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Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in Olg Models

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Listed:
  • Alexander Gorokhovsky

    (Dept. of Mathematics University of Colorado at Boulder)

  • Anna Rubinchik

    (Dept. of Economics; University of Haifa)

Abstract

We propose a criterion for determining whether a local policy analysis can be made in a given equilibrium in an overlapping generations model. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The equilibrium is not necessarily a steady state; for example, demographic and type composition of the population or individuals' endowments can change over time. However, asymptotically, the equilibrium should be stationary. The two limiting stationary paths at either end of the timeline do not have to be the same. If they are, conditions for local uniqueness are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. In addition, we illustrate our main result using a textbook model with a single physical good, a two-period life-cycle and a single type of consumer. In this model we show how to calculate a response to a policy change using the implicit function theorem.

Suggested Citation

  • Alexander Gorokhovsky & Anna Rubinchik, 2019. "Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in Olg Models," Cowles Foundation Discussion Papers 2179, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2179
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    References listed on IDEAS

    as
    1. Kehoe, Timothy J. & Levine, David K., 1984. "Regularity in overlapping generations exchange economies," Journal of Mathematical Economics, Elsevier, vol. 13(1), pages 69-93, April.
    2. Kehoe, Timothy J & Levine, David K, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Econometrica, Econometric Society, vol. 53(2), pages 433-453, March.
    3. Gale, David, 1973. "Pure exchange equilibrium of dynamic economic models," Journal of Economic Theory, Elsevier, vol. 6(1), pages 12-36, February.
    4. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66(6), pages 467-467.
    5. Shinichi Nishiyama & Kent Smetters, 2007. "Does Social Security Privatization Produce Efficiency Gains?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1677-1719.
    6. Chris Shannon & William R. Zame, 2002. "Quadratic Concavity and Determinacy of Equilibrium," Econometrica, Econometric Society, vol. 70(2), pages 631-662, March.
    7. Castro, Sofia B.S.D. & Dakhlia, Sami & Gothen, Peter B., 2010. "Direct perturbations of aggregate excess demand," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 562-571, July.
    8. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
    9. John Geanakoplos & Donald J. Brown, 1985. "Comparative Statics and Local Indeterminacy in OLG Economies: An Application of the Multiplicative Ergodic Theorem," Cowles Foundation Discussion Papers 773, Cowles Foundation for Research in Economics, Yale University.
    10. Mertens, Jean-François & Rubinchik, Anna, 2019. "Regularity And Stability Of Equilibria In An Overlapping Generations Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 699-729, March.
    11. Burke, Jonathan L., 1990. "A benchmark for comparative dynamics and determinacy in overlapping-generations economies," Journal of Economic Theory, Elsevier, vol. 52(2), pages 268-303, December.
    12. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    13. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    14. Sterk, Vincent & Tenreyro, Silvana, 2018. "The transmission of monetary policy through redistributions and durable purchases," Journal of Monetary Economics, Elsevier, vol. 99(C), pages 124-137.
    15. Araujo, A., 1988. "The non-existence of smooth demand in general banach spaces," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 309-319, September.
    16. 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.
    17. Geanakoplos, John D. & Polemarchakis, Heraklis M., 1991. "Overlapping generations," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 35, pages 1899-1960, Elsevier.
    18. Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.
    19. Muller, Walter III & Woodford, Michael, 1988. "Determinacy of equilibrium in stationary economies with both finite and infinite lived consumers," Journal of Economic Theory, Elsevier, vol. 46(2), pages 255-290, December.
    20. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    21. Balasko, Yves & Cass, David & Shell, Karl, 1980. "Existence of competitive equilibrium in a general overlapping-generations model," Journal of Economic Theory, Elsevier, vol. 23(3), pages 307-322, December.
    22. Krueger, Dirk & Ludwig, Alexander & Villalvazo, Sergio, 2021. "Optimal taxes on capital in the OLG model with uninsurable idiosyncratic income risk," Journal of Public Economics, Elsevier, vol. 201(C).
    23. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    24. Gorokhovsky, Alexander & Rubinchik, Anna, 2018. "Regularity of a general equilibrium in a model with infinite past and future," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 35-45.
    25. Santos, Manuel S. & Bona, Jerry L., 1989. "On the structure of the equilibrium price set of overlapping-generations economies," Journal of Mathematical Economics, Elsevier, vol. 18(3), pages 209-230, June.
    26. Mertens, Jean-François & Rubinchik, Anna, 2015. "Pareto Optimality Of The Golden Rule Equilibrium In An Overlapping Generations Model With Production And Transfers," Macroeconomic Dynamics, Cambridge University Press, vol. 19(8), pages 1780-1799, December.
    27. Debreu, Gerard, 1974. "Excess demand functions," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 15-21, March.
    28. S. Demichelis & H. Polemarchakis, 2007. "The determinacy of equilibrium in economies of overlapping generations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 461-475, September.
    29. Mas-Colell, Andreu & Zame, William R., 1991. "Equilibrium theory in infinite dimensional spaces," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 34, pages 1835-1898, Elsevier.
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    More about this item

    Keywords

    Overlapping generations; Implicit function theorem; Determinacy; Time-invariance; Comparative statics;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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