Estimation of continuous-time linear DSGE models from discrete-time measurements

We provide a general state space framework for estimation of the parameters of continuous-time linear DSGE models from data that are only available at discrete points in time. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, which allows avoiding discretization errors. Using the Kalman filter, we construct the exact likelihood for data sampled either as stocks or flows, and estimate frequency-invariant parameters by maximum likelihood. We address the aliasing problem arising in multivariate settings and provide conditions for precluding it, which is required for local identification of the parameters in the continuous-time economic model. We recover the unobserved structural shocks at measurement times from the reduced-form residuals in the state space representation by exploiting the underlying causal links imposed by the economic theory and the information content of the discrete-time observations. We illustrate our approach using an off-the-shelf real business cycle model. We conduct extensive Monte Carlo experiments to study the finite sample properties of the estimator based on the exact discrete-time representation, and show they are superior to those based on a naive Euler-Maruyama discretization of the economic model. Finally, we estimate the model using postwar U.S. macroeconomic data, and offer examples of applications of our approach, including historical shock decomposition at different frequencies, and estimation based on mixed-frequency data. JEL classification: C13, C32, C68, E13, E32, J22 Key words: DSGE models, continuous time, exact discrete-time representation, stock and flow variables, Kalman filter, maximum likelihood, aliasing, structural shocks