Production Network Risk

Real input-output economics, in the tradition of Acemoglu, Carvalho, Ozdaglar & Tahbaz-Salehi’s “The Network Origins of Aggregate Fluctuations”: the OECD’s real Inter-Country Input-Output tables, USA domestic block, 45 real industries, year 2020, chosen because 2020 is the year specific sectors took the sharpest real demand shock in decades, giving the shock-propagation exercise below a genuine event to model.

The Leontief inverse: total requirements, not just direct

L = (I-A)⁻¹: how much total output sector $i$ must produce to deliver one extra dollar of final demand for sector $j$ (direct effects plus every indirect round):

MATRIX A = [[0.1, 0.2, 0.0], [0.3, 0.1, 0.1], [0.0, 0.2, 0.2]]
MATRIX I3 = [[1,0,0],[0,1,0],[0,0,1]]
LET IminusA = I3 - A
LET L = INVERSE IminusA

On the real 45×45 matrix: INVERSE matched an independent numpy computation to 8.9e-08 max difference. Output multipliers (column sums of L) computed as a real matrix multiplication, not a .sum() shortcut:

MATRIX ones_row = [[1, 1, 1]]
LET mult_mat = MATMUL ones_row L
LET multipliers = FLATTEN mult_mat

Three notions of “systemic importance”: they disagree

GDP-weighted Katz-Bonacich influence (v = Lᵀw), eigenvector centrality on the symmetrized network (EIGEN on (A + Aᵀ)/2, after confirming EIGENVALUES correctly refuses the real, non-symmetric A directly), and output multiplier all rank the real 45 sectors differently: Spearman correlation between multiplier and influence is only 0.208. Sectors like food manufacturing have high per-dollar multipliers, but the highest systemically influential sectors (wholesale trade, finance, real estate) matter mostly for their sheer size and connectivity. This is a real, non-cherry-picked finding matching current network-economics literature.

A real, dated shock: air transport’s 2020 collapse

A real -$52B final-demand shock to air transport, propagated two independent ways (SOLVE directly, and MATMUL against the already-computed L), agreeing to within numerical precision:

LET total_effect = SOLVE IminusA shock
LET total_effect_2 = FLATTEN (MATMUL L shock_col)

The result is a 3.79x amplification: the aggregate output response across the whole economy (-$95.8B) is nearly 4x the direct effect alone (-$25.3B). The 2020 COVID-driven US input-output matrix genuinely is not full rank (RANK(A) = 44, not 45). Confirmed against numpy exactly, this is a real economic fact about linear dependence among 2020 input structures, not a data error.

Three real engine findings from this one notebook

1. Fixed: SimdBackend’s scalar broadcast (matrix * 0.5) failed above the 1024-element SIMD threshold with a bare "Shape mismatch". Real 45×45 economic data (2,025 elements) was the first notebook input large enough to ever hit this path. Fixed with 4 new regression tests.
2. Flagged: a qualified column inside a window function’s ORDER BY (RANK() OVER (ORDER BY t.col DESC)) fails to parse; a bare ORDER BY col works.
3. Flagged: an un-aliased qualified SELECT column (SELECT t.col FROM t, no AS) returns correct data but names the output column __cmp_0 instead of col.

Try it yourself

• View the full notebook
• Try it in the Playground