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Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints

Author

Listed:
  • S. Boragan Aruoba

    (University of Maryland)

  • Pablo Cuba-Borda

    (Federal Reserve Board)

  • Kenji Higa-Flores

    (University of Maryland)

  • Frank Schorfheide

    (University of Pennsylvania CEPR, NBER, PIER)

  • Sergio Villalvazo

    (University of Pennsylvania)

Abstract

We develop an algorithm to construct approximate decision rules that are piecewise-linear and continuous for DSGE models with an occasionally binding constraint. The functional form of the decision rules allows us to derive a conditionally optimal particle ?lter (COPF) for the evaluation of the likelihood function that exploits the structure of the solution. We document the accuracy of the likelihood approximation and embed it into a particle Markov chain Monte Carlo algorithm to conduct Bayesian estimation. Compared with a standard bootstrap particle ?lter, the COPF signi?cantly reduces the persistence of the Markov chain, improves the accuracy of Monte Carlo approximations of posterior moments, and drastically speeds up computations. We use the techniques to estimate a small-scale DSGE model to assess the e?ects of the government spending portion of the American Recovery and Reinvestment Act in 2009 when interest rates reached the zero lower bound.

Suggested Citation

  • S. Boragan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2020. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," PIER Working Paper Archive 20-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:20-037
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    References listed on IDEAS

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    Cited by:

    1. Leonardo Melosi & Giorgio Primiceri & Andrea Tambalotti, 2021. "Introduction to the Special Issue in Memory of Alejandro Justiniano," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 1-3, July.
    2. Sophocles Mavroeidis, 2021. "Identification at the Zero Lower Bound," Econometrica, Econometric Society, vol. 89(6), pages 2855-2885, November.
    3. Enrique Mendoza & Sergio Villalvazo, 2020. "FiPIt: A Simple, Fast Global Method for Solving Models with Two Endogenous States & Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 37, pages 81-102, July.
    4. Daisuke Ikeda & Shangshang Li & Sophocles Mavroeidis & Francesco Zanetti, 2020. "Testing the Effectiveness of Unconventional Monetary Policy in Japan and the United States," IMES Discussion Paper Series 20-E-10, Institute for Monetary and Economic Studies, Bank of Japan.
    5. Sophocles Mavroeidis, 2021. "Identification at the Zero Lower Bound," Papers 2103.12779, arXiv.org, revised May 2021.
    6. Damioli, Giacomo & Gregori, Wildmer Daniel, 2021. "Diplomatic relations and cross-border investments in the European Union," Working Papers 2021-02, Joint Research Centre, European Commission (Ispra site).
    7. Guido Ascari & Sophocles Mavroeidis, 2020. "The unbearable lightness of equilibria in a low interest rate environment," Papers 2006.12966, arXiv.org, revised Nov 2021.
    8. Giovannini, Massimo & Pfeiffer, Philipp & Ratto, Marco, 2021. "Efficient and robust inference of models with occasionally binding constraints," Working Papers 2021-03, Joint Research Centre, European Commission (Ispra site).
    9. Calo, Silvia & Gregori, Wildmer Daniel & Petracco Giudici, Marco & Rancan, Michela, 2021. "Has the Comprehensive Assessment made the European financial system more resilient?," Working Papers 2021-08, Joint Research Centre, European Commission (Ispra site).

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    More about this item

    Keywords

    Bayesian Estimation; E?ective Lower Bound on Nominal Interest Rates; Nonlinear Filtering; Nonlinear Solution Methods; Particle MCMC;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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