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Differentiable, Filter Free Bayesian Estimation of DSGE Models Using Mixture Density Networks

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  • Chris Naubert

Abstract

I develop a methodology for Bayesian estimation of globally solved, non-linear macroeconomic models. A novel feature of my method is the use of a mixture density network to approximate the distribution of initial states. I use the methodology to estimate a medium-scale, two-agent New Keynesian model with irreversible investment and a zero lower bound on nominal interest rates. Using simulated data, I show that the method is able to recover the “true” parameters when using the mixture density network approximation of the initial state distribution. This contrasts with the case when the initial states are set to their steady-state values.

Suggested Citation

  • Chris Naubert, 2025. "Differentiable, Filter Free Bayesian Estimation of DSGE Models Using Mixture Density Networks," Staff Working Papers 25-3, Bank of Canada.
    • Handle: RePEc:bca:bocawp:25-3
    DOI: 10.34989/swp-2025-3
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    References listed on IDEAS

    as
    1. Villemot, Sébastien, 2011. "Solving rational expectations models at first order: what Dynare does," Dynare Working Papers 2, CEPREMAP, revised Dec 2025.
    2. Bilbiie, Florin O., 2008. "Limited asset markets participation, monetary policy and (inverted) aggregate demand logic," Journal of Economic Theory, Elsevier, vol. 140(1), pages 162-196, May.
    3. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

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