On the effectiveness of sunspots in incomplete markets

Abstract

This note reexamines the conditions under which extrinsic uncertainty, or sunspots, may leave invariant the equilibrium allocations in general equilibrium models. Conventional wisdom, following the Philadelphia folk theorem of Shell [10], is that Pareto-optimality of equilibrium allocations (combined with risk aversion) is a necessary and sufficient condition for this property to hold in most general classes of models. Thus ineffectiveness of sunspots is typically associated with the case of complete markets, where the first welfare theorem holds, and not with incomplete markets, where equilibrium allocations are generically inefficient (as shown, e.g., in Geanakoplos and Polemarchakis [5]). Here however, we stress that it is not the Pareto-optimality property per se but the very question of insurability of sunspots that plays a crucial role in order to obtain an extended version of the "ineffectiveness theorem" of Cass and Shell [4]. Numerous papers have already demonstrated the significant influence of non-insurable sunspots, see notably Cass [3], Cass and Shell [4], Guesnerie and Laffont [7] and the papers recently appearing in the Mini-Symposium [8]. We take here the opposite viewpoint, that is, in a world with both intrinsic and extrinsic uncertainty we assume that agents can completely insure themselves against the extrinsic uncertainty while markets remain incomplete with respect to intrinsic uncertainty. Given the special decomposable structure of the equilibrium equations involved, it is then easy to extend the argument of Cass and Shell [4] to show that here again sunspots will not matter, although equilibrium allocations are typically inefficient. This paper can thus be seen to provide a robust counter-example to the Philadelphia folk theorem. Other known robust counter-examples are Benveniste and Cass [2] in the case of "segregated markets" and Goenka [6] in the case of