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Rational Bubbles in Non-Linear Business Cycle Models: Closed and Open Economies

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  • Robert Kollmann

Abstract

This paper studies rational bubbles in non-linear dynamic general equilibrium models of the macroeconomy. The term ‘Rational bubble’ refers to multiple equilibria due to the absence of a transversality condition (TVC) for capital. The lack of TVC can be due to an OLG population structure. If a TVC is imposed, the macro models considered here have a unique solution. Bubbles reflect self-fulfilling fluctuations in agents’ expectations about future investment. In contrast to explosive rational bubbles in linearized models (Blanchard (1979)), the rational bubbles in non-linear models here are bounded. Bounded rational bubbles provide a novel perspective on the drivers and mechanisms of business cycles. I construct bubbles (in non-linear models) that feature recurrent boom-bust cycles characterized by persistent investment and output expansions which are followed by abrupt contractions in real activity. Both closed and open economies are analyzed. In a non-linear two-country model with integrated financial markets, bubbles must be perfectly correlated across countries. Global bubbles may, thus, help to explain the synchronization of international business cycles.

Suggested Citation

  • Robert Kollmann, 2020. "Rational Bubbles in Non-Linear Business Cycle Models: Closed and Open Economies," Working Papers ECARES 2020-02, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/301557
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    References listed on IDEAS

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    1. Kollmann, Robert, 1995. "Consumption, real exchange rates and the structure of international asset markets," Journal of International Money and Finance, Elsevier, vol. 14(2), pages 191-211, April.
    2. Backus, David K & Kehoe, Patrick J & Kydland, Finn E, 1994. "Dynamics of the Trade Balance and the Terms of Trade: The J-Curve?," American Economic Review, American Economic Association, vol. 84(1), pages 84-103, March.
    3. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448, Elsevier.
    4. Andrew B. Abel & N. Gregory Mankiw & Lawrence H. Summers & Richard J. Zeckhauser, 1989. "Assessing Dynamic Efficiency: Theory and Evidence," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 1-19.
    5. David K. Backus & Patrick J. Kehoe & Finn E. Kydland, 1992. "Dynamics of the trade balance and the terms of trade: the J-curve revisited," Discussion Paper / Institute for Empirical Macroeconomics 65, Federal Reserve Bank of Minneapolis.
    6. Alberto Martin & Jaume Ventura, 2018. "The Macroeconomics of Rational Bubbles: A User's Guide," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 505-539, August.
    7. Coeurdacier, Nicolas & Kollmann, Robert & Martin, Philippe, 2010. "International portfolios, capital accumulation and foreign assets dynamics," Journal of International Economics, Elsevier, vol. 80(1), pages 100-112, January.
    8. Kollmann, Robert & Kim, Jinill & Kim, Sunghyun H., 2011. "Solving the multi-country Real Business Cycle model using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 35(2), pages 203-206, February.
    9. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    10. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS
    11. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January.
    12. Olivier J. Blanchard & Mark W. Watson, 1982. "Bubbles, Rational Expectations and Financial Markets," NBER Working Papers 0945, National Bureau of Economic Research, Inc.
    13. Tom D. Holden, 2023. "Existence and Uniqueness of Solutions to Dynamic Models with Occasionally Binding Constraints," The Review of Economics and Statistics, MIT Press, vol. 105(6), pages 1481-1499, November.
    14. Kollmann, Robert, 1991. ""Essays on International Business Cycles", PhD thesis, Economics Department, University of Chicago, 1991," MPRA Paper 69905, University Library of Munich, Germany.
    15. Backus, David K. & Smith, Gregor W., 1993. "Consumption and real exchange rates in dynamic economies with non-traded goods," Journal of International Economics, Elsevier, vol. 35(3-4), pages 297-316, November.
    16. Philippe Bacchetta & Cédric Tille & Eric van Wincoop, 2012. "Self-Fulfilling Risk Panics," American Economic Review, American Economic Association, vol. 102(7), pages 3674-3700, December.
    17. King, Robert G. & Rebelo, Sergio T., 1999. "Resuscitating real business cycles," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 14, pages 927-1007, Elsevier.
    18. Holden, Tom D., 2016. "Existence, uniqueness and computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 127430, ZBW - Leibniz Information Centre for Economics.
    19. Guido Ascari & Paolo Bonomolo & Hedibert F. Lopes, 2019. "Walk on the Wild Side: Temporarily Unstable Paths and Multiplicative Sunspots," American Economic Review, American Economic Association, vol. 109(5), pages 1805-1842, May.
    20. Kollmann, Robert, 1996. "Incomplete asset markets and the cross-country consumption correlation puzzle," Journal of Economic Dynamics and Control, Elsevier, vol. 20(5), pages 945-961, May.
    21. Holden, Tom, 2016. "Computation of solutions to dynamic models with occasionally binding constraints," EconStor Preprints 130143, ZBW - Leibniz Information Centre for Economics.
    22. Olivier Jean Blanchard & Stanley Fischer, 1989. "Lectures on Macroeconomics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262022834, December.
    23. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    24. 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.
    25. J. B. Taylor & M. Woodford (ed.), 1999. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 1, number 1.
    26. 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.
    27. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
    28. Dellas, Harris, 1986. "A real model of the world business cycle," Journal of International Money and Finance, Elsevier, vol. 5(3), pages 381-394, September.
    29. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g7084aa4m is not listed on IDEAS
    30. Stracca, Livio, 2004. "Behavioral finance and asset prices: Where do we stand?," Journal of Economic Psychology, Elsevier, vol. 25(3), pages 373-405, June.
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    More about this item

    Keywords

    rational bubbles; boom-bust cycles; business cycles in closed and open economies; non-linear DSGE models; Long-Plosser model; Dellas model;
    All these keywords.

    JEL classification:

    • E1 - Macroeconomics and Monetary Economics - - General Aggregative Models
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • F3 - International Economics - - International Finance
    • F4 - International Economics - - Macroeconomic Aspects of International Trade and Finance
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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