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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

    (Stanford University)

  • Inna Tsener

Abstract

We study a class of infinite-horizon nonlinear dynamic economic models in which preferences, technology and laws of motion for exogenous variables can change over time either deterministically or stochastically, according to a Markov process with time-varying transition probabilities, or both. The studied models are nonstationary in the sense that the decision and value functions are time-dependent, and they cannot be generally solved by conventional solution methods. We introduce a quantitative framework, called extended function path (EFP), for calibrating, solving, simulating and estimating such models. We apply EFP to analyze a collection of challenging applications that do not admit stationary Markov equilibria, including growth models with anticipated parameters shifts and drifts, unbalanced growth under capital augmenting technological progress, anticipated regime switches, deterministically time-varying volatility and seasonal fluctuations. Also, we show an example of estimation and calibration of parameters in an unbalanced growth model using data on the U.S. economy. Examples of MATLAB code are provided.

Suggested Citation

  • Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2015. "A Tractable Framework for Analyzing a Class of Nonstationary Markov Models," Economics Working Papers 15105, Hoover Institution, Stanford University.
  • Handle: RePEc:hoo:wpaper:15105
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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. Yongyang Cai & Kenneth L. Judd, 2023. "A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems," Quantitative Economics, Econometric Society, vol. 14(2), pages 651-687, May.
    7. Christian vom Lehn & Thomas Winberry, 2022. "The Investment Network, Sectoral Comovement, and the Changing U.S. Business Cycle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 137(1), pages 387-433.
    8. 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.
    9. 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.
    10. Nicoletta Batini & Luigi Durand, 2024. "Accounting for Nature in Economic Models," Working Papers Central Bank of Chile 1014, Central Bank of Chile.
    11. 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.
    12. Taylor, John, 2018. "Taylor Rules and Forward Guidance: A Rule is not a Path," CEPR Discussion Papers 13383, C.E.P.R. Discussion Papers.
    13. Andrew Binning, 2022. "An Efficient Application of the Extended Path Algorithm in Matlab with Examples," Treasury Working Paper Series 22/02, New Zealand Treasury.
    14. 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.
    15. 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.
    16. Naubert, Christopher, 2019. "Monetary Policy and Redistribution: A Look under the Hatch with TANK," CEPR Discussion Papers 14159, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    nonstationary models; unbalanced growth; time varying transition probabilities; time varying parameters; anticipated shock; shooting method; parameter shift; parameter drift; regime switch; stochastic volatility; capital augmenting; seasonality; Fair and Taylor; extended path; Smolyak method;
    All these keywords.

    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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