TAILIEUCHUNG - DYNAMIC HIGHER ORDER EXPECTATIONS

New Zealand’s university graduation rates were high by OECD standards in 2007. The Times Higher World University Ranking suggests that New Zealand ranks 19th out of 30 OECD countries in terms of where their top universities score – this being the University of Auckland in New Zealand’s case. New Zealand has a high number of science graduates (fourth in the OECD). The number of engineering graduates, however, is close to the bottom of the OECD (22nd in the OECD). At the secondary school level, the picture is mixed. While 15-year-olds perform well above average on reading, scientifi c, and mathematics. | DYNAMIC HIGHER ORDER EXPECTATIONS KRISTOFFER P. NIMARK Abstract. In models where privately informed agents interact agents may need to form higher order expectations . expectations of other agents expectations. This paper develops a tractable framework for solving and analyzing linear dynamic rational expectations models in which privately informed agents form higher order expectations. The framework is used to demonstrate that the well-known problem of the infinite regress of expectations identified by Townsend 1983 can be approximated to an arbitrary accuracy with a finite dimensional representation under quite general conditions. The paper is constructive and presents a fixed point algorithm for finding an accurate solution and provides weak conditions that ensure that a fixed point exists. To help intuition Singleton s 1987 asset pricing model with disparately informed traders is used as a vehicle for the paper. Keywords Dynamic Higher Order Expectations Private Information Asset Pricing 1. Introduction Many economic decisions involve predicting the actions of other agents. For instance hrms in oligopolistic markets may need to predict how much production capacity their competitors will invest in and traders in hnancial markets may need to predict how much other traders will be willing to pay for an asset at the next trading opportunity. In settings where all agents are identical and share the same information this becomes a trivial problem An individual agent can predict the behavior of other agents by introspection since all agents will choose the same action in equilibrium. The problem becomes more interesting if the common information assumption is relaxed because predicting the actions of others is then distinct from predicting ones own s actions. But since other agents face a symmetric problem in order to predict the behavior of agents that form expectations about the actions of others an individual agent needs to predict other agents expectations .

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