Statistical & Clinical Analysis
Oaxaca-Blinder Decomposition Formula: Explained Endowment vs. Unexplained Pay Gap
Decompose mean log-wage differentials (Y_A - Y_B) into Explained Endowment differences (X_A - X_B) * beta_A and Unexplained Coefficient/Return differences using Ronald Oaxaca & Alan Blinder’s 1973 counterfactual identity.
Separating observable qualification differences (Endowments) from unequal returns (Coefficients) in pay-equity audits!
Published simultaneously in 1973 by Ronald L. Oaxaca (International Economic Review) and Alan S. Blinder (Journal of Human Resources), the Oaxaca-Blinder twofold decomposition splits the raw mean log-wage differential Delta_Y = Y_bar_A - Y_bar_B between Reference Group A and Comparison Group B by adding and subtracting counterfactual Group-B endowments valued at Group-A returns (X_bar_B * beta_A): Delta_Y = (X_bar_A - X_bar_B) * beta_A + [Delta_Y - (X_bar_A - X_bar_B) * beta_A]!
The first term E = (X_bar_A - X_bar_B) * beta_A measures the Explained Characteristics / Endowment effect (how much of the gap stems from differences in mean schooling/tenure X), while the residual U = Delta_Y - E captures differences in intercepts and slopes (unexplained / structural return differences)! When Y_bar_A = 2.62, Y_bar_B = 2.38 (total gap = 0.2400 log points), X_bar_A = 16.2 yr, X_bar_B = 14.4 yr, and beta_A = 0.095, Explained Endowment E = (16.2 - 14.4) * 0.095 = 0.1710 log points (71.25% of the gap) and Unexplained U = 0.0690 (28.75%)!
| Pay-Equity Decomposition Component | Formula (Group A Reference Coefficients) | Log-Point Value & Share of 0.2400 Gap |
|---|---|---|
| Total Mean Log-Wage Gap (Y_A - Y_B) | 2.62 - 2.38 | 0.2400 log points (100.0%) |
| Explained Endowment Effect (X_A - X_B)*beta_A | (16.2 - 14.4) * 0.095 | 0.1710 log points (71.25% Explained) |
| Unexplained Return/Intercept Gap (Delta_Y - E) | 0.2400 - 0.1710 | 0.0690 log points (28.75% Unexplained) |
Oaxaca-Blinder Explained Endowment Component E = (X_bar_A - X_bar_B) * beta_A
Evaluates the counterfactual endowment contribution in log-wage points using Group A’s slope beta_A (B4).
=IF(B6 = B7, "Zero Total Mean Gap", ROUND((B2 - B3) * B4, 4))Explained Share of Total Raw Differential (%) = E / (Y_bar_A - Y_bar_B) * 100
Computes the percentage of the raw mean log-wage differential explained by observable characteristic differences.
=IF(B6 = B7, "Zero Total Mean Gap", ROUND(((B2 - B3) * B4) / (B6 - B7) * 100, 2))Try the example
Use the original values or change them to test your understanding.