On trees and logs (Q1877165)

The authors critically examine the Lucas tree model (LT-model) in asset pricing theory extended to include heterogeneous agents and multiple goods. Dividend streams of the trees are specified in terms of a particular good; different trees pay out indifferent goods. Equilibrium implications of the LT-model are weighted against those of the benchmark real assets model (RA-model) in financial equilibrium theory. As a conclusion, the LT-model has certain embedded structure that makes it significantly different from the RA-model, and the goal of the paper is to highlight this structure and the implications it may lead to. In particular, specializing households' preferences to be additively separable (over time) as well log-linear, the authors show that for a large set of initial endowments, the LT-model, even with potentially complete financial markets, admits a peculiar financial equilibrium in which all stocks but one are redundant. Also it is investigated why the LT-model is so much at variance with RA-model, and new results are uncovered on uniqueness of financial equilibria. Portfolio constraints possible in LT-models but not in RA-model are discussed.