Business Cycle Asymmetries: Characterisation and Testing based on Markov-Switching Autoregressions

We propose testing for business cycle first-moment asymmetries in Markov-switching autoregressive (MS-AR) models. We derive the parametric restrictions on MS-AR models that rule out types of asymmetries such as deepness, steepness, and sharpness, and set out a testing procedure based on Wald statistics which have standard asymptotics. For a two-regime model, such as that popularised by Hamilton (1989), we show that deepness implies sharpness (and vice versa) while the process is always non-step. We illustrated with two and three-state MS-AR models of US GNP growth, and models of US investment and consumption growth. Our findings are compared with those obtained from standard non-parametric tests, which are unable to distinguish between first-moment asymmetries and heteroscedasticity.