Before revision:  It is shown theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and relationships , unlike the current indirect effects formulations. The indirect requirements matrices for the US economy using aggregated input-output tables for multiple years are also presented and briefly analyzed.
After revision:  It is shown theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and relationships . The proposed requirements matrices for the US economy using aggregated input-output tables for multiple years are also presented and briefly analyzed.