The volatility of Australian traded goods’ prices

Abstract

It is generally accepted that the Australian economy is continually subject to unanticipated shocks, particularly, unexpected swings in the prices of Australia's internationally- traded goods. This article empirically investigates the nature and extent of volatility in import and export prices faced by the Australian production sector. It estimates multivariate GARCH models of the stochastic processes generating the prices of imports and exports, and of important components of exports and imports. This article proposes an index of volatility, which is used to provide a summary measure of the extent of volatility in a multivariate context. The overall conclusion is that the price growth rates for Australia's traded goods exhibit considerable time variation in volatility and that these price growth rates are highly and positively correlated with each other.

Acknowledgements

A. Woodland gratefully acknowledges the Australian Research Council for financial support for this research and the exceptional research assistance provided by Ponnuthurai Ainkaran. We thank, without implicating, Andy Tremayne for valuable comments on a earlier draft of this article. The opinions expressed in this article should not be interpreted as representing the views of BIS Shrapnel.

Notes

¹ The export of agricultural and mineral resources has been the mainstay of Australia's economy for many years and continues to be a significant contributor to Gross Domestic Product (GDP). Commodities produced in these sectors generate about 60% of the value of total exports.

² Bollerslev et al. (1992) and Pagan (1996) provide surveys of numerous studies that implement GARCH models. An alternative to the GARCH model for modelling changing variance is stochastic volatility models. Kim et al. (1998) provides a comparison of stochastic volatility and GARCH models.

³ The effects of prices, incomes and exchange rate volatility upon Australia's trade flows were investigated by McKenzie (1998), but he did not model the volatility of traded goods prices themselves.

⁴ The original ARCH model proposed by Engle (1982) has been extended in a number of ways to dozens of ARCH- and GARCH-type models. Palm (1996) provides a survey of many types of GARCH models that collectively may be described as members of the extended GARCH family. The theoretical properties of these models are discussed in Bera and Higgins (1995).

⁵ Kroner and Ng (1998) discuss the relationship between several alternative multivariate models, including BEKK, and show that they can be derived from a more general specification. For a recent review of alternative multivariate GARCH models, see Bauwens et al. (2006).

⁶ This catalogue now supercedes Catalogue 6405 called ‘Export Price Index’ and Catalogue 6414 entitled ‘Import Price Index’.

⁷ The inclusion of the category of miscellaneous manufactures would further increase this percentage coverage to 94. However, to include it as a separate category would overtax the ability of the data to identify the parameters of the models to be estimated. It could have been aggregated with the other manufacturing category, since their price series are very highly correlated. Nevertheless, because of this, the expected gain in information would not be very large.

⁸ The model used to carry out the ADF test was a random walk model with a constant, drift and four lags. That is, .

⁹ That is, each conditional variance and covariance only depends upon its own value in the previous period (GARCH term) and upon the corresponding product of disturbances in the previous period (ARCH term). The restriction allows only N free parameters so that the coefficients for covariance terms are given in terms of coefficients for the variance terms.

¹⁰ This means that the variance for one price depends only on the past variance for that price and on the past disturbance for that price; it does not depend on the past variance for the other prices or the covariances or the past disturbances of other prices. This restriction does not imply that the covariances are zero, merely that the covariance matrix is more highly structured.

¹¹ These plots are available for interested readers.

¹² These parameter values were chosen after some experimentation to provide plots that were informative, meaning not very flat and not at the zero and unity extremes.

¹³ Our calculations and discussion have been in terms of the volatility of the prices. It is straightforward to apply our methodology to the price growth rates and, hence, to compute indices of the volatility of price growth rates.

¹⁴ For example, to obtain the expectation of p_i , choose k as the i-th unit vector with component i equal to 1 and 0 for every other component. To obtain the expectation E(p_ip_j ), choose k as the vector with components i and j both equal to 1 and 0 for every other component. To obtain the expectation E(p _i ²), choose k as the vector with component i equal to 2 and 0 for every other component. In this manner, all moments of the lognormal random vector p may be readily obtained by appropriate evaluation of the moment generating function for a multivariate normal variable.