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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 high-dimensional 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.