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Notation cheat sheet

In the multi-regional model, every row and column is a country–sector pair. D and N are the two results most users work with.

SymbolNameIn wordsUnits
A (Adom, Aimp)Direct requirementsInputs bought per dollar of a sector’s output, split into domestic and imported$ / $
LTotal requirements (Leontief inverse)All the output needed across the whole supply chain per dollar of final demand$ / $
VSupply (Make) tableProduction of each commodity by each domestic industry$
U (Udom, Uimp)Use tableCommodities bought by each industry as inputs, split into domestic and imported$
xIndustry outputTotal output of each industry: the row sums of V$
qCommodity outputTotal domestic output of each commodity: the column sums of V$
y (ydom, yimp)Final demandPurchases by households, government, investment, and exports, split into domestic and imported$
ynabFinal demand for the national accounting balanceFinal demand for domestic production: ydom plus exports$
EEmissionsEmissions of each gas by each sector, weighted by AR6 GWPskg CO₂e
BDirect emission intensitiesEmissions of each gas per dollar of a sector’s own output, in CO₂ekg CO₂e / $
MTotal emission intensities by gasB × L: emissions of each gas across the supply chain per dollar, in CO₂ekg CO₂e / $
DDirect emission factorsB summed over gases: CO₂e emitted by the sector itself per dollar of outputkg CO₂e / $
NTotal emission factorsD × L, or M summed over gases: CO₂e across the whole supply chain per dollar of purchaseskg CO₂e / $
A_marginMargin coefficientsTrade and transport margins paid to each margin sector per dollar of a commodity at producer price$ / $
φProducer share of purchaser price1 ÷ (1 + Σ A_margin): converts producer-price factors to purchaser price$ / $
PIPrice indexU.S. BEA chain-type price index for gross output, by sector (2017 = 100)index

Applies to: 2026-rc.1 · Last reviewed: 2026-rc.1