Existence Of Rational Expectations Equilibrium Research Articles

Rational expectations equilibria in a Ramsey model of optimal growth with non-local spatial externalities

This work provides a rigorous treatment concerning the formation of rational expectations equilibria in a general class of spatial economic models under the effect of externalities, using techniques from calculus of variations and optimal control. Using detailed estimates for a parametric optimisation problem, the existence of rational expectations equilibria is proved via a fixed-point theorem, and they are characterised in terms of a nonlocal Euler-Lagrange equation. The study of the individual optimisation problem, formulated according to Ramsey's model, is performed via a convex relaxation to the space of BV capital paths and measure-valued consumptions, and allows to obtain existence, uniqueness, regularity and stability properties for the optimisers in a rigorous and original way.

On Equilibrium Existence in a Finite-Agent, Multi-Asset Noisy Rational Expectations Economy

Abstract We introduce a novel method of proving existence of rational expectations equilibria (REE) in multi-dimensional CARA-Gaussian environments. Our approach is to construct a mapping from agents’ initial beliefs (which are characterized by a positive semidefinite matrix), to their updated beliefs, after reaching and observing equilibrium; we then show Brouwer’s fixed point theorem applies. We apply our approach to a finite-market version of Admati (1985), which is a multi-asset noisy REE asset pricing model with dispersed information. We present an algorithm to numerically solve for equilibrium of the finite model, as well as several examples illustrating the difference in equilibrium behavior between the finite and infinite models. Our method can be applied to any multi-dimensional REE model with Gaussian uncertainty and behavior that is linear in agents’ information.

Inflation Forecasts and Monetary Policy

Proposals for 'inflation targeting' as a strategy for monetary policy leave open the important operational question of how to determine whether current policies are consistent with the long-run inflation target. An interesting possibility is that the central bank might target current private-sector forecasts of inflation, either those made explicitly by professional forecasters or those implicit in asset prices. We address the issue of existence and uniqueness of rational expectations equilibria when the central bank uses private-sector forecasts as a guide to policy actions. In a dynamic model which incorporates both sluggish price adjustment and shocks to aggregate demand and aggregate supply, we show that strict targeting of inflation forecasts is typically inconsistent with the existence of rational expectations equilibrium, and that policies approximating strict inflation-forecast targeting are likely to have undesirable properties. We also show that economies with more general forecast-based policy rules are particularly susceptible to indeterminacy of rational expectations equilibria. We conclude that, although private-sector forecasts may contain information useful to the central bank, ultimately the monetary authorities must rely on an explicit structural model of the economy to guide their policy decisions.

On the generic existence of fully revealing price equilibria

In an asset trading model, the generic existence of rational expectations equilibrium established by Radner requires an assumption which is not shown to be generic. A regularity condition is imposed on the relative risk aversion of the utility function to eliminate the assumption.

The generic existence of rational expectations equilibrium in the higher dimensional case

The study of the generic existence of rational expectations equilibrium has concentrated on three cases, according to whether the space of “states of private information” has dimension less than, equal to, or greater than the price space. Previous results have shown that in the first case fully revealing equilibria exist generically and in the second case there are open sets of environments with no equilibrium. This paper shows that in the third case there is a residual set of environments which permits equilibria which are arbitrarily close to fully revealing.

On the existence of rational expectations equilibrium

We prove a theorem on the existence of rational expectations general economic equilibrium when agents condition on prices as well as on private information, and maximize the expectation of a state-dependent utility function. The key to the result is a new idealization of what it means for a set of empirical distributions to support agents' expectations. This idealization depends on the notion that agents compare their expectations with continuous versions of the random empirical distributions that are generated by the workings of the economy. The existence theorem covers all strictly concave utility functions, arbitrary distributions of the state variable, and situations in which the dimension of the state variable is large relative to the number of commodities.