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Complex eigenvalues and trend-reverting fluctuations

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Author Info
Costas Azariadis
James Bullard
Lee E. Ohanian

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Abstract

Autoregressions of quarterly or annual aggregate time series provide evidence of trend-reverting output growth and of short-term dynamic adjustment that appears to be governed by complex eigenvalues. This finding is at odds with the predictions of reasonably parameterized, convex one-sector growth models, most of which have positive real characteristic roots. We study a class of one-sector economies, overlapping generations with finite life spans of L greater than or equal to 3, in which aggregate saving depends nontrivially on the distribution of wealth among cohorts. If consumption goods are weak gross substitutes near the steady state price vector, we prove that the unique equilibrium of a life cycle exchange economy converges to the unique steady state via damped oscillations. We also conjecture that this form of trend reversion extends to production economies with a relatively flat factor-price frontier, and we test this conjecture in several plausible parameterizations of 55-period life cycle economies.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Staff Report with number 255.

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Date of creation: 1998
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Handle: RePEc:fip:fedmsr:255

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Keywords: Time-series analysis Econometric models Regression analysis

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Rotemberg, Julio J & Woodford, Michael, 1996. "Real-Business-Cycle Models and the Forecastable Movements in Output, Hours, and Consumption," American Economic Review, American Economic Association, vol. 86(1), pages 71-89, March.
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  4. Basu, Susanto & Fernald, John G, 1997. "Returns to Scale in U.S. Production: Estimates and Implications," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 249-83, April.
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  5. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-47, April. [Downloadable!] (restricted)
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  6. Bernanke, Ben & Gertler, Mark, 1989. "Agency Costs, Net Worth, and Business Fluctuations," American Economic Review, American Economic Association, vol. 79(1), pages 14-31, March. [Downloadable!] (restricted)
  7. Kehoe, Timothy J. & Levine, David K. & Mas-Colell, Andreu & Woodford, Michael, 1991. "Gross substitutability in large-square economies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 1-25, June. [Downloadable!] (restricted)
  8. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 82(3), pages 430-50, June. [Downloadable!] (restricted)
  9. Burnside, Craig & Eichenbaum, Martin & Rebelo, Sergio, 1993. "Labor Hoarding and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 101(2), pages 245-73, April. [Downloadable!] (restricted)
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  10. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October. [Downloadable!] (restricted)
  11. Hansen, G D, 1993. "The Cyclical and Secular Behaviour of the Labour Input: Comparing Efficiency Units and Hours Worked," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 71-80, Jan.-Marc. [Downloadable!] (restricted)
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  12. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September. [Downloadable!] (restricted)
  13. Ramey, Garey & Watson, Joel, 1997. "Contractual Fragility, Job Destruction, and Business Cycles," The Quarterly Journal of Economics, MIT Press, vol. 112(3), pages 873-911, August.
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  14. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  15. Timothy Cogley & James M. Nason, 1993. "Output dynamics in real business cycle models," Working Papers in Applied Economic Theory 93-10, Federal Reserve Bank of San Francisco.
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  16. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-73, September. [Downloadable!] (restricted)
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  17. Christopher A. Sims, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," NBER Working Papers 0430, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  18. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October. [Downloadable!] (restricted)
  19. 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. [Downloadable!] (restricted)
  20. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Discussion Paper / Institute for Empirical Macroeconomics 24, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  21. Laitner, John, 1990. "Tax Changes and Phase Diagrams for an Overlapping Generations Model," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 193-220, February. [Downloadable!] (restricted)
  22. Rios-Rull, Jose-Victor, 1996. "Life-Cycle Economies and Aggregate Fluctuations," Review of Economic Studies, Blackwell Publishing, vol. 63(3), pages 465-89, July. [Downloadable!] (restricted)
  23. repec:cup:macdyn:v:1:y:1997:i:1:p:7-44 is not listed on IDEAS
  24. Gali, Jordi, 1996. "Multiple Equilibria in a Growth Model with Monopolistic Competition," Economic Theory, Springer, vol. 8(2), pages 251-66, August.
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  25. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June. [Downloadable!] (restricted)
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  26. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. James Bullard & Bruce D. Smith, 2001. "The value of inside and outside money: expanded version," Working Papers 2001-011, Federal Reserve Bank of St. Louis. [Downloadable!]
  2. James Bullard & Bruce D. Smith, 2001. "The value of inside and outside money," Working Papers 2000-027, Federal Reserve Bank of St. Louis. [Downloadable!]
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  3. FAIRISE, Xavier & FÈVE, Patrick, 2002. "Labor Adjustment Costs and Complex Eigenvalues," IDEI Working Papers 156, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
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  4. Costas Azariadis & James Bullard & Bruce Smith, 2000. "Private and public circulating liabilities," Working Papers 2000-012, Federal Reserve Bank of St. Louis. [Downloadable!]
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