IDEAS home Printed from https://ideas.repec.org/p/fip/fedgfe/96642.html
   My bibliography  Save this paper

Finite-State Markov-Chain Approximations: A Hidden Markov Approach

Author

Listed:

Abstract

This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and transition probability matrix. The method can be used for multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made arbitrarily small if enough grid points are used. We compare our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find our method leads to more parsimonious discretizations and more accurate solutions, and the discretization matters for the welfare costs of risk, the marginal propensities to consume, and the amount of wealth inequality a life-cycle model can generate.

Suggested Citation

  • Eva F. Janssens & Sean McCrary, 2023. "Finite-State Markov-Chain Approximations: A Hidden Markov Approach," Finance and Economics Discussion Series 2023-040, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:96642
    DOI: 10.17016/FEDS.2023.040
    as

    Download full text from publisher

    File URL: https://www.federalreserve.gov/econres/feds/files/2023040pap.pdf
    File Function: Full text
    Download Restriction: no
    File URL: https://libkey.io/10.17016/FEDS.2023.040?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    2. Joseph Altonji & Disa Hynsjo & Ivan Vidangos, 2023. "Individual Earnings and Family Income: Dynamics and Distribution," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 49, pages 225-250, July.
    3. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, December.
    4. Galindev, Ragchaasuren & Lkhagvasuren, Damba, 2010. "Discretization of highly persistent correlated AR(1) shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1260-1276, July.
    5. Krueger, D. & Mitman, K. & Perri, F., 2016. "Macroeconomics and Household Heterogeneity," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 843-921, Elsevier.
    6. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    7. Chunzan Wu & Dirk Krueger, 2021. "Consumption Insurance against Wage Risk: Family Labor Supply and Optimal Progressive Income Taxation," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(1), pages 79-113, January.
    8. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    9. Duan, Jin-Chuan & Simonato, Jean-Guy, 2001. "American option pricing under GARCH by a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 25(11), pages 1689-1718, November.
    10. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    11. Nikolay Gospodinov & Damba Lkhagvasuren, 2014. "A Moment‐Matching Method For Approximating Vector Autoregressive Processes By Finite‐State Markov Chains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 843-859, August.
    12. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    13. Leland E. Farmer, 2021. "The discretization filter: A simple way to estimate nonlinear state space models," Quantitative Economics, Econometric Society, vol. 12(1), pages 41-76, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nikolay Gospodinov & Damba Lkhagvasuren, 2014. "A Moment‐Matching Method For Approximating Vector Autoregressive Processes By Finite‐State Markov Chains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 843-859, August.
    2. Rabitsch, Katrin & Stepanchuk, Serhiy & Tsyrennikov, Viktor, 2015. "International portfolios: A comparison of solution methods," Journal of International Economics, Elsevier, vol. 97(2), pages 404-422.
    3. Jordan Roulleau-Pasdeloup, 2022. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Papers 2209.05081, arXiv.org, revised Feb 2023.
    4. Karen Kopecky & Richard Suen, 2010. "Finite State Markov-chain Approximations to Highly Persistent Processes," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 13(3), pages 701-714, July.
    5. Daniel Harenberg & Alexander Ludwig, 2019. "Idiosyncratic Risk, Aggregate Risk, And The Welfare Effects Of Social Security," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 60(2), pages 661-692, May.
    6. Kuehn Lars-Alexander & Petrosky-Nadeau Nicolas & Zhang Lu, "undated". "An Equilibrium Asset Pricing Model with Labor Market Search," GSIA Working Papers 2010-E63, Carnegie Mellon University, Tepper School of Business.
    7. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    8. Leland E. Farmer, 2021. "The discretization filter: A simple way to estimate nonlinear state space models," Quantitative Economics, Econometric Society, vol. 12(1), pages 41-76, January.
    9. Laczó, Sarolta & Rossi, Raffaele, 2020. "Time-consistent consumption taxation," Journal of Monetary Economics, Elsevier, vol. 114(C), pages 194-220.
    10. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    11. Kal, Süleyman Hilmi & Arslaner, Ferhat & Arslaner, Nuran, 2015. "The dynamic relationship between stock, bond and foreign exchange markets," Economic Systems, Elsevier, vol. 39(4), pages 592-607.
    12. Gaia Garino & Lucio Sarno, 2004. "Speculative Bubbles in U.K. House Prices: Some New Evidence," Southern Economic Journal, John Wiley & Sons, vol. 70(4), pages 777-795, April.
    13. Dmitry Kulikov, 2012. "Testing for Rational Speculative Bubbles on the Estonian Stock Market," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 4(1).
    14. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    15. Maliar, Lilia & Maliar, Serguei & Tsener, Inna, 2022. "Capital-skill complementarity and inequality: Twenty years after," Economics Letters, Elsevier, vol. 220(C).
    16. Geert Bekaert & Eric C. Engstrom & Nancy R. Xu, 2022. "The Time Variation in Risk Appetite and Uncertainty," Management Science, INFORMS, vol. 68(6), pages 3975-4004, June.
    17. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    18. Sergei Koulayev & Marc Rysman & Scott Schuh & Joanna Stavins, 2016. "Explaining adoption and use of payment instruments by US consumers," RAND Journal of Economics, RAND Corporation, vol. 47(2), pages 293-325, May.
    19. Pami Dua & Divya Tuteja, 2015. "Global Recession and Eurozone Debt Crisis: Impact on Exports of China and India," Working Papers id:7386, eSocialSciences.
    20. Hanno Foerster, 2019. "The Impact of Post-Marital Maintenance on Dynamic Decisions and Welfare of Couples," Boston College Working Papers in Economics 982, Boston College Department of Economics.

    More about this item

    Keywords

    numerical methods; Kullback–Leibler divergence; misspecified model; earnings process;
    All these keywords.

    JEL classification:

    • 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
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:fip:fedgfe:96642. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ryan Wolfslayer ; Keisha Fournillier (email available below). General contact details of provider: https://edirc.repec.org/data/frbgvus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.