Modeling the conditional volatility asymmetry of business cycles in four OECD countries: A multivariate GARCH approach

Abstract

There are many studies on the business cycle indicators in the past decades, but mostly focusing on the asymmetric and non-linear features of business cycles incorporated into the conditional mean equation rather than the conditional variance formulation. Recently, the hypothesis of volatility asymmetry in business cycle indicators has been re-examined by, for instance, Ho and Tsui (2003 and 2004) using univariate asymmetric power ARCH (APARCH) and EGARCH models. However, the main drawback of univariate GARCH analysis is that it fails to capture the co-movement of macroeconomic variables. These co-movement relationships are important issues emphasised by the business cycle researchers, yet not much work has been done on formally modelling co-movements of asymmetric conditional volatilities in the context of multivariate GARCH setting. Our study extends the constant conditional correlation framework proposed by Bollerslev (1990) and the time-varying conditional correlation approach by Tse and Tsui (2002). We propose three new bivariate asymmetric GARCH models to accommodate the individual conditional heteroskedastic effects and the possibly varying conditional correlation relationships of asymmetric volatilities of the business cycles indicators in the selected OECD countries including Canada, Italy, the UK and the US. Using indices of industrial production as proxies for business cycles indicators, we detect statistically significant evidence of asymmetric conditional volatility in the UK and US. Additionally, we find that the conditional correlations are significantly time-varying, and that the strength of varying correlations may be linked to the degree of economic integration between the countries. These findings have the following implications: • if business cycles are conditionally heteroskedastic and exhibit volatility asymmetry, then any theory without such properties is inadequate. • the GARCH structure is consistent with the hypothesis of rational expectations in macroeconomics as rational economic agents make decisions based on all available information (see Hong and Lee, 2001 for details). • since movements in the financial markets are inextricably linked to the overall health of the economy, adequate accommodation of macroeconomic uncertainty such as conditional volatilities of business cycles would help researchers understand more about the causes of changes in financial market volatilities, and • it is vital to understand the domestic macroeconomic policy implications of asymmetric volatility and the corresponding policy co-ordinations among major international trading partners.