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 discrete-time data. Our approach relies on the exact discrete-time representation of the equilibrium dynamics, hence avoiding discretization errors. We construct the exact likelihood for data sampled either as stocks or flows, based on the Kalman filter, and provide necessary and sufficient conditions for local identification of the frequency-invariant structural parameters of the underlying continuous-time 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 implied by the economic model. We illustrate our approach using an off-the-shelf real business cycle model. Extensive Monte Carlo experiments show that the finite sample properties of our estimator are superior to those of an estimator relying on a naive Euler–Maruyama discretization of the economic model. In an application to postwar U.S. macroeconomic data, we estimate the model using series sampled at mixed frequencies, and combinations of series sampled as stocks and flows, and we provide a historical decomposition of the effects of shocks on observables into those stemming from structural supply and demand shocks.