Modelling Volatility Asymmetry of Business Cycles in the US

Document Type

Conference Proceeding


Faculty of Business and Law


School of Accounting, Finance and Economics




Ho, K. Y., Tsui, A. K., & Zhang, Z. (2007). Modelling Volatility Asymmetry of Business Cycles in the US. In proceedings of MODSIM 2007 International Congress on Modelling and Simulation. Christchurch, New Zealand: Modelling and Simulation Society of Australia and New Zealand.


Most studies on the asymmetric and non-linear properties of US business cycles exclude the dimension of asymmetric conditional volatility. Engle (1982) proposes an autoregressive conditional heteroskedasticity (ARCH) model to capture the time-varying volatility of inflation rates in the United Kingdom. Weiss (1984) finds evidence of ARCH in the US industrial production. The ARCH model is then extended to generalized ARCH (GARCH) models by Bollerslev (1986) and exponential GARCH models by Nelson (1991). Recently Stock and Watson (2002) find that a substantial reduction in the variability of the US output growth since the early 1980s can be explained by a reduction in the variance of macroeconomic shocks. However, a few researchers have attempted to formally model asymmetries in the conditional variance of business-cycle variables (see Brunner 1992, Hamori 2000, and Ho and Tsui 2001, 2003 and 2004). All these studies are confined to univariate GARCH analysis. One major drawback of the univariate GARCH framework is that it does not capture the co-movement of business-cycle variables, nor analyze the empirical evidence of asymmetric volatilities in the context of multivariate GARCH approach. In this paper, we use the multivariate GARCH framework to investigate the evidence of asymmetric volatility and time-varying conditional correlations between sectors of the monthly US industrial production (IIP) indices in 1961-1997. We propose three new multivariate asymmetric GARCH models, which are developed based on a synthesis and improvement of the methodologies of Ding et al (1993), Sentana (1995) and Tse and Tsui (2002), including the VC-Quadratic GARCH (VC-QGARCH) model, VC-Leveraged GARCH (VC-LGARCH) model, and VC-Threshold GARCH (VC-TGARCH) model. Our proposed models are computationally manageable and are capable of capturing features of volatility asymmetry and the path of time-varying correlations. The issues of conditional heteroskedasticity and volatility asymmetry of business cycles are important because of their implications on macroeconomic and business cycle theory, measurement and forecasting. If business cycles are conditionally heteroskedastic and exhibit volatility asymmetry, then any theory assuming the absence of either of these properties is most likely inadequate. It is crucial to understand the potential macroeconomic policy implications of asymmetric volatility shocks for economies. If negative shocks induce greater future volatilities on IIP than positive shocks of the same magnitude, this might further vindicate the implementation of macroeconomic stabilisation measures by the government in times of recession. We use monthly data from the OECD website Source OECD: Main Economic Indicators for the 5 sectoral IIP of the US: the Consumer Good (CG), the Investment Good (IG), the Manufacturing (M), the Non-Durables (ND) and the Raw Materials (RM) with 444 observations. The results show that negative shocks have a greater impact on future volatilities than positive shocks of the same magnitude for the 5 sectoral IIP series in the U.S. Most parameter estimates of the time-varying conditional correlation coefficient equation are significant at the 5% level, indicating that dynamic correlations probably exist among the 5 main industrial groups/sectors. The estimates of the time-invariant component of the correlation coefficient equation, ρ, are significantly positive constant conditional correlations models, which is consistent with Lucas’ (1977) observation More importantly, the pattern of conditional correlations and the magnitude of ρ differ among the 10 sectoral pairs, ranging from a low of 0.2763 (IGND pair) to 0.7652 (M-RM pair) and 0.8363 (CGM pair). This is consistent with results from the VC-LGARCH model. The findings on asymmetric effects have policy implications for government to consider the effective countercyclical measures during recessions.