Rationalizability of Rational Expectations Equilibria on Asset Markets with Asymmetric Information and Learning from Prices

This paper analyses conditions for rationalizability of rational expectations equilibria of asset market models with asymmetric information and learning from current prices. In such models, traders are asymmetrically informed about the liquidation value of an asset. However, they take into account that the actual asset price reveals other agents' private information and so each agent's asset demand will depend on the asset price not only for the usual reason but also because of the informational content of the asset price. Following Guesnerie (1992), the game-theoretical concept of rationalizability is used in order to asses whether such a rational expectations equilibrium can be justified as the result of a mental process of reasoning of the agents. A rational expectations equilibrium is said to be eductively stable or strongly rational, if it is the unique rationalizable solution of the model. Thus, this concept make use of the fact that the rational expectations equilibrium of the model might be represented as a Bayesian-Nash equilibrium of a specific game played by the agents. Hence, a rational expectations equilibrium is eductively stable, if there is only one consistent way of 'forecasting the forecasts of others'. Based on the well known asset market model of Grossman (1976), it is shown that the unique rational expectations equilibrium of this model is eductively stable only if additional restrictions are met. In particular, the asset price in the rational expectations equilibrium must not be too informative --- the informativeness of the equilibrium asset price has to be lower than an endogenously determined upper bound. As is shown, this stability condition requires in the end that the private signals are more informative regarding the unknown asset return than the asset price. The underlying problem is the well known problem of 'forecasting the forecasts of others' that is described by Keynes (1936) in his famous 'beauty contest' example: The extraction of information from the market price requires a precise idea of the other traders' behavior. If the asset price is not very informative, it is not quite important for the individual trader to anticipate correctly what the other firms believe and do. Therefore the rational expectations equilibrium is likely to be eductively stable in this case. Equivalent conditions are derived for a version of the model with a continuum of traders and also for a version with a finite number of traders, where following Kyle (1989), each agent takes into consideration that his decisions will affect the resulting asset price. In both models, the 'schizophrenia problem' described by Hellwig (1980) is not present. However, the condition for eductive stability remains the same: The rational expectations equilibria of these models are eductively stable only if equilibrium asset prices are not too informative.