# 3.2.2  Decomposing the volatility

It is of interest to assess the source of this volatility in the terms of trade. Gillitzer and Kearns (2005) suggest a way to decompose the variance of the terms of trade into the variance of export and import prices and their covariance. The log terms of trade, tott, is the difference between detrended log export and log import prices where and are log export and import prices respectively and dtis calculated by averaging the export and import prices and detrending using an HP filter as shown in (6). The purpose of this detrending is to remove common trends between export and import prices.

(6)

The variance of the terms of trade can therefore be decomposed as in (7). Using this method, the terms of trade is split into the periods 1900 to 1979 and 1980 to 2005 and the results are displayed in Table 9 below. The table also splits the series into 20 year periods to get a better appreciation of how the volatility and contributions to the volatility have changed over time.

(7)

Export price volatility made the larger contribution to terms of trade volatility in the period from 1900 to 1979 while import price volatility made the larger contribution in the period from 1980 to 2005. However, if the 20 year periods are examined in more detail, the results vary. For example, in the period between 1900 and 1920 import price volatility made a significantly larger contribution to total terms of trade volatility than export price volatility. This pattern was reversed for the periods 1921 to 1940 and 1941 to 1960 where export price volatility made a significantly larger contribution. Although the pattern was again reversed for the three periods after 1960, when import price volatility made the larger contribution. The volatility in the terms of trade was highest in the period 1921 to 1940 and only just higher than the period 1941 to 1960. However, this has reduced dramatically, with volatility in the 1981 to 2000 period approximately five times lower than the period 1921 to 1940.

Table 9 – Decomposing the Log Terms of Trade Variance
Export Component Import Component -2 x Covariance Component Terms of Trade Variance
Variance
1900-1920 0.006 0.020 -0.008 0.018
1921-1940 0.022 0.004 0.001 0.027
1941-1960 0.015 0.004 0.005 0.024
1961-1980 0.007 0.008 0.005 0.019
1981-2000 0.002 0.007 -0.004 0.005
2001-2005 0.009 0.012 -0.016 0.005
1900-1979 0.013 0.009 0.001 0.023
1980-2005 0.004 0.008 -0.005 0.007
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