What Is the One‑Third Rule?
Key takeaway
– The one‑third rule is a simple, empirical shortcut used in growth accounting to estimate how much a change in capital per worker (capital intensity) affects labor productivity. It states that a 1% rise in capital per worker raises labor productivity by about 0.33% (one‑third of the change), holding other factors constant. The remaining productivity change is attributed to technology (total factor productivity) or other residual factors. (Source: Investopedia)
What the rule expresses (formula)
– %Δ Labor productivity ≈ (1/3) × %Δ (capital per worker) + %Δ Technology (TFP)
– Rearranged to infer technology change:
%Δ Technology ≈ %Δ Labor productivity − (1/3) × %Δ (capital per worker)
Why the rule exists
– The rule is a rule‑of‑thumb that comes from growth‑accounting ideas and common estimates of the elasticity of output per worker with respect to capital per worker (roughly one third in many historical estimates). It’s used to split observed productivity growth into a capital‑driven component and a residual labeled “technology” (or total factor productivity).
Practical example
– Suppose a firm observes overall labor productivity rising 6% over a year. Over that year, capital per worker (machines, equipment, software per labor hour) rose 6%.
– Contribution of increased capital: (1/3) × 6% = 2%
– Implied contribution of technology/TFP: 6% − 2% = 4%
– Interpretation: about one‑third of the productivity gain is attributable to rising capital intensity; the rest reflects technology, efficiency, or other unmeasured factors.
Important assumptions and limitations
– Ceteris paribus: the rule assumes other variables are unchanged (no simultaneous changes in skill levels, institutions, labor quality, or measurement methods).
– Aggregate approximation: it is an empirical shortcut, not a precise structural identity. It can vary by industry, country, and time period.
– Diminishing returns and heterogeneity: returns to capital per worker may diminish and differ across sectors; one‑third is a central estimate, not a universal constant.
– Measurement issues: measuring “labor productivity” and “capital per worker” is difficult—especially in service sectors—and measurement error will affect decomposition results.
– Residual interpretation: the “technology” term is a residual and bundles many effects (organizational change, shifts in labor quality, regulatory changes, measurement error), so it is not pure technological progress.
Factors that affect labor productivity
– Physical capital: machines, tools, technology and capital intensity (capital per worker).
– Human capital: education, skills, experience, health of the workforce.
– Technological change: new production techniques, software, automation, process innovation.
– Organizational and managerial practices: workflow, incentives, training, quality control.
– Infrastructure and institutions: transport, communications, rule of law, regulatory environment.
– Scale and specialization: economies of scale, industry structure, international trade.
– Measurement and composition effects: shifts between sectors (e.g., manufacturing → services) can change measured productivity without underlying changes in worker output.
How businesses can use the one‑third rule — practical steps
1. Measure baseline metrics
– Track labor productivity (output per hour or value added per worker) and capital per worker over consistent time periods.
2. Compute the rule‑of‑thumb contribution
– Use the formula: estimated capital contribution = (1/3) × %Δ (capital per worker).
– Infer residual (“technology”) = observed %Δ productivity − estimated capital contribution.
3. Interpret cautiously
– Treat numbers as approximate indicators of where to investigate further (capital, technology, training, processes).
4. Run targeted experiments
– Incrementally increase capital intensity (new machines, software) in pilots and measure productivity change to estimate firm‑specific elasticity.
5. Combine with qualitative analysis
– Pair numbers with worker surveys, process audits, and management assessments to distinguish true technological gains from measurement or compositional effects.
6. Do cost‑benefit analyses
– If capital investment is expected to raise productivity by x% (using firm‑specific evidence), compare expected gains to costs and financing implications.
7. Monitor over time and by unit
– Break results down by plant, department, or product line to identify where capital investments or technology have the strongest impact.
How policymakers can use the one‑third rule — practical steps
1. Monitor national and sectoral data
– Compute productivity and capital‑per‑worker trends to identify lagging sectors.
2. Prioritize policies aligned to sources of productivity growth
– If residual (technology) explains much growth, promote R&D, innovation policy, and knowledge diffusion.
– If capital intensity is low, consider tax incentives, public investment in infrastructure, or credit access for equipment.
3. Invest in human capital
– Complement capital accumulation with education, training, and health to raise labor’s ability to use capital productively.
4. Track outcomes and adjust
– Evaluate whether investments raise measured productivity as expected and adjust policy levers.
5. Consider complementary reforms
– Improve institutions, competition, and business climate to amplify the returns to capital and technology.
Practical checklist for applying the rule responsibly
– Use firm/sector/country‑specific data rather than blindly applying the 1/3 value.
– Check for structural breaks (technology shocks, regulatory changes) that change elasticities.
– Use the rule as a diagnostic, not a definitive attribution of causality.
– Combine quantitative decomposition with qualitative investigation.
– Report uncertainty and alternative explanations when presenting results to stakeholders.
Conclusion
– The one‑third rule is a useful, simple rule‑of‑thumb to decompose productivity changes into capital‑driven and residual (technology/other) components. It helps focus attention on whether rising productivity is mainly due to more capital per worker or to improvements in technology and efficiency. However, because it rests on empirical averages and simplifying assumptions, it should be used cautiously and supplemented with firm‑ or sector‑level analysis and careful measurement.
Source
– Investopedia. “One‑Third Rule.” https://www.investopedia.com/terms/o/one-third-rule.asp (accessed via user‑provided source).