ECOS2025 Chap.9 Growth Accounting and Demographic Change
Growth Accounting and Demographic Change
This chapter recomputes capital, labour and total factor productivity contributions before turning to population structure. It treats the Solow residual as a noisy diagnostic, explains the temporary opportunity created by a demographic dividend and shows why persistent low fertility can later raise dependency and fiscal pressure.
What this chapter covers
- 01
Factor-share weights
- 02
Capital contribution
- 03
Labour contribution
- 04
Residual interpretation
- 05
Demographic dividend
- 06
Ageing pressure
Worked example · free
A checked growth decomposition
- +1Capital contributes 3.5 percentage points.
- +1Labour contributes 1.3 percentage points.
- +1The residual contributes 2.2 percentage points.
- +1Verify that all contributions sum to 7.0 points and qualify the residual.
Key terms
- Growth accounting
- A decomposition of output growth into weighted input contributions and an unexplained residual.
- Factor share
- The output weight assigned to capital or labour in the growth-accounting calculation.
- Demographic dividend
- Potential growth gains from a rising working-age share relative to dependants.
- Dependency ratio
- A comparison of dependent age groups with the working-age population that supports them.
Growth Accounting and Demographic Change FAQ
Why must the contributions add back to output growth?
The residual is defined as what remains after weighted input contributions are removed. If the total does not match output growth, the factor share, arithmetic or units are wrong.
Is a demographic dividend automatic?
No. A favourable age structure creates potential labour and saving gains, but education, employment, health, investment and institutions determine whether that opportunity becomes actual growth.
Why can very low fertility become a problem?
After the initial transition, the workforce can shrink and old-age dependency can rise. That changes labour supply, saving, care needs and pressure on public budgets.
How does the capital share affect the residual?
A larger capital share assigns more observed growth to capital and less to labour, changing what remains unexplained. The residual therefore depends on an empirical assumption as well as arithmetic.
Can productivity offset demographic drag?
Higher participation, skills, automation and better allocation can raise output per worker even as workforce growth slows. These responses reduce pressure but do not make population structure irrelevant.
What is the narrow Solow effect of lower fertility?
Lower population growth reduces required investment per worker and can raise steady-state capital per worker. Welfare, implementation and later ageing require additional analysis outside that narrow result.
How should growth accounting and demographic analysis be combined?
Compute capital, labour and residual contributions first, keeping percentage points and factor shares explicit. Then ask how age structure changes labour quantity, participation, saving, fiscal pressure and human-capital investment. A demographic dividend is not automatic: productive employment and complementary capital must absorb the larger working-age share.
Later ageing can reverse some channels while technology, migration, retirement rules and participation offset others. Keep the Solow result narrow and use institutional evidence to explain why similar population shifts produce different outcomes across Japan, Korea and China.
Exam move
Recompute the chapter example without notes and keep every result in percentage points. Write the output growth total first, calculate capital's weighted contribution, calculate labour's weighted contribution and subtract both to obtain the residual. Perform the add-back check before offering any interpretation. Then vary the capital share and observe how the residual changes even though the observed growth rates stay fixed.
Repeat the calculation with a second original data set and include a negative or very small residual so you can explain that the method does not guarantee a positive technology story. Build a limitations list beside the formula: hours, utilisation, human capital, input quality, omitted capital and measurement error.
For each item, say whether better measurement would likely reallocate growth from the residual toward an observed input. This turns the caveat into a mechanism. Draw the demographic transition as a sequence and write one sentence on the opportunity phase and one on the later ageing phase.
Lower fertility can reduce capital dilution in Solow and raise the working-age share during transition, yet persistent low fertility can later shrink labour-force growth and raise old-age dependency. Add employment, education, health and productive investment as conditions that determine whether the potential dividend is realised. Practise an answer on one-child policy with two distinct layers.
Use the Solow diagram to show the effect of lower population growth under its assumptions, then evaluate distribution, implementation and long-run ageing outside the model. Do not let a curve shift settle the policy judgment. For Korea, write a short paragraph on why automation, participation and skills may offset some demographic drag without making demography irrelevant.
Finish with a chart audit: the bars in the worked example must match the printed 3.5, 1.3 and 2.2 contributions and sum to 7.0. Any revised number must be recomputed in both prose and figure. Numerical consistency is part of the economic argument because a residual built from mismatched values cannot support a productivity conclusion.
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