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This paper uses several methods to study the interrelationship among Divisia monetary aggregates, prices, and income, allowing for nonstationary, nonlinearities, asymmetries, and time-varying relationships among the series. We propose a multivariate regime switching unobserved components model to obtain transitory and permanent components for each series, allowing for potential recurrent and structural changes in their dynamics. Each component follows distinct two-state Markov processes representing low or high phases. Since the lead-lag relationship between the phases can vary over time, rather than pre-imposing a structure to their linkages, the proposed flexible framework enables us to study their specific lead-lag relationship over each one of their cycles and over each U.S. recession in the last 40 years. The decomposition of the series into permanent and transitory components reveals striking results. First, we find a strong nonlinear association between the components of money and prices-all low phases of the transitory component of prices were preceded by tight transitory and permanent money phases. We also find that most recessions were preceded by tight money phases (its cyclical and permanent components) and high transitory price phases (with the exception of the 2001 and 2009-2010 recessions). In addition, all recessions were associated with a decrease in transitory and permanent income.

Nonlinear Relationship Between Permanent and Transitory Components of Monetary Aggregates and the Economy