Estimating dynamic equilibrium models using mixed frequency macro and financial data

We provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency, along with macro series at standard lower frequency. Our formulation of the macro-finance model in continuous time conveniently accounts for the difference in observation frequency. We suggest the use of martingale estimating functions (MEF) to infer the structural parameters of the model directly through a nonlinear scheme. This method is compared to regression-based methods and the generalized method of moments (GMM). We illustrate our approaches by estimating various versions of the AK-Vasicek model with mean-reverting interest rates. We provide asymptotic theory and Monte Carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of US macro and financial data.