
Rich by Accident: the Second Welfare Theorem with a Redundant Asset Under Imperfect Foresight
Abstract
We consider a multiperiod (Tperiod) model with no uncertainty where short term bonds coexist with a long term bond. Markets are complete with just the short term bonds so that under the usual hypothesis of perfect foresight, the long term bond is redundant by no arbitrage in that it has no allocational implications. We dispense with perfect foresight, derive appropriate no arbitrage conditions and show that the presence of the long term bond has significant allocational implications. Specifically, in the model with just the short term bond, we show that a T dimensional subset of efficient allocations can arise as Walrasian equilibria whereas the dimension of efficient allocations is one less than the number of households (assumed to be much larger than T). In the model with the both types of bonds, essentially all efficient allocations might arise as Walrasian equilibria; minute errors in forecasting prices might generate all income transfers that are consistent with efficiency. We argue that the beneficiaries of such unanticipated income transfers are determined not by the superiority of forecasts but rather by accident.
Introduction
What allocational role might a redundant financial asset play in an intertemporal Walrasian setting? Traditional wisdom would suggest none, since by definition, a redundant financial asset can be replicated by trading other assets dynamically at market prices so that any trader is indifferent between holding it and ignoring it, and so its presence in no way alters the possibilities of income transfers across periods/states. But notice that this conclusion might not be valid if the market prices are not correctly anticipated. That is, this conclusion relies entirely on the feature that the axiom of perfect foresight is built into the particular equilibrium concept, Radner equilibrium, used in the analysis. We dispense with perfect foresight and show that essentially all intertemporally efficient allocations can arise as Walrasian equilibria when a redundant asset is traded.
WP048