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Trend-reverting fluctuations in the life-cycle model

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Aggregate time series provide evidence of short term dynamic adjustment that appears to be governed by complex or negative real eigenvalues. This finding is at odds with the predictions of reasonably parameterized, convex one-sector growth models with complete markets. We study life cycle economies in which aggregate saving depends non-trivially 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 non-monetary steady state via damped oscillations. We also discuss examples and extensions. ; Earlier title: Complex Eigenvalues and Trend-Reverting Fluctuations

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  • Costas Azariadis & James B. Bullard & Lee E. Ohanian, 2001. "Trend-reverting fluctuations in the life-cycle model," Working Papers 1998-015, Federal Reserve Bank of St. Louis.
  • Handle: RePEc:fip:fedlwp:1998-015
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    1. 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 655-673, September.
    2. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
    3. Taylor, John B, 1980. "Aggregate Dynamics and Staggered Contracts," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 1-23, February.
    4. José-Víctor Ríos-Rull, 1996. "Life-Cycle Economies and Aggregate Fluctuations," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 465-489.
    5. Azariadis, Costas & Smith, Bruce, 1998. "Financial Intermediation and Regime Switching in Business Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 516-536, June.
    6. Sims, Christopher A, 1980. "Comparison of Interwar and Postwar Business Cycles: Monetarism Reconsidered," American Economic Review, American Economic Association, vol. 70(2), pages 250-257, May.
    7. 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.
    8. Bruce D. Smith, 1991. "Interest on Reserves and Sunspot Equilibria: Friedman's Proposal Reconsidered," Review of Economic Studies, Oxford University Press, vol. 58(1), pages 93-105.
    9. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    10. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June.
    11. Woodford, Michael, 1994. "Monetary Policy and Price Level Determinacy in a Cash-in-Advance Economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 345-380.
    12. Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 381-399.
    13. Taylor, John B, 1979. "Estimation and Control of a Macroeconomic Model with Rational Expectations," Econometrica, Econometric Society, vol. 47(5), pages 1267-1286, September.
    14. Boyd, John H. & Smith, Bruce D., 1997. "Capital Market Imperfections, International Credit Markets, and Nonconvergence," Journal of Economic Theory, Elsevier, vol. 73(2), pages 335-364, April.
    15. Bruce D. Smith & John H. Boyd, 1998. "Capital market imperfections in a monetary growth model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 241-273.
    16. Huang, He & İmrohorogˇlu, Selahattin & Sargent, Thomas J., 1997. "Two Computations To Fund Social Security," Macroeconomic Dynamics, Cambridge University Press, vol. 1(1), pages 7-44, January.
    17. 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.
    18. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
    19. Boldrin, Michele & Montrucchio, Luigi, 1986. "On the indeterminacy of capital accumulation paths," Journal of Economic Theory, Elsevier, vol. 40(1), pages 26-39, October.
    20. 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.
    21. Valerie R. Bencivenga & Elisabeth Huybens & Bruce D. Smith, 2002. "What to stabilize in the open economy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1289-1307, November.
    22. 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 249-283, April.
    23. Michele Boldrin, 1988. "Paths of Optimal Accumulation in Two-Sector Models," UCLA Economics Working Papers 464, UCLA Department of Economics.
    24. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    25. Timothy J. Kehoe, 1985. "Multiplicity of Equilibria and Comparative Statics," The Quarterly Journal of Economics, Oxford University Press, vol. 100(1), pages 119-147.
    26. 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.
    27. 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.
    28. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    29. Smith, Bruce D, 1994. "Efficiency and Determinacy of Equilibrium under Inflation Targeting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 327-344.
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    2. Hippolyte d’Albis & Emmanuelle Augeraud-Véron & Marie Bessec, 2004. "Démographie et fluctuations économiques," Revue économique, Presses de Sciences-Po, vol. 55(3), pages 429-437.
    3. Raouf Boucekkine & David De la Croix & Omar Licandro, 2011. "Vintage Capital Growth Theory: Three Breakthroughs," Working Papers 565, Barcelona Graduate School of Economics.
    4. Xavier Fairise & Patrick Fève, 2006. "Labor adjustment costs and complex eigenvalues," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 95-110, September.
    5. Mitra, Kaushik & Evans, George W. & Honkapohja, Seppo, 2013. "Policy change and learning in the RBC model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(10), pages 1947-1971.
    6. Loumrhari, Ghizlan, 2016. "Vieillissement démographique et réforme paramétrique des retraites. Les enseignements d’un modèle EGC-GI pour le Maroc [Ageing and pension reform. A computational olg model for Morocco]," MPRA Paper 74077, University Library of Munich, Germany.
    7. D'ALBIS Hippolyte & AUGERAUD-VÉRON Emmanuelle, 2009. "Continuous-Time Overlapping Generations Models," LERNA Working Papers 09.15.291, LERNA, University of Toulouse.
    8. Brito, Paulo & Dilão, Rui, 2010. "Equilibrium price dynamics in an overlapping-generations exchange economy," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 343-355, May.
    9. de la Croix, David & Pierrard, Olivier & Sneessens, Henri R., 2013. "Aging and pensions in general equilibrium: Labor market imperfections matter," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 104-124.
    10. Hippolyte d'Albis & Emmanuelle Augeraud-véron, 2009. "Competitive Growth In A Life-Cycle Model: Existence And Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 459-484, May.
    11. Charles Ka Yui Leung & Nan‐Kuang Chen, 2010. "Stock Price Volatility, Negative Autocorrelation And The Consumption–Wealth Ratio: The Case Of Constant Fundamentals," Pacific Economic Review, Wiley Blackwell, vol. 15(2), pages 224-245, May.
    12. Orrego, Fabrizio, 2011. "Habit formation and sunspots in overlapping generations models," Working Papers 2011-013, Banco Central de Reserva del Perú.
    13. Nils-Petter Lagerlöf, 2006. "The Galor-Weil Model Revisited: A Quantitative Exercise," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(1), pages 116-142, January.
    14. Pedro Gomis-Porqueras & Solmaz Moslehi & Vivianne Vilar, 2013. "The Fiscal Theory of the Price Level When All Income is Taxed," Monash Economics Working Papers 09-13, Monash University, Department of Economics.
    15. Wilson, Matthew S., 2020. "A real business cycle model with money as a sunspot variable," Journal of Economics and Business, Elsevier, vol. 109(C).
    16. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    17. Erasmo Papagni, 2008. "The Long-run Effects of Household Liquidity Constraints and Taxation on Fertility, Education, Saving, and Growth," Discussion Papers 11_2008, D.E.S. (Department of Economic Studies), University of Naples "Parthenope", Italy.
    18. Peter Stemp & Ric Herbert, 2006. "Solving Non-Linear Models with Saddle-Path Instabilities," Computational Economics, Springer;Society for Computational Economics, vol. 28(2), pages 211-231, September.
    19. Jeremy Greenwood & Ananth Seshadri & Guillaume Vandenbroucke, 2002. "The baby boom and baby bust: some macroeconomics for population economics," Proceedings, Federal Reserve Bank of San Francisco, issue Nov.
    20. Costas Azariadis & Leo Kaas, 2007. "Is dynamic general equilibrium a theory of everything?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(1), pages 13-41, July.
    21. Fabrizio Orrego, 2014. "Habit formation and indeterminacy in overlapping generations models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 225-241, January.
    22. Etro, Federico, 2017. "Research in economics and macroeconomics," Research in Economics, Elsevier, vol. 71(3), pages 373-383.

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    Keywords

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