macro chapter 2 basic facts about prosperity and growth

The Long Run
Economic Growth, Long-run
Unemployment and Structural
Economic Policy

Basic Theory and
Empirics about
Prosperity and
Growth
2 Some facts about prosperity and growth
3 Capital accumulation and growth the basic solow model
4 Wealth accumulation and capital mobility: the Solow model


Some facts about prosperity and growth

An Inquiry into the Nature and Causes of the Wealth of Nations. This was the title Adam
Smith gave his famous book published in 1776, a book which greatly advanced
economics as a scientific discipline. Already in the title Adam Smith stated what he
considered to be the most important issue in economics: what is it that makes a nation
prosperous, to the benefit of its citizens? Smith was clear from the very beginning about
how prosperity should be measured:
The annual labour of every nation is the fund which originally supplies it with all the necessaries
and conveniences of life which it annually consumes, and which consists always either
in the immediate produce of that labour, or in what is purchased with that produce from other
nations.
According therefore as this produce, or what is purchased with it, bears a greater or
smaller proportion to the number of those who are to consume it, the nation will be better or
worse supplied with all the necessaries and conveniences for which it has occasion.
(Opening remarks of 'Introduction and Plan of the Work' of
The Wealth of Nations, 1 776).
In modem economic language. Smith says that the average level of prosperity in a
country can be measured by the country's GDP or income per person. It is not necessarily
all of the annual income that is consumed during the year, but what is not consumed is
saved. and becomes either investment or an export surplus. In both uses it adds to the
national wealth and thereby becomes a source of future consumption. Consumption is
thus always rooted in production and income. and in so far as consumption is a good
proxy for the economic well-being of people, annual GDP or income per person is a relevant
measure of prosperity. Clearly, not only the avemge income per person but also the
distrilJUtion of income across persons is of interest. However. for a given degree of income
inequality, an increase in average GDP per person is to the benefit of everybody.
According to Adam Smith's view, it is the annual/eve/ of GDP per person that is of
importance. Nevertheless, in Book One we will be much concerned with economic
growth, i.e. the annual increase in GDP per person. We are interested in growth, not as an
end in itself, but because the way a country can reach a higher level of income is through n
process of growth.

Figure 2.1 gives some clear illustrations of the importance of gradual growth for
reaching higher, or falling to lower, levels of income per person. The figure shows GOP per worker (GOP per person in the labour force), no: GOP per capita (GOP per person in the
population) for reasons to be explained.
1 Around 19 60, three
African nations. Botswana, Nigeria and Uganda, were all at about the same level of GDP
per worker, and this level was very low by international standards. Over the subsequent
40 years, GDP per worker in Botswana grew at an impressive average rate of about 6 per
cent per year, while the growth rates of Nigeria and Uganda were - 1.2 per cent and
1.4 per cent. respectively. This implied that around the year 2000 the level of GDP per
worker in Botswana was more than 10 times greater than in Nigeria and Uganda. By
2000 Botswana had not become extremely rich, but rather than having. as Nigeria and
Uganda, a GDP per worker at or below 3 per cent of the US level, Botswana had reached a
level of 3 6 per cent ofUS income per capita. The differences in the conditions of life caused
by these different growth experiences are not ditncult to imagine.
Both Jamaica and Hong Kong had a GDP per worker of around 20 per cent of that in
the USA in 1960. From that time until2000, Jamaica grew at an average rate of0.2 per
cent a year, while Hong Kong grew at an annual rate of 5.5 per cent. Today Hong Kong is
one of the world's rich areas. with a GDP per worker of about 80 per cent of the US level,
while Jamaica is relatively poor at around 11 per cent of the US level.
In 1960 Venezuela was one of the world's richest countries with a GDP per worker of
83 per cent of the US level. while Italy was considerably behind at 55 per cent of the US
level. However. until 2000, average annual growth in Italy was 2.9 per cent, but in
Venezuela it was negative. Today it is Italy, not Venezuela, that is one of the world's
richest countries, with a GDP per worker at 84 per cent of the US level. Venezuela has
fallen to 28 per cent of the US level.

What allows a country to escape from poverty, or to achieve prosperity, is a process of
growth over a succession of years. Therefore one of the most important questions in
economics. probably the most important one. is: what creates growth? Growth theory and
growth empirics are fascinating subjects in economics. We start in this chapter by stating
and discussing some empirical regularities concerning prosperity and growth. These
'stylized facts' constitute important knowledge in themselves. They will also be used later
on as yardsticks: the growth theory to be presented \.viii be held up against the empirical
facts.

2.2 measuring the wealth of a nation

Agreeing with Adam Smith that the ratio of the annual 'produce' to 'the number of those
who are to consume it' is a relevant measure of the average standard of living in a nation,
we will use GDP per person as a proxy for living standards. You are assumed to know
about statistics such as GDP . total consumption. total investment, etc .. from an earlier
course in macroeconomics. We will therefore only discuss a lew aspects of measuring
economic welfare by GDP per person.
Suppose we would like to compare the standard ofliving bea.veen a highly developed
country such as the US, and a somewhat less developed country with relatively fewer
transactions in the olllcial market economy and relatively more sell~sulllciency. The GDP
of each country is the value of the 'olllcial' marketed production.
First. a comparison between the two countries requires that their GDPs be measured
in the same currency, say US dollars. For this purpose we need an exchange rate that
converts amounts denominated in the currency of the less developed country, the peso
say, into amounts in dollars. It may be misleading to use the olllcial prevailing exchange
rate between the peso and the dollar since prevailing exchange rates are volatile. A 10 per
cent increase in the peso relative to dollars from one month to the next will typically not
reflect that the less developed country has become 10 per cent richer compared to the US
in one month. It will rather be a reflection of some change in expectations. Current
exch ange rates are not appropriate for converting GDPs if one is interested in standards of
living. Instead one should use a rate of conversion that reflects purchasing power. The
total cost of a relevant bundle of goods representing the 'necessaries and conveniences' of
life should be computed in the two countries, and the purchasing-power-adjusted
exch ange rate could then be defined as the relation between the two total costs. If the
bundle has a total cost of 1000 dollars in the US, and a cost of 100,000 pesos in the less
developed country, the purchasing-power-adjusted exchange rate is one dollar for
100 pesos. One should use this computed exchange rate to convert the GDP of the less
developed country into a purchasing-power-adjusted GDP in US dollars.
A second issue is whether GDP per person should mean GDP per capita. where the
GDP is divided by the size of the total population. or whether it should mean GDP per
worker, where the GDP is only divided by the size of the labour Ioree, which is the population
size times the labour force participation rate? The less developed country will typically
have a larger informal sector and relatively more people living from non-marketed
home production. If one divides the olllcial GDP of the country, the value of the marketed
production, by the size of the entire population. one will probably underestimate the
prosperity of the country in a comparison with the highly developed country. Dividing the
ofllcial GDP by the size of the ofllcial labour Ioree can be a way of correcting for this bias.
since the olllcial labour force does not include those working only in the informal sector.
(If the productivity in the formal and the in formal sector are identical, the correction
should be perfect.) Generally. using GDP per worker as our measure of the standard of
living makes at least some correction lor cross-country dillerences in the degree of
participation in the formal economy.
Table 2.1 shows that it may indeed make a difference whether one considers GDP per
capita or per worker. For instance. measured by GDP per capita, Egypt and Pakistan are
only 13 per cent and 6 percent as rich as the US in the year 2000, respectively. Measured by GDP per worker. they are still not rich compared to the US . but they are considerably
less poor. now at 21 per cent and 11 per cent of th e US level. respectively. Th is reflects the
low participation rates in Egypt and Pakistan.
According to GDP per capita, Ireland was 79 per cent as rich as the US in 2000. but
measuring by GDP per worker. Ireland was just as rich as the US. The dillerence is a reflection
of the much higher participation rate in the US. Also note that according to GDP per
capita, Denmark is richer than the Netherlands. but according to GDP per worker it is a bit
poorer, reflecting the higher participation rate in Denmark. For the examples oflreland vs.
the US, and Denmark vs. the Netherlands, the dHTerences in participation rates are probably
not caused by diflerences in the relative sizes of the unofllcial sectors. but rather by
'true' differences in labour force participation . Nevertheless, it can still be argued that GDP
per worker is a more appropriate measure of economic standards ofliving than GDP per
capita, because home production and leisure should also count.
GDP per worker is closer to a productivity measure th an GDP per capita. In the growth
models presented in the subsequent chapters. average labour productivity is a key variable.
and productivity has a closer correspondence to GDP per worker than to GDP per
capita. Since we want a close correspondence bet\<veen our empirical and theoretical
variables, this is another reason lor studying GDP per worker. 2
The statistics used lor international comparison in this book are of the purchasingpower-
adjusted type, and we will mainly use GDP per worker as a proxy for the standard
of living and for labour productivity . Data \>Viii. to a large extent, come from a database
called the Penn World Table (PWT), which is an attempt to create internationally comparable
statistics relevant lor growth issues for the countries of the world lor a considerable
period (for many developed countries 19 50- 2000, and lor most other countries
1960- 2000). 3 The PWT does not cover all countries in the world. Among the exceptions are nations that were formerly part of the Soviet Union and other formerly planned
economies ofEastern Europe.

2.2 rich and poor and growing or declining

We have already given some illustrations of the enormous differences between rich and
poor countries, and of the fact that some countries have managed to develop from poor to
not so poor through a good growth performance. We now go into more detail about the
issues of poverty and prosperity. and about moving in and out of these categories.
The world income distribution
Some countries are poor and some are rich, but is there any sign that the world income
distribution has become more equal over, say. the last 40 years? We can investigate this
by means of so-called Lorenz curves. Figure 2. 2 shows two Lorenz curves for the world,
one lor 1960 and one lor 1998. A point (x. y) on a Lorenz curve indicates that the fraction
x of the people in the world with the smallest incomes earns the fraction y of all the income
in the world. For instance. the Lorenz curve for 1960 shows that in that year. the 60 per
cent of the world population that lived in the poorest countries earned around 15 per cent
of the world's income. In 1998 the corresponding llgure was around 20 per cent.
The curves are based on average GDP per worker and assume that nll people living in
a specific country, not just all people in the labour force. have an income equal to the
average per worker GDP recorded in the PWT, in the country and for the year in question.


We thus attribute to each individual in a country an artificial income equal to the
recorded average GDP per worker. The Lorenz curves have been constructed from such
personal incomes and population sizes (you will be asked to do a similar construction
yourself in Exercise 2 ). The procedure may seem a bit odd, but in this way we can base the
Lorenz curves on data for average GDP per worker.
Absolute equality corresponds to a Lorenz curve identical to the 45° line. or diagonal.
The further the Lorenz curve is below the diagonal. the more unequal is the income distribution.
Therefore the area between the diagonal and the Lorenz curve. as a fraction of the
entire area below the diagonal. is an aggregate measure of inequality. This measure,
called the Gini coefficient. is a number between zero and one, and the closer it is to one the
more ina:ruality there is. The Gini coelllcients for 19 60 and 199 8 are shown in Fig. 2.2,
and they are 0 . 59 and 0 .52, respectively. Because of the particular construction of the
Lorenz curves based on GDP per worker. these Gini coefllcients are not comparable to traditional
coetllcients computed lor the income distribution of a specific country. However,
they should be comparable to each other.
Investigating the Lorenz curves and the Gini coelllcients reveals that there were enormous
income dillerences in the world both in 1960 and in 1998. Between the two years
the world income distribution does seem to have become more equal, but not much, and
not at the bottom.
Our investigation of the world income distribution is a bit crude. Most of the improvement
indicated by Fig. 2.2 comes from the relatively good growth performances of some
heavily populated countries. in particular China, but also India and Pakistan (as illustrated
in Table 2.3 below). This does not necessarily mean that Fig. 2.2 gives a distorted
impression, but in the construction we have completely neglected the influence of
inequality within countries by attributing the same income to all persons in each country.
If. for instance, the personal income distribution in China has become more unequal over
the period considered, Fig. 2.2 will exaggerate the degree to which the per~~ona/ world
income distribution has become more equal. Furthermore, the data lor the three heavily
populated counties mentioned above are not the best. It is interesting to note that more
thorough studies of the evolution in the world income distribution, which account lor
inequality within countries, reach conclusions similar to the one appearing from our
more crude analysis. 4
Some countries are rich and some are poor. the differences are enormous, and it has pretty much
stayed like that in relative terms over the last 40 years. However, there is some tendency
towards a more equal world income distribution. but not lllltcl! at the bottom.
Two features should be noted. First, the Lorenz curve and the associated Gini
coelllcient illustrate the income distribution in relative terms. If the Lorenz curve had been
completely unchanged from 1960 to 1998 it would mean that the percentage change in income per capita in the world's poorest country would have been the same as in the
richest country. In absolute terms the poorest country would be much less poor by 1998
than in 1960. Indeed, the world average income per worker (computed '>\lith population
sizes as weights) increased from 19 60 to 1999 by an average annual rate ofl .9 per cent.
corresponding more or less to a doubling over the full period. The fact that the Lorenz
curve is relatively unchanged at the bottom means that the poorest countries have also
enjoyed most of this increase. On the other hand. if the world income distribution is
unchanged in relative terms, and incomes generally increase, then the absolute differences
between the poorest and the richest increase.
Second. it is not exactly the same countries that are the poorest (or the richest) in 1960
and 1998. The fact that the 10 percent of people living in the poorest countries earned only
around 1.5 per cent of world income in 1960 as well as in 1998 does not mean that it is
impossible to escape from poverty. There were some countries that did move out of the
group of the poorest countries by having high growth (compared to the world). However,
the other countries that took their place among the poorest had sulllciently bad growth
experiences to ensure that the group of poorest countries did not increase their share of the
world's income.
Prosperity and poverty, growth and decline
The movement in and out of the groups of the poorest and of the most prosperous countries
is illustrated in Table 2.2. The table states some statistics for the countries that were
among the 15 poorest in terms of GDP per worker in 1960 and in 1998, and for the 15
richest countries in both years (still only including countries for which data are available
from the PWT). The average annual growth rates between 1960 and 1998 reported in
Table 2.2 have been calculated as (In y 98 - In y 60)/38, where y 1 is GDP per worker in year
t. We use here a general property that will be used throughout the book: if the relative
change in a Yariable is not too large, it is approximately equal to the variable's absolute
change in (natural) logs. 5
Table 2.2 illustrates again the enormous di1Ierences between the rich and the poor,
but also a fair amount of income mobility. Some countries are among the 15 poorest both
in 1960 and 1998, but other countries have left the group of the poorest. For instance, in
1960 China was among the poorest w ith a level of GDP per worker at 4. 3 per cent of that
in the US . By 1998 China had advanced to 8. 9 per cent of the US level. This was achieved
by an average annual growth rate in GDP per worker of 3.8 per cent, bringing China
safely out of the group of the 15 poorest nations in 1998, which all had a GDP per worker
of less than 4 per cent of the US level.
Other countries that moved out of the bottom 15 are, for example. Lesotho and
Romania. Over the same 3 8 years countries such as Mozambique and Niger moved the
other way, into the group of the poorest, by having very bad growth performances. Their
GDP per worker fell from being around 9 per cent of the US level down to less than 3. 5 per
cent.

At the rich end there was also a substantial amount of mobility. Most impressively,
Hong Kong and Ireland. starting at levels of GDP per worker relative to the US of 19 per
cent and 43 per cent. respectively, moved into the top 15. and ended at levels 79 per cent
and 91 per cent. respectively. Most spectacular drop outs of the top 15 are Argentina,
Venezuela and New Zealand.
Table 2.2 reveals another interesting, and perhaps surprising, fact: even among the
world's 15 richest countries in 1998, there are substantial differences in income per
worker, ranging from 73 per cent of. to above. the US level.

Since a country can move from poor to rich through a process of growth. and vice
versa, it is of interest to look directly at growth performances. Table 2.3 shows the bottom
20 and the top 20 lor growth in GDP per worker between 1960 and 1998. It is not
surprising to find the so-called 'tiger economies' of East Asia in the top 20: Taiwan. Hong
Kong, South Korea, and also Japan. It is perhaps more surprising (if you had not read the
previous sections) to find the African country Botswana near the very top. and to lind
countries like the Republic of Congo. China. India, Pakistan and Syria on the list.
The countries at the top oft he top 20 are often called 'growth miracles' . Likewise. the
countries in the bottom 20 can be called 'growth disasters'. Note that lor many of these
countries, average growth rates between 19 60 and 1998 were actually negative.
The countries of the world that are neither in the growth top 20 nor the bottom 20
have had annual growth rates between 3 per cent (the slowest growing countries in top
20) and 0.3 per cent (the fastest grm.ving countries in the bottom 20): see for instance
Table A at the end of Book One. Altogether, our insights can be summarized as follows:
Growth mtes vary substantially between countries. and by the process of growing or declining
quickly. a country cnn move from being relatively poor to being relatively riel!, or from being
relatively rich to being relatively poor.
Hidden in the data is another interesting fact. Consider the tiger economies. Taiwan,
Hong Kong and South Korea (Singapore could be included, but does not appear in
Table 2.3 because oflack of data for 1998)which all grew very quickly between 1960 and
1998, with average annual GDP growth rates per worker above 5 per cent. Other South-
East Asian countries such as Thailand and i\'lalaysia also grew quickly over the same
period. on average around or above 4 per cent per year. We know. however. that over the
preceding 38 years they grew much more slowly. In fact. in the 1960s some economists
worried about the prospects for countries in South Asia. 6 All the growth miracles of
South-East Asia experienced breaks in their growth rates from lower to higher values
somewhere around the early 19 60s. Similar growth breaks have occurred lor several
other countries in the growth top 20.
Growth crm brenk in a country. tuming.fmm a high rate to a low one or vice versa.
You may perhaps think that this is a trivial fact: there is nothing inevitable about
grm.vth. However. it illustrates once again that the light against poverty is not a hopeless
one. In particular, one cannot point to a continent or part of the world in which the break
in growth from low to high should be impossible. We stress this because sometimes in the
public debate it is taken for granted that countries in some parts of the world, sub-Saharan
Africa or the Middle East for instance. will never be able to grow out of poverty. The data
simply do not support such an idea. There are no growth-preventing areas in the world,
but there may be grm.vth -preventing policies or circumstances (such as civil war. lor
instance).

Most of all, Stylized fact 3 raises again the perhaps most important question in
economics: how can a country create a positive growth break? What kinds of policies can
do that? Growth theory and empirics. as presented in the coming chapters. can contribute
some possible answers.

2.3 Convergence

An interesting idea in economics would, if it were true, imply that poverty should
disappear by itself.
Absolute convergence
Figure 2.3 plots the log of annual GDP per worker for the period 1950 to 2000 lor a
selection of OECD member countries in 1998. A glance at the Hgure suggests that all the
countries tend to approach one and the same 'growth path' . Since lny,-lny,_1 is
(approximately) the rate of growth in y ,. in a Hgure showing In y, against timet. constant
growth corresponds to a straight line, and the slope of the line is the growth rate.
Figure 2.3 suggests a tendency for countries to approach one and the same upward
sloping straight line, perhaps more or less a line corresponding to the USA.
Figures like Fig. 2.3 (drawn lor even longer periods, up to 100 years and more) were
presented by William J. Baumol in a famous article from 1986, suggesting some of
the 'laws' discussed below. 7 Such ligures open up the fascinating possibility that the diflerences with respect to output and income per person between the countries of the
world automatically vanish in the long run. This possibility is sufficiently intriguing to
have a name of its m<Vn:
The Hypothesis of Absolute Convergence. Tn the long nm GDP per worker (or per capita) converges to one and
the same growth path in all countries. so that all countries converge on the same level of income per worker.
A main reason why this hypothesis is so fascinating is the implication that poverty
should disappear by itself in the long run. It is worth thinking about what this would
imply for the relevance of, say, foreign aid policies. It would not make such policies irrelevant
altogether. It could be argued that the speed by which poverty disappears is so slow,
and the current poverty problems so severe. that foreign aid is currently needed. However,
other things being equal. if poverty disappears by itself. it certainly makes foreign aid less
necessary than if some countries are caught in poverty traps.
The hypothesis of absolute convergence implies that countries with relatively low levels
of GDP per worker in an initial year will grow relatively fa st after that initial year. 8 In other
words, average growth in GDP per worker from year 0 to year T. say, should be negatively
correlated with GDP per worker in year 0 . Indexing cow1tries by i. and denoting country
i's GDP per worker in year t by y~ .. the following equation (where the left-hand side is the
approximate average annual growth rate in GDP per worker, {3 0 is a constant. and {3 1 is a
positive parameter) should then be expected to lit well:
In y~. - ln y;) _ {3 {3 ;
T = o- J lnyo, (1)
Figure 2.4 plots the average annual growth rate of GDP per worker from 19 51 to 2000
against the log of GDP per worker in 19 51 lor all OECD member countries in 2 000 lor
which data were available from the PWT.
The country points in Fig. 2.4 are nicely located along a decreasing straight line. The
line that has been drawn in the figure is a best flt to the points according to a standard
statistical method. ordinary least squares (OLS) estimation, wh ich is described in the
flgure legend and in the statistical appendix to this book. The line has the particular
formula:
(2)
Figures 2.3 and 2.4 seem to support the hypothesis of absolute convergence. but they
only present data for some countries. This would not be so much of a problem if those
countries were randomly selected and representative. However, they are not. Both ligures
have, in diflerent ways. selected countries which had relatively high and relatively similar
GDPs per worker in 2000. Figure 2.4, lor instance, focuses on the club of relatively rich
OECD members in 2000. The countries in Fig. 2.4 that had relatively low GDPs per
worker around 19 SO must h ave gro\<Vn relatively fast to be able to join the rich club in 2000. The selection of countries thus has a bias in favour of the hypothesis we are testing.
This problem is known as the 'sample selection bias' problem, and was noted in the
present context by the economist J. Bradford DeLong in an article in 1988.9
To avoid the sample selection bias problem one should try to get a more representative
sample. One way to proceed is as follows: in order to have good standardized data for
a large number of countries, consider the somewhat shorter period from 1960 to 2000,
and include all countries lor which the relevant data for this period are available from the
PWT. This is what we will do, except that we exclude countries for which the data quality
is relatively poor according to tbe PWT itself. 10
Figure 2.5 plots the average growth rate of GDP per worker from 1960 to 2000
against the log of GDP per worker in 1960 lor all countries fuliHling the criteria
mentioned. The nice negative relationship has disappeared. The slope of the line of best
IH has even become positive. but the line fits so poorly that we cannot attach any
statistical signillcance to its slope. Since absolute convergence implies a clear negative relationship, we have to draw the sad conclusion: the hypothesis ofabsolute convergence does
not hold.
Conditional convergence
Thinking a bit more about it, absolute convergence is too much to hope for. We know that
the countries in Fig. 2. 5 diller considerably with respect to basic structural characteristics.
For instance. some countries have higher rates of saving and investment than others.
Savings and investment accumulate as capital. and capital is productive. We should
therefore expect countries with higher savings rates to have higher GDP per worker, but
then GDP per worker ca1mot converge to one and the same level for all countries.
Similarly. some countries spend a larger fraction of GDP on education (investing in
human capital) than others, and education makes labour more productive. Countries
with higher investment rates in human capital should therefore be expected to approach
higher levels of GDP per worker. A third structural characteristic likely to be important is
population growth. Higher population growth means that a larger number of people
will come to share the physical and human capital accumulated in the past. Other
characteristics being equal. this should pull GDP per capita down, again preventing
absolute convergence.
Consider t\ovo countries with the same level of GDP per worker in an initial year zero,
and suppose that the first country has more favourable structural characteristics than the
second. Since the first country will then approach a higher level of GDP per worker than the second. it will also have higher average growth in GDP per worker over a period after
year zero. Such reasoning h as led to a weaker notion of convergence:
The Hypothesis of Conditional Convergence. A country's i11come per worker (or per capita) converges to a
country-specific long-run growth path which is given f1y the basic structural characteristics of tile cou11try. Tile
jitrther below its own long-ru11 growth path a country su1rts. tile jnster it will grow. l11come per worker therefore
converges to the same level across cou11tries conditional on the countries being structurally alike.
Again the convergence hypothesis implies a relationship between the initial level of
and the subsequent growth in GDP per worker: other things (basic structural characteristics)
being equal. countries with relatively low levels of GDP per worker ill an initial year will grow
relatively fast after that initial year. The crucial addition compared to the absolute convergence
hypothesis is the phrase 'other things being equal'. According to the hypothesis
of conditional convergence, it is only after controlling appropriately for structural diilerences
that one should find a negative relationship between initial GDP per worker and
subsequent growth. The correct equation would not be (1) above. but perhaps an
equation like
(3)
where zi is a vector of variables capturing country-specific structural characteristics. and
y is a function expressing their influence.
The hypothesis of conditional convergence does not imply that poverty would disappear
by itself in the long run. Nevertheless, conditional convergence is also a fascinating
possibility. It does imply that if a poor country can manage somehow to achieve the same
structural characteristics as rich countries, it will become as rich in due time. What are
the implications of conditional convergence for the relevance of foreign aid? Certainly.
conditional convergence gives more room for foreign aid than does absolute convergence.
since condition al convergence means that a country may be caught in poverty due to bad
structural characteristics. However, the kind of policy indicated is not so much a traditional
one of transfers to the poor countries ('<\lith a reservation like the one we made in
connection with absolute convergence). Rather, the conditional convergence hypothesis
points to the importance of supporting poor countries in improving their internal structures.
This could, for instance. be a policy of assisting a country in building up sound
Hnancial and educational systems.
To work seriously with an equation like (3). for example testing it against data, one
must have an idea of how to handle the structural variables. Which economic variables
should be included in zi, and what should the function y look like? We h ave argued
intuitively above that the rates of investment in physical and human capital and the
population growth rate should probably be included, but this does not tell us how they
should enter. A good answer will require some growth theory, as presented in the coming
chapters. At this stage it will be illustrative to consider a speciHc version of (3 ), which is for
now postulated. but will be rooted in theory later on. So, assume that (among) the relevant
structural ch aracteristics of country i are the rate of investment in physical capital
(the GDP share of gross investment in physical capital), si, and the population growth rate,
11i. Assume further that (for reasons that will become clear in Chapter 5) the appropriate Consider the same countries and years as in Fig. 2. 5. Measures; and n; as the country's
average gross investment rate and its average population growth rate. respectively, over
the period 1960 to 2000 (these can also be computed from data in the PWT, and are
included in Table A of Book One) . Assume that the appropriate value of the parameter fJ 2
is 0.020 (Chapter 5 will explain this value). Finally, create a diagram like Fig. 2.5, still
with In y~0 along the horizontal axis, but now measure the growth rate adjusted for
cozmtry-specijic structural characteristics. (In Y~l- In y~0)/40 - (J 2 [ln s; - ln(n; + 0.075)],
up along the vertical axis. Figure 2.6 then results.
The points in Fig. 2. 6 do seem to be clustered around a negatively sloped straight line.
Hence. controlling for some structural dillerences makes the negative relationship
between initial GDP per worker and subsequent growth visible again, and we have not
even controlled for all the structural characteristics that should be important on a priori
grounds. Education has not been taken into account, but will be later on. This will make
the picture even more compatible with conditional convergence. Based on theoretical and
empirical work. most economists believe that if one puts the right structural characteristics
into z;, and does it in the right way (assuming the right y). then indeed one will end
up with a significant and positive estimate of the fJ 1 in (3 ). That is, if one controls appropriately
for the influence of structural characteristics. growth in GDP per worker is
negatively correlated with the initial level of GDP per worker lor the countries of the
world. This accords with the hypothesis of conditional convergence.

Club convergence
According to the hypothesis of conditional convergence. the long-run growth path of
each country is given entirely by the country's structural characteristics. It is independent
of the country's initial level of GDP per worker: the starting point has no influence on the
long-run growth path. Some economists doubt that this i~ really true. They argue that
indeed the initial position of a country may have an influence on the level of the growth
path that the country is approaching in the long run. In this way history can have a
permanent impact - its influence is not washed out in the long run.
What these economists have in mind is that there is a certain threshold value of GDP
per worker (or perhaps there are several thresholds. but here we present the idea in its
simplest version), which may be country-specific, such that if a country happens to start
below that value, it will converge to one growth path. and if it happens to start above. it
will converge to another path. The two growth paths may have the same constant growth
rate. but they diller with respect to their levels: the first path lies below the second.
Figure 2. 7 gives an illustration of club convergence.
The meaning of the term ;club' is that countries that start oil' on the same side of the
threshold value are in the same category. Stating the hypothesis comprehensively. what
must be changed from the definition of conditional convergence above is that the longrun
growth path depends not only on structural characteristics. but also on the
economy's starting point.
The Hypothesis of Conditional Convergence. A country's income per worker (or per capitn) converges to a
long-rem growth path that depends on the country's basic structural characteristics and on whether its initial GDP per
mpita is nbove or below a spec(fic threshold value. The further below the relevnnt growth path a country starts out. the
faster it will grow. Income per worker therefore converges to the same level across countries conditional 011 the
countries being structurally nlike mtd on the countries startillB 011 the same side of their respective threshold values.

One can write down sound economic growth models that support the idea of conditional
convergence. as well as models supporting the idea of club convergence. Likewise,
some empirical analyses are in favour of conditional convergence. and some are in favour
of club convergence. At present the issue of conditional or club convergence is unsettled.
An interesting implication of the idea of club convergence is that it may provide a
rationale for traditional foreign aid policy. Giving high transfers to a developing country
over some period may bring the country's income per capita above the threshold level,
and thereby initiate a growth process eventually leading the country to higher levels of
income than would have been reached without the transfers. even after the transfers are
no longer given. A foreign aid policy of giving temporary transfers to the poor countries
can thus have permanent beneficial ellects, according to the idea of club convergence.
We may sum up our discussion of convergence below in Stylized fact 4 . The reader
should be warned. however, that the issue of convergence is perhaps a bit more controversial
than our use of the word 'fact' suggests:
Convergence: lf one controls appropriately for structural dij)'erences between the countries
of tile world. a lower initial val11e of GDP per worker tends to be associated with a higher
subsetJuent growth rate in GDP per worker. This accords with the idea that in the long nm
income and GDP per worker converge to a country-spec~flc growth path which is given by the
country's basic structural c/wracteristics. and possibly also by its initial position.

2.4 The long run growth process
The previous section was concerned with the relationship between the growth processes
in dillerent countries. Now we will focus on the long-run growth process within a single
and steadily growing economy, that is. on growth along the country's own long-run
growth path. To separate convergence to the growth path from the long-run growth path
itself. we should look at very long series for GDP per person. It turns out that indeed many
of the countries that industrialized early have had relatively constant growth in GDP per
person over quite long periods.
Steady long-run growth
Figure 2.8 shows the evolution oft he log of GDP per capita in a number of Western countries
for periods exceeding 100 years. and it also shows the linear trends. Disregarding
shorter run fluctuations and the infl uences from great wars and depressions, Fig. 2.8
shows for each country a remarkable tendency towards a constant and positive rate of
grm.vth in output per capita.
Over periods of more titan 130 years, probably up to 200 years. many countries in Westem
Europe and North America have lwd relatively constant ann11al rates of growth in GDP per
capita in ~he range 1.5-2 per cent.
Because of a lack of very long nm data lor GDP per worker, Fig. 2.8 shows GDP per
capita. However, there is good reason to believe that GDP per worker has also grown at constant (slightly lower) rates in the countries considered. since participation rates h ave
typically increased gradually.
The countries that have experienced relatively constant growth have typically had
remarkably constant factor income shares over long periods as well. The 'law' of stable
income shares is illustrated in Fig. 2. 9. which shows the evolution of the income share of
labour for six OECD countries, five of which also appear in Fig. 2 .8 . Not only does labour's
share not show any long-run trend. the relatively constant labour share turns out to be
relatively close to 2/3 in all the countries. There are considerable short-run cyclical movements
in labour's share (not so visible from Fig. 2.9). but the long-run evolution in the
labour income share is fairly precisely described as being constant.
Consider a Western economy that has experienced steady annual growth in GDP per
worker. y 1 = YJL1, where Y1 and L1 are the GDP and the number of workers in year t.
respectively. Labour's share in year tis w1L)Y1
, where w1 is the average real wage per
worker. We can rewrite labour's share as wJ(YJL1) = wJy(' Hence, if y 1 has grown at a
relatively constant rate, and labour's share has stayed relatively constant, the average
real wage rate must have been increasing by more or less the same rate as GDP per
worker. Steady growth in GDP per worker, and a constant labour income share implies
steady grovvth in the real wage.
During the long periods of relatively constant growth rates in GDP per worker in the typical
Westem economy. labour's share of GDP has stayed relatively constant, and (hence) the
average real wage of a worker has grown by approximately the same rate as GDP per worker.
If labour's share has been relatively constant, so must the share of all other production
factors since this latter share is one minus labour's share. Let us call the other factors
'capital', including into this category not only reproducible physical capital. but also, for
example. land and other natural resources.
Let the total capital input in year t be denoted by K1• If we denote the rate of return on
capital by r1, then capital's share is r1K1/Y1 = r J(Y JK1) . Hence. constancy of capital's share
implies that the real rate of return on capital, ru and the output-capital ratio, Y JKu must
have been changing by the same rates.
Over long periods there should be no systematic differences between the trends in the
real rates of return on dillerent types of assets. If the rate of return on capital (as defined
here) over a long period increased by one hall' of a per cent per year, say, while over the
same period the real rate of interest on bonds stayed constant. investment in real capital
would soon become much more advantageous than buying bonds. This would direct portfolios
away from bonds and towards real capital, which would tend to equalize the rates of
returns between bonds and capital.
In the long run the trend of the rate of return on capital must. therefore, be anchored
by the trend of real interest rates on bonds. Figure 2.10 reports on the long-run behaviour
of real interest rates over long periods in some Western countries. The figure shows that
real interest rates (as computed in the figure) fluctuate a lot. but there is no tendency for
real interest rates to be systematically increasing or decreasing over long periods: they
have no long-run trend. upwards or downwards. For purposes of long-run analysis, real
interest rates. and hence the real rate of return on capital. may therefore be treated as if
they were constant.
If capital's share, r,/(Y,/K,), and the rate of return on capital, r,. have both been
relatively constant, then the output- capital ratio, Y JK,. and the capital- output ratio,
KJY" must also have been constant. We can rewrite the capital- output ratio as KjY1 =
(KjL1)/(YjL,! = kjy,. where we have denoted the capital- labour ratio. or capital intensity,
K,/Lt' by k, . Constancy of K,/Y, implies that the capital intensity grows at the same
rate as GDP per worker.
During the long periods of relatively constant growth in GDP per worker in the typical
Western economy, capital's share ar1d the rate of retum on capital have shown no trend.
(therefore) tile capital-output ratio has been relatively constant, and the capital intensity has
grown by approximately the same rate as GDP per worker.
Balanced growth
The empirical regularities in our Stylized facts 5- 7 are much inspired by a famous lecture
given by the British economist Nicholas Kaldor, who pioneered the approach of setting up
the stylized facts and constructing theories to explain them. 11 All three facts can be
~::xpre:;:.eu compreh eu:;ivdy by lhree fuudameulal cou:.laudes: lhe growlh rate ofGDP per
worker is relatively constant. the functional income distribution between labour and
'capital' is relatively constant, and the rate of return on 'capital' is relatively constant. All
the other features in our list of facts follow from these constancies (convince yourselfofthis).
The stylized facts have given rise to an idealized picture of the long-run growth
process called 'balanced growth'. Consider an economy that fulfils the three constancies
with an annual grovvth rate. g, in GDP per worker. a constant annual growth rate. n, in
the number of workers, and for which total annual consumption is a constant fraction,
1 - s, of total annual GDP (a realistic long-run feature for a typical western economy).
Since Y1 = y ,L,, onehas ln Y, - In Y,_1 = (In y,- ln y1_ 1) +(In L, - In L1_ 1) i: g+ 11, so
GDP grows at a constant rate equal to the sum of the growth rate of GDP per worker and
the population growth rate. Hence total consumption, (1 -s)Y,. and total investment, sY1,
must also be grovving at the rate, g + n. Finally. since K1 = k1L1, and k, is growing at the
same rate as y 1• total capital is growing at the rate, g + 11 .
Balanced Growth. 11 The growth process follows a balanced growth path if (Wl' per worker, consumption per
worker. the real wage rate, and the capital intensity all grow at one and the same constant rate, g, the labour force
(population) grows at constant rate, n. GDP. consumption, and capital grow at the common rate. g + n, the
capital- output ratio is constant, and tile rate ofretum 011 capital is co11stant.
Along a balanced gro\.vth path the capital- output ratio is constant. In fact. the
constancy of the capital- output ratio is a main motivating factor behind the definition of income shares and the absence of a trend in the rate of return on capital, where we argued
for the latter by pointing to the long-run behaviour of real interest rates. However, it
should be mentioned that there is some controversy about whether long-run
capital-output ratios are really constant. Direct estimates of the long-run evolution of
capital- output ratios, most notably some by the British economist and economic
historian Angus MaddL~on. suggest that the capital- output ratio may be close to constant
in the US in the long run, but in several other countries the ratio seems to have been
gradually increasing over the last 100 years. 13
When we tum to growth models in the subsequent chapters, balanced growth will be
of theoretical importance. If a growth model predicts that the economy \>\Till converge to or
move a long a specific long-run growth path, then this path should be a balanced growth
path, because of the empirical plausibility ofbalanced growth. Long-run accordance with
balanced growth will thus be used as an 'empirical consistency check' of growth models.