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On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective

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  • Bennett T. McCallum

Abstract

Many macroeconomic models involving rational expect at ions give rise to an infinity of solution paths, even when the models are linear in all variables. Some writers have suggested that this non-uniqueness constitutes a serious weakness for the rational expectations hypothesis. One purpose of the present paper is to argue that the non-uniqueness in question is not properly attributable to the rationality hypothesis but, instead, is a general feature of dynamic models involving expectations. It is also argued that there typically exists, in a very wide class of linear rational expectations models, a single solution that excludes "bubble" or "bootstrap" effects -- ones that occur only because they are arbitrarily expected to occur. A systematic procedure for obtaining solutions free from such effects is introduced and discussed. In addition, this procedure is used to interpret and reconsider several prominent examples with solution multiplicities, including ones developed by Fischer Black and John B. Taylor.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 0684.

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Date of creation: Jun 1981
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Publication status: published as McCallum, Bennett T. "On Non-Uniqueness in Rational Expectations Models: An Attempt at Perspective." Journal of Monetary Economics, Vol. 11, No. 2, (March 1983) pp. 139-168.
Handle: RePEc:nbr:nberwo:0684

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  1. Hahn, Frank, 1969. "On Money and Growth," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 1(2), pages 172-87, May.
  2. Robert J. Shiller, 1975. "Rational Expectations and the Dynamic Structure of Macroeconomic Models:A Critical Review," NBER Working Papers 0093, National Bureau of Economic Research, Inc.
  3. Miguel Sidrauski, 1967. "Inflation and Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 75, pages 796.
  4. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  5. Flood, Robert P & Garber, Peter M, 1980. "Market Fundamentals versus Price-Level Bubbles: The First Tests," Journal of Political Economy, University of Chicago Press, vol. 88(4), pages 745-70, August.
  6. Black, Fischer, 1974. "Uniqueness of the price level in monetary growth models with rational expectations," Journal of Economic Theory, Elsevier, vol. 7(1), pages 53-65, January.
  7. Taylor, John B, 1977. "Conditions for Unique Solutions in Stochastic Macroeconomic Models with Rational Expectations," Econometrica, Econometric Society, vol. 45(6), pages 1377-85, September.
  8. Blanchard, Olivier J, 1979. "Backward and Forward Solutions for Economies with Rational Expectations," American Economic Review, American Economic Association, vol. 69(2), pages 114-18, May.
  9. Aoki, Masanao & Canzoneri, Matthew, 1979. "Reduced Forms of Rational Expectations Models," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 59-71, February.
  10. Sargent, Thomas J & Wallace, Neil, 1973. "The Stability of Models of Money and Growth with Perfect Foresight," Econometrica, Econometric Society, vol. 41(6), pages 1043-48, November.
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