  Most solved dynamic structural macrofinance models are non-linear and/or
non-Gaussian state-space models with high-dimensional and complex structures.
We propose an annealed controlled sequential Monte Carlo method that delivers
numerically stable and low variance estimators of the likelihood function. The
method relies on an annealing procedure to gradually introduce information from
observations and constructs globally optimal proposal distributions by solving
associated optimal control problems that yield zero variance likelihood
estimators. To perform parameter inference, we develop a new adaptive SMC$^2$
algorithm that employs likelihood estimators from annealed controlled
sequential Monte Carlo. We provide a theoretical stability analysis that
elucidates the advantages of our methodology and asymptotic results concerning
the consistency and convergence rates of our SMC$^2$ estimators. We illustrate
the strengths of our proposed methodology by estimating two popular
macrofinance models: a non-linear new Keynesian dynamic stochastic general
equilibrium model and a non-linear non-Gaussian consumption-based long-run risk
model.
