Rational Expectations Models with a Continuum of Convergent Solutions

49 Pages Posted: 11 Jul 2007 Last revised: 14 Aug 2010

See all articles by Michael L. Mussa

Michael L. Mussa

International Monetary Fund (IMF) - Research Department; National Bureau of Economic Research (NBER)

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Date Written: September 1984

Abstract

This paper examines five examples of rational expectations models with a continuum of convergent solutions and demonstrates serious difficulties in the economic interpretation of these solutions. The five examples are (1) a model of optimal capital accumulation with a negative rate of time preference, (2) Taylor's (1977) linear rational expectations model of macroeconomic equilibrium; (3) Calvo's (1984) model of contract setting and price dynamics; (4) Obstfeld's (1984) equilibrium model of monetary dynamics with individual optimizing agents; and (5) Calvo's (1978) life-cycle model of savings and asset valuation. In every case, when these models yield a continuum of convergent infinite horizon solutions, these solutions fail to exhibit economically appropriate, forward looking dependence of the endogenous variables on the paths of the exogenous forcing variab1es--a difficulty that does not arise under the circumstances where these models yield unique convergent infinite horizon solutions. Further, the three models that have natural finite horizon versions, either lack finite horizon solutions or have solutions that do not converge to any of the infinite horizon solutions. Again, this difficulty arises only under the circumstances where these models have a continuum of infinite horizon solutions.

Suggested Citation

Mussa, Michael L., Rational Expectations Models with a Continuum of Convergent Solutions (September 1984). NBER Working Paper No. t0041, Available at SSRN: https://ssrn.com/abstract=579738

Michael L. Mussa (Contact Author)

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