We propose testing for business cycle 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-steep. We illustrate with two and three-state MS models of US GNP growth, and with models of US output and employment. Our findings are compared with those obtained from standard non-parametric tests
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