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A tractable framework for analyzing a class of nonstationary Markov models

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  • Lilia Maliar
  • Serguei Maliar
  • John B. Taylor
  • Inna Tsener

Abstract

We consider a class of infinite‐horizon dynamic Markov economic models in which the parameters of utility function, production function, and transition equations change over time. In such models, the optimal value and decision functions are time‐inhomogeneous: they depend not only on state but also on time. We propose a quantitative framework, called extended function path (EFP), for calibrating, solving, simulating, and estimating such nonstationary Markov models. The EFP framework relies on the turnpike theorem which implies that the finite‐horizon solutions asymptotically converge to the infinite‐horizon solutions if the time horizon is sufficiently large. The EFP applications include unbalanced stochastic growth models, the entry into and exit from a monetary union, information news, anticipated policy regime switches, deterministic seasonals, among others. Examples of MATLAB code are provided.

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  • Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
  • Handle: RePEc:wly:quante:v:11:y:2020:i:4:p:1289-1323
    DOI: 10.3982/QE1360
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    2. Sposi, Michael, 2022. "Demographics and the evolution of global imbalances," Journal of Monetary Economics, Elsevier, vol. 126(C), pages 1-14.
    3. Arellano, Cristina & Maliar, Lilia & Maliar, Serguei & Tsyrennikov, Viktor, 2016. "Envelope condition method with an application to default risk models," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 436-459.
    4. Martin Seneca, 2020. "Risk Shocks and Monetary Policy in the New Normal," International Journal of Central Banking, International Journal of Central Banking, vol. 16(6), pages 185-232, December.
    5. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    6. Christian vom Lehn & Thomas Winberry, 2022. "The Investment Network, Sectoral Comovement, and the Changing U.S. Business Cycle," The Quarterly Journal of Economics, Oxford University Press, vol. 137(1), pages 387-433.
    7. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    8. Lilia Maliar & John B. Taylor, 2019. "Forward Guidance: Is It Useful Away from the Lower Bound?," NBER Working Papers 26053, National Bureau of Economic Research, Inc.
    9. Ernst, Ekkehard & Semmler, Willi & Haider, Alexander, 2017. "Debt-deflation, financial market stress and regime change – Evidence from Europe using MRVAR," Journal of Economic Dynamics and Control, Elsevier, vol. 81(C), pages 115-139.
    10. Maliar, Lilia & Taylor, John B., 2018. "Forward Guidance: Is It Useful After the Crisis?," CEPR Discussion Papers 13383, C.E.P.R. Discussion Papers.
    11. Andrew Binning, 2022. "An Efficient Application of the Extended Path Algorithm in Matlab with Examples," Treasury Working Paper Series 22/02, New Zealand Treasury.
    12. Lilia Maliar & Serguei Maliar, 2016. "Ruling Out Multiplicity of Smooth Equilibria in Dynamic Games: A Hyperbolic Discounting Example," Dynamic Games and Applications, Springer, vol. 6(2), pages 243-261, June.
    13. vom Lehn, Christian, 2020. "Labor market polarization, the decline of routine work, and technological change: A quantitative analysis," Journal of Monetary Economics, Elsevier, vol. 110(C), pages 62-80.
    14. Maliar, Lilia & Naubert, Christopher, 2019. "TANK Models with Amplification and no Puzzles: the Magic of Output Stabilization and Capital," CEPR Discussion Papers 14159, C.E.P.R. Discussion Papers.

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    9. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    10. Maliar, Lilia & Maliar, Serguei & Winant, Pablo, 2021. "Deep learning for solving dynamic economic models," Journal of Monetary Economics, Elsevier, vol. 122(C), pages 76-101.
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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy

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