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Information, trade and incomplete markets.

Article Excerpt
Abstract The no-trade result of Milgrom and Stokey, J Econ Theory 26:17-27 (1982), states that if rational traders begin with an ex-ante Pareto optimal allocation then the arrival of information cannot generate trade. This paper allows traders to trade before and after the arrival of information. If there are enough securities to hedge against all payoff relevant risk, then the preinformation-arrival allocation is Pareto optimal and information arrival has no effect. This no-retrade result is the competitive analog of the no-trade result of Milgrom and Stokey (1982). However, information generically generates trade when markets are state-contingent incomplete.

Keywords Trade * Incomplete markets * Risk sharing

JEL Classification Numbers D52 * D82

1 Introduction

A standard interpretation of the no-trade theorem in the fundamental paper by Milgrom and Stokey (1982) is that the arrival of new private information cannot generate trade between rational traders in an ongoing security market. The usual intuition offered for this theorem is as follows. Suppose that traders' initial security holdings are Pareto optimal and that some traders receive new information. If this new information generates trade then the trade must be for speculative purposes. But any trader who has not received the information would not want to trade as each such trader would know that he is being taken advantage of by the informed traders. (1)

This reasoning is game theoretic; it is not based on the decision making that is usually employed in competitive markets. Under some circumstances the no-trade result applies to rational expectations equilibrium, but the logic above does not apply. There are two reasons for this. First, to make the argument above carefully requires setting up a game and employing a game theoretic equilibrium concept. This requires knowledge assumptions that are irrelevant in competitive equilibrium analysis. In a competitive market no trader reasons about, or needs to reason about, the knowledge, payoffs or rationality of any other trader. In a rational expectations equilibrium every trader makes rational inferences about relevant information from market statistics. But this requires only rationality and knowledge of the equilibrium relationship; it does not require higher order knowledge assumptions. (2) Second, if one attempts to employ the reasoning above one typically does not get a rational expectations equilibrium even in settings in which traders might trade for risk sharing purposes as well as for speculation. Blume and Easley (1990) show that for a broad class of classical economies, there is no game whose Bayes Nash equilibrium is a rational expectations equilibrium unless stringent restrictions are placed on the distribution of information. These restrictions exclude economies in which informed traders can take advantage of uninformed traders.

Milgrom and Stokey (1982) also provide a non-game theoretic analysis in which they show that if beliefs satisfy a restriction, and if traders begin with a Pareto optimal allocation of state contingent consumptions, then the arrival of public information does not generate rational expectations equilibrium trade. Kreps (1977) provides a similar rational expectations equilibrium result as a No-Speculation theorem. Judd, Kubler, and Schmedders (2003) show in a Lucas asset pricing model with infinitely lived assets forming dynamically complete markets that the volume of trade is zero beyond the first period.

The reason that no trade occurs is that, under the belief restriction, the arrival of information preserves equality of marginal rates of substitution across traders. The allocations are assumed to be ex ante Pareto optimal, so consumers begin with a common marginal rate of substitution. Information arrival changes marginal rates of substitution, but since traders have a common interpretation of the signal, equality of marginal rates of substitution across traders is preserved and the original allocation remains an equilibrium allocation. Thus there is no trade even though beliefs have changed.

This result has two key assumptions: the Pareto optimality of the original allocation and the belief restriction. The Pareto optimality of the initial allocation is usually interpreted as arising from a previous round of trade on competitive markets. The first welfare theorem implies that if the markets are complete then any competitive equilibrium allocation will be Pareto optimal. So in an ongoing complete market, in which there are no new liquidity reasons for trade (no exogenous changes in endowments), the initial allocation at each trading date will be Pareto optimal. Numerous authors, including Milgrom and Stokey (1982), note that completeness of markets matters for this claim. We show that if markets are state-contingent incomplete, then for the generic economy the arrival of new information does generate trade. In this theorem we do not impose any restrictions on beliefs. Even if agents have common priors, the arrival of new information generically generates trade in state-contingent incomplete markets economies. This occurs because with incomplete markets the arrival of new information creates new insurance opportunities.

The belief restriction is that consumers share an understanding of the information generating process. In Bayesian terms a sufficient restriction is that they have a common likelihood function. In a standard statistical problem assuming a correct, and therefore common, likelihood function is natural. It is less natural in a consumer decision problem. Suppose one begins with consumers who have preferences over random consumptions defined on a state space consisting of the payoff relevant states and the signals. Then we typically derive a consumer's beliefs over the space of signals and states as well as his utility function from the expected utility theorem. This approach places no restrictions on beliefs. We show that without the belief restriction the arrival of new information generically generates trade even when consumers begin with a...

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