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Complex eigenvalues and trend-reverting fluctuations

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  • Costas Azariadis
  • James Bullard
  • Lee E. Ohanian

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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Bibliographic Info

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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Related research

Keywords: Time-series analysis ; Econometric models ; Regression analysis;

References

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  1. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June.
  2. Sims, Christopher A, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," American Economic Review, American Economic Association, vol. 70(2), pages 250-57, May.
  3. Blanchard, Olivier J, 1985. "Debt, Deficits, and Finite Horizons," Journal of Political Economy, University of Chicago Press, vol. 93(2), pages 223-47, April.
  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.
  5. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  6. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
  7. 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.
  8. Rios-Rull, Jose-Victor, 1996. "Life-Cycle Economies and Aggregate Fluctuations," Review of Economic Studies, Wiley Blackwell, vol. 63(3), pages 465-89, July.
  9. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Working Paper Series, Macroeconomic Issues 90, Federal Reserve Bank of Chicago.
  10. Kehoe, Timothy J, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, MIT Press, vol. 100(1), pages 119-47, February.
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  12. 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.
  13. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
  14. 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.
  15. 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.
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  18. 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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  20. 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.
  21. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  22. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
  23. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1993. "Labor Hoarding and the Business Cycle," NBER Working Papers 3556, National Bureau of Economic Research, Inc.
  24. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics.
  25. HUANG, HE & IMROHOROG[caron]LU, SELAHATTIN & SARGENT, THOMAS J., 1997. "Two Computations To Fund Social Security," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 7-44, January.
  26. repec:cup:macdyn:v:1:y:1997:i:1:p:7-44 is not listed on IDEAS
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Citations

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Cited by:
  1. Costas Azariadis & James Bullard & Bruce Smith, 2000. "Private and public circulating liabilities," Working Papers 2000-012, Federal Reserve Bank of St. Louis.
  2. Fairise, Xavier & Fève, Patrick, 2002. "Labor Adjustment Costs and Complex Eigenvalues," IDEI Working Papers 156, Institut d'Économie Industrielle (IDEI), Toulouse.
  3. James Bullard & Bruce D. Smith, 2001. "The value of inside and outside money," Working Papers 2000-027, Federal Reserve Bank of St. Louis.
  4. Colucci, Domenico, 2003. "Steady states in the OLG model with seignorage and long-lived agents," Research in Economics, Elsevier, vol. 57(4), pages 371-381, December.
  5. 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.
  6. Lucas, Deborah, 1999. "Price and interest rate dynamics induced by multiperiod contracts," The North American Journal of Economics and Finance, Elsevier, vol. 10(2), pages 315-338.

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