Leontief coefficients — Algeria (2000-2019)

What one dinar of final demand mobilises across the whole Algerian economy. 5,508 coefficients, seventeen years from 2000 to 2019, eighteen branches — technical coefficients and the Leontief matrix, with output multipliers.

An input-output table says what each branch buys from the others. Normalising it by output gives the technical coefficients: how much of product i one dinar of product j requires. Inverting it gives something else entirely — (I − A)⁻¹, what output of i must total, chain effects included, for one dinar of final demand for j to be met. That is the object economists use to assess an investment, a sectoral policy or a demand shock, and nobody publishes it for Algeria.

The ordering of the multipliers was assumed nowhere, and comes out of the textbook. In 2019: 1.21 for miscellaneous industries and 1.28 for business services, which buy little; 1.35 for agriculture; 1.44 for hydrocarbons, extractive and therefore weakly linked despite their weight; then 2.58 for metals and machinery and 2.95 for textiles, whose supply chains are long. One dinar of textile demand mobilises close to three dinars of output; one dinar of hydrocarbons, one and a half.

Four checks, three mathematical and one economic. The spectral radius of the technical matrix must stay below one — beyond it the economy would consume more than it produces and the inverse would not exist; here it runs 0.60 to 0.63. The inversion is exact to 10⁻¹⁶: (I − A) · L = I. The Leontief matrix dominates the identity, its diagonal between 1.0001 and 2.63, with no negative coefficient. And the reconstruction — L times net final demand must recover published output.

The model's boundary is measured and shipped on every row. Reconstruction comes out 5.7% low. That is not noise: branch 16, Trade, weighs exactly that share of intermediate consumption and has no supply row in the source table. It has a column — it buys — and a gross output, but its product flows through trade margins, which offset between branches and sum to zero. Setting that as its supply row pushes the spectral radius to 1.06 and the model ceases to exist. The eighteen branches kept are therefore exact among themselves; the nineteenth is missing, and two columns of the file say by how much, year by year.

Five years are not published, all for the same verified reason. 2008, 2009, 2010, 2020 and 2021 have no "trade margins" row in the source table, and without it the resource side no longer decomposes: their reconstruction comes out at 40%, which has nothing to do with the missing branch. We do not publish a matrix whose check fails.

A methodological lesson, because it nearly cost us the product. A first measurement left trade margins out of the deductions and gave 40% error on every year — enough to conclude impossibility and abandon. A product's resources equal its output plus imports, taxes and the margins added to it; forgetting one term of the balance wrongly disqualifies a model that holds.

Unit and reading. The coefficients are dimensionless: dinars per dinar. The file is in long form — one row per (year, origin branch, destination branch) — with the technical coefficient, the Leontief coefficient, the destination branch's multiplier, and both boundary measures. It reads alongside our "Input-Output Tables", from which it derives.