Portfolio choice, life-cycle and idiosyncratic income risk : the semi-external habit formation approach

In line with Campbell and Cochrane (1999) and Gomes and Michaelides (2003), we study the implications of various types of habit formation in a further examination of some asset pricing puzzles. Precisely, we build an overlapping generations economy consisting of different types of agents characterized by their earning profiles, idiosyncratic earning risk and mortality. Agents, confronted with a liquidity constraint, decide on their consumption level as well as their portfolio allocation. We focus here on various forms of external habit, depending on the reference group, distinguishing three of them: pure macro external habit, external habit conditional on the occupational group and a semi external habit. The third type is the true counterpart of the external habit model with a representative agent in our economy populated by agents of different age, earnings and endogenous asset holdings. Thanks to the inclusion of a second state variable, we track each agent"s level of habit, yet making sure that he does not endogenize the impact of his current consumption choice on tomorrow"s level of habit. Our main guess is that the semi-external specification enables to obtain, extend and improve the previous results of external habit models in the heterogeneous agents model framework