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Constructing Pure-Exchange Economies with Many Equilibria
We develop a restart algorithm based on Scarf’s (1973) algorithm for computing approximate Brouwer fixed points. We use the algorithm to compute all of the equilibria of a general equilibrium pure-exchange model with four consumers, four goods, and 15 equilibria. The mathematical result that motivates the algorithm is a fixed-point index theorem that provides a sufficient condition for uniqueness of equilibrium and a necessary condition for multiplicity of equilibria. Examining the structure of the model with 15 equilibria provides us with a method for constructing higher dimensional models ...
Report
The Incredible Taylor Principle
This paper discusses the extent to which the Taylor principle can solve the indeterminacy of equilibria in economies where the monetary authority follows an interest rate feedback rule. We first show that only the limiting behavior of the feedback rule matters, so identifying in the data if the Taylor principle holds cannot be achieved. Second, we show that the competitive equilibrium under interest rate feedback rules is nominally determined if the Taylor principle holds and, in addition, two ad-hoc restrictions on equilibrium are satisfied. These require equilibrium inflation to be bounded ...
Working Paper
The Incredible Taylor Principle
This note addresses the role of the Taylor principle to solve the indeterminacy of equilibria in economies in which the monetary authority follows an interest rate rule. We first study the role of imposing two additional ad-hoc restrictions on the definition of equilibrium. Imposing the equilibrium to be locally unique never delivers a unique outcome. Imposing the equilibrium to be bounded, renders the outcome unique only if the inflation target is the Friedman rule. Second, we show that the Taylor principle is strongly time inconsistent - in a sense we make very precise - and that policies ...