Introduction to growth: some facts Prof. Hartmut Lehmann Dipartimento di Scienze Economiche.

Introduction to growth: some facts

Prof. Hartmut Lehmann

Dipartimento di Scienze Economiche

Main stylized facts on growth (fact 1)

1) Enormous variation in per capita income (pci) across economies - for example, poorest countries in the world have pci with less than 5% of pci in richest countries

We see this in table 1 (taken from Jones)

Table 1“Rich countries”

Country

(GDP data in 1985 U.S. $)

GDP per cap. 1997 $U.S.

(PPP)

GDP per

Worker 1997 $U.S. (PPP)

Labor force participation rate 1997

Avg. Annual growth rate

1960-97

Years to double

U.S.A 20,049 40,834 0.49 1.4 50

Japan 16,003 25,264 0.63 4.4 16

France 14,650 31,986 0.46 2.3 30

Italy (other data source)

13,478 30,920 0.43 2.0 35

U.K. 14,472 29,295 0.49 1.9 37

Spain 10,685 29,396 0.36 3.5 20

Table 1, continued“Poor” Countries

Country GDP per cap. 1997 $U.S. (PPP)

GDP per




1960-97

Years to double

China 2,387 3,946 0.60 3.5 20

India 1,624 4,156 0.39 2.3 30

Zimbabwe 1,242 2,561 0.49 0.4 192

Uganda 697 1,437 0.49 0.5 146

Table 1, continued“Growth Miracles”


GDP per




1960-97

Years to double

Hong Kong 18,811 28,918 0.65 5.2 13

Singapore 17,559 36,541 0.48 5.4 13

Taiwan 11,729 26,779 0.44 5.6 12

South Korea

10,131 24,325 0.42 5.9 12

Table 1, continued“Growth Disasters”


GDP per




1960-97

Years to double

Venezuela 6,760 19,455 0.35 -0.1 -517

Madagascar 577 1,334 0.43 -1.5 -46

Mali 535 1,115 0.48 -0.8 -85

Chad 392 1,128 0.35 -1.4 -48

How to measure income levels in international comparisons?

• Column 1 shows GDP per capita with purchasing power parity (PPP) exchange rate – explains why U.S. is richest country in the world. Simple example of PPP exchange rate: Economist’s exchange rates based on prices of McDonald’s Big Mac around the world. PPP exchange rate based on prices of many goods.

How to measure income levels in international comparisons?

• Column 2 shows GDP per worker. We get this by dividing GDP per capita by Labor Force participation rate (column 1 / column 3)GDP per worker often taken as a productivity measure (i.e. output produced per worker), while GDP per capita taken as welfare measure (output that can be used for consumption and investment per person).BUT, case can be made for using GDP per worker as measure to compare welfare across countries, because home production and shadow economy activities are not included in official GDP, while GDP per worker gives measured output divided by measured input.

Income levels in international perspective

• Table 1 shows rich versus poor countries in the first two panels – tremendous differences in GDP per capita between e.g. U.S. and Uganda: U.S. is roughly 29 times richer than Uganda on this measure.

• Since labor force participation is the same in both countries, the main reason for this great divergence cannot be the effort that a society puts into economic activity (we can take labor force participation as a rough measure of “effort”). Instead, technology drives these differences as we shall see later.

Income levels in international perspective, continued

• Figure 1 shows that in 1995 more than half the world’s population has a GDP per worker that is less or equal to 10% of the U.S. GDP per worker.

• Most of these people live in China (1/4 of world population) and India (1/6 of world population).

• Figure 2 shows how that the distribution of world income has become somewhat more equal since 1960. There has been a fall in the share of world population living in countries with low percentages of US GDP per worker and a rise in the share of world population living in countries with high percentages of US GDP per worker.

Figure 1

Figure 2


2) Rates of economic growth vary substantially across countries

Last two columns of table 1 are directly related to growth.

Average growth rates – change in ln (GDP/worker) – vary widely among the shown countries. Within the groups shown there are also great differences as there are between groups (e.g. growth miracles vs. growth disasters)

Main stylized facts on growth (fact 2), continued

• Last column shows how long it takes to double income.

Lucas introduced the rule of thumb that 70/g gives t* , where t* is the time it takes to double income and g is the growth rate (in percentage)

{y(t)=y0egt shows income at time t as a function of initial income (y0) and an exponential growth rate g (as a fraction).

We have t* when y(t)= 2y0, so 2y0= y0egt*

t*= log2/g, Since log20.7 and multiplying by 100, we get Lucas’ rule of thumb: t*= 70/g}


• The main message from the last column of table 1 is that small differences in growth rates if they persist over even moderate time spans can lead to very large differences in per capita income.


3) Growth rates are not generally constant over time. For the world as a whole growth rates were close to zero for most of history, but increased sharply in the 20th century. Individual countries show changing growth rates over time.

Figure 1.3 shows world GDP per capita since 1500. Note the very flat slopes between 1500 and 1850, with growth accelerating in second half of 19th century and taking off in 20th century. World per capita GDP was roughly $500 in 1500 and was in 2000 about 10 times as large.

Figure 3

Main stylized facts on growth (fact 3), continuedA simple thought experiment shows that the world could not have grown

at a rate of 2% since e.g. 1750. Assume that it had actually grown at such a rate, then every 35 years its per capita income would have doubled. over 250 years income would have roughly risen by a factor of 27 = 128 if in 2000 per capita GDP of the world were $20,000 it would have been $150 in 1750 (at prices of 2000). But today even the poorest country has a per capita income of $300. even over 250 years the world’s per capita GDP could not have grown at a rate of 2%; given the actual per capita GDP of the world of about $5000 there must have been long stretches of ~ zero growth in human history.

{Note: we do the thought experiment because we do not have really reliable data going back much beyond 1850.}


• Examples of varying average annual growth rates of GDP per worker within countries

India: 1960-1997: 2.3% 1960-1980: 1.3% 1980-1997: 3.5%

China: 1960-1997: 3.5% 1960-1979: 1.9% 1979-1997: 5.0% (!market-oriented

reforms)


4) A country’s relative position in the world’s distribution of per capita incomes can change over time.

Countries that are “poor” can become “rich”, e.g. the NICs in table 1;

Countries that are “rich” can become “poor”, e.g. Argentina – one of the richest countries in the world at beginning of 20th century, now having only 1/3 of U.S. per capita income.

Other stylized facts

In US over last century:• Real rate of return to capital – r – shows no trend.• Shares of income going to capital – rK/Y – and

going to labor – wL/Y – show no trend; they are roughly 0.3 and 0.7 respectively.

• Average growth rate of output per person has been positive and relatively constant over time (see Figure 4)

Figure 4

Other stylized facts, continued

• Growth in output and trade volume (trade volume= exports + imports) are strongly correlated.

• Both skilled and unskilled workers migrate from relatively poor to relatively rich countries/regions. returns to both skilled and unskilled labor must be higher in high-income countries/regions.

Caveat: are other measures of development not better in grasping well-being of a society?

• Using other measures (e.g. human development index) we might get for a specific country another picture than when we use pci, but the rank correlation across countries between pci and other measures is very high focusing on pci growth is legitimate.

The simplest Solow model

• 2 equations

1. A production function, which transforms inputs (e.g. iron ore) into output (e.g. steelworks, computers…)

2. A capital accumulation equation (explaining what factors drive the accumulation of capital in the economy)

The simplest Solow model – production function

• Here we assume 2 inputs – K, L – and an homogeneous output, Y

(1)

• This equation is characterized by constant returns to scale (CRS), i.e. F(aK, aL) = aY for any a>1, we have:

1, LKLKFY

aYLaKaLaKaLaKF 11,

The simplest Solow model – production function (continued)

• If:– w = wage for each unit of labor– r = rental rate of 1 unit of capital per period– p = 1 (price level set to 1 for mathematical

convenience)

• And:– We have perfect competition in product and

labor markets


profit maximizing firms will solve the following problem:

wLrKLKFLK

),(max,


K

Yr

K

F

1 so 11

111

0

1

11

L

Y

L

Fw

L

Y

L

LK

L

LLKLKLK

L

F

wL

Fw

L

F


IMPORTANT:

Share of value of output going to L = 1- (constant)

11Y

wL

L

Yw


IMPORTANT:

Share of value of output going to K = (constant)

As indicated by stylized fact 5 from introduction into growth, shares going to labor and capital are constant (at least in U.S.).

Y

rK

K

Yr

K

F


YYYYK

K

YL

L

Y 111

Note: Every CRS production function has this property,

i.e. that payments going to inputs consume entire output.

Growth accounting

Y = BKL1- B = “Hicks-neutral” productivity term

Taking logs: Log Y = log B + log K + (1-) log L

Differentiating with respect to time:

ty"productivir Multifacto"or ty"productivifactor Total" is Where

:get we termscapitaper In 1

1 1

1111

B

B

B

B

k

k

y

y

B

B

L

L

L

L

K

K

L

L

Y

Y

B

B

L

L

K

K

Y

Y

dt

dL

Ldt

dK

Kdt

dB

Bdt

dY

Y

Growth accounting (continued)Table for the US – Years 1948 - 1998

1948-98 1948-73 1973-79 1979-90 1990-95 1995-98

Output per hour 2.5 3.3 1.3 1.6 1.5 2.5

Contribution from:

Capital per hour worked 0.8 1.0 0.7 0.7 0.5 0.8

IT 0.3 0.1 0.3 0.5 0.4 0.8

Other Capital services 0.6 0.9 0.5 0.3 0.1 0.0

Labor Composition 0.2 0.2 0.0 0.3 0.4 0.3

TFP or MFP 1.4 2.1 0.6 0.5 0.6 1.4

Source: Bureau of Labor Statistics(Already discussed that TFP/MFP is low or not existing in LDC’s)

Growth in international perspective

Growth of GDP in transition countries (CEE &FSU)

Growth accounting – transition countries




Introduction to growth: some facts Prof. Hartmut Lehmann Dipartimento di Scienze Economiche.

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