The Treasury

Global Navigation

Personal tools

3.2  Volatility

3.2.1  Measuring volatility

The previous section illustrated that there is no evidence of a secular decline in New Zealand’s terms of trade and in fact the past three decades have seen an upward trend. This section looks at the volatility in the terms of trade to see if it has also changed over time.

As illustrated in Figure 1, New Zealand has experienced some large fluctuations in its terms of trade. These have been a result of both export price movements as well as import price movements. For example, the oil price shocks of the mid-1970s had a large impact on import prices while the Korean War of 1950 saw a considerable increase in export prices through the price of wool. Some measures of volatility of the terms of trade are summarised in Table 7 which also shows how volatility has changed over time. The series is again split into the familiar periods of pre-1973 and post-1973 as in the trend discussion above. It is found that volatility (measured by the variance) is almost 70% less in the post-1973 period than the 1900 to 1973 period.[12] Also displayed in Table 7 is a measure of the range of the terms of trade relative to the mean. This has fallen by over 50% between the period 1900 to 1973 and 1974 to 2005.

Table 7 – Measures of Volatility in New Zealand’s Log Goods Terms of Trade
  1900-2005 1900-1973 1974-2005
Variance 0.020 0.023 0.007
Range/Mean* 0.651 0.632 0.311

* The estimate is based on the actual terms of trade data (not logarithms).

Table 7 shows how the volatility has changed between the two periods. However, these two periods are arbitrary and chosen by “eye-balling” a graph. It is therefore of interest to test whether a structural break is present in the volatility of the terms of trade. In their paper, Gillitzer and Kearns (2005) apply the Bai and Perron (1998) test to see whether there are any statistically significant breaks in the mean of the absolute log difference in the terms of trade and it is this methodology that is repeated here and displayed in Table 8.

Both the UDMax test and the WDMax test, which test for an unknown number of breaks, reject zero breaks against an unknown number of breaks at the 1% significance level. The BIC information criterion indicates that there is one break while the LWZ criterion does not find evidence of any breaks. After allowing for one break, the SupF test cannot reject one break in favour of two or two breaks in favour of three at the 5% significance level. The sequential test using the results of the SupF test therefore finds one break in the volatility of the terms of trade and the Bai and Perron test selects the most likely date as 1980.

Table 8 – Results of Bai and Perron (1998) Test for Structural Break in Volatility of Terms of Trade
Double maximum tests Information criteria SupF(i+1|i) Sequential test Break dates
UDMax BIC SupF(2|1) 1 break 1980
26.951*** 1 break 7.748*    
WDMax LWZ SupF(3|2)    
27.484*** 0 breaks 4.180    

The double maximum tests are tests for an unspecified number of breaks against the null of zero breaks. Both the WDMax and UDMax test statistics evaluate an F-statistic for 1-5 breaks, with the breakpoints selected by global maximisation of the sum of squared residuals. The UDMax statistic weights the five F-statistics equally, while the WDMax statistic weights the F-statistics such that the marginal p-values are equal across the number of breaks. The WDMax test statistic reported is for a 1% significance level test. The LWZ statistic is a modified Schwarz criterion. The SupF(i+1|I) test is a test for i+1 breaks against the null of i breaks. The sequential test selects the number of breaks stepwise from zero breaks using the SupF test. The break dates are those identified by minimising the sum of squared errors conditional on the number of breaks found.

***, ** and * represent significance at the 1%, 5%, and 10% levels of significance respectively.

Figure 6 below displays the absolute log difference in the terms of trade and the means of the two periods selected by the Bai and Perron (1998) test. It is clear that volatility is significantly lower in the period after 1980. It also illustrates that there have been some periods when the volatility in the terms of trade has been significant. Specifically the period between the two World Wars looks to have been a period of significant volatility as well as more one-off periods like the early 1950s and mid-1970s. Another interesting observation is that although the period between 1900 and 1980 experienced higher volatility on average than the period after 1980, this appears to be a result of an increased number of one-off shocks rather than generalised volatility. Section 4.1.2 will go into the reasons why this is likely to have occurred.

Figure 6 – Goods Terms of Trade Volatility[13]
Source: Author’s calculation


  • [12]A similar observation was observed for Australia in the work by Gillizter and Kearns (2005) in that the volatility of its terms of trade has also reduced significantly. It would be interesting to see if this reduction in volatility is more of a world-wide phenomenon, but that is beyond the scope of this paper.
Page top