The paper considers the use of directed acyclic graphs (DAGs), and their construction from observational data with PC-algorithm TETRAD II, in providing over-identifying restrictions on the innovations from a vector autoregression. Results from Sims’ 1986 model of the US economy are replicated and compared using these data-driven techniques. The directed graph results show Sims’ six-variable VAR is not rich enough to provide an unambiguous ordering at usual levels of statistical significance. A significance level in the neighborhood of 30 % is required to find a clear structural ordering. Although the DAG results are in agreement with Sims’ theory-based model for unemployment, differences are noted for the other five variables: income, money supply, price level, interest rates, and investment. Overall the DAG results are broadly consistent with a monetarist view with adaptive expectations and no hyperinflation.