Palma Ratio Formula: Top 10% to Bottom 40% National Income Share & Middle-50% Check

José Gabriel Palma’s striking empirical discovery: Deciles 5–9 almost always capture ~50% of national income!

Cambridge economist José Gabriel Palma (2011, Development and Change — formalized for UN SDG / OECD reporting by Alex Cobham and Andy Sumner, 2013) demonstrated that across over 130 countries, the "administrative/middle" 50% of households between the 40th and 90th percentiles (Deciles 5–9) nearly always capture ~50% of gross national income—meaning almost ALL cross-country inequality variation is a tug-of-war over the OTHER half of national income between the richest 10% (Decile 10) and the poorest 40% (Deciles 1–4)!

Accordingly, the Palma Ratio = Top_10%_Income_Share / Bottom_40%_Income_Share measures how many times more national income goes to the richest 10% than to the entire poorest 40% combined! In Nordic social democracies (Top 10% ≈ 24%, Bottom 40% ≈ 24%), Palma ≈ 1.00; in typical OECD economies (Top 10% = 31.5%, Bottom 40% = 17.5%, Middle 50% = 51.0%), Palma = 1.800; and in high-inequality economies (Top 10% = 44%, Bottom 40% = 11%), Palma reaches 4.000!

Palma Inequality Ratio = Top_10%_Income_Share / Bottom_40%_Income_Share

Divides Top 10% income share (B2, %) by Bottom 40% income share (B3, %) while verifying valid national share bounds (B2 + B3 < 100%).

=IF(OR(B2 <= 0, B3 <= 0, B2 + B3 >= 100), "Invalid Decile Income Shares", ROUND(B2 / B3, 3))

Implied Middle-50% (Deciles 5–9) Income Share = 100 - Top_10% - Bottom_40%

Verifies Palma’s middle-class stability proposition (~45%–55% of national income).

=IF(OR(B2 <= 0, B3 <= 0, B2 + B3 >= 100), "Invalid Decile Income Shares", ROUND(100 - B2 - B3, 2))

Further reading

• Microsoft Support — ROUND function