IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v151y2023ics0165188923000350.html
   My bibliography  Save this article

Analyzing Linear DSGE models: the Method of Undetermined Markov States

Author

Listed:
  • Roulleau-Pasdeloup, Jordan

Abstract

I show that a class of Linear DSGE models with one endogenous state variable can be represented as a three-state Markov chain. I develop a new analytical solution method based on this representation, which amounts to solving for a vector of Markov states and one transition probability. These two objects constitute sufficient statistics to compute in closed form objects that have routinely been computed numerically: impulse response function, cumulative sum, present discount value multiplier. I apply the method to a standard New Keynesian model that features optimal monetary policy with commitment.

Suggested Citation

  • Roulleau-Pasdeloup, Jordan, 2023. "Analyzing Linear DSGE models: the Method of Undetermined Markov States," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:dyncon:v:151:y:2023:i:c:s0165188923000350
    DOI: 10.1016/j.jedc.2023.104629
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188923000350
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2023.104629?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
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boppart, Timo & Krusell, Per & Mitman, Kurt, 2018. "Exploiting MIT shocks in heterogeneous-agent economies: the impulse response as a numerical derivative," Journal of Economic Dynamics and Control, Elsevier, vol. 89(C), pages 68-92.
    2. Francesco Bianchi & Leonardo Melosi, 2017. "Escaping the Great Recession," American Economic Review, American Economic Association, vol. 107(4), pages 1030-1058, April.
    3. Florin O. Bilbiie, 2019. "Optimal Forward Guidance," American Economic Journal: Macroeconomics, American Economic Association, vol. 11(4), pages 310-345, October.
    4. Hafedh Bouakez & Michel Guillard & Jordan Roulleau-Pasdeloup, 2017. "Public Investment, Time to Build, and the Zero Lower Bound," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 23, pages 60-79, January.
    5. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    6. Jordi Gali, 1999. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," American Economic Review, American Economic Association, vol. 89(1), pages 249-271, March.
    7. Justiniano, Alejandro & Primiceri, Giorgio E. & Tambalotti, Andrea, 2010. "Investment shocks and business cycles," Journal of Monetary Economics, Elsevier, vol. 57(2), pages 132-145, March.
    8. Jordi Gali, 2013. "Notes For A New Guide To Keynes (I): Wages, Aggregate Demand, And Employment," Journal of the European Economic Association, European Economic Association, vol. 11(5), pages 973-1003, October.
    9. Michael McLeay & Silvana Tenreyro, 2020. "Optimal Inflation and the Identification of the Phillips Curve," NBER Macroeconomics Annual, University of Chicago Press, vol. 34(1), pages 199-255.
    10. He Nie & Jordan Roulleau-Pasdeloup, 2023. "The promises (and perils) of control-contingent forward guidance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 49, pages 77-98, July.
    11. Harald Uhlig, 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper / Institute for Empirical Macroeconomics 101, Federal Reserve Bank of Minneapolis.
    12. Florin O. Bilbiie & Fabio Ghironi & Marc J. Melitz, 2012. "Endogenous Entry, Product Variety, and Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 120(2), pages 304-345.
    13. Adrien Auclert & Bence Bardóczy & Matthew Rognlie & Ludwig Straub, 2021. "Using the Sequence‐Space Jacobian to Solve and Estimate Heterogeneous‐Agent Models," Econometrica, Econometric Society, vol. 89(5), pages 2375-2408, September.
    14. Gauti Eggertsson & Bulat Gafarov & Saroj Bhatarai, 2014. "Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing," 2014 Meeting Papers 1292, Society for Economic Dynamics.
    15. Carlstrom, Charles T. & Fuerst, Timothy S. & Paustian, Matthias, 2015. "Inflation and output in New Keynesian models with a transient interest rate peg," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 230-243.
    16. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014, April.
    17. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    18. Robert B. Barsky & Christopher L. House & Miles S. Kimball, 2007. "Sticky-Price Models and Durable Goods," American Economic Review, American Economic Association, vol. 97(3), pages 984-998, June.
    19. Nakata, Taisuke & Schmidt, Sebastian, 2019. "Conservatism and liquidity traps," Journal of Monetary Economics, Elsevier, vol. 104(C), pages 37-47.
    20. Xavier Gabaix, 2020. "A Behavioral New Keynesian Model," American Economic Review, American Economic Association, vol. 110(8), pages 2271-2327, August.
    21. 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.
    22. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78-121.
    23. 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.
    24. Bilbiie, Florin O. & Känzig, Diego R. & Surico, Paolo, 2022. "Capital and income inequality: An aggregate-demand complementarity," Journal of Monetary Economics, Elsevier, vol. 126(C), pages 154-169.
    25. Ellen R. McGrattan, 2012. "Capital Taxation During the U.S. Great Depression," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1515-1550.
    26. Pascal Michaillat, 2012. "Do Matching Frictions Explain Unemployment? Not in Bad Times," American Economic Review, American Economic Association, vol. 102(4), pages 1721-1750, June.
    27. Gauti B. Eggertsson & Benjamin Pugsley, 2006. "The Mistake of 1937: A General Equilibrium Analysis," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 24(S1), pages 151-190, December.
    28. Florin O. Bilbiie, 2022. "Neo-Fisherian Policies and Liquidity Traps," American Economic Journal: Macroeconomics, American Economic Association, vol. 14(4), pages 378-403, October.
    29. Oliver Pfäuti & Fabian Seyrich, 2022. "A Behavioral Heterogeneous Agent New Keynesian Model," Discussion Papers of DIW Berlin 1995, DIW Berlin, German Institute for Economic Research.
    30. Karel R. S. M. Mertens & Morten O. Ravn, 2014. "Fiscal Policy in an Expectations-Driven Liquidity Trap," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(4), pages 1637-1667.
    31. 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.
    32. Christian K. Wolf, 2021. "Interest Rate Cuts vs. Stimulus Payments: An Equivalence Result," NBER Working Papers 29193, National Bureau of Economic Research, Inc.
    33. Michael Woodford, 2011. "Simple Analytics of the Government Expenditure Multiplier," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 1-35, January.
    34. Flodén, Martin, 2008. "A note on the accuracy of Markov-chain approximations to highly persistent AR(1) processes," Economics Letters, Elsevier, vol. 99(3), pages 516-520, June.
    35. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    36. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    37. Leeper, Eric M. & Walker, Todd B. & Yang, Shu-Chun S., 2010. "Government investment and fiscal stimulus," Journal of Monetary Economics, Elsevier, vol. 57(8), pages 1000-1012, November.
    38. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
    39. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
    40. Eric Sims & Jing Cynthia Wu & Ji Zhang, 2023. "The Four-Equation New Keynesian Model," The Review of Economics and Statistics, MIT Press, vol. 105(4), pages 931-947, July.
    41. Uhlig, H.F.H.V.S., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Other publications TiSEM cc1b2469-9d2f-445a-a2b3-1, Tilburg University, School of Economics and Management.
    42. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    43. 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.
    44. George-Marios Angeletos & Chen Lian, 2021. "Determinacy without the Taylor Principle," NBER Working Papers 28881, National Bureau of Economic Research, Inc.
    45. Tanaka, Ken’ichiro & Toda, Alexis Akira, 2013. "Discrete approximations of continuous distributions by maximum entropy," Economics Letters, Elsevier, vol. 118(3), pages 445-450.
    46. Gauti B. Eggertsson & Michael Woodford, 2003. "Optimal Monetary Policy in a Liquidity Trap," NBER Working Papers 9968, National Bureau of Economic Research, Inc.
    47. Bennett T. McCallum, 2002. "The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models," GSIA Working Papers 2003-25, Carnegie Mellon University, Tepper School of Business.
    48. Valerie A. Ramey & Sarah Zubairy, 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 850-901.
    49. Harald Uhlig, 2010. "Some Fiscal Calculus," American Economic Review, American Economic Association, vol. 100(2), pages 30-34, May.
    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. Gordon, Grey, 2021. "Efficient VAR discretization," Economics Letters, Elsevier, vol. 204(C).
    2. He Nie & Jordan Roulleau-Pasdeloup, 2023. "The promises (and perils) of control-contingent forward guidance," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 49, pages 77-98, July.
    3. Chunbing Cai & Jordan Roulleau-Pasdeloup, 2023. "Simple Analytics of the Government Investment Multiplier," Papers 2302.11212, arXiv.org, revised Sep 2023.
    4. Timothy S. Hills & Taisuke Nakata, 2018. "Fiscal Multipliers at the Zero Lower Bound: The Role of Policy Inertia," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 50(1), pages 155-172, February.
    5. Lemoine, Matthieu & Lindé, Jesper, 2023. "Fiscal stimulus in liquidity traps: Conventional or unconventional policies?," European Economic Review, Elsevier, vol. 151(C).
    6. 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.
    7. 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.
    8. Alisdair McKay & Christian K. Wolf, 2023. "What Can Time‐Series Regressions Tell Us About Policy Counterfactuals?," Econometrica, Econometric Society, vol. 91(5), pages 1695-1725, September.
    9. 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.
    10. Valerie A. Ramey, 2020. "The Macroeconomic Consequences of Infrastructure Investment," NBER Chapters, in: Economic Analysis and Infrastructure Investment, pages 219-268, National Bureau of Economic Research, Inc.
    11. Adrien Auclert & Ludwig Straub & Matthew Rognlie, 2019. "Micro Jumps, Macro Humps: monetary policy and business cycles in an estimated HANK model," 2019 Meeting Papers 1449, Society for Economic Dynamics.
    12. Alexis Akira Toda, 2021. "Data-Based Automatic Discretization of Nonparametric Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1217-1235, April.
    13. Florin O. Bilbiie, 2022. "Neo-Fisherian Policies and Liquidity Traps," American Economic Journal: Macroeconomics, American Economic Association, vol. 14(4), pages 378-403, October.
    14. Sims, Eric & Wolff, Jonathan, 2018. "The state-dependent effects of tax shocks," European Economic Review, Elsevier, vol. 107(C), pages 57-85.
    15. Gregory E. Givens, 2022. "Unemployment, Partial Insurance, And The Multiplier Effects Of Government Spending," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 571-599, May.
    16. Damba Lkhagvasuren & Erdenebat Bataa, 2023. "Finite-State Markov Chains with Flexible Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 611-644, February.
    17. Böhl, Gregor & Lieberknecht, Philipp, 2021. "The hockey stick Phillips curve and the effective lower bound," Discussion Papers 55/2021, Deutsche Bundesbank.
    18. Roulleau-Pasdeloup, Jordan, 2020. "Optimal monetary policy and determinacy under active/passive regimes," European Economic Review, Elsevier, vol. 130(C).
    19. Mr. Jiaqian Chen & Ms. Era Dabla-Norris & Carlos Goncalves & Zoltan Jakab & Jesper Lindé, 2023. "Can Fiscal Consolidation help Central Banks Fight Inflation?," IMF Working Papers 2023/260, International Monetary Fund.
    20. Julio Carrillo & Celine Poilly, 2013. "How do financial frictions affect the spending multiplier during a liquidity trap?," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 16(2), pages 296-311, April.

    More about this item

    Keywords

    Linear DSGE models; Markov chains; Impulse Response Functions;
    All these keywords.

    JEL classification:

    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

    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:eee:dyncon:v:151:y:2023:i:c:s0165188923000350. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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.