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BEA Input-Output Matrix Explorer

The U.S. industry direct-requirements matrix A from the Bureau of Economic Analysis (BEA) input–output accounts, 71 industries, 1997–2023. Explore its structure, its powers, its inverse, and how it changes over time — each angle reveals a different economic meaning for "matrix operations."

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Direct requirements matrix A

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What you're looking at. A[i,j] is the dollar value of industry i's output consumed by industry j per dollar of j's total output, after BEA's "redefinitions" that assign each industry a primary commodity. Column sums are bounded by 1: an industry can't spend more on intermediate inputs than it earns. The remainder is value added (compensation, taxes, profits).

Why this object matters. A²[i,j] is what industry i's suppliers need from industry j per dollar of i's output, summed over all suppliers. The geometric series I + A + A² + A³ + … sums all orders of indirect supply, and equals the Leontief inverse (I − A)⁻¹ when A's spectral radius is below 1 (which it always is here, because the value-added share is positive). That inverse, applied to a final-demand vector, is the textbook input-output multiplier model.

Data: BEA Input-Output Accounts, "Commodity-by-Industry Direct Requirements, After Redefinitions" at the summary level, 1997–2023 (released Sep 2024). At the summary level, after redefinitions, commodities and industries share the same 71-code list and each industry produces only its primary commodity — so BEA's CxI direct-requirements table is effectively the industry-by-industry direct-requirements (A) matrix used in the standard Leontief inverse. Detail-level tables require an explicit market-share step (D · B) to square them up; we don't need that here. Computed client-side from a 1.1 MB JSON blob with ml-matrix and D3.