RDP 8608: Exchange Rate Regimes and the Volatility, of Financial Prices: The Australian Case 4. Empirical Results
July 1986
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(a) Some Preliminaries
In estimating the VARs for the pre- and post-float sample periods we have included all interest rates in levels and all exchange rates as trade weighted indexes in natural logarithms. The data used are on a daily basis from 16 November 1981 until 31 December 1985. As there may have been some turbulance in Australian financial markets just prior to and just after the floating of the Australian dollar on 12 December 1983, we have omitted observations around the float to give pre- and post-float sample periods which are more homogeneous within exchange rate regimes and more suitable for comparison across regimes. The sample periods used are 16 November 1981 to 31 October 1983 for the pre-float period and 2 April 1984 to 31 December 1985 for the post-float period – sample sizes of 503 and 447 observations respectively.
Using the methodology described in Section 2 we have fitted to each sample period VARs comprising the following eight financial prices: the Australian trade-weighted index (AUSTWI); the Australian 90 day bank accepted bill rate (AUSRATE); the United States TWI (USTWI); the U.S. 90 day prime bankers' acceptances rate (USRATE); West Germany's TWI (DMTWI); the West German 90 day interbank deposits rate (DMRATE); Japan's TWI (JAPTWI); and the Japanese 90 day Gensaki rate (JAPRATE).^{[8]} The VAR for the pre-float sample period required five lags and a first order time trend to induce multivariate white noise residuals (innovations), while for the post-float sample period four lags and a first order time trend were required.
(b) The Estimated VARs
Convenient summaries of the estimated VARs are provided in Tables 1 and 2 for the pre- and post-float periods. These tables contain the results of F tests for the significance of blocks of coefficients in each equation of the VARs (i.e., tests of Granger-causality). Each entry is the minimum level of significance required to reject the null hypothesis that the column variable does not help forecast (Granger-cause) the row variable. As we are more concerned in this paper with the behaviour of Australian financial prices in the two periods, the marginal significance levels in the first two rows of the tables are the most important (i.e., the significance levels for the tests for Granger-causality running from each variable to the two Australian variables).
Equation |
Explanatory Variable | ||||||||
---|---|---|---|---|---|---|---|---|---|
AUSTWI | AUSRATE | USTWI | USRATE | DMTWI | DMRATE | JAPTWI | JAPRATE | FOREIGN | |
AUSTWI | – | .0001 | .5309 | .0089 | .4716 | .9568 | .8757 | .1811 | .0233 |
AUSRATE | .0497 | – | .3647 | .2852 | .3364 | .9248 | .9483 | .2875 | .1230 |
USTWI | .7019 | .7618 | – | .0267 | .1024 | .4381 | .0009 | .3211 | – |
USRATE | .1830 | .1397 | .0211 | – | .3524 | .7380 | .3286 | .2823 | – |
DMTWI | .0871 | .0522 | .4122 | .8078 | – | .0718 | .7618 | .0161 | – |
DMRATE | .0366 | .5848 | .0857 | .2161 | .0857 | – | .1589 | .8164 | – |
JAPTWI | .7371 | .7655 | .1624 | .2071 | .5879 | .2700 | – | .4794 | – |
JAPRATE | .2008 | .3097 | .4017 | .2413 | .8646 | .0244 | .6255 | – | – |
Equation |
Explanatory Variable | ||||||||
---|---|---|---|---|---|---|---|---|---|
AUSTWI | AUSRATE | USTWI | USRATE | DMTWI | DMRATE | JAPTWI | JAPRATE | FOREIGN | |
AUSTWI | – | .4268 | .0003 | .4258 | .0335 | .0087 | .0780 | .4703 | .0004 |
AUSRATE | .1394 | – | .0772 | .0116 | .2192 | .1303 | .0631 | .2211 | .1267 |
USTWI | .1340 | .3757 | – | .2198 | .7930 | .7603 | .8947 | .8079 | – |
USRATE | .9746 | .5160 | .8024 | – | .5855 | .2924 | .9207 | .8874 | – |
DMTWI | .0779 | .0078 | .0001 | .0287 | – | .2424 | .0009 | .5315 | – |
DMRATE | .6932 | .8161 | .0026 | .0325 | .1318 | – | .0052 | .0001 | – |
JAPTWI | .8751 | .4613 | .0641 | .7060 | .4434 | .6947 | – | .9394 | – |
JAPRATE | .4051 | .6766 | .0037 | .0061 | .0081 | .0632 | .2889 | – | – |
From Table 1 we note that, with one exception, the hypothesis that each of the foreign variables does not Granger-cause either Australian interest rates or TWI cannot be rejected, at commonly used levels of significance, in the pre-float period. The exception is the lags of US interest rates which appear to feed strongly into the AUSTWI. A test for the joint significance of all foreign variables (the marginal significance levels for which are in the final column) indicates that the null hypothesis can be rejected at the 5 per cent level in the case of the AUSTWI, while it can't be rejected for AUSRATE. There is, however, strong evidence that AUSRATE Granger-causes AUSTWI while there is weaker evidence of feedback from the AUSTWI into AUSRATE.
By comparison, the results in Table 2 for the post-float period indicate much stronger effects of foreign variables on AUSTWI and a relatively exogenous AUSRATE. Both the USTWI and DMRATE strongly Granger-cause AUSTWI while there is also evidence, although not as strong, that both DMTWI and JAPTWI have some influence on AUSTWI. Moreover, the null hypothesis that the foreign variables have no joint impact on AUSTWI is easily rejected. The evidence for this appears stronger than for the corresponding test in the pre-float VAR, suggesting that AUSTWI is relatively more endogenous under a floating exchange rate regime, as one would anticipate.
From the corresponding tests for AUSRATE presented in the second row of Table 2, we can note that there is slightly stronger evidence of individual foreign variables having some impact on AUSRATE than in the pre-float period. The USTWI, USRATE and JAPTWI all Granger cause AUSRATE at the 10 per cent level of significance. However, the hypothesis that the foreign variables have no joint impact on AUSRATE cannot be rejected, as in the case of the pre-float VAR. The results with respect to the relationship between AUSRATE and AUSTWI indicate no significant impact of one upon the other for the post-float VAR. Taken together, these results suggest that in the post-float period AUSRATE is relatively exogenous – there is no net effect from the foreign variables and no effect from AUSTWI. They also support the notion that floating exchange rates allow an independent monetary policy.
As one might anticipate, there is little or no evidenceof feedback from either Australian variable into any foreign variable. This accords with the idea of Australia being relatively unimportant in world financial markets. There is, however, fairly strong evidence of relationships among the individual foreign variables.
The results of these Granger-causality tests provide limited evidence to suggest a greater impact of foreign financial prices upon the Australian dollar (as measured by AUSTWI) under a floating exchange rate regime compared to that under a fixed exchange rate regime. The evidence with respect to the Australian interest rate, however, is inconclusive. It suggests that foreign financial prices had little direct, net impact on Australian short-term interest rates under either regime, although they may have had an impact via the exchange rate in the fixed rate regime.
Another important finding of these Granger-causality tests is the change in relationship between AUSTWI and AUSRATE in the move from a fixed exchange rate regime to a floating exchange rate regime. While there appears to be a strong relationship between the two variables in the pre-float period, with AUSRATE strongly Granger-causing AUSTWI and some evidence of feedback, this relationship appears to have been broken by moving to a floating exchange rate regime where neither variable Granger-causes the other.
(c) The Variance Decompositions
As noted in Sections 2 and 3 above, in order to decompose the k-step forecast variance into percentage contributions from the individual variables, we are required to make assumptions regarding the contemporaneous causal ordering of the variables. The sensitivity of the results (for the percentage contributions, though not the forecast variances themselves) to the ordering assumed will depend on the degree of contemporaneous correlation among the innovations – i.e., the contemporaneously non-forecastable part of each variable. Since these are of some interest in themselves, we present the correlations in upper-triangular matrix form for the pre- and post-float periods in Tables 3 and 4 respectively. Examination of these tables will help identify possible areas of sensitivity with regard to assumed causal ordering.
AUSTWI | AUSRATE | USTWI | USRATE | DMTWI | DMRATE | JAPTWI | JAPRATE | |
---|---|---|---|---|---|---|---|---|
AUSTWI | 1 | .4641 | −.0479 | .0482 | −.0366 | .1322 | .0248 | .0421 |
AUSRATE | 1 | −.0118 | .0802 | .0035 | .0062 | −.0034 | .0019 | |
USTWI | 1 | .4248 | −.5167 | .0208 | −.5159 | .0105 | ||
USRATE | 1 | −.3281 | .0035 | −.2605 | −.0247 | |||
DMTWI | 1 | −.0195 | .2898 | .0082 | ||||
DMRATE | 1 | .0041 | −.0936 | |||||
JAPTWI | 1 | −.0488 | ||||||
JAPRATE | 1 |
AUSTWI | AUSRATE | USTWI | USRATE | DMTWI | DMRATE | JAPTWI | JAPRATE | |
---|---|---|---|---|---|---|---|---|
AUSTWI | 1 | −.1918 | −.0197 | −.0276 | .1547 | −.0154 | .0489 | .0273 |
AUSRATE | 1 | −.0017 | −.0065 | .0098 | −.0527 | .0018 | .0225 | |
USTWI | 1 | .2571 | −.7985 | −.0128 | −.2739 | −.0458 | ||
USRATE | 1 | −.2072 | .0236 | −.1424 | −.1144 | |||
DMTWI | 1 | −.0322 | .0497 | .0225 | ||||
DMRATE | 1 | .0646 | .0709 | |||||
JAPTWI | 1 | .0206 | ||||||
JAPRATE | 1 |
The correlations presented in Tables 3 and 4 indicate very little in the way of contemporaneous correlation between the innovations in Australian and foreign variables. This is especially the case for AUSRATE, while the exchange rate appears to be correlated to a certain extent with the DMTWI in the post-float period. This reflects a greater endogeneity in the floating exchange rate regime than under the fixed exchange rate regime, as one would expect. These correlations suggest that the variance decompositions are likely to be insensitive to our maintained hypothesis that the Australian variables do not contemporaneously cause the foreign variables.^{[9]}
However, the correlation between innovations in AUSTWI and AUSRATE in the pre-float period suggests that some caution is required in ordering these two variables. The differences in these correlations (.46 for the pre-float period and −.19 for the post-float period) also suggests that the relationship between interest rate and exchange rate movements has changed in the move to a floating exchange rate regime.^{[10]} This concurs with the findings of the Granger-causality tests in the previous section in suggesting that the interdependence between interest rates and exchange rate movements has been reduced in a floating exchange rate regime – i.e., that the independence of monetary policy has been increased.
As the correlations presented above suggest, the variance decomposition for the pre-float period are sensitive to the causal ordering assumption for AUSTWI and AUSRATE. However, the nature of the AUSTWI variable in the pre-float period suggests that assuming AUSRATE does not contemporaneously cause AUSTWI makes more sense on a priori grounds. Observation of the AUSTWI variable on a given day is calculated on the basis of the previous day's trading in New York. In the pre-float period, the authorities used this to set the US$/$A exchange rate each morning for that day's trading. The AUSRATE variable, by comparison, is measured during the current day's trading; hence, the AUSTWI is intertemporally prior to it. Moreover, this ordering accords with the exchange rate regime in the pre-float period. The exchange rate was not determined by market forces; it was relatively fixed. We maintain this contemporaneous causal ordering for the post-float VAR for consistency; however, it makes little difference to the post-float results.
We present the variance decompositions for AUSTWI and AUSRATE for both the pre- and post-float periods in Tables 5 through 8. To simplify the analysis, we have aggregated the foreign contribution to avoid the need for assumptions about causal ordering for these variables. The total foreign contribution is independent of the relative ordering of the individual foreign exchange and interest rate variables.
Days Ahead |
Forecast Variance |
Per cent Due to Innovations in | AUSTWI ROWTWI |
||
---|---|---|---|---|---|
Foreign | AUSTWI | AUSRATE | |||
0 | .21 | 3.1 | 96.9 | – | 1.21 |
1 | .39 | 4.6 | 95.3 | .1 | 1.21 |
2 | .57 | 5.8 | 92.7 | 1.5 | 1.22 |
3 | .74 | 6.9 | 91.0 | 2.3 | 1.21 |
4 | .85 | 7.9 | 89.7 | 2.4 | 1.17 |
5 | .95 | 8.9 | 88.4 | 2.7 | 1.14 |
6 | 1.03 | 9.7 | 87.1 | 3.2 | 1.11 |
7 | 1.11 | 10.6 | 85.3 | 4.1 | 1.09 |
8 | 1.20 | 11.4 | 83.2 | 5.4 | 1.07 |
9 | 1.29 | 12.2 | 80.8 | 7.0 | 1.06 |
10 | 1.39 | 13.1 | 78.1 | 8.8 | 1.06 |
15 | 1.87 | 16.4 | 64.0 | 19.6 | 1.05 |
20 | 2.40 | 18.5 | 52.7 | 28.8 | 1.07 |
30 | 3.34 | 21.5 | 40.7 | 37.8 | 1.09 |
Days Ahead |
Forecast Variance |
Per cent Due to Innovations in | AUSTWI ROWTWI |
||
---|---|---|---|---|---|
Foreign | AUSTWI | AUSRATE | |||
0 | .71 | 4.1 | 95.9 | – | 2.40 |
1 | 1.32 | 9.5 | 90.4 | .1 | 2.26 |
2 | 1.81 | 8.6 | 91.1 | .3 | 2.12 |
3 | 2.23 | 9.0 | 90.8 | .2 | 1.97 |
4 | 2.58 | 8.8 | 91.0 | .2 | 1.87 |
5 | 2.90 | 8.9 | 90.9 | .2 | 1.80 |
6 | 3.18 | 9.2 | 90.6 | .2 | 1.74 |
7 | 3.45 | 10.2 | 89.4 | .4 | 1.70 |
8 | 3.70 | 10.7 | 88.6 | .7 | 1.67 |
9 | 3.94 | 11.5 | 87.6 | .9 | 1.64 |
10 | 4.17 | 12.2 | 86.6 | 1.2 | 1.62 |
15 | 5.29 | 15.3 | 81.8 | 2.9 | 1.57 |
20 | 6.40 | 18.9 | 75.4 | 5.7 | 1.57 |
30 | 8.73 | 25.0 | 63.0 | 12.0 | 1.62 |
Days Ahead |
Forecast Variance |
Per cent Due to Innovations in | AUSRATE ROWRATE |
||
---|---|---|---|---|---|
Foreign | AUSTWI | AUSRATE | |||
0 | .08 | 1.0 | 21.6 | 77.4 | 2.48 |
1 | .21 | 1.2 | 16.3 | 82.5 | 2.81 |
2 | .34 | 2.9 | 14.8 | 82.3 | 3.01 |
3 | .49 | 4.0 | 14.4 | 81.6 | 3.15 |
4 | .67 | 5.1 | 14.6 | 80.3 | 3.33 |
5 | .86 | 5.9 | 14.6 | 79.5 | 3.50 |
6 | 1.04 | 6.6 | 14.4 | 79.0 | 3.63 |
7 | 1.21 | 7.4 | 14.1 | 78.5 | 3.73 |
8 | 1.37 | 8.1 | 13.8 | 78.1 | 3.81 |
9 | 1.52 | 8.8 | 13.5 | 77.7 | 3.85 |
10 | 1.65 | 9.4 | 13.2 | 77.4 | 3.89 |
15 | 2.11 | 12.6 | 11.7 | 75.7 | 3.84 |
20 | 2.35 | 15.2 | 10.7 | 74.1 | 3.69 |
30 | 2.60 | 17.9 | 9.7 | 72.4 | 3.42 |
Days Ahead |
Forecast Variance |
Per cent Due to Innovations in | AUSRATE ROWRATE |
||
---|---|---|---|---|---|
Foreign | AUSTWI | AUSRATE | |||
0 | .03 | 1.0 | 3.6 | 95.4 | 2.65 |
1 | .06 | 3.0 | 3.4 | 93.6 | 2.94 |
2 | .09 | 3.8 | 4.3 | 91.9 | 2.94 |
3 | .12 | 4.9 | 5.4 | 89.7 | 2.98 |
4 | .15 | 6.3 | 6.3 | 87.4 | 2.96 |
5 | .18 | 7.7 | 7.2 | 85.1 | 3.01 |
6 | .21 | 9.2 | 7.9 | 82.9 | 3.01 |
7 | .23 | 10.5 | 8.7 | 80.8 | 3.01 |
8 | .26 | 11.8 | 9.3 | 78.9 | 3.04 |
9 | .28 | 13.1 | 9.8 | 77.1 | 3.03 |
10 | .31 | 14.3 | 10.3 | 75.4 | 3.02 |
15 | .42 | 19.9 | 11.8 | 68.3 | 3.04 |
20 | .51 | 24.5 | 12.4 | 63.1 | 3.03 |
30 | .67 | 32.2 | 12.2 | 55.6 | 3.00 |
The decomposition for AUSTWI for both periods, presented in Tables 5 and 6, indicate little differences in the source of the forecast variance in percentage terms between the two exchange rate regimes. Over short horizons (with which we are more concerned since for longer horizons income and relative price variables are likely to be important) most of the variance comes from its own innovations. The percentage contribution of the foreign sector appears marginally higher in the post-float period whereas the percentage contribution of AUSRATE is marginally higher in the pre-float period. These margins, however, are very small over horizons of up to 10 days (two market weeks).
Much more noticeable in Tables 5 and 6 are the forecast variances at various horizons – the measures of the predictability of AUSTWI. The forecast variance in the post-float period is about three times larger than that in the pre-float period, over all horizons. While this is strongly supportive of the theoretical prior that exchange rates are more volatile under a floating exchange rate regime, there is still a possibility that world exchange rates have similarly been more volatile in the post-float period. To obtain a measure which corrects for this possibility, we have constructed a variable which measures the standard error of the forecast of AUSTWI relative to the average standard error of forecasts for exchange rates in the rest of the world (i.e., USTWI, DMTWI and JAPTWI). This is presented in the final column of Tables 5 and 6.
These standardised measures show that for all horizons the forecast variance is larger under the floating exchange rate regime than under the fixed exchange rate regime. Even allowing for possible changes in volatility of world exchange rates, AUSTWI is relatively more volatile under a flexible exchange rate regime. It is also interesting to note that the differences in volatility are much larger over short horizons, falling as the horizon lengthens. This suggests that over longer horizons the flexible peg (or fixed, as we have called it) exchange rate may be considered approximately flexible; an assumption often encountered in the literature.
Turning to the results for AUSRATE in Tables 7 and 8, it can be seen that the interest rate is relatively more exogenous in the post-float period. For short horizons of up to seven days, some 10 per cent less of its variance comes from its own innovations in the pre-float period (than in the post-float period), with the bulk of this being attributed to AUSTWI. At longer horizons the difference disappears and reverses for horizons of 15 days and over. The contribution of foreign variables is relatively small in both periods, with no sizable differences apparent until the horizon exceeds ten days.
Again, while there are only modest differences in the variance decompositions, the sizes of the k-step forecast variances are very different between the two periods. The forecast variance in the pre-float period is some three to four times larger than that in the post-float period, for all horizons. This suggests that the interest rate is relatively less volatile under a floating exchange rate regime, as theory suggests. This conclusion is supported by the measure of the standard error of the forecast relative to the average of that for the rest of the world. At all horizons apart from the first two, the ratio has fallen with the move to a floating exchange rate regime.
Further evidence, which supports this result that the interest rate has become relatively exogenous (with respect to the other variables in the VAR) since the float, is presented in Table 9. This table shows the marginal significance levels for the test of the null hypothesis that the variable concerned is a random walk. The random walk hypothesis is soundly rejected for the exchange rate in both the pre- and post-float periods, and for the interest rate in the pre-float period. However, at least at levels of significance of two per cent or less, the random walk hypothesis can not be rejected for the interest rate during the post-float period.^{[11]}
Pre-Float | Post-Float | |
---|---|---|
AUSTWI | .0003 | .0001 |
AUSRATE | .0001 | .0205 |
Footnotes
These data are more fully described in Appendix D. The Gensaki rate is only available for the post-float period. Prior to this, the rate for unconditional call money is used. The results of the analysis without Japan, presented in Appendix A, are essentially the same as those to be presented below. All the trade weighted indexes are expressed in natural logarithms and then scaled up by a factor of 100. Interest rates are in level form and unsealed, i.e., an interest rate of 10 per cent is expressed as 10.0. [8]
This is the standard “small country” assumption. Since, for the purposes of this paper, we are only interested in the net foreign contribution to volatility, we do not need to be concerned about the ordering of the foreign variables themselves. The net foreign contribution is invariant to the ordering of these foreign variables. [9]
Bilson (1984) argues that such a negative correlation is predicted by the Dornbusch (1976) model of floating exchange rates. [10]
Each entry in Table 9 is the minimum level of significance required to reject the null hypothesis that, in the given equation of the VAR, the coefficient on the first lag of the own variable is unity and all other coefficients are zero. These tests are biased against the null hypothesis of a unit root. However, essentially the same values were obtained from an unbiased sequential procedure. Under this procedure, we first tested the null hypothesis that the relevant VAR equation was a first order univariate autoregressive model. This hypothesis could not be rejected for the post-float interest rate at a level of significance of less than 2.8 per cent. An AR(1) model for this variable was then estimated. The null hypothesis that the parameter was unity could not be rejected at a level of significance less than 2.5 per cent, using the table of adjusted significance levels in Fuller (1976, p.371). For a discussion of this adjustment, see Fuller (1976, pp.366–385). [11]