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

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  • S. Borağan Aruoba
  • Pablo Cuba-Borda
  • Kenji Higa-Flores
  • Frank Schorfheide
  • Sergio Villalvazo

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. Borağan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2020. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," NBER Working Papers 27991, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:27991
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    4. Aruoba, S. Borağan & Mlikota, Marko & Schorfheide, Frank & Villalvazo, Sergio, 2022. "SVARs with occasionally-binding constraints," Journal of Econometrics, Elsevier, vol. 231(2), pages 477-499.
    5. 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.
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    7. Villalvazo, Sergio, 2024. "FDI flows and sudden stops in small open economies," Journal of Macroeconomics, Elsevier, vol. 79(C).
    8. 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.
    9. Harding, Martín & Lindé, Jesper & Trabandt, Mathias, 2022. "Resolving the missing deflation puzzle," Journal of Monetary Economics, Elsevier, vol. 126(C), pages 15-34.
    10. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano & Mertens, Elmar, 2023. "Shadow-rate VARs," Discussion Papers 14/2023, Deutsche Bundesbank.
    11. Ascari, Guido & Mavroeidis, Sophocles & McClung, Nigel, 2023. "Coherence without rationality at the zero lower bound," Journal of Economic Theory, Elsevier, vol. 214(C).
    12. 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.
    13. James A. Duffy & Sophocles Mavroeidis & Sam Wycherley, 2022. "Cointegration with Occasionally Binding Constraints," Papers 2211.09604, arXiv.org, revised Jul 2023.
    14. Boehl, Gregor & Strobel, Felix, 2024. "Estimation of DSGE models with the effective lower bound," Journal of Economic Dynamics and Control, Elsevier, vol. 158(C).
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    18. Luisa Corrado & Stefano Grassi & Aldo Paolillo, 2021. "Identifying Economic Shocks in a Rare Disaster Environment," CEIS Research Paper 517, Tor Vergata University, CEIS, revised 18 Jul 2024.
    19. 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.
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    22. 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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    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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