Subir Chattopadhyay

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agents equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agents consumption is bounded away from zero eventually, the other agents consumption is zero eventually--so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agents consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.

Optimality in stochastic OLG models: Theory for tests

We consider general OLG economies under uncertainty, with short maturity assets and with dividend paying assets of infinite maturity and fiat money, and study the optimality properties of equilibria with a sequence of asset markets that are sequentially complete. We provide necessary and sufficient conditions, in terms of asset prices and dividends, for equilibria to be conditionally Pareto optimal. These results provide a theoretical basis for empirical investigation.

The unit root property and optimality: a simple proof

Consider a pure exchange OLG economy under stationary Markov uncertainty with one good and with sequentially complete markets. It is known that an interior stationary equilibrium allocation at which the agents common matrix of intertemporal rates of substitution has a Perron root which is less than or equal to one is conditionally Pareto optimal. We provide a simple and direct proof of this fact.

The Cass criterion, the net dividend criterion, and optimality

Abel, Mankiw, Summers, and Zeckhauser [Assessing dynamic efficiency: theory and evidence, Rev. Econ. Stud. 56 (1989) 1-20] propose the net dividend criterion as an easy to use sufficient condition for optimality in general stochastic overlapping generations economies with production. We provide examples based on the criterion due to Cass [On capital overaccumulation in the aggregative neoclassical model of economic growth: a complete characterization, J. Econ. Theory 4 (1972) 200-223] and its extensions, the usual tools for such problems, to show that the net dividend criterion need not give the right answer. We identify the flaw in their proof. We also provide an alternative condition which, by an argument unrelated to theirs, is a sufficient condition for optimality when dividends are nonnegative and then argue that the condition is not innocuous since it cannot be verified in actual economies.

Pareto Optimal Improvements for Sunspots: The Golden Rule as a Target for Stabilization

SummaryThe stationary sunspot equilibria of a simple one good OLG economy are considered. These equilibria are known to be suboptimal. We show that, for any such equilibrium allocation, there always exists a Pareto optimal improvement which has the additional property of reaching the Golden Rule in finite time, i.e., the monetary steady state acts as a target. We also show that, in general, periodic allocations cannot be used as targets. The result is interpreted as a welfare theoretical justification for stabilization policy.

Sunpsots and cycles reconsidered1

Abstract We develop a sufficient condition for the existence of stationary sunspot equilibria in a one good OLG economy. This condition is of a global nature (unlike the usual local indeterminacy condition) and lets us prove existence even for independent sunspot processes. We use this result to show that the assumption that second period consumption is a normal good is essential to obtaining two of the results in Azariadis and Guesnerie [Azariadis and Guesnerie, 1986. Rev Economic Studies 53, 725–737], namely, that (a) whenever sunspot equilibria with two states of nature exist, cycles of period two also exist, and that (b) for a given economy, the set of matrices generating two state stationary sunspot equilibria is a connected set.

Contingent commodities and implementation

In this note we consider the problem whether contingent commodity allocations can be used when the states are not directly contractible. In such a setting a contingent commodity allocation takes the form of a social choice function, and the question is whether this function is implementable (in the sense of full implementation). Using only very mild assumptions on the rule for selecting contingent commodity allocations, we derive a strong negative result which also proves to be robust with respect to different solution concepts employed for implementation. These findings have interesting implications for the interpretation of Arrow-Debreu economies.

INFORMATION, STABILIZATION, AND WELFARE: THE CASE OF SUNSPOTS

The stationary sunspot equilibria of a simple OLG economy with heterogeneous agents areconsidered. These equilibria are known to be suboptimal. The focus of the paper is on the efficacy,based on welfare economic considerations and informational requirements, of government policy insuch an environment.The main result is that knowledge of (a) the sunspot equilibrium net trades, (b) weak interval typeinformation on two parameters, and (c) weak set type information on the location of some optimalstationary allocation, is sufficient to induce a competitive location of some optimal stationaryallocation, is sufficient to induce a competitive equilibrium which is a pareto optimal Paretoimprovement over the sunspot allocation which has the further property of reaching a Pareto optimalstationary allocation in finite time.The result are interpreted as demonstrating that in a simple model with a sunspot environment, policyis very effective and that welfare economic considerations lead to stabilization.