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Analyzing Linear DSGE models: the Method of Undetermined Markov States

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  • 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
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    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

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