Financial & Accounting
Verdoorn’s Law (Kaldor’s Second Growth Law) Formula: Dynamic Productivity & Employment Elasticity
Forecast manufacturing labor-productivity growth g_p = a + b * g_Y and induced employment growth g_E = (1 - b) * g_Y - a from output expansion g_Y using Petrus J. Verdoorn (1949) and Nicholas Kaldor’s (1966) increasing-returns law.
Why 1% faster industrial output expansion raises labor productivity by ~0.48% via learning-by-doing!
Petrus Johannes Verdoorn (1949, L’Industria) and Nicholas Kaldor (1966, Causes of the Slow Rate of Economic Growth of the United Kingdom — Kaldor’s Second Growth Law) discovered a remarkably stable empirical regularity across industrial economies: labor-productivity growth g_p (output per worker-hour) scales linearly with output growth g_Y via g_p = a + b * g_Y, where autonomous technical progress a ≈ 1%–1.5%/yr and the Verdoorn coefficient b ≈ 0.45–0.50 reflects dynamic economies of scale, division of labor, and Arrow learning-by-doing!
Because output growth equals productivity growth plus employment growth (g_Y = g_p + g_E), Verdoorn’s Law simultaneously implies g_E = g_Y - g_p = (1 - b) * g_Y - a! At autonomous drift a = 0.012 (1.2%/yr), Verdoorn elasticity b = 0.48, and manufacturing output growth g_Y = 0.065 (6.5%/yr), labor productivity grows at 4.32%/yr while employment expands at 2.18%/yr (slowing to g_p = 2.64%/yr if output growth cools to 3.0%)!
| Manufacturing Output Growth g_Y (a=1.2%, b=0.48) | Verdoorn Productivity Growth g_p (%) | Induced Employment Growth g_E (%) |
|---|---|---|
| Industrial Expansion g_Y = 6.50%/yr | 4.32% / yr | +2.18% / yr Net Job Creation |
| Moderate Expansion g_Y = 3.00%/yr | 2.64% / yr | +0.36% / yr Near-Jobless Growth |
| Invalid Elasticity b < 0 or b >= 1 | Outside Verdoorn Regime | "Requires Verdoorn Coefficient 0 < b < 1" |
Verdoorn-Kaldor Labor Productivity Growth Rate (%) = ROUND((a + b * g_Y) * 100, 2)
Evaluates annual percentage labor-productivity growth from autonomous technical progress a (B2), Verdoorn coefficient b (B3 in (0, 1)), and output growth rate g_Y (B4).
=IF(OR(B3 <= 0, B3 >= 1, B4 < -0.5, B4 > 1), "Requires Verdoorn Coefficient 0 < b < 1", ROUND((B2 + B3 * B4) * 100, 2))Implied Industrial Employment Growth Rate (%) = ROUND((g_Y - (a + b * g_Y)) * 100, 2)
Computes residual employment growth g_E = (1 - b) * g_Y - a in percentage points per year.
=IF(OR(B3 <= 0, B3 >= 1, B4 < -0.5, B4 > 1), "Requires Verdoorn Coefficient 0 < b < 1", ROUND((B4 - (B2 + B3 * B4)) * 100, 2))Try the example
Use the original values or change them to test your understanding.