Many recent papers have tried to identify behavioral disturbances in vector autoregressions (VAR's) by imposing restrictions on the long-run effects of shocks. This paper argues that this approach will support reliable structured inferences only if the underlying economy satisfies strong restrictions. Absent restrictions linking long-run and short-run dynamics, every decomposition of a VAR is essentially equally consistent with any long-run restriction. Further, dynamic common factor restrictions must hold if the scheme is to work properly in small models estimated using time-aggregated data. The paper illustrates possible consequences of failure of these assumptions using bivariate models to identify aggregate supply and demand disturbances.