Economic data are collected at various frequencies but econometric
estimation typically uses the coarsest frequency. This article develops a Gibbs sampler for estimating vector autoregression (VAR) models with
mixed and irregularly sampled data. The Gibbs sampler allows efficient
likelihood inference and uses simple conjugate posteriors even in highdimensional parameter spaces, avoiding a non-Gaussian likelihood
surface even when the Kalman filter applies. Two examples studying
the relationship between financial data and the real economy illustrate
the methodology and demonstrates efficiency gains from the mixed
frequency estimator.