Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to US Consumption and Income

Stylized facts show that the average growth rates of US per capita consumption and income differ in recession and expansion periods. Since a linear combination of such series does not have to be a constant mean process, standard cointegration analysis between the variables, to examine the permanent income hypothesis, may not be valid. To model the changing growth rates in both series, we introduce a multivariate Markov trend model, which allows for different growth rates in consumption and income during expansions and recessions. The deviations from the multivariate Markov trend are modelled by a vector autoregressive model. Bayes estimates of this model are obtained using Markov chain Monte Carlo methods. The empirical results suggest that there exist a cointegration relation between US per capita disposable income and consumption, after correction for a multivariate Markov trend.<BR><BR>