Modelling Volatility Asymmetry of Business Cycles in the U.S

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.