Applying shape and phase restrictions in generalized dynamic categorical models of the business cycle

To match the NBER business cycle features it is necessary to employ Generalised dynamic categorical (GDC) models that impose certain phase restrictions and permit multiple indexes. Theory suggests additional shape restrictions in the form of monotonicity and boundedness of certain transition probabilities. Maximum likelihood and constraint weighted bootstrap estimators are developed to impose these restrictions. In the application these estimators generate improved estimates of how the probability of recession varies with the yield spread.