Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation

David Childers, Jesus Fernandez-Villaverde, Jesse Perla, Christopher Rackauckas and Peifan Wu

No 30573, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: We propose a methodology to take dynamic stochastic general equilibrium (DSGE) models to the data based on the combination of differentiable state-space models and the Hamiltonian Monte Carlo (HMC) sampler. First, we introduce a method for implicit automatic differentiation of perturbation solutions of DSGE models with respect to the model's parameters. We can use the resulting output for various tasks requiring gradients, such as building an HMC sampler, to estimate first- and second-order approximations of DSGE models. The availability of derivatives also enables a general filter-free method to estimate nonlinear, non-Gaussian DSGE models by sampling the joint likelihood of parameters and latent states. We show that the gradient-based joint likelihood sampling approach is superior in efficiency and robustness to standard Metropolis-Hastings samplers by estimating a canonical real business cycle model, a real small open economy model, and a medium-scale New Keynesian DSGE model.

JEL-codes: C01 C10 C11 E0 (search for similar items in EconPapers)
Date: 2022-10
New Economics Papers: this item is included in nep-dge, nep-ecm and nep-ets
Note: EFG
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Citations: View citations in EconPapers (3)

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Working Paper: Differentiable State-Space Models and Hamiltonian Monte Carlo Estimation (2022)
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