‘Infinite Higher-Order Beliefs and First-Order Beliefs: An Equivalence Result” by Zhen Huo
University of Amsterdam
In beauty-contest models with dispersed information, the rational-expectations equilibrium is a fixed point that involves agents' infinite higher-order beliefs about economic fundamentals. This paper shows that the equilibrium policy rule is equivalent to that of a pure forecasting problem that involves only first-order beliefs. This forecast is conditional on a modified information process which discounts the precision of idiosyncratic shocks by the degree of strategic complementarity. The result holds for any linear Gaussian signal process (static or persistent, stationary or non-stationary, exogenous or endogenous), and also extends to models in which agents choose multiple actions. Theoretically, this result provides a sharp characterization of the equilibrium; practically, it provides a straightforward method to solve models with complicated information structures. We use the result to establish general equilibrium properties and apply it to a number of environments with dynamic information.