Jones: Introduction to Economic Growth

Jones, C., 1998. Introduction to Economic Growth. New York.

Why are we so rich and they are so poor? That is a fundamental question driving theories of economic growth. This was famously explored by Smith in The Wealth of Nations. More recently, this was explored by Solow. “Solow’s theories helped to clarify the role of the accumulation of physical capital and emphasized the importance of technological progress as the ultimate driving force behind sustained economic growth” (2). This work continued apace throughout the 60s and 70s, eventually building to contributions made by Romer and Lucas. These authors focused on human capital and the importance of ideas for economic growth. Barro quantified many of these ideas.

The book is an exploration of economic growth theory from the perspective of the relationship between observation and theory. The author uses the analogy of astronomy in the hard sciences.
1: Per-capita income varies between countries

2: Economic growth rates vary from country to country

3: Growth not entirely consistent over time

4: Countries can become wealthy or poor

5: US has seen steady growth

“Facts” about the US over the last century: Kaldor: “…economic theorists should begin with a summary of the ‘stylized’ facts a theory was supposed to explain” (14). First fact: “…the rate of return to capital is roughly constant…” (14). Secondly: the labor share has been mostly constant across history, looking specifically at the US. The combination of stylized fact one and two is that the ratio of K/Y is relatively stable. The third stylized fact alters one of Kaldor’s facts: there is relative consistent growth in economic growth.

6: Growth in output and trade are related (15)

7: Skilled and unskilled workers show a tendency to move from poor to rich countries

Three questions explored here: Why are some rich and some poor? What drives economic growth? And finally: how do some countries transition so quickly to becoming rich?

Solow’s Model:

Assumptions: world comprised of countries producing a single good. No international trade because there is only one good. Consumers have a percentage that they save for future consumption and a percentage that they use for consumption.

The model is constructed around two equations: production function and capital accumulation.

The production function acts as a saturating curve with respect to increases in capital relative to workers: there are diminishing returns on investment. Secondly, capital accumulation change is equal to the amount of investment minus the amount of depreciation.

Consumers save a portion of their income, which is invested, or rented, for use in production.

Capital accumulation per worker is determined by three things. It is increased with investment in workers, it is decreased with depreciation and the new term is change in the size of labor relative to capital.

A basic Solow diagram is shown that compares two plotted equations. One is a saturating curve that represents the amount of investment per person. The second curve is a line that represents the amount of new capital investment required per person required to keep the ratio of capital to worker consistent. Both equations begin at 0,0. When capital growth occurs per worker, capital deepening takes place. When per worker change is not taking place but capital grows, capital widening takes place. The amount of capital per worker constantly tries to approach the point where both lines intersect.

What happens if there is an increase in the investment rate? The saturating curve that represents the amount of investment per person shifts up. This starts a process of capital deepening.

What happens if there is an increase in the population growth? That shifts the degree of the relationship between the amount of capital investment required to keep the amount of capital per worker constant. “Investment per worker is now no longer high enough to keep the capital-labor ratio constant in the face of the rising population. Therefore, the capital-labor ratio begins to fall…At this point, the economy has less capital per worker than it began with and is therefore poorer: per capita output is ultimately lower after the increase in population growth…” (31-2).

The Steady State: “By definition, the steady-state quantity of capital per worker is determined by the condition that…” capital change is equal to zero (32).

“This equation reveals the Solow model’s answer to the question ‘Why are we so rich and they so poor?’ Countries that have higher savings/investment rates will tend to be richer…” (32). More capital/worker equals more output/worker. If you have high population growth, you will have lower production because you will have lower capital/worker: ie, these countries will focus on just trying to keep the capital/labor ratio stable and will have to emphasize capital widening with less of an opportunity to explore capital deepening.

These effects are then explored vis-à-vis empirical evidence: real GDP is compared to savings rate and real GDP is compared to population growth rates. There is seen to be a correlation (though the later graph, figure 2.7, doesn’t appear to display this correlation as well as claimed).

This model fails to describe increased per capital growth because output per unit of labor, and thus per person, is constant.

“To generate sustained growth in per capita income in this model, we must follow Solow and introduce technological progress to the model” (36). This is done through the variable a which increases labor’s productivity. This technology assumption is exogenously imposed.

“A situation in which capital, output, consumption, and population are growing at constant rates is called balanced growth path” (37).

“If the economy begins with a capital-technology ratio that is below its steady-state level…the capital-technology ratio {k~=K/AL} will rise gradually over time. Why? Because the amount of investment being undertaken exceeds the amount needed to keep the capital-technology ratio constant” (39).

“This exercise {Figure 2.10} illustrates two important points. First, policy changes in the Solow model increase growth rates, but only temporarily along the transition to the new steady state. That is, policy changes have no long-run growth effect. Second, policy changes can have level effects. That is, a permanent policy change can permanently raise (or lower) the level of per capita output” (41-3).

Some key aspects of the Solow Model: per capita growth happens because of exogenously imposed technology variables. Also, the reason some countries are better off than others is because they save and invest more, and thus increase the amount of capital per worker which makes them more efficient. There is also a more subtle explanation of why some countries grow more quickly than others: if their capital technology ratio (k~) is below the steady-state level for the long run, it will climb back quickly to that level. This might be an explanation for why Germany and Japan built back up their capital stocks so quickly after WWII. “Or it may explain why an economy that increases its investment rate will grow rapidly as it makes the transition to a higher output-technology ratio” (44-5). This may be applicable in situations like South Korea, for example.

Exploring output: as a stylized fact, output per person decreased after 1973. This was the case throughout the advanced countries. It remained relatively low into the end of the 1990s. Some thought that high energy prices could be the culprit, but this is improbable as real energy prices in the late 80s were lower than they were before the shock. Another thought is that the decreased productivity has to do with a transition from a manufacturing economy to a service economy. Another explanation blames a slow-down in funding for R&D in the late 1960’s. Alternatively, growth may have been artificially high in the 50s and 60s because of the rebuilding efforts after WWII.

The “New Economy” saw productivity increase in the late 1990s. This can be partially attributed to the increased use of information technology. Also, some posit that ICT can explain the slow-down in growth and the later improvement: the time-lag associated with diffusing new technologies in the early 1970s created productivity slowdowns that were only circumvented over 20 years later.

Ch. 3:

An influential paper by Mankiw, Romer and Weil put the Solow model to an empirical test, found that it was quite good, but added human capital to make it better. This extends the Solow model to include different levels of education and skills.

H, or the degree to that labor is skilled, is calculated based upon investment in education which rises at a relatively constant rate. For example, if someone invests one extra year on education, wages are expected to rise by about 10% for a life-time (Bils and Klenow (2000)). The amount that individuals invest in education is given exogenously.

K is also gathered by investing some output instead of consuming everything.

“Countries are rich because they have high investment rates in physical capital, spend a large fraction of time accumulating skills…, have low population growth rates, and have high levels of technology” (57).

An additional discussion about convergence and differences in growth rates. A piece by Gerschenkron (1952) and “backward” economies and how they grow faster to catch up is sited, as well as a piece by Abramovitz (1986).

Technology transfer may be a plausible cause of convergence, but the neoclassical model provides other explanations. “Why…do we see convergence among some sets of countries but a lack of convergence among the countries of the world as a whole? The neoclassical growth model suggests an important explanation for these findings” (66). “Among countries that have the same steady state, the convergence hypothesis should hold: poor countries should grow faster on average than rich countries” (68). This explains why there is convergence in some areas, but not all areas, as not every country has the same steady state, but countries who do have the same steady state are incentivized by structural forces to converge technologically.

There is then a brief discussion of income distribution, historical trends and future possible developments.

Ch. 4:

Neoclassical growth models explore the accumulation of physical and human capital in relation to labor stocks and technology, which is determined exogenously. Endogenous technological determination is crucial for the further establishment of economic growth models.

Romer writes about ideas. Ideas are nonrivalrous. Most goods are rivalrous, as my use of it excludes your use of it. Not ideas. An additional distinction made by Romer is that of excludability and non-excludability. “…the economics of ‘ideas’ is intimately tied to the presence of increasing returns to scale and imperfect competition” (83). Increasing returns to scale is seen in the initial costs of the development of an idea: these costs are fixed and may be large. Therefore, companies must charge a price that is above their marginal costs in order to recoup these fixed costs.

Authors like North (1981) see the imposition of intellectual property rights regimes as being crucial for the establishment of sustained economic growth because this incentivized innovation.

Ch. 5:

Endogenous technological change is explored through the lenses of Romer’s model. “The Romer model endogenizes technological progress by introducing the search for new ideas by researches interested in profiting from their inventions” (97).

As was the case with the Solow model, there are two main elements in the Romer model of endogenous technological change: an equation describing the production function and a set of equations describing how the inputs for the production function evolve over time” (98). “The Romer economy consists of three sectors: a final-goods sector, an intermediate-goods sector, and a research sector” (111).

The book continues and lays out different approaches to exploring technology endogenously and technology transfer issues.