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From Sunspots to Black Holes: Singular dynamics in macroeconomic models

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We present conditions for the emergence of singularities in DGE models. We distinguish between slow-fast and impasse singularity types, review geometrical methods to deal with both types of singularity and apply them to DGE dynamics. We find that impasse singularities can generate new types of DGE dynamics, in particular temporary determinacy/indeterminacy. We illustrate the different nature of the two types of singularities and apply our results to two simple models: the Benhabib and Farmer (1994) model and one with a cyclical fiscal policy rule.

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  • Brito, Paulo & Costa, Lu s F. & Dixon, Huw David, 2016. "From Sunspots to Black Holes: Singular dynamics in macroeconomic models," Cardiff Economics Working Papers E2016/6, Cardiff University, Cardiff Business School, Economics Section.
    • Handle: RePEc:cdf:wpaper:2016/6
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    1. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    2. Joseph E. Stiglitz, 2011. "Rethinking Macroeconomics: What Failed, And How To Repair It," Journal of the European Economic Association, European Economic Association, vol. 9(4), pages 591-645, August.
    3. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
    4. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
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    Cited by:

    1. Anton Bondarev, 2021. "Games Without Winners: Catching-up with Asymmetric Spillovers," Dynamic Games and Applications, Springer, vol. 11(4), pages 670-703, December.
    2. Abad, Nicolas & Lloyd-Braga, Teresa & Modesto, Leonor, 2020. "The failure of stabilization policy: Balanced-budget fiscal rules in the presence of incompressible public expenditures," Journal of Economic Dynamics and Control, Elsevier, vol. 120(C).
    3. Paulo Brito, 2017. "Government Debt, Fiscal Rules and Singular Growth Dynamics," Dynamic Modeling and Econometrics in Economics and Finance, in: Bettina Bökemeier & Alfred Greiner (ed.), Inequality and Finance in Macrodynamics, pages 43-74, Springer.

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    More about this item

    Keywords

    slow-fast singularities; impasse singularities; macroeconomic dynamics; temporary indeterminacy;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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