managed by monetary policy.
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