Intermediate MacroeconomicsLecture 2 - Growth Facts & the Malthusian Model

Zsofia L. Barany

Sciences Po

2014 January

Hall and Jones 1999, QJE:

In 1988 output per worker in the United States was more than 35times higher than output per worker in Niger. In just over ten days

the average worker in the United States produced as much as anaverage worker in Niger produced in an entire year.

Lucas 2000, JEP:

How did the world economy of today, with its vast differences inincome levels and growth rates, emerge from the world of two

centuries ago, in which the richest and the poorest societies hadincome differing by perhaps a factor of two, and in which no

society had ever enjoyed sustained growth in living standards?

Measuring growth

I growth: the change in output per capita over time → proxyfor standards of living

I output per capita: real GDP/population

I alternatively: real GDP/worker → gives a sense ofproductivity change

I there are other important measures of development such as:life expectancy, infant mortaility, education

I is it development what we want to measure? or somethingelse? welfare?

I there are two reasons why GDP per capita is the preferredmeasure:

1. more data available2. theories have predictions mainly in terms of income

I growth theory is concerned with changes in real GDP percapita over a very long horizon

I comparisons over a long period of time are difficultI even if nominal income data is available, we need price indices

to transform it to real dataI adjustment for quality changes and the introduction of new

goods is difficult

I to compare across countries: use adjustment of nominal GDPaccording to PPP

I the growth rate is gt = (yt − yt−1)/yt−1I growth is exponential, if the growth rate, g is close to

constant → yt ≈ (1 + g)ty0I even a very small difference in g can result in huge disparities

in the level of output per capita in 100 years

Small, sustained differences matterImplications for human welfare are ENORMOUS

0  

200  

400  

600  

800  

1000  

1200  

1400  

1600  

1800  

2000  

1%   1.50%   2%   3%  

GDP  pe

r  cap

ita  

growth  rate  

year  0  

year  10  

year  20  

year  50  

year  100  

”Once one starts to think about [economic growth] it is hard tothink about anything else.”

Robert Lucas

Economic growth is important.

The main data sources are:

I historical data from Angus Maddison

I data since 1950 from Summer-Heston, also known as thePenn World Tables

I there are many websites where you can find data on economicgrowth: World Bank, OECD, ...

⇒ average real incomes in the US and in Western Europe are

I 10 to 30 times larger than 100 years ago

I 50 to 300 times larger than 200 years ago

From stagnation to growth

1. stagnation: average income at the beginning of the industrialrevolution was not far above subsistence levels → growth inper capita income before must have been very lowthere was growth in total output, but the population alsoincreased by a lot→ Malthusian model

2. modern growth: since the industrial revolution most of thedeveloped economies have been growing per capita at 1.5-2percent annually2 percent means a doubling of output per capita in 35 years,i.e. each generation can enjoy double the living standards ofits parents!→ Solow model

Facts of post industrial revolution growth

1. since the industrial revolution most countries are growing; thedeveloped economies have been growing at around 1.5-2percent annually per capita

2. looking at many countries at the same point in time (across-section) we see that there is a positive correlationbetween the investment share (investment/GDP) and thelevel of output per capita

↔ those who invest more are usually richer

however, there is no correlation between the investment rateand the growth rate!

3. the cross-section also shows a negative correlation between thegrowth rate of population and the level of output per capita

countries where the population is growing faster are typicallypoorer

note that their total output can be growing fast, but this isoffset by the fast growth of the population

4. there is no convergence in general in output per capita acrosscountries

5. a group of developed countries is similar in terms of growthand the level of output per capita

→ they have converged

the rest of the countries are significantly different both fromeach other, and from the developed countries

GDP per capita in 1820 and 1998 (in 1990$)

1820 1998 growth rate

Western Europe 1202 18137 1.5%America, Canada, Oceania 1202 25767 1.7%Eastern Europe 683 5550 1.2%Former USSR 688 3907 1.0%Latin America 691 5837 1.2%Japan 669 20662 1.9%China 600 2993 0.9%East Asia (incl China and Japan) 556 1405 0.5%West Asia 607 5623 1.3%Africa 420 1444 0.7%World average 667 5729 1.2%

Source: Maddison

I world income differences were small until the 19th century(industrial revolution), most countries were at subsistencelevel, since then, there has been a huge divergence betweencountries - mainly due to the persistent growth of richcountries

I average real incomes in the US, Germany, Japan exceed thosein Bangladesh, Kenya by 10 to 20 times

I output per worker in the US is more than 35 times higher thanoutput per worker in Niger

I outside the developed countries there are examples foreverything: some have successfully caught up, and some whohave fallen behind

I growth miracles of the Asian tigers, 1960-90: Singapore,Taiwan, Hong Kong, South Korea, where g is larger than 5%:y doubles in less than 15 years

I China: g=6.3%, India: g=3.8% during 1980-2000

From stagnation to modern growth

Source: Maddison

Large differences in income and productivity in 2000

country % of world pop GDP per capita GDP per worker

USA 5% $33308 $64537Japan 2% $24671 $38737France 1% $22371 $49136UK 1% $22188 $44650China 21% $3746 $6174India 17% $2480 $6216Honduras 0.1% $2054 $6380Niger 0.2% $875 $1822

Source: Penn World Tables

Large differences in income and productivity in 2000

Source: Penn World Tables

A very skewed distribution

I the world income (or productivity) distribution is very skewed

I essentially because of the presence of two large countries,China and India, near the bottom 10%

I the difference between GDP per capita and GDP per workerfor the 0-10 and 10-20 bars is mainly due to China

Question: Will poor countries remain much poorer than the richcountries, or will they catch up? → is there chance forconvergence?

Is there convergence across countries? 1.

Is there convergence across countries? 2.

Is there convergence across countries? 3.

Convergence

I important difference: there seems to be conditionalconvergence, but not absolute convergence

I absolute convergence: poor countries grow faster than richcountries

I conditional convergence: among similar countries - that sharea given set of institutional, behavioral, cultural, socialcharacteristics - poorer countries grow faster than the richer(and catch up with similar countries)

Objective of growth models

is to address the following type of questions:

I why is there growth?

I why are some countries poorer than others?

I why is output per worker lower in some countries?

I why do some countries grow faster?

I is there convergence over time among countries?

The Malthusian model

The Malthusian model

I based on Thomas Malthus: An Essay on the Principle ofPopulation from 1798

I he did not formalize a model, but his ideas can be easilytranslated into a formal model

I (probably) motivated by the growth facts (or lack of growth inincome per capita) that he witnessedremember, this is from the stagnation period prior to theindustrial revolution

I main statement: any advance in the technology to producefood would lead to further population growth

I ⇒ technological advance ⇒ increase in population ⇒ nolong-run change in the standard of living

Some notation

I for now we abstract from the unemployed and the inactive, sototal population = number of workers

I upper case letters denote aggregates:Y - aggregate output, I - aggregate investment, K aggregatecapital, N - total number of workers, L total amount of land,C - aggregate consumption

I lower case letters denote per capita (⇔ per worker) values:y - output per capita, k - capital per capita, l - land percapita, c - consumption per capita

Assumptions

these are exogenous to the model, we assume they are true

1. production function: Y = z · F (L,N)

I where z is total factor productivity (TFP)

I L is total land, and N is labor input

I the function F (·, ·)I has constant returns to scale (CRS):

for any λ > 0 constant F (λL, λN) = λF (L,N)

I is increasing in both its arguments, at a decreasing rate

→ these are all properties of the neoclassical productionfunction (more details next week)

Assumptions

2. the growth of population depends on consumption per capita:

I N ′ = N + births − deaths = N + N(birth rate − death rate)⇒ N ′ = N · g(c)

I N ′ is population in the next period

I g is an increasing function of c

I what is the rational for this assumption?

Results

Using the CRS property of the production function we can expressoutput per capita as:

y =Y

N=

z · F (L,N)

N= z

F (L,N)

N= z · F

(L

N, 1

)︸ ︷︷ ︸

f (l)

= z · f (l)

⇒ output per capita depends on land per capita

Everything that is produced is consumed (remember no capital, nosaving, no investment in this model):

c = y = z · f (l)

The evolution of the population can then be written as:

N ′ = N · g(c) = N · g(y) = N · g(z · f (l))

Steady stateGiven the equation for the evolution of population, we can drawthe following diagram:

N∗ is a steady state: N∗ = N = N ′

Why is N∗ is a steady state ( a resting point) of the economy?

I imagine that the economy is in a situation where N < N∗,what happens to N?

I similarly what if N > N∗?

What does g(z · f

(LN

))· N have to look like for there to be a

steady state?

So the economy will reach the population where N = N ′ = N∗.Here it is true that

N ′ = N · g(c∗) ⇔ 1 = g(c∗) ⇒ c∗ = g−1(1)

At this level of per capita consumption we know how much landper capita there is:

c∗ = y∗ ⇔ c∗ = z · f (l∗) ⇒ l∗ = f −1(

c∗

z

)Since we know how much total land there is, i.e. we know L, thisgives us the level of population:

l∗ =L

N∗⇔ N∗ =

L

l∗

Or to show it in some graphs:

I to find the equilibrium per capita consumption, c∗, we need tosolve the equation: g(c∗) = 1

I this implies that the long-run standard of living (per capitaconsumption) is entirely determined by the function g(·)

I so improvements in the production technology (increase in z),or the acquisition of more land (increase in L) lead to higheraggregate labor, and higher aggregate consumption, but donot lead to a change in the long-run standard of living

An increase in productivity, z

Transitional dynamics - productivity increase

I the economy does not jump to the new steady state, as ittakes time for the population to adjust

I transitional dynamics: the description of the path of thedifferent endogenous variables of the model as the economyadjusts to the new steady state

So what happens if z increases, say from za to zb? Starting fromthe old steady state with N = N∗a , the transitional dynamicscaused by a higher z are:

1. y increases immediately (from production function), so cincreases immediately (from market clearing condition)

2. ⇒ N2 will be larger than N∗a (from population growthfunction), but probably smaller than N∗b

3. ⇒ y2 is still above y∗b = y∗, so c2 > c∗b = c∗

4. ⇒ N3 is probably still below N∗b , so

5. ⇒ y3 > y∗ and c3 > c∗, so N3 > N∗b⇒ . . . and N keeps growing until cn = c∗

Transitional dynamics - productivity increase

Population control

I Malthus’s proposal to increase the standards of living waspopulation control

I if the state would limit the number of children families canhave, that would reduce population growth for each level ofconsumption per capita

I the function g(c) would shift down

I the effects of such a policy in the Malthusian model is indeedthat in the long run per capita consumption increases, i.e.living standards rise

Population control

Summary of the Malthusian model

I the model provides a good explanation for the pre industrialrevolution growth facts

I GDP per capita is roughly constant → stagnationI population growth is higher when living standards riseI mainly agricultural production

I this model does not explain the patterns after the industrialrevolution

I there is sustained growth in GDP per capita → moderneconomic growth

I there is a demographic transition: decline in the growth rate ofthe population

I there is a structural transformation: from agriculturalproduction to industries and to services

What is missing from the Malthusian model?

I Malthus did not consider the role of capital accumulation→ capital fundamentally different from land:

I land is in limited supplyI capital is reproducable, it can be accumulated

I Malthus did not predict the effects of economic forces onfertility:it is true that a higher standard of living reduces death rates,but it also reduces birth rates

I the opportunity cost of raising a large familyI the role of human capital: quantity vs quality trade-off