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3 Institutions, technological progress and growth

3 Institutions, technological progress and growth

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Figure 12.6

Protection from expropriation and GDP per person

There is a strong positive relation

between the degree of protection from

expropriation and the level of GDP per

person.

Source: Daron Acemoglu, ‘Understanding institutions’, Lionel Robbins Lectures,

2004, London School of Economics, http://­

economics.mit.edu/files/1353



Kenya’s index is 6. Kenya is below

the regression line, which means that

Kenya has lower GDP per person than

would be predicted based just on the



index.



Log GDP per capita per person, PPP, in 1995



248  THE CORE The long run

LUX

USA

CHE

JPN

NOR

DNK

BEL

CAN

AUT

FRA

ISL NLD

AUS

ITA

GBR

SWEFIN

IRL

NZL

ESP

PRT

SGP



HKG



10



ARE

KWT



MLT

GRC

BHS CHL

OMN SAU

VEN

URY

MEX GAB

ZAF

BWAMYS

CRI COL

TTOTHA BRA

TURPOL



ARG

PAN

IRN

GTM



TUN

ECU

DOM DZA



PER



PHL

SYR

BOLGUY

AGO

LKA

ZWE

HND

NIC

CMR

GIN

CIV

COG

SEN

PAKGHA

VNM

TGO

KEN

UGA

BGD NGA

BFA

MDG

ZMB

NER

YEM

MOZ MWI



SDN

HTI

ZAR

MLI



SLE

ETH



6

4



KOR

CZE



HUN

RUS



ROM



PRY

JAM

JOR

MAR

EGY



SUR SLV



8



ISR



QAT BHR



BGR



IDN

CHN



IND

GMB



MNG



TZA



6



8



10



Average protection against risk of expropriation, 1985–1995



constructed for each of these countries by an international business organisation. The positive correlation between the two is striking (the figure also plots the regression line). Low

protection is associated with a low GDP per person (at the extreme left of the figure are Zaire

and Haiti); high protection is associated with a high GDP per person (at the extreme right are

the United States, Luxembourg, Norway, Switzerland and the Netherlands).

What does ‘protection of property rights’ mean in practice? It means a good political system, in which those in charge cannot expropriate or seize the property of the citizens. It

means a good judicial system, where disagreements can be resolved efficiently, rapidly and

fairly. Looking at an even finer degree of detail, it means laws against insider trading in the

stock market, so people are willing to buy stocks and so provide financing to firms; it means

clearly written and well-enforced patent laws, so firms have an incentive to do research and

develop new products. It means good antitrust laws, so competitive markets do not turn into

monopolies with few incentives to introduce new methods of production and new products.

The list obviously goes on. (A particularly dramatic example of the role of institutions is given

in the next Focus box.)



Focus



The importance of institutions: North Korea and South Korea

Following the surrender of Japan in 1945, Korea formally

acquired its independence but became divided at the 38th

parallel into two zones of occupation, with Soviet armed

forces occupying the north and US armed forces occupying

the south. Attempts by both sides to claim jurisdiction over

all of Korea triggered the Korean War, which lasted from

1950 to 1953. At the armistice in 1953, Korea became formally divided into two countries, the Democratic People’s

Republic of North Korea in the north and the Republic of

Korea in the south.



M12 Macroeconomics 85678.indd 248



An interesting feature of Korea before separation was

its ethnic and linguistic homogeneity. The north and the

south were inhabited by essentially the same people, with

the same culture and the same religion. Economically, the

two regions were also highly similar at the time of separation. PPP GDP per person, in 1996 dollars, was roughly the

same, about $700 in both the north and south.

Yet, 50 years later, as shown in Figure 12.7, GDP per

person was 10 times higher in South Korea than in North

Korea: $12,000 versus $1,100! On the one hand, South



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Chapter 12  Technological progress and growth   249







intervention but also private ownership and legal protection of private producers. North Korea relied on central

planning. Industries were quickly nationalised. Small firms

and farms were forced to join large cooperatives, so they

could be supervised by the state. There were no private

property rights for individuals. The result was the decline

of the industrial sector and the collapse of agriculture.

The lesson is sad, but transparent; institutions matter very

much for growth.



Korea had joined the OECD, the club of rich countries.

On the other, North Korea had seen its GDP per person

decrease by nearly two-thirds from its peak of $3,000 in

the mid-1970s and was facing famine on a large scale. (The

graph, taken from the work of Daron Acemoglu, stops in

1998. But, if anything, the difference between the two

Koreas has become larger since then.)

What happened? Institutions and the organisation

of the economy were dramatically different during that

period in the south and in the north. South Korea relied on

a capitalist organisation of the economy, with strong state



GDP per capita



14,000



PPP GDG per person (1996 dollars)



Source: Daron Acemoglu, ‘Understanding institutions’, Lionel Robbins Lectures,

2004, London School of Economics, http://economics.mit.edu/files/1353



South Korea

North Korea



12,000

10,000

8,000

6,000

4,000

2,000

0

1950



1960



1970



1980



1990



1998



Figure 12.7

PPP GDP per person: North and South Korea, 1950–98



This still leaves one essential question: Why do poor countries not adopt these good institutions? The answer is that it is hard! Good institutions are complex and difficult for poor

countries to put in place. Surely, causality runs both ways in Figure 12.5: low protection

against expropriation leads to low GDP per person. But it is also the case that low GDP per

person leads to worse protection against expropriation. Poor countries are often too poor to

afford a good judicial system and to maintain a good police force, for example. Thus, improving institutions and starting a virtuous cycle of higher GDP per person and better institutions

are often difficult. The fast-growing countries of Asia have succeeded. (The following Focus

box explores the case of China in more detail.) Some African countries appear also to be succeeding; others are still struggling.





M12 Macroeconomics 85678.indd 249



A quote from Gordon Brown, a former

UK prime minister, ‘In establishing the

rule of law, the first five centuries are

always the hardest!’



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250  THE CORE The long run



Focus



What is behind Chinese growth?

From 1949 – the year in which the People’s Republic of

China was established – to the late 1970s, China’s economic system was based on central planning. Two major

politico-economic reforms, the Great Leap Forward in

1958 and the Cultural Revolution in 1966, ended up as

human and economic catastrophes. Output decreased by

20% from 1959 to 1962, and it is estimated that 25 million people died of famine during the same period. Output

again decreased by more than 10% from 1966 to 1968.

After Chairman Mao’s death in 1976, the new leaders

decided to introduce market mechanisms progressively

in the economy. In 1978, an agricultural reform was put

in place, allowing farmers, after satisfying a quota due to

the state, to sell their production in rural markets. Over

time, farmers obtained increasing rights to the land and,

today, state farms produce less than 1% of agricultural

output. Outside of agriculture, and also starting in the late

1970s, state firms were given increasing autonomy over

their production decisions, and market mechanisms and

prices were introduced for an increasing number of goods.

Private entrepreneurship was encouraged, often taking the

form of ‘Town and Village Enterprises’, collective ventures

guided by a profit motive. Tax advantages and special

agreements were used to attract foreign investors.

The economic effects of these cumulative reforms have

been dramatic. Average growth of output per worker has

increased from 2.5% between 1952 and 1977 to more than

9% since then.

Is such high growth surprising? One could argue that

it is not. Looking at the 10-fold difference in productivity between North Korea and South Korea we saw in the

previous Focus box, it is clear that central planning is a

poor economic system. Thus, it would seem that, by moving from central planning to a market economy, countries

could easily experience large increases in productivity.

The answer is not so obvious, however, when one looks at

the experience of the many countries that, since the late

1980s, have indeed moved away from central planning.

In most Central European countries, this transition was

typically associated with an initial 10% to 20% drop in

GDP, and it took five years or more for output to exceed

its pre-transition level. In Russia and in the new countries

carved out of the Soviet Union, the drop was even larger

and longer lasting. (Many transition countries now have

strong growth, although their growth rates are far below

that of China.)



M12 Macroeconomics 85678.indd 250



In Central and Eastern Europe, the initial effect of

transition was a collapse of the state sector, only partially

compensated by slow growth of the new private sector. In

China, the state sector has declined more slowly, and its

decline has been more than compensated by strong private

sector growth. This gives a proximate explanation for the

difference between China and the other transition countries. But it still begs the question: How was China able to

achieve this smoother transition?

Some observers offer a cultural explanation. They

point to the Confucian tradition, based on the teachings

of Confucius, which still dominates Chinese values and

emphasises hard work, respect of one’s commitments, and

trustworthiness among friends. All these traits, they argue,

are the foundations of institutions that allow a market

economy to perform well.

Some observers offer an historical explanation. They

point to the fact that, in contrast to Russia, central planning in China lasted only for a few decades. Thus, when

the shift back to a market economy took place, people still

knew how such an economy functioned and adapted easily

to the new economic environment.

Most observers point to the strong rule of the Communist Party in the process. They point out that, in contrast to

Central and Eastern Europe, the political system did not

change, and the government was able to control the pace

of transition. It was able to experiment along the way, to

allow state firms to continue production while the private

sector grew and to guarantee property rights to foreign

investors (in Figure 12.5, China has an index of property

rights of 7.7, not far from its value in rich countries). With

foreign investors has come the technology from rich countries, and in time the transfer of this knowledge to domestic firms. For political reasons, such a strategy was simply

not open to governments in Central and Eastern Europe.

The limits of the Chinese strategy are clear. Property

rights are still not well established. The banking system is

still inefficient. So far, however, these problems have not

stood in the way of growth.

For more on China’s economy, read Gregory Chow,

China’s Economic Transformation, 3rd edition (Chichester:

Wiley, 2014).

For a comparison between transition in Eastern Europe

and China, read Jan Svejnar, ‘China in light of the performance of Central and East European economies’, IZA Discussion Paper 2791, May 2007.



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Chapter 12  Technological progress and growth   251







12.4  The facts of growth revisited

We can now use the theory we have developed in this and the previous chapter to interpret

some of the facts we saw previously (see Chapter 10).



Capital accumulation versus technological progress in rich

countries since 1985

Suppose we observe an economy with a high growth rate of output per worker over some

period of time. Our theory implies this fast growth may come from two sources:







It may reflect a high rate of technological progress under balanced growth.

It may reflect instead the adjustment of capital per effective worker, K/AN, to a higher

level. As we saw in Figure 12.4, such an adjustment leads to a period of higher growth,

even if the rate of technological progress has not increased.



Can we tell how much of the growth comes from one source and how much comes from

the other? Yes. If high growth reflects high balanced growth, output per worker should

be growing at a rate equal to the rate of technological progress (see Table 10.1). If high

growth reflects instead the adjustment to a higher level of capital per effective worker, this

adjustment should be reflected in a growth rate of output per worker that exceeds the rate

of technological progress.

Let’s apply this approach to interpret the facts about growth in rich countries we saw in

Table 10.1. This is done in Table 12.2, which gives the average rate of growth of output per

worker (gY - gN) for 1985 to 2014 and the average rate of technological progress, gA, for

1985 and 2013 for selected countries in Europe – including Denmark, France, Germany,

Italy, Spain, Sweden and the United Kingdom, together with Japan and the United States

we looked at in Table 10.1. Note two differences between Tables 10.1 and 12.2. First, as

suggested by the theory, Table 12.2 looks at the growth rate of output per worker, whereas

Table 10.1, which was focusing on the standard of living, looked at the growth rate of output per person; the differences, however, are rather small. Second, because of data limita- ➤ In the United States, for example, the

tions, Table 12.2 starts in 1985 rather than in 1950. The rate of technological progress, gA, ratio of employment to population

is constructed using a method introduced by Robert Solow; the method and the details of decreased slightly from 60.1% in 1985

to 59% in 2014. Thus, output per person

construction are given in the appendix to this chapter.

and output per worker grew at virtually

Table 12.2 leads to two conclusions. First, over the period 1985–2014, output per worker the same rate over this period.

has grown at rather similar rates across the selected countries. In particular, there was little or

no catching up of the United States by the other countries. This is in contrast to the numbers

in Table 10.1 which looked at the period 1950–2014 and showed substantial convergence to

the United States. Put another way, much of the convergence happened between 1950 and

1985, and since then appears to have slowed down or even stopped.

Table 12.2  Average annual rates of growth of output per worker and technological

progress in selected rich countries since 1985



Denmark

France

Germany

Italy

Netherlands

Spain

Sweden

United Kingdom

United States

Japan



Rate of growth of output per

worker (%) 1985–2014



Rate of technological

progress (%) 1985–2014



1.3

1.3

1.0

0.7

0.9

1.0

1.8

1.9

1.7

1.6



0.6

1.4

1.1

0.3

0.5

0.3

0.8

1.4

1.4

1.7



Source: Calculations from OECD Productivity Statistics.



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252  THE CORE The long run

Second, growth since 1985 has come from technological progress only in a few cases,

while in most cases it has come from unusually high capital accumulation. This conclusion

follows from the fact that only in some countries has the growth rate of output per worker

been roughly equal to the rate of technological progress. This is what we would expect when

countries are growing along their balanced growth path. In many European economies (with

the exception of France and Germany among the selected countries in Table 12.2), the rate

of growth of output per worker has been substantially higher than the rate of technological

progress, which means that growth in these countries has come from an unusual increase in

the ratio of capital to output, or capital accumulation.

Note what this conclusion does not say. It does not say that capital accumulation was

irrelevant in countries that have been growing along their balanced growth path. Capital

accumulation was such as to allow these countries to maintain a roughly constant ratio of

output to capital and achieve balanced growth.



Capital accumulation versus technological progress in China

Going beyond growth in OECD countries, one of the striking facts of Chapter 10 was the high

growth rates achieved by a number of Asian countries in the last three decades. This raises

again the same questions as those we just discussed: Do these high growth rates reflect rapid

technological progress, or do they reflect unusually high capital accumulation?

To answer these questions, we shall focus on China, because of its size and because of

the astonishingly high output growth rate, nearly 10% since the late 1970s. Table 12.3 gives the

average rate of growth, gY, the average rate of growth of output per worker, gY - gN, and

the

average rate of technological progress, gA, for two periods, 1978 to 1995 and 1996 to 2011.

Warning! Chinese data for output, ➤

employment and the capital stock (the

Table 12.3 yields two conclusions. From the late 1970s to the mid-1990s, the rate of techlatter is needed to construct gA) are

nological progress was close to the rate of growth of output per worker. China was roughly

not as reliable as similar data for OECD

on a (rapid) balanced growth path. Since 1996, however, although growth of output per

countries. Thus, the numbers in the

worker has remained high, the contribution of technological progress has decreased. Put

table should be seen as more tentative

another way, more recently, growth in China has come partly from unusually high capital

than those in Table 12.2.

accumulation – from an increase in the ratio of capital to output.

Table 12.3  Average annual rate of growth of output per worker and technological progress

in China, 1978–2011

Period



1978–1995

1996–2011



Rate of growth of

output (%)

10.1

9.8



Rate of growth of

output per worker

(%)



Rate of technological

progress (%)



7.4

8.8



7.9

5.9



Source: Penn World Table version 8.1.



We can look at it another way. Recall, from Table 12.1, that under balanced growth

gK = gY = gA + gN. To see what investment rate would be required if China had balanced

growth, go back to equation (12.3) and divide both sides by output, Y, to get:

I

K

= (d + gA + gN)

Y

Y

Let’s plug in numbers for China for the period 1996–2011. The estimate of d, the depreciation rate of capital in China, is 5% a year. As we just saw, the average value of gA for the

period was 5.9%. The average value of gN, the rate of growth of employment, was 0.9%.

The average value of the ratio of capital to output was 2.9. This implies a ratio of investment

of output required to achieve balanced growth of (5% + 5.9% + 0.9%) * 2.9 = 34.2%.



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Chapter 12  Technological progress and growth   253







The actual average ratio of investment to output for 1995–2011 was a much higher 47%.

Thus, both rapid technological progress and unusually high capital accumulation explain

high Chinese growth. If the rate of technological progress were to remain the same, this suggests that, as the ratio of capital to output stabilises, the Chinese growth rate will decrease,

closer to 6% than to 9.8%.

Where does technological progress in China come from? A closer look at the data suggests

two main channels. First, China has transferred labour from the countryside, where productivity is low, to industry and services in the cities, where productivity is much higher. Second,

China has imported the technology of more technologically advanced countries. It has, for

example, encouraged the development of joint ventures between Chinese firms and foreign

firms. Foreign firms have come with better technologies and, over time, Chinese firms have

learned how to use them. To relate to our discussion, growth has come largely through imitation, the importation and adaptation of modern technologies from more advanced countries.

As China catches up and gets closer to the technology frontier, it will have to shift from imitation to innovation, and thus modify its growth model.



Summary





When we think about the implications of technological

progress for growth, it is useful to think of technological progress as increasing the amount of effective labour

available in the economy (i.e. labour multiplied by the

state of technology). We can then think of output as

being produced with capital and effective labour.







In steady state, output per effective worker and capital per

effective worker are constant. Put another way, output per

worker and capital per worker grow at the rate of technological progress. Put yet another way, output and capital

grow at the same rate as effective labour, thus at a rate

equal to the growth rate of the number of workers plus

the rate of technological progress.







When the economy is in steady state, it is said to be on

a balanced growth path. Output, capital and effective

labour are all growing ‘in balance’, that is at the same rate.







The rate of output growth in steady state is independent

of the saving rate. However, the saving rate affects the

steady-state level of output per effective worker. And

increases in the saving rate will lead, for some time, to

an increase in the growth rate above the steady-state

growth rate.







Technological progress depends on: (1) the fertility of

R&D, how spending on R&D translates into new ideas

and new products; and (2) the appropriability of the

results of R&D, which is the extent to which firms benefit

from the results of their R&D.







When designing patent laws, governments must balance

their desire to protect future discoveries and provide incentives for firms to do R&D with their desire to make existing

discoveries available to potential users without restrictions.







Sustained technological progress requires that the right

institutions are in place. In particular, it requires wellestablished and well-protected property rights. Without

good property rights, a country is likely to remain poor.

But in turn, a poor country may find it difficult to put in

place good property rights.







France, Japan, the United Kingdom and the United States

have experienced roughly balanced growth since 1950.

Growth of output per worker has been roughly equal to

the rate of technological progress. Growth in China is a

combination of a high rate of technological progress and

unusually high investment, leading to an increase in the

ratio of capital to output.



Key terms

state of technology 237

effective labour 237

labour in efficiency

units 237

balanced growth 241



M12 Macroeconomics 85678.indd 253



research and development

(R&D) 243



patents 245

technology frontier 246



rate of growth of total factor

productivity 257



fertility of research 243



property rights 247



rate of tfp growth 257



appropriability of

research 243



Solow residual 257



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254  THE CORE The long run



Questions and problems

Quick check

All ‘Quick check’ questions and problems are available on

MyEconLab.

1.Using the information in this chapter, label each of the following statements true, false or uncertain. Explain briefly.

a. Writing the production function in terms of capital and

effective labour implies that as the level of technology

increases by 10%, the number of workers required to

achieve the same level of output decreases by 10%.

b. If the rate of technological progress increases, the investment rate (the ratio of investment to output) must increase

to keep capital per effective worker constant.

c. In steady state, output per effective worker grows at the

rate of population growth.

d.In steady state, output per worker grows at the rate of

technological progress.

e. A higher saving rate implies a higher level of capital per

effective worker in the steady state and thus a higher rate

of growth of output per effective worker.

f. Even if the potential returns from research and development (R&D) spending are identical to the potential

returns from investing in a new machine, R&D spending

is much riskier for firms than investing in new machines.

g.The fact that one cannot patent a theorem implies that

private firms will not engage in basic research.

h. Because eventually we will know everything, growth will

have to come to an end.



3.Sources of technological progress: leaders versus

followers

a. Where does technological progress come from for the economic leaders of the world?

b.Do developing countries have other alternatives to the

sources of technological progress you mentioned in part

(a)?

c. Do you see any reasons why developing countries may

choose to have poor patent protection? Are there any dangers in such a policy (for developing countries)?



Dig Deeper

All ‘Dig deeper’ questions and problems are available on

MyEconLab.

4.For each of the economic changes listed in (a) and (b), assess

the likely impact on the growth rate and the level of output over

the next five years and over the next five decades.

a.A permanent reduction in the rate of technological

progress.

b. A permanent reduction in the saving rate.

5.Measurement error, inflation and productivity growth

Suppose that there are only two goods produced in an economy:

haircuts and banking services. Prices, quantities and the number of workers occupied in the production of each good for year

1 and for year 2 are given in the following table:

Year 1



i. Technology has not played an important part in Chinese

economic growth.

2.R&D and growth

a. Why is the amount of R&D spending important for growth?

How do the appropriability and fertility of research affect

the amount of R&D spending?

How do each of the policy proposals listed in (b) to (e) affect the

appropriability and fertility of research, R&D spending in the

long run, and output in the long run?



Haircuts

Banking



Year 2



P1



Q1



W1



P2



Q2



W2



10

10



100

200



50

50



12

12



100

230



50

60



a. What is nominal GDP in each year?

b. Using year 1 prices, what is real GDP in year 2? What is the

growth rate of real GDP?

c. What is the rate of inflation using the GDP deflator?



b. An international treaty ensuring that each country’s patents are legally protected all over the world. This may be

a part of the proposed Trans-Pacific Partnership.



d. Using year 1 prices, what is real GDP per worker in year 1

and year 2? What is labour productivity growth between

year 1 and year 2 for the whole economy?



c. Tax credits for each euro of R&D spending.



Now suppose that banking services in year 2 are not the same

as banking services in year 1. Year 2 banking services include

telebanking, which year 1 banking services did not include. The

technology for telebanking was available in year 1, but the price

of banking services with telebanking in year 1 was $13, and

no one chose to purchase this package. However, in year 2, the



d.A decrease in funding of government-sponsored conferences between universities and corporations.

e. The elimination of patents on breakthrough drugs, so the

drugs can be sold at a low cost as soon as they become

available.



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Chapter 12  Technological progress and growth   255







price of banking services with telebanking was $12, and everyone chose to have this package (i.e. in year 2 no one chose to

have the year 1 banking services package without telebanking).

(Hint: Assume that there are now two types of banking services:

those with telebanking and those without. Rewrite the preceding table but now with three goods: haircuts and the two types

of banking services.)



technology, K is the level of capital stock and H is the level of the

human capital stock.



e. Using year 1 prices, what is real GDP for year 2? What is

the growth rate of real GDP?



e. Low tax rates



f. What is the rate of inflation using the GDP deflator?



g. Low population growth



g. What is labour productivity growth between year 1 and

year 2 for the whole economy?



EXPLORE FURTHER



h. Consider this statement: ‘If banking services are mismeasured – for example, by not taking into account the introduction of telebanking – we will overestimate inflation

and underestimate productivity growth.’ Discuss this

statement in light of your answers to parts (a) to (g).

6.Suppose that the economy’s production function is:

Y = 2K2AN



that the saving rate, s, is equal to 16%, and that the rate of

depreciation, d, is equal to 10%. Suppose further that the number of workers grows at 2% per year and that the rate of technological progress is 4% per year.

a. Find the steady-state values of the variables listed in (i) to

(v):

i.The capital stock per effective worker

ii.Output per effective worker

iii.The growth rate of output per effective worker

iv.The growth rate of output per worker

v.The growth rate of output

b. Suppose that the rate of technological progress doubles to

8% per year. Recompute the answers to part (a). Explain.

c. Now suppose that the rate of technological progress is

still equal to 4% per year, but the number of workers now

grows at 6% per year. Recompute the answers to (a). Are

people better off in (a) or in (c)? Explain.

7.Discuss the potential role of each of the factors listed in (a) to

(g) on the steady-state level of output per worker. In each case,

indicate whether the effect is through A, through K, through

H, or through some combination of A, K and H. A is the level of



a. Geographic location

b.Education

c. Protection of property rights

d. Openness to trade

f. Good public infrastructure



8.Growth accounting

The appendix to this chapter shows how data on output, capital

and labour can be used to construct estimates of the rate of growth

of technological progress. We modify that approach in this problem to examine the growth of capital per worker. The function:

Y = K 1/3(AN)2/3

gives a good description of production in rich countries. Following the same steps as in the appendix, you can show that:

(2/3)gA = gY - (2/3)gN - (1/3)gK

= (gY - gN) - (1/3)(gK - gN)

where gY denotes the growth rate of Y.

a. What does the quantity gY - gN represent? What does the

quantity gK - gN represent?

b. Rearrange the preceding equation to solve for the growth

rate of capital per worker.

c. Look at Table 12.2. Using your answer to part (b), substitute in the average annual growth rate of output per

worker and the average annual rate of technological progress for the United States for the period 1985 to 2013 to

obtain a crude measure of the average annual growth of

capital per worker. (Strictly speaking, we should construct

these measures individually for every year, but we limit

ourselves to readily available data in this problem.) Do the

same for the other countries listed in Table 12.2 (where

data goes to 2014). How does the average growth of capital per worker compare across the countries in Table 12.2?

Do the results make sense to you? Explain.



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256  THE CORE The long run



Further reading





For more on growth, both theory and evidence, read Charles

Jones’s Introduction to Economic Growth, 3rd edition (New

York: W.W. Norton, 2013). Jones’s web page, (http://web

.stanford.edu/~chadj/) is a useful portal to the research on

growth.







For more on patents, see The Economist’s Special Report:

Patents and Technology, 20 October 2005.







For more on growth in two large, fast-growing countries,

read the article by Barry Bosworth and Susan M. Collins,

‘Accounting for growth: comparing China and India’,

Journal of Economic Perspectives, 2008, 22(1), 45–66.







For the role of institutions in growth, read ‘Growth

theory through the lens of development economics’, by

Abhijit Banerjee and Esther Duflo, Handbook of Economic

Growth (Amsterdam: Elsevier, 2005), Chapter  7. Read

sections 1 to 4.



M12 Macroeconomics 85678.indd 256







For more on institutions and growth, look at the slides from

the 2004 Lionel Robbins Lecture ‘Understanding institutions’

given by Daron Acemoglu. These are found at http://economics.mit.edu/files/1353



On two issues we have not explored in the text:





Growth and global warming. Read the Stern Review on

the Economics of Climate Change (2006). You can find it at

www.wwf.se/source.php/1169157. (The report is long.

Read just the executive summary.)



● Growth and the environment. Read The Economist’s

Survey on the Global Environment, ‘The great race’, 4 July

2002, and the update titled ‘The Anthropocene: a manmade world’, 26 May 2011.



30/05/2017 10:45



Chapter 12  Technological progress and growth   257







APPENDIX



Constructing a measure of technological progress

In 1957, Robert Solow devised a way of constructing an estimate of technological progress. The method, which is still

in use today, relies on one important assumption: that each

factor of production is paid its marginal product.

Under this assumption, it is easy to compute the contribution of an increase in any factor of production to the increase

in output. For example, if a worker is paid €30,000 a year,

the assumption implies that his or her contribution to output

is equal to €30,000. Now suppose that this worker increases

the amount of hours worked by 10%. The increase in output

coming from the increase in hours will therefore be equal to

:30,000 * 10%, or €3,000.

Let’s write this more formally. Denote output by Y, labour

by N and the real wage by W/P. The symbol, ∆, means

‘change in’. Then, as we just established, the change in output

is equal to the real wage multiplied by the change in labour:

∆Y =



W

∆N

P



Divide both sides of the equation by Y, divide and multiply

the right side by N and rearrange:

∆Y

WN ∆N

=

Y

PY N

Note that the first term on the right (WN/PY) is equal to

the share of labour in output – the total wage bill in euros

divided by the value of output in euros. Denote this share by

a. Note that ∆Y/Y the rate of growth of output, and denote

it by gY. Note similarly that ∆N/N is the rate of change of the

labour input, and denote it by gN. Then the previous relation

can be written as:

gY = agN

More generally, this reasoning implies that the part of output growth attributable to growth of the labour input is equal

to a times gN. If, for example, employment grows by 2% and

the share of labour is 0.7, then the output growth due to the

growth in employment is equal to 1.4% (0.7 times 2%).

Similarly, we can compute the part of output growth

attributable to growth of the capital stock. Because there

are only two factors of production, labour and capital, and

because the share of labour is equal to a, the share of capital

in income must be equal to (1 - a). If the growth rate of

capital is equal to gK, then the part of output growth attributable to growth of capital is equal to (1 - a) times gK. If, for

example, capital grows by 5%, and the share of capital is 0.3,

then the output growth due to the growth of the capital stock

is equal to 1.5% (0.3 times 5%).

Putting the contributions of labour and capital together,

the growth in output attributable to growth in both labour

and capital is equal to [agN + (1 - a)gK].



M12 Macroeconomics 85678.indd 257



We can then measure the effects of technological progress by computing what Solow called the residual, the

excess of actual growth of output gY over the growth

attributable to growth of labour and the growth of capital

[agN + (1 - a)gK]:

Residual K gY - [agN + (1 - a)gK]

This measure is called the Solow residual. It is easy to

compute. All we need to know to compute it are the growth

rate of output, gY, the growth rate of labour, gN, and the

growth rate of capital, gK, together with the shares of labour,

a, and capital, (1 - a).

To continue with our previous numerical examples,

suppose employment grows by 4%, the capital stock

grows by 5% and the share of labour is 0.7 (so the share

of capital is 0.3). Then the part of output growth attributable to growth of labour and growth of capital is equal to

2.9% (0.7 * 2% + 0.3 * 5%). If output growth is equal,

for example, to 4%, then the Solow residual is equal to

1.1% (4% - 2.9%).

The Solow residual is sometimes called the rate of growth

of total factor productivity (or the rate of TFP growth, for

short). The use of ‘total factor productivity’ is to distinguish

it from the rate of growth of labour productivity, which is

defined as (gY - gN), the rate of output growth minus the

rate of labour growth.

The Solow residual is related to the rate of technological

progress in a simple way. The residual is equal to the share of

labour times the rate of technological progress:

Residual = agA

We shall not derive this result here. But the intuition for

this relation comes from the fact that what matters in the production function Y = F(K, AN) (equation (12.1)) is the product of the state of technology and labour, AN. We saw that to

get the contribution of labour growth to output growth, we

must multiply the growth rate of labour by its share. Because

N and A enter the production function in the same way, it is

clear that to get the contribution of technological progress

to output growth, we must also multiply it by the share of

labour.

If the Solow residual is equal to zero, so is technological

progress. To construct an estimate of gA, we must construct

the Solow residual and then divide it by the share of labour.

This is how the estimates of gA presented in the text are

constructed.

In the numerical example we saw previously, the Solow

residual is equal to 1.1% and the share of labour is equal to

0.7. So, the rate of technological progress is equal to 1.6%

(1.1% divided by 0.7).



30/05/2017 10:45



258  THE CORE The long run

Remember the definitions of productivity growth you

have seen in this chapter:

(a)Labour productivity growth (equivalently, the rate of

growth of output per worker): gY - gN.

(b)The rate of technological progress: gA.

In steady state, labour productivity growth (gY - gN)

equals the rate of technological progress gA. Outside of



M12 Macroeconomics 85678.indd 258



steady state, they need not be equal. An increase in the

ratio of capital per effective worker, due, for example, to an

increase in the saving rate, will cause gY - gN to be higher

than gA for some time.

Source: The original presentation of the ideas discussed in this appendix is found in

Robert Solow’s article, ‘Technical change and the aggregate production function’,

Review of Economics and Statistics, 1957, 312–320.



30/05/2017 10:45



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