Labor Economics & Human Capital
Acemoglu-Pischke Firm-Sponsored General Training Formula
Calculate Daron Acemoglu and Jorn-Steffen Pischke’s (1998, 1999) optimal firm-paid general training intensity tau* = (theta_comp * p_skill) / c_tr under compressed wage structures versus Gary Becker’s (1964) zero-sponsorship benchmark.
Explain why real firms pay for portable coding bootcamps and German apprenticeships!
Gary Becker (1964) proved that in a frictionless competitive labor market where outside wages w(tau) rise dollar-for-dollar with general productivity f(tau) = f_0 + p_skill * tau, firms earn zero post-training margin f(tau) - w(tau) = 0 and never pay a cent for general training (tau_Becker = 0)! Daron Acemoglu and Jorn-Steffen Pischke (1998, 1999) overturned that puzzle by showing that search frictions, asymmetric employer information, or collective wage floors compress outside wage growth so w’(tau) = (1 - theta_comp) * p_skill < f’(tau) = p_skill! Because the Firm Rent Wedge Delta(tau) = f(tau) - w(tau) = theta_comp * p_skill * tau widens with skill, the employer profitably sponsors general training up to f’(tau*) - w’(tau*) = C’(tau*) => tau* = (theta_comp * p_skill) / c_tr under quadratic training cost C(tau) = 0.5 * c_tr * tau^2!
Verify on Marginal_Skill_Productivity p_skill = 40.00 (B2), Wage_Compression_Factor theta_comp = 0.35 (35% firm rent capture, B3), and Training_Cost_Slope c_tr = 7.00 (B4): Optimal Firm-Sponsored General Training is tau* = (0.35 * 40.00) / 7.00 = 2.0000 skill units (vs Social First-Best tau_FB = 40.00 / 7.00 = 5.7143 units and Becker Frictionless tau = 0 at theta_comp = 0!); Net Firm Training Profit is 0.35 * 40 * 2.00 - 0.5 * 7.00 * (2.00^2) = 28.00 - 14.00 = 14.00; and Worker Wage Gain from Free General Training is (1 - 0.35) * 40 * 2.00 = 52.00!
| Human Capital Training Metric (p_skill=40, theta_comp=0.35, c_tr=7) | Formula | Verified Output |
|---|---|---|
| Firm-Sponsored General Training (tau*) | (theta_comp * p_skill) / c_tr | 2.0000 units |
| First-Best Social Training Benchmark (tau_FB) | p_skill / c_tr | 5.7143 units |
| Net Employer Training Profit (Pi_firm) | theta_comp*p_skill*tau* - 0.5*c_tr*(tau*)^2 | 14.00 |
| Worker Free-Training Wage Gain | (1 - theta_comp) * p_skill * tau* | 52.00 |
Acemoglu-Pischke Optimal Firm-Sponsored Training Intensity tau* Formula
Set B3 = 0 (zero wage compression) to reproduce Gary Becker’s (1964) classic competitive benchmark tau* = 0, Pi_firm = 0!
=LET(p_sk, B2, th_cm, B3, c_tr, B4, IF(OR(p_sk <= 0, th_cm < 0, th_cm > 1, c_tr <= 0), "Invalid Training Input", ROUND((th_cm * p_sk) / c_tr, 4)))Net Employer Training Rent & Worker Wage Gain Formula
Notice that stronger wage compression (higher theta_comp) increases firm-paid general training and shrinks deadweight underinvestment relative to tau_FB!
=IF(ISTEXT(E2), E2, ROUND(B3 * B2 * E2 - 0.5 * B4 * (E2 ^ 2), 2))Try the example
Use the original values or change them to test your understanding.