ECON2000 Chap.3 Convergence and Productivity
Convergence and Productivity
Convergence questions ask whether initially poorer economies grow faster and catch richer economies. The Solow answer is conditional: growth is faster when an economy lies farther below its own steady state, but countries can have different steady states because productivity, saving, depreciation, education and labour conditions differ.
Development accounting then applies production logic across countries to divide income gaps into measured factor gaps and a productivity remainder. Misallocation provides one mechanism for lower measured productivity when resources are prevented from reaching firms with higher marginal products.
The chapter compares absolute with conditional convergence, separates time-series growth accounting from cross-sectional development accounting and keeps regression evidence distinct from causal identification.
What this chapter covers
- 01
Distance from steady state
- 02
Absolute convergence
- 03
Conditional convergence
- 04
Cross-country testing
- 05
Development accounting
- 06
Misallocation and TFP
Worked example · free
Comparing distances, not income ranks
- +1A is at 60% of its steady state.
- +1B is at 50% of its steady state.
- +2B is proportionally farther below its own destination despite having higher current income.
- +1Conditional convergence therefore predicts faster growth for B, other model conditions held fixed.
Key terms
- Absolute convergence
- The claim that poorer economies grow faster without conditioning on structural steady-state differences.
- Conditional convergence
- The prediction that growth depends on distance from each economy's own parameter-dependent steady state.
- Development accounting
- A cross-country decomposition of income differences into measured factors and a productivity remainder.
- Misallocation
- A distribution of resources that prevents inputs from reaching uses with the highest marginal product.
- Productivity remainder
- The income component not explained by measured factors under the selected production structure.
Convergence and Productivity FAQ
Do all poor countries grow faster?
No. The Solow mechanism predicts faster growth when an economy is farther below its own steady state. A poor country can be close to a low steady state because of weak productivity or other parameters, while a richer country can be farther below a much higher destination.
How is conditional convergence tested?
Empirical work relates subsequent growth to initial income while controlling for variables that influence the steady state, such as saving, population growth, human capital or productivity proxies. The interpretation remains conditional on model specification and does not automatically identify a causal policy effect.
Why can misallocation lower TFP?
Aggregate factor totals can remain unchanged while productive firms receive too little capital and labour. Moving inputs away from their higher marginal products lowers aggregate output. Development accounting records the unexplained output loss as lower measured productivity even if firm technologies themselves did not change.
Is a productivity residual directly observed?
No. It is calculated after selecting a production function, measuring inputs and applying factor weights. Its size can reflect technology, institutions, allocation, utilisation, omitted inputs and error. The residual is a useful diagnostic, but interpreting a cause requires additional evidence.
Exam move
Draw two convergence paths with different steady states and practise explaining why income rank does not reveal distance from destination. Then write a comparison table: growth accounting uses changes through time, while development accounting uses gaps across economies. For empirical questions, label the dependent variable, the initial-condition variable and the controls that proxy for steady-state determinants.
Ask whether the result tests a model implication, decomposes a gap or estimates a causal effect. Use a simple two-firm allocation example to show how total capital and labour can remain fixed while output changes. Finish every residual explanation with the phrase under the chosen production and measurement assumptions to keep the inference appropriately conditional.
Work with ratios to steady state rather than income levels alone. Construct examples where the poorer economy is closer to a low destination and where the richer economy is farther below a high destination; explain how the predicted growth ranking changes. In a separate table, list saving, depreciation, education and productivity as steady-state determinants, and write the direction each has in the baseline model.
For development accounting, keep observed factors in one column and the productivity remainder in another. Change an input-quality assumption and observe how the remainder changes, which demonstrates that it is calculated rather than directly measured. When reading regression evidence, identify what is conditioned on and whether the coefficient is descriptive, a model test or causal.
Add a two-firm misallocation diagram showing marginal products before and after a distortion. The best final paragraph connects the empirical result back to the model while admitting measurement and identification limits, rather than declaring that a correlation proves one institutional mechanism. Prepare one counterexample to the claim that poorer always means faster.
Give the poorer economy a low steady state and the richer economy a higher but more distant destination, then compare their proportional gaps. For data questions, write one sentence on variable measurement and one on identification. That pair prevents a conditional correlation from becoming an unsupported causal policy recommendation and keeps the Solow prediction attached to its assumptions.
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