²⁹One inconvenient aspect of the model as specified is that it does not exhibit a stationary distribution of idiosyncratic permanent noncapital income; the longer the economy lasts, the wider is the distribution. This problem can be remedied by assuming a constant probability of death, and replacing deceased households with newborns whose initial idiosyncratic permanent income matches the mean idiosyncratic permanent income of the population. For a fully worked-out general equilibrium version of such a model, see Carroll, Slacalek, and Tokuoka (2011).