Macroeconomics — Comparing Growth Models

Macroeconomics — The Growth Debate Is About Whether Saving Changes the Level or the Growth Rate

This chapter sets the Solow model of Chapter 11 side by side with the endogenous growth models of Chapter 12. It sets out what each model predicts about the question “why do some countries catch up quickly while others do not,” and which side the data support.

1. Predictions by model

What saving and research do
Model	Higher saving rate	Source of long-run growth per person	Convergence
Solow	Raises only the steady-state level	Exogenous technological progress	Conditional convergence
Solow with human capital	Raises the level by more, with a longer transition	Exogenous technological progress	Conditional convergence (slow)
AK	Raises the growth rate permanently	Accumulation of broad capital	No convergence
Idea-based (Romer)	Research workforce and incentives set the growth rate	R&D	Depends on technology diffusion

2. The speed of convergence

Mankiw, Romer and Weil (1992) found that adding human capital to the Solow model explains much of the income gap between countries, and estimated the speed of conditional convergence, controlling for saving rates and population growth, at about 2% a year. At 2% a year, it takes about 35 years for the gap to the steady state to halve.

The half-life of convergence

t_{1/2} = \frac{\ln 2}{\lambda} \approx \frac{0.693}{0.02} \approx 35\text{ years}

λ is the speed of convergence. With a capital share of 1/3, the Solow model predicts much faster convergence, but including human capital in broad capital slows convergence and brings it closer to the data.

3. Development accounting: where do income differences come from?

When the gap in output per person between rich and poor countries is split into capital, human capital and productivity (TFP), a large share not explained by differences in factor inputs remains as TFP differences (Hall and Jones 1999, among others). In other words, poor countries are poor mainly not because they have little capital but because they produce less with the same capital and labour. Institutions, geography and culture are debated as the fundamental causes of those productivity differences.

4. The East Asian growth debate

The rapid growth of East Asia from the 1960s to the 1990s gave rise to two interpretations.

Accumulation view: Young, Krugman and others argued that most growth came from high investment rates, rising labour participation and expanding education, and that TFP growth was modest. By the logic of the Solow model, growth driven by accumulation alone eventually slows.
Assimilation view: other researchers argued that the process of rapidly absorbing and learning advanced technology is itself bound up with investment, so accumulation and technological progress are hard to separate.

Both views agree that rapid catch-up is possible during the transition, but that as a country nears the frontier its growth rate converges to the rate of technological progress. Near the frontier, the source of growth becomes innovation rather than imitation.

5. Criteria for judging policy

Policy statements that differ by model
Policy	Solow assessment	Endogenous growth assessment
Encouraging saving	Raises the level; sacrifices consumption in the transition	May raise the growth rate
R&D subsidies	Outside the model, since technology is exogenous	Raises growth by correcting undersupply
Investment in education	Raises the level through human capital	Raises the capacity to produce ideas
Better property rights and institutions	Raises the level through investment incentives	Raises growth through innovation incentives

Check your understanding

If the steady-state income gap between two countries is 40% and the speed of convergence is 3% a year, how many years does it take for the gap to shrink to 20%? The half-life is $\ln 2/0.03\approx 23$ years. If the same gap arose from different saving rates under the AK model, it would widen rather than shrink. Whether conditional convergence is observed in the data is the test that separates the two models.

References

N. Gregory Mankiw, David Romer and David Weil, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics (1992)
Robert Hall and Charles Jones, “Why Do Some Countries Produce So Much More Output per Worker than Others?,” Quarterly Journal of Economics (1999)
Alwyn Young, “The Tyranny of Numbers,” Quarterly Journal of Economics (1995)
Paul Romer, “Endogenous Technological Change,” Journal of Political Economy (1990)