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 capitaconsumption and income differ in recession and expansion periods.Since a linear combination of such series does not have to be a constant meanprocess, standard cointegration analysis between the variables, toexamine the permanent income hypothesis, may not be valid. To model thechanging growth rates in both series, we introduce a multivariate Markov trendmodel, which allows for different growth rates in consumption and incomeduring expansions and recessions. The deviations from the multivariateMarkov trend are modelled by a vector autoregressive model. Bayes estimates ofthis model are obtained using Markov chain Monte Carlo methods. The empiricalresults suggest that there exist a cointegration relation between US percapita disposable income and consumption, after correction for amultivariate Markov trend.