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 Gen- eralised dynamic categorical (GDC) models that impose certain phase re- strictions and permit multiple indexes. Theory suggests additional shape re- strictions in the form of monotonicity and boundedness of certain transitio… n probabilities. Maximum likelihood and constraint weighted bootstrap esti- mators 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.