On Trees and Logs

In this paper we contrast the main workhorse model in asset pricing theory, the Lucas (1978) tree model (LT-Model), to a benchmark model in financial equilibrium theory, the real assets model (RA-Model). It is commonly believed that the two models entail similar conclusions since the LT-Model is a special case of the RA-Model. But this is simply wrong: implications of these models can be strikingly at odds. Indeed, under the widely used log-linear specification of households' preferences, we show that for a large set of initial endowments the LT-Model - even with potentially complete financial markets - admits only peculiar financial equilibria in which the stock market is completely degenerate, in that all stocks offer the same investment opportunity - and yet, allocation is Pareto optimal. We investigate why the LT-Model is so much at variance with the RA-Model, and uncover new results on uniqueness of equilibria and portfolio constraints obtaining in the LT-Model, but not in the RA-Model.Keywords: Lucas tree model, equilibrium theory, peculiar financial equilibrium, nonuniqueness of equilibria, portfolio constraints