International Trade & Global Value Chains
Vertical Specialization (VS) & VAX Export Ratio Formula
Calculate Hummels, Ishii, and Yi’s (2001) Vertical Specialization Foreign Value Added in Exports VS = (M_int / Y_gross) * X_gross, Domestic Value Added (DVA), and Johnson-Noguera VAX ratio.
Stop double-counting imported semiconductors and components as domestic export GDP!
When an assembly hub imports $180B of foreign chips and displays to produce $600B of gross electronics output and ships $250B abroad, customs statistics record $250B of Gross Exports — vastly overstating domestic value added! David Hummels, Jun Ishii, and Kei-Mu Yi (2001) defined Direct Vertical Specialization (VS, or Foreign Value Added in Exports FVA) as VS = (Imported_Intermediates / Gross_Output) * Gross_Exports! Subtracting VS from Gross_Exports isolates Domestic Value Added in Exports DVA = X_gross - VS, and dividing by X_gross yields Robert Johnson and Guillermo Noguera’s (2012) Value-Added-to-Gross Export Ratio VAX = DVA / X_gross = 1 - (M_int / Y_gross)!
Verify on Imported_Intermediates M_int = 180 ($B, B2), Sector_Gross_Output Y_gross = 600 ($B, B3 -> 30.0% foreign input share), Gross_Exports X_gross = 250 ($B, B4), and Pure_Domestic_Partner_Imports M_partner = 150 ($B, B5): Foreign Value Added in Exports VS is (180 / 600) * 250 = $75.00B; Domestic Value Added in Exports DVA is 250 - 75 = $175.00B; VAX Ratio is 175 / 250 = 0.7000 (70.00%); and while Headline Gross Bilateral Surplus appears to be 250 - 150 = +$100.00B, True Value-Added Bilateral Balance (DVA - M_partner) is only 175 - 150 = +$25.00B! Test pure assembly M_int = 510 ($B, 85% imported inputs): DVA plunges to $37.50B (VAX = 0.1500)!
| Global Value Chain TiVA Metric (M_int=180, Y=600, X=250, M_part=150) | Formula | Verified Output |
|---|---|---|
| Vertical Specialization / Foreign VA (VS) | (M_int / Y_gross) * X_gross | $75.00B |
| Domestic Value Added in Exports (DVA) | X_gross - VS | $175.00B |
| Johnson-Noguera VAX Ratio | DVA / X_gross = 1 - (M_int / Y_gross) | 0.7000 (70.00%) |
| Value-Added Bilateral Balance (vs +100 Gross) | DVA - M_partner | +$25.00B |
Hummels-Ishii-Yi (2001) Vertical Specialization (VS) Formula
Enforce accounting identities 0 <= M_int < Y_gross and 0 < X_gross <= Y_gross!
=LET(m_in, B2, y_gr, B3, x_gr, B4, IF(OR(m_in < 0, y_gr <= 0, m_in >= y_gr, x_gr <= 0, x_gr > y_gr, B5 < 0), "Invalid GVC Input", ROUND((m_in / y_gr) * x_gr, 2)))Domestic Value Added (DVA) & VAX Ratio Formula
Track VAX over time: a falling VAX ratio signals deeper multi-country supply-chain fragmentation rather than declining export competitiveness!
=IF(ISTEXT(E2), E2, ROUND(1 - (B2 / B3), 4))Try the example
Use the original values or change them to test your understanding.