Estimating and Identifying Vector Autoregressions Under Diagonality and Block Exogeneity Restrictions

I show how to estimate and identify a large-scale vector autoregression when the variables in a subset of the system are mutually independent after conditioning on a separate set of variables (diagonality), and when the conditioning variables are independent of the former subset (block exogeneity). Least squares estimation is efficient, and restrictions only on the set of common variables are sufficient to fully identify the economic structure. This approach will be most useful when using VARs to estimate the responses of a cross-section of variables, such as industry-level output or prices, to aggregate shocks.