Consumption with Heterogeneous Preferences and Heterogeneous Income Processes

Recent research on earnings dynamics reveals a great deal of heterogeneity in all parameters that govern underlying processes. In particular, there appears to be considerable heterogeneity in the trend, with some workers having a strong positive trend, and other having no trend, or, even a negative trend. Within the suggested framework and using income data, it is possible to decompose any change in earnings into a transitory component and a permanent component. What we cannot do as econometricians is to determine whether a particular change was anticipated or unanticipated by the worker. The latter requires a dynamic structural model of consumption, and, obviously, consumption data. Estimating a structural model of consumption with an underlying income process is now standard. The problem is incorporating all the heterogeneity in income processes and preference parameters in such estimation. This paper circumvents this problem. It is motivated by the observation that associated with every structural model of dynamic consumption and saving choice there is a distribution for the expectation errors. These serially uncorrelated surprises exhibit various higher order dynamics depending on the way in which underlying income and interest rate processes are modelled. In this paper, we initially investigate how different income processes proposed in the literature manifest themselves in the higher order behaviour of the expectation errors. For this, we use a standard life cycle model of consumption with CRRA utility function. We allow for a great deal of heterogeneity across agents in income process parameters and intertemporal allocation parameters. Our investigation of expectation errors under different scenarios reveals very interesting results. It is these results upon which we base our identification for our empirical work. In the second part of the paper, we estimate a joint distribution of the intertemporal allocation parameters by fitting a parametric distribution to expectation errors conditioned on observed income shocks.