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Most solved dynamic structural macrofinance models are non-linear and/ornon-Gaussian state-space models with high-dimensional and complex structures.We propose an annealed controlled sequential Monte Carlo method that deliversnumerically stable and low variance estimators of the likelihood function. Themethod relies on an annealing procedure to gradually introduce information fromobservations and constructs globally optimal proposal distributions by solvingassociated optimal control problems that yield zero variance likelihoodestimators. To perform parameter inference, we develop a new adaptive SMC$^2$algorithm that employs likelihood estimators from annealed controlledsequential Monte Carlo. We provide a theoretical stability analysis thatelucidates the advantages of our methodology and asymptotic results concerningthe consistency and convergence rates of our SMC$^2$ estimators. We illustratethe strengths of our proposed methodology by estimating two popularmacrofinance models: a non-linear new Keynesian dynamic stochastic generalequilibrium model and a non-linear non-Gaussian consumption-based long-run riskmodel.

Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models