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Chapter 5: Conditional Convergence and Long-
Run Economic Growth
Chapter Summary:
The previous chapters introduced a model of growth which was based on
the accumulation of capital per worker (capital deepening). The assumption of
diminishing marginal returns led to the conclusion that there was an ultimate
limit to growth in income per worker: the so called “steady state”. In this
chapter, alternative models are discussed which allow for continuous growth.
One factor that allows for this possibility is a broader interpretation of
capital to include human and infrastructure capital. The marginal returns to
investment in human and infrastructure capital augment the returns to physical
The second factor that might lead to continuous growth is technological
progress. The Solow model assumes that technological progress is exogenous:
that the technology parameter A grows at a constant rate. In this case the
accumulation of capital per worker will not end; technological progress offsets
the impact of diminishing returns on the average product of capital. Output per
worker will grow at a constant rate; but one of the more interesting aspects of
this model is that growth in output per worker will grow faster than the rate of
technological progress. This is due to the additional capital accumulation
induced by the higher level of output per worker.
returns to private R&D spending should experience faster rates of technological
progress. The Romer model is a prominent example of endogenous growth
theory. In this case, the private return on investment in R&D is dependent on
such things as the efficiency of the regulatory process, the size of the market for
the innovation, or the security of intellectual property rights.
Chapter Outline:
I. Conditional Convergence in Practice
A. Recent Research on the Determinants of Economic Growth
B. Examples of Conditional Convergence
II. Long Run Economic Growth
A. Models with Constant Average Product of Capital
B. Exogenous Technological Progress
1. The Steady State Growth Rate
III. Conclusion: What We Know About Economic Growth
Teaching Tips:
1. A good introduction to the themes of this chapter and a fine way to introduce
students to a quality economics blog is to direct them to this entry:
2. The “Back to Reality” discussion of pop star Bono’s meeting with the author is
sure to generate some heated discussion about the effectiveness about
4. A side by side comparison of the assumptions, specifications, and results of
5. One of the strengths of the book is that it is allows students to see the way the
process by which various assumptions in the modeling process lead to different
theoretical results; and the data available concerning real world results can
6. In the Romer model, spending on R&D is used as a proxy for technology
progress, and that there are no diminishing returns to technology. This implies
that there are no diminishing returns to R&D spending?
Answers to review questions, pg. 117
1. The exogenous growth in technology would lead to positive growth rates in
both output and output per worker. The growth would come from two sources:
2. Differences in the growth rates can be explained by differences in the factors
that determine the steady state level of income in each region. As saw in chapter
4, differences in savings rates, population growth and technology can have
significant effects on the steady state level of income. East Asian countries are
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Answers to Problems for discussion, pg. 117
3. a. The key to understanding Galton’s fallacy is to recognize that some of the
variation in height is due to chance. For the sake of clarity, let us take an
example where height is entirely due to chance: the height of the father has no
predictive power on the height of the son. In particular, suppose that the height
Applying the logic outlined above to the case of rich and poor countries,
we find that the appearance of convergence is possible even though incomes are
not becoming more equal. At any particular point in time, the distribution of
income per person will be determined to a certain extent by “chance”– that is, by
events and circumstances not described in our growth model. These can have
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b. In part “a” to this question, we recognized that part of the growth rate of
income per person is due to chance. But obviously, the theory of growth we
learned in the text suggests that much of it can be predicted by specific factors- in
c. Conditional convergence implies that rich and poor countries with different
steady states will not converge, but their will be groups of countries for which
convergence will be observed. . If technological change allows steady state