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

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  • Aruoba, Boragan
  • Cuba-Borda, Pablo
  • Hilga-Flores, Kenji
  • Schorfheide, Frank
  • Villalvazo, Sergio

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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  • Aruoba, Boragan & Cuba-Borda, Pablo & Hilga-Flores, Kenji & Schorfheide, Frank & Villalvazo, Sergio, 2020. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," CEPR Discussion Papers 15388, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:15388
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    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. Ascari, Guido & Mavroeidis, Sophocles, 2022. "The unbearable lightness of equilibria in a low interest rate environment," Journal of Monetary Economics, Elsevier, vol. 127(C), pages 1-17.
    5. Harding, Martín & Lindé, Jesper & Trabandt, Mathias, 2022. "Resolving the missing deflation puzzle," Journal of Monetary Economics, Elsevier, vol. 126(C), pages 15-34.
    6. 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.
    7. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Modelling and Estimating Large Macroeconomic Shocks During the Pandemic," CREATES Research Papers 2021-08, Department of Economics and Business Economics, Aarhus University.
    8. 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.
    9. Guido Ascari & Sophocles Mavroeidis, 2020. "The unbearable lightness of equilibria in a low interest rate environment," Papers 2006.12966, arXiv.org, revised Dec 2021.
    10. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Identifying Economic Shocks in a Rare Disaster Environment," CEIS Research Paper 517, Tor Vergata University, CEIS, revised 19 Nov 2021.
    11. 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.
    12. Andras Fulop & Jeremy Heng & Junye Li, 2022. "Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models," Papers 2201.01094, arXiv.org.
    13. 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.

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    Keywords

    Bayesian estimation; Effective 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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