Economics Chapter 9 Homework Make some or all of the discussion intuitive rather

207

CHAPTER 9

Economic Growth II: Technology,

Empirics, and Policy

Notes to the Instructor

Chapter Summary

This chapter continues the presentation of the Solow growth model started in Chapter 8. The chapter

begins by adding labor–augmenting technological progress to the model. This addition completes the

Solow growth model. Once the complete model is developed, it is used to address how public policy

affects growth and development. The last section of the chapter examines some of the weaknesses of the

Solow growth model and introduces the student to endogenous growth theory. In addition, there is an

appendix on growth accounting based on the Solow growth model.

Building on the lessons of Chapter 8, the three sections of this chapter teach the following lessons:

1. Technological progress is the sole determinant of growth in living standards in the long run.

Comments

This chapter expands the Solow growth model of Chapter 8 to explain sustained growth in output per

capita and thus the ongoing rise in the standard of living. The chapter also discusses endogenous growth

1. The Meaning of Effective Worker

The analysis of population growth often seems easy to students while that of technological progress seems

2. Why Does Technological Progress Reduce k?

Students find it counterintuitive that technological progress reduces the capital–labor ratio, probably

because of the difficulty of interpreting the concept of effective worker. To emphasize that, the lower k

3. Confusion Among a Number of Similar Graphs and Variants of

the Model

The following are suggestions to correct such confusion:

(a) Make some or all of the discussion intuitive rather than mathematical; see Supplements 8–9

and 9-7.

(b) Stress that there is ultimately just one model with a number of special cases. The entire

4. Difficulties Relating the Model to the Real World

The Solow model can be roughly calibrated to the U.S. economy. As discussed in Chapter 9 of the

textbook, if depreciation is ten percent of GDP and the capital stock is 2.5 times one year’s GDP, we can

compute the depreciation rate by dividing

δ

k = 0.1y by k = 2.5y to obtain:

δ

k /k = (0.1y)/(2.5y),

δ

= 0.04.

Use of the Dismal Scientist Web Site

Go to the Dismal Scientist Web site and download data for total business fixed investment and investment

in information technology and software over the past 40 years. Compute the ratio of investment in

information technology and software to total business fixed investment. How has this ratio changed over

time? Discuss whether the data are consistent with the pickup in trend productivity growth during the late

1990s.

Lecture Notes | 209

Chapter Supplements

This chapter contains the following supplements:

9-1 More on the Convergence Hypothesis

9-3 The Economics of Ideas

9-5 Corruption and Growth

9-7 The Solow Growth Model: An Intuitive Approach—Part Two

9-9 More on the New Economy (Case Study)

9-10 Additional Readings

210 | CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy

Lecture Notes

Introduction

The Solow growth model as developed in Chapter 8 showed how changes in the capital stock

and population growth affect the long–run level of output of the economy. This chapter adds

changes in technology to complete the model. The complete Solow growth model can then be

9-1 Technological Progress in the Solow Model

Chapter 8 provided an explanation of persistently rising output, but we have not yet explained

rising living standards. To do so, we incorporate technological progress, meaning that we are

able to produce more output with a given amount of capital and labor.

The Efficiency of Labor

Technological progress is a slightly trickier process to incorporate into the model. The reason is

that it can enter the production function in different ways; it may increase the productivity of

capital or labor. The simplest form to analyze is labor–augmenting technological progress.

Return to the production function and amend it so that

This assumption makes analysis simple since increases in the productivity of labor now

look just like increases in population. If either L or E increases, output is affected in just the

same way. For this reason we call L × E the number of effective workers. In other words, labor–

The Steady State With Technological Progress

Now redefine k to be capital per effective worker (k = K/LE), and likewise, y = Y/LE. The

analysis of technological progress is now exactly analogous to that of population growth. The

economy will be in steady state with k constant when

The Effects of Technological Progress

In steady state, output, capital, and consumption per worker are all growing at the rate g. The

model can now explain rising living standards. According to the Solow model, technological

progress is the only source of rising living standards over time. The analysis of the Golden Rule

is again altered when we have technological progress. The condition for maximum consumption

per effective worker is

MPK – δ = n + g.

!Figure 9-1

!Table 9-1

9-2 From Growth Theory to Growth Empirics

Thus far, we have used the Solow model to help us understand how policy might influence

economic growth. We now turn to the question of how well the model fits the empirical facts.

Balanced Growth

Data for the United States bear out the predictions of the Solow model for technological progress

FYI: Economic Possibilities for Our Grandchildren

Since the Industrial Revolution, economic growth has raised living standards of people

worldwide. John Maynard Keynes, writing in 1930, projected that continued rapid economic

growth would raise living standards by four to eight times over the next 100 years. He saw such

growth as ensuring that most basic needs and material desires would be satisfied. He expected

the workweek to be much shorter and that the main problem facing society would be how to use

Convergence

The differences in living standards around the world are staggering. Yet the Solow model

suggests that economies are likely to converge toward the same steady state—at least if they

possess similar technologies and have similar rates of saving and population growth. If the

differences between rich and poor countries are just due to the fact that rich countries have more

capital, then we would expect poor countries to accumulate capital faster and so eventually catch

up with richer ones.

!Supplement 9–1,

“More on the

Convergence

Hypothesis”

!Supplement 9–2,

“Convergence of

education.

Factor Accumulation Versus Production Efficiency

Cross–country differences in income per person arise either because of differences in capital per

person (physical capital and human capital) or because of differences in the efficiency with

which factors are employed. Although results vary from study to study, research has shown that

Case Study: Good Management as a Source of Economic

Growth

Differences in incomes across nations occur in part because of differences in production

efficiency. The same is true about businesses. One possible reason is differences in management

practices. A recent study finds significant variation in management practices across firms in the

United States, the United Kingdom, France, and Germany. In each country, some firms are

efficiently managed and others are poorly managed. But the distribution of management quality

9-3 Policies to Promote Growth

What are the policy implications of the Solow growth model?

Evaluating the Rate of Saving

A natural starting point for evaluating the saving rate is to see if the U.S. economy is above the

Golden Rule, since we know that policymakers could then make everybody better off by

discouraging saving. We need to compare the growth rate

(n + g) with the return to capital net of depreciation (MPK – δ).

The following are true for the U.S. economy:

Lecture Notes | 213

Changing the Rate of Saving

Although the Solow model as set out here excluded the government for simplicity, we know

from the analysis of the classical model that national saving depends on both private saving and

government saving. One way, therefore, for policymakers to change the saving rate is by

increasing public saving—running government surpluses rather than government deficits. Recall

Allocating the Economy’s Investment

Although the Solow model assumes a single capital good, it is helpful to distinguish three

different types of capital. First, there is private physical capital: the factories, machinery, and the

like firms use to produce goods. Second, there is public physical capital—that is, capital goods,

such as the interstate highway system, that the government provides. Such goods are often

known as infrastructure. And third, there is human capital, or the knowledge and skills of people

in the economy.

Case Study: Industrial Policy in Practice

A long–standing debate in economics revolves around whether governments should promote

certain industries or firms because of their importance to the economy. This debate in the United

States goes back to the early days of the country and the Tariff of 1789, which was intended to

help develop domestic manufacturing. One example supporters of industrial policy often point to

is the success of the Internet—a government–sponsored defense project that, by all estimation,

Establishing the Right Institutions

As noted earlier, nations have differences in per–capita income because of differences in factor

accumulation and differences in production efficiency. In turn, nations may have different levels

of production efficiency because they have different political and legal institutions that affect the

allocation of scarce resources. For example, the extent of legal protection afforded shareholders

and creditors may influence the functioning of capital markets and thus the allocation of capital

!Supplement 3–2,

“What Is Capital”

214 | CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy

A comparison of the economic performance between North and South Korea highlights

well the importance of institutions for economic success. Both nations shared a common

government, economy, heritage, and culture for many centuries. After World War II, Korea was

Case Study: The Colonial Origins of Modern Institutions

A nation’s geographical latitude is strongly correlated with its income per capita. Nations near

the equator typically have a lower income per capita than nations farther away from the equator.

This finding holds for both the northern and southern hemispheres. Some economists argue that

this correlation is due to the direct effect of tropical climates on productivity in agriculture and

industry—hot climates are associated with more disease and generally poorer results in

agriculture. Recent work by Daron Acemoglu, Simon Johnson, and James Robinson goes

beyond the direct effect of climate on productivity to consider the indirect effect of climate on

institutions. These authors argue that the presence of tropical disease dissuaded Europeans from

settling in tropical areas and opting instead to establish permanent settlements in more temperate

Encouraging Technological Progress

Having gone through the Solow model in some detail, we are left with a somewhat disturbing

conclusion from the point of view of our theory. Explaining growing living standards means

explaining technological progress, which is exogenous in the model. Economists do not yet have

a very good understanding of the sources of technological progress. Nonetheless, government

policies are often directed to encouraging technological progress. Such policies include tax

breaks for research and development and government funding of basic research. More broadly,

government subsidization of education, by improving the skills of the work force, may increase

the efficiency of labor.

Case Study: Is Free Trade Good for Economic Growth?

As Adam Smith noted, international trade allows countries to specialize in productive activities

in which they have a comparative advantage. So one might expect that countries that are open to

trade would have higher living standards than countries that are closed to trade. The empirical

evidence shows that countries that are more open to trade indeed do experience more rapid

9-4 Beyond the Solow Model: Endogenous Growth Theory

How to incorporate the process of technological change into a growth model?

The Basic Model

Start with a production function

Y= AK,

where A is a constant measuring the amount of output produced for each unit of capital. This is

known as an AK model. The production function does not exhibit diminishing returns to capital.

If s is the fraction of income saved, then

A Two–Sector Model

The AK model developed above is the simplest example of an endogenous growth model. A

more sophisticated version incorporates two sectors: a manufacturing sector that produces goods

and services for either consumption or investment in physical capital K and a research sector

composed of universities that produce knowledge, E, which is used in both sectors.

The economy can be described by three equations:

The Microeconomics of Research and Development

There are three microeconomic facts of research and development (R&D):

2. Research is profitable because innovations give firms temporary monopoly power.

3. Firms build on the innovations of other firms.

!Supplement 9–3,

“The Economics

of Ideas”

!Supplement 9–4,

“Green Growth”

216 | CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy

The Process of Creative Destruction

Economist Joseph Schumpeter proposed that economic growth occurs through a process known

as “creative destruction.” His theory viewed new firms as continually entering the marketplace,

having monopoly power over their innovations, and reaping the profits that induced the firms to

enter the market in the first place. Consumers benefit from the greater choice of products, but

existing firms now face competition. Some of these established firms cannot compete and go out

9-5 Conclusion

While the Solow model explains the long–run determination of the capital stock and teaches us

where to focus our attention, if we want to explain economic growth, it is unsatisfactory in that it

takes as exogenous precisely those variables identified as sources of growth—population change

Appendix: Accounting for the Sources of Economic Growth

Growth accounting attempts to decompose overall output growth into its constituent sources:

changes in labor, capital, and technology.

Increases in the Factors of Production

First, we hold the technology constant. Recall the following definitions from Chapter 3:

MPK = F(K + 1, L) – F(K, L);

MPL = F(K, L + 1) – F(K, L).

Given a change in capital ∆K and a change in labor ∆L, we then have

∆Y = (MPK × ∆K) + (MPL × ∆L).

Now divide through by Y, multiply and divide the first term on the right–hand side by K,

multiply and divide the second term on the right–hand side by L, and rearrange to obtain

Lecture Notes | 217

Technological Progress

To include technological progress, write the production function as

Y = A × F(K, L),

The Sources of Growth in the United States

Table 9-2 in the text presents decade–by–decade decompositions of U.S. economic growth into

its constituent sources.

Case Study: The Slowdown in Productivity Growth

Economic growth slowed sharply after the early 1970s. This slowdown was worldwide and has

been attributed to a decline in the rate of technological progress. The downshift in growth meant

that living standards for many countries rose more slowly in the 1970s and 1980s than they had

2. faster obsolescence of capital in the 1970s due to the large changes in oil prices;

4. a decline in inventiveness.

The worldwide slowdown in growth that began in the early 1970s seems to have ended

sometime in the mid–1990s. In the United States, GDP per person has grown by 2 percent per

year since 1995, compared with just 1.5 percent per year from 1972 to 1995. This increase in the

growth rate has been described by some observers as the dawning of a “New Economy.”

Economists are not completely certain as to why growth suddenly surged in the 1990s, but

many suspect that it had something to do with advances in computing and other information

!Table 9-2

!Supplement 9–8,

“More on the

Productivity

!Supplement 9–9,

“More on the

New Economy”

218 | CHAPTER 9 Economic Growth II: Technology, Empirics, and Policy

Case Study: Growth in the East Asian Tigers

Many businesspeople, economists, and other commentators have noted the phenomenal

economic success of certain countries in East Asia—particularly Hong Kong, Singapore, South

The Solow Residual in the Short Run

This appendix shows how we may infer the effect of technological change on the economy by

using the techniques of growth accounting. Any variation in output that cannot be explained by

changes in capital or labor, so the reasoning goes, must be the result of technological progress.

This unexplained change in output is known as the Solow residual. The Solow residual has, in

fact, fluctuated substantially in the past. It rises during expansions and falls during recessions.

Economist Edward Prescott has argued that such fluctuations in technology are an important

during times when business has slowed, but this activity is not generally accounted for in the

National Income Accounts’ measures of output. As a result, output and the Solow residual

appear lower than they actually are during recessions. The evidence on labor hoarding and

cyclical mismeasurement of output, however, is not clear–cut, and so the debate goes on between

proponents and critics of real business cycle theory.

!Figure 9-2

ADDITIONAL CASE STUDY

9-1 More on the Convergence Hypothesis

The Solow growth model suggests that economies with similar rates of population growth and

technological progress should exhibit similar levels of per–capita income in the long run, regardless of

their initial capital stock. During the adjustment to steady state, countries with a lower capital stock will

grow faster than those with higher capital stocks. This is known as the convergence hypothesis. Some

recent theories of endogenous growth, by contrast, do not imply convergence. Rather, they suggest that

there may be constant or increasing returns to capital and, hence, no tendency for convergence in per–

capita income.

There is as yet no consensus on whether or not countries do exhibit convergence in per–capita income.

Figure 1 shows a scatterplot of growth rates since 1960 against output per worker in 1960. The simple

convergence hypothesis suggests that these variables should be negatively related: Countries with higher

GDP per person should grow more slowly. Such a relationship is not apparent in Figure 1, casting doubt

1 G. Mankiw, D. Romer, and D. Weil, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics 107, no. 2 (May

1992): 407–38. Mankiw, Romer, and Weil suggest that a production function such as Y = (K × L × H)1/3, where H is human capital, might describe