Consumption and wealth in the long run : an integrated unobserved component approach

The ratio of consumption to total household wealth (i.e., tangible assets plus unobserved human wealth) is commonly calculated from the estimation of a log-linear version of the household intertemporal budget constraint as a cointegrating relationship between consumption, assets and earnings (i.e., the variable "cay"). The evidence in favor of a stable cointegrating relationship between these variables in the US is weak however. This paper follows an alternative empirical approach using an unobserved component model applied to US data over the period 1951Q4-2016Q4. The regression of consumption on assets and earnings is augmented with an integrated unobserved component. The results strongly support the presence of such an integrated component in the consumption equation. The consumption-to-wealth ratio calculated from this model is much less persistent than the traditional "cay" variable. Its predictive ability for future excess stock returns - while diminished compared to that of the standard "cay" variable - is statistically and economically significant. We further show that - contrary to what has been suggested in the literature recently - the non-stationarity of the standard "cay" variable cannot be dealt with by allowing for regime shifts in its mean.