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In our Bayesian graphical VAR (BGVAR) model, the contemporaneous and temporal causal structures of the structural VAR model are represented by two different graphs. We also provide an efficient Markov chain Monte Carlo algorithm to estimate jointly the two causal structures and the parameters of the reduced\u2010form VAR model. The BGVAR approach is shown to be quite effective in dealing with model identification and selection in multivariate time series of moderate dimension, as those considered in the economic literature. In the macroeconomic application the BGVAR identifies the relevant structural relationships among 20 US economic variables, thus providing a useful tool for policy analysis. The financial application contributes to the recent econometric literature on financial interconnectedness. The BGVAR approach provides evidence of a strong unidirectional linkage from financial to non\u2010financial super\u2010sectors during the 2007\u20132009 financial crisis and a strong bidirectional linkage between the two sectors during the 2010\u20132013 European sovereign debt crisis. 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