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

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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 filter (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 filter, the COPF significantly 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 effects of the government spending portion of the American Recovery and Reinvestment Act in 2009 when interest rates reached the zero lower bound.

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  • S. Boragan Aruoba & Pablo A. Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2020. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," International Finance Discussion Papers 1272, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgif:1272
    DOI: 10.17016/IFDP.2020.1272
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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. Guido Ascari & Sophocles Mavroeidis, 2020. "The unbearable lightness of equilibria in a low interest rate environment," Papers 2006.12966, arXiv.org, revised Jul 2021.
    3. Daisuke Ikeda & Shangshang Li & Sophocles Mavroeidis & Francesco Zanetti, 2020. "Testing the effectiveness of unconventional monetary policy in Japan and the United States," Papers 2012.15158, arXiv.org, revised May 2021.
    4. 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.
    5. Sophocles Mavroeidis, 2021. "Identification at the Zero Lower Bound," Papers 2103.12779, arXiv.org, revised May 2021.
    6. 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).
    7. 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).
    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).

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    More about this item

    Keywords

    Bayesian estimation; Nonlinear filtering; Nonlinear solution methods; Particle MCMC; ZLB;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • E40 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - General
    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

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