Financial & Accounting
Mincer Earnings Function Formula: Return to Schooling & Concave Experience Wage Profile
Model human-capital earnings EXP(beta_0 + r_s*S + beta_1*X + beta_2*X²), marginal return to work experience (beta_1 + 2*beta_2*X), and peak-earnings career horizon X* = -beta_1 / (2*beta_2) using Jacob Mincer’s 1974 log-wage equation.
The single most estimated equation in labor economics: Jacob Mincer’s 1974 semi-log human-capital curve!
Jacob Mincer (1974, Schooling, Experience, and Earnings, NBER) unified formal education investment (S years of schooling, returning r_s per year) with concave post-schooling on-the-job training (X years of work experience, where beta_1 > 0 and beta_2 < 0 capture diminishing net training investment over the career lifecycle): ln(W) = beta_0 + r_s * S + beta_1 * X + beta_2 * X^2!
Differentiating ln(W) with respect to X gives the instantaneous marginal wage growth from an extra year of experience: d(ln W)/dX = beta_1 + 2 * beta_2 * X, which hits zero at career peak experience X_peak = -beta_1 / (2 * beta_2)! With beta_0 = 7.85, schooling return r_s = 0.095 (9.5%/yr), S = 16 yr (bachelor’s degree), beta_1 = 0.045, X = 10 yr, and beta_2 = -0.0007, predicted geometric-mean earnings EXP(ln W) = $17,154.23 (baseline real dollars) and marginal experience return is (0.045 - 0.014) = 3.10%/yr (tapering to 1.00%/yr at X = 25 yr)!
| Career Stage (S = 16 yr Schooling, r_s = 9.5%) | Predicted Geometric Mean Wage EXP(ln W) | Marginal Return to +1 Yr Experience |
|---|---|---|
| Mid-Career X = 10 Years Experience | $17,154.23 | +3.10% / yr |
| Senior Career X = 25 Years Experience | $22,387.92 | +1.00% / yr (Approaching X_peak = 32.1 yr) |
| Negative Schooling S < 0 or Convex beta_2 >= 0 | Invalid Profile | "Invalid Mincer Human-Capital Inputs" |
Mincer Predicted Geometric-Mean Earnings W = EXP(beta_0 + r_s*S + beta_1*X + beta_2*X²)
Exponentiates Mincer’s log-earnings equation across schooling S >= 0 (B4), experience X >= 0 (B6), and concave quadratic coefficient beta_2 < 0 (B7).
=IF(OR(B3 < 0, B4 < 0, B5 <= 0, B6 < 0, B7 >= 0), "Invalid Mincer Human-Capital Inputs", ROUND(EXP(B2 + B3 * B4 + B5 * B6 + B7 * (B6 ^ 2)), 2))Marginal Percentage Return to Experience (%) = (beta_1 + 2 * beta_2 * X) * 100
Evaluates instantaneous percentage wage gain from one additional year of labor-market experience at X = B6.
=IF(OR(B3 < 0, B4 < 0, B5 <= 0, B6 < 0, B7 >= 0), "Invalid Mincer Human-Capital Inputs", ROUND((B5 + 2 * B7 * B6) * 100, 2))Try the example
Use the original values or change them to test your understanding.