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Rational Expectations Models with a Continuum of Convergent Solutions

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  • Michael Mussa

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.

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  • Michael Mussa, 1984. "Rational Expectations Models with a Continuum of Convergent Solutions," NBER Technical Working Papers 0041, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberte:0041
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    1. Obstfeld, Maurice, 1984. "Multiple Stable Equilibria in an Optimizing Perfect-Foresight Model," Econometrica, Econometric Society, vol. 52(1), pages 223-228, January.
    2. John Kareken & Neil Wallace, 1981. "On the Indeterminacy of Equilibrium Exchange Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 96(2), pages 207-222.
    3. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    4. Calvo, Guillermo A., 1978. "On the indeterminacy of interest rates and wages with perfect foresight," Journal of Economic Theory, Elsevier, vol. 19(2), pages 321-337, December.
    5. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    6. Taylor, John B, 1977. "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica, Econometric Society, vol. 45(6), pages 1377-1385, September.
    7. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, vol. 52(3), pages 665-680, May.
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    Cited by:

    1. Behzad T. Diba & Herschel I. Grossman, 1985. "The Impossibility of Rational Bubbles," NBER Working Papers 1615, National Bureau of Economic Research, Inc.
    2. Qin Xiao & Gee Kwang Randolph Tan, 2007. "Signal Extraction with Kalman Filter: A Study of the Hong Kong Property Price Bubbles," Urban Studies, Urban Studies Journal Limited, vol. 44(4), pages 865-888, April.
    3. Qin Xiao & Yunhua Liu, 2010. "The residential market of Hong Kong: rational or irrational?," Applied Economics, Taylor & Francis Journals, vol. 42(7), pages 923-933.
    4. Behzad T. Diba & Herschel I. Grossman, 1986. "On the Inception of Rational Bubbles in Stock Prices," NBER Working Papers 1990, National Bureau of Economic Research, Inc.

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