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Parametric continuity of stationary distributions

Author

Listed:
  • John Stachurski

    () (CORE)

  • Cuong Le Van

    () (CERMSEM)

Abstract

The paper gives conditions under which stationary distributions of Markov models depend continuously on the parameters. It extends a well-known parametric continuity theorem for compact state space to the unbounded setting of standard econometrics and time series analysis. Applications to several theoretical and estimation problems are outlined.

Suggested Citation

  • John Stachurski & Cuong Le Van, 2004. "Parametric continuity of stationary distributions," Cahiers de la Maison des Sciences Economiques b04059, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b04059
    as

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    References listed on IDEAS

    as
    1. Mark Huggett, 2003. "When Are Comparative Dynamics Monotone?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(1), pages 1-11, January.
    2. Schenk Hopp , Klaus Reiner, 2002. "Is There A Golden Rule For The Stochastic Solow Growth Model?," Macroeconomic Dynamics, Cambridge University Press, vol. 6(04), pages 457-475, September.
    3. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-952, July.
    4. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    5. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Manuel S. Santos, 2006. "Convergence Properties of the Likelihood of Computed Dynamic Models," Econometrica, Econometric Society, vol. 74(1), pages 93-119, January.
    6. Mirman, Leonard J. & Morand, Olivier F. & Reffett, Kevin L., 2008. "A qualitative approach to Markovian equilibrium in infinite horizon economies with capital," Journal of Economic Theory, Elsevier, vol. 139(1), pages 75-98, March.
    7. Futia, Carl A, 1982. "Invariant Distributions and the Limiting Behavior of Markovian Economic Models," Econometrica, Econometric Society, vol. 50(2), pages 377-408, March.
    8. Manuel S. Santos & Adrian Peralta-Alva, 2005. "Accuracy of Simulations for Stochastic Dynamic Models," Econometrica, Econometric Society, vol. 73(6), pages 1939-1976, November.
    9. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, vol. 66(2), pages 409-426, March.
    10. Danthine, Jean-Pierre & Donaldson, John B, 1981. "Stochastic Properties of Fast vs. Slow Growing Economies," Econometrica, Econometric Society, vol. 49(4), pages 1007-1033, June.
    11. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    12. repec:cup:macdyn:v:6:y:2002:i:4:p:457-75 is not listed on IDEAS
    13. Ricard Torres, 1990. "Stochastic Dominance," Discussion Papers 905, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Citations

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    Cited by:

    1. Stephane Verani & Till Gross, 2012. "Financing constraints, firm dynamics, and international trade," Finance and Economics Discussion Series 2012-68, Board of Governors of the Federal Reserve System (U.S.).
    2. Stephane Verani, 2018. "Aggregate Consequences of Dynamic Credit Relationships," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 44-67, July.
    3. repec:eee:jetheo:v:173:y:2018:i:c:p:18-55 is not listed on IDEAS
    4. Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2008. "A foundation for the solution of consumption-saving behavior with a borrowing constraint and unbounded marginal utility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 695-708, March.
    5. Moritz Kuhn, 2013. "Recursive Equilibria In An Aiyagari‐Style Economy With Permanent Income Shocks," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54, pages 807-835, August.
    6. Stephane Verani, 2018. "Aggregate Consequences of Dynamic Credit Relationships," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 29, pages 44-67, July.
    7. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.

    More about this item

    Keywords

    Stationary distribution; parametric continuity; Markov process; Solow-Phelps golden rule; Foias operator; V norm-like function; Feller property;

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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