One-Third Rule: What it Means and How It Works

The one-third rule is a simple rule of thumb used in growth accounting to estimate how changes in capital per worker affect labor productivity. It says that roughly one-third of a percentage increase in capital per hour of labor translates into a percentage increase in labor productivity; the remainder of output growth is attributed to other factors (often measured as technological progress).

Definition and formula

• Rule of thumb: A 1% increase in capital per worker (or per labor hour) produces about a 0.33% increase in labor productivity.
• Algebraic form (stylized):
  ΔProductivity% ≈ (1/3) × Δ(Capital per labor-hour)% + Δ(Technology)%

The formula is used to separate how much of productivity growth is explained by increases in physical capital versus improvements in technology (or other residual factors).

Example

If capital per labor-hour rises by 6%, the one-third rule implies productivity would rise by about 2% from capital. If observed productivity rises by 6% total, the remaining 4% would be attributed to technological improvements or other factors.

Why it matters

• Labor productivity—how much output a worker produces in an hour—drives real GDP per person and is closely linked to standards of living.
• Understanding the sources of productivity growth (capital versus technology/human capital) helps policymakers and firms decide where to invest.

Measurement challenges and limitations

• The rule is a simplification and an empirical “stylized fact,” not a strict law. Elasticities vary across industries and countries.
• Valuing productivity in services is harder than in goods-producing sectors, making measurements less precise for many economies.
• The rule implicitly holds other influences constant; in reality, human capital, institutions, and technology usually change simultaneously with capital accumulation.
• It doesn’t identify the mechanisms of technological change—only attributes the unexplained residual to “technology” in growth-accounting frameworks.

Policy implications

When an economy lacks human capital or labor participation:
– Invest in education and training to raise worker skills.
– Encourage policies that increase labor supply (e.g., immigration, incentives to raise participation).
– Increase physical capital investment and promote technological innovation to raise productivity.

Historical context

Large technological shifts (for example, during the Industrial Revolution) dramatically increased capital intensity and technology, boosting hourly productivity and, over time, living standards.

Key takeaways

• The one-third rule: roughly one-third of increases in capital per worker show up as productivity gains.
• It’s a useful, simple guide for attributing productivity growth between capital investment and technology.
• Use it cautiously—measurements and elasticities vary, and many factors jointly influence productivity.