Intermediate Macroeconomics

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1 Intermediate Macroeconomics Lecture 2 - Growth Facts & the Malthusian Model Zsófia L. Bárány Sciences Po 2014 January

2 Hall and Jones 1999, QJE: In 1988 output per worker in the United States was more than 35 times higher than output per worker in Niger. In just over ten days the average worker in the United States produced as much as an average worker in Niger produced in an entire year.

3 Lucas 2000, JEP: How did the world economy of today, with its vast differences in income levels and growth rates, emerge from the world of two centuries ago, in which the richest and the poorest societies had income differing by perhaps a factor of two, and in which no society had ever enjoyed sustained growth in living standards?

4 Measuring growth growth: the change in output per capita over time proxy for standards of living output per capita: real GDP/population alternatively: real GDP/worker gives a sense of productivity change there are other important measures of development such as: life expectancy, infant mortaility, education is it development what we want to measure? or something else? welfare? there are two reasons why GDP per capita is the preferred measure: 1. more data available 2. theories have predictions mainly in terms of income

5 growth theory is concerned with changes in real GDP per capita over a very long horizon comparisons over a long period of time are difficult even if nominal income data is available, we need price indices to transform it to real data adjustment for quality changes and the introduction of new goods is difficult to compare across countries: use adjustment of nominal GDP according to PPP the growth rate is g t = (y t y t 1 )/y t 1 growth is exponential, if the growth rate, g is close to constant y t (1 + g) t y 0 even a very small difference in g can result in huge disparities in the level of output per capita in 100 years

6 Robert Lucas Small, sustained differences matter Implications for human welfare are ENORMOUS GDP per capita year 0 year 10 year 20 year 50 year % 1.50% 2% 3% growth rate Once one starts to think about [economic growth] it is hard to think about anything else.

7 The main data sources are: historical data from Angus Maddison data since 1950 from Summer-Heston, also known as the Penn World Tables there are many websites where you can find data on economic growth: World Bank, OECD,... average real incomes in the US and in Western Europe are 10 to 30 times larger than 100 years ago 50 to 300 times larger than 200 years ago

8 From stagnation to growth 1. stagnation: average income at the beginning of the industrial revolution was not far above subsistence levels growth in per capita income before must have been very low there was growth in total output, but the population also increased by a lot Malthusian model 2. modern growth: since the industrial revolution most of the developed economies have been growing per capita at percent annually 2 percent means a doubling of output per capita in 35 years, i.e. each generation can enjoy double the living standards of its parents! Solow model

9 Facts of post industrial revolution growth 1. since the industrial revolution most countries are growing; the developed economies have been growing at around percent annually per capita 2. looking at many countries at the same point in time (a cross-section) we see that there is a positive correlation between the investment share (investment/gdp) and the level of output per capita those who invest more are usually richer however, there is no correlation between the investment rate and the growth rate!

10 3. the cross-section also shows a negative correlation between the growth rate of population and the level of output per capita countries where the population is growing faster are typically poorer note that their total output can be growing fast, but this is offset by the fast growth of the population

11 4. there is no convergence in general in output per capita across countries 5. a group of developed countries is similar in terms of growth and the level of output per capita they have converged the rest of the countries are significantly different both from each other, and from the developed countries

12 GDP per capita in 1820 and 1998 (in 1990$) growth rate Western Europe % America, Canada, Oceania % Eastern Europe % Former USSR % Latin America % Japan % China % East Asia (incl China and Japan) % West Asia % Africa % World average % Source: Maddison

13 world income differences were small until the 19th century (industrial revolution), most countries were at subsistence level, since then, there has been a huge divergence between countries - mainly due to the persistent growth of rich countries average real incomes in the US, Germany, Japan exceed those in Bangladesh, Kenya by 10 to 20 times output per worker in the US is more than 35 times higher than output per worker in Niger outside the developed countries there are examples for everything: some have successfully caught up, and some who have fallen behind growth miracles of the Asian tigers, : Singapore, Taiwan, Hong Kong, South Korea, where g is larger than 5%: y doubles in less than 15 years China: g=6.3%, India: g=3.8% during

14 From stagnation to modern growth Source: Maddison

15 Large differences in income and productivity in 2000 country % of world pop GDP per capita GDP per worker USA 5% $33308 $64537 Japan 2% $24671 $38737 France 1% $22371 $49136 UK 1% $22188 $44650 China 21% $3746 $6174 India 17% $2480 $6216 Honduras 0.1% $2054 $6380 Niger 0.2% $875 $1822 Source: Penn World Tables

16 Large differences in income and productivity in 2000 Source: Penn World Tables

17 A very skewed distribution the world income (or productivity) distribution is very skewed essentially because of the presence of two large countries, China and India, near the bottom 10% the difference between GDP per capita and GDP per worker for the 0-10 and bars is mainly due to China Question: Will poor countries remain much poorer than the rich countries, or will they catch up? is there chance for convergence?

18 Is there convergence across countries? 1.

19 Is there convergence across countries? 2.

20 Is there convergence across countries? 3.

21 Convergence important difference: there seems to be conditional convergence, but not absolute convergence absolute convergence: poor countries grow faster than rich countries conditional convergence: among similar countries - that share a given set of institutional, behavioral, cultural, social characteristics - poorer countries grow faster than the richer (and catch up with similar countries)

22 Objective of growth models is to address the following type of questions: why is there growth? why are some countries poorer than others? why is output per worker lower in some countries? why do some countries grow faster? is there convergence over time among countries?

23 The Malthusian model

24 The Malthusian model based on Thomas Malthus: An Essay on the Principle of Population from 1798 he did not formalize a model, but his ideas can be easily translated into a formal model (probably) motivated by the growth facts (or lack of growth in income per capita) that he witnessed remember, this is from the stagnation period prior to the industrial revolution main statement: any advance in the technology to produce food would lead to further population growth technological advance increase in population no long-run change in the standard of living

25 Some notation for now we abstract from the unemployed and the inactive, so total population = number of workers upper case letters denote aggregates: Y - aggregate output, I - aggregate investment, K aggregate capital, N - total number of workers, L total amount of land, C - aggregate consumption lower case letters denote per capita ( per worker) values: y - output per capita, k - capital per capita, l - land per capita, c - consumption per capita

26 Assumptions these are exogenous to the model, we assume they are true 1. production function: Y = z F (L, N) where z is total factor productivity (TFP) L is total land, and N is labor input the function F (, ) has constant returns to scale (CRS): for any λ > 0 constant F (λl, λn) = λf (L, N) is increasing in both its arguments, at a decreasing rate these are all properties of the neoclassical production function (more details next week)

27 Assumptions 2. the growth of population depends on consumption per capita: N = N + births deaths = N + N(birth rate death rate) N = N g(c) N is population in the next period g is an increasing function of c what is the rational for this assumption?

28 Results Using the CRS property of the production function we can express output per capita as: y = Y ( ) z F (L, N) F (L, N) L = = z = z F N N N N, 1 = z f (l) }{{} f (l) output per capita depends on land per capita Everything that is produced is consumed (remember no capital, no saving, 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))

29 Steady state Given the equation for the evolution of population, we can draw the following diagram: N is a steady state: N = N = N

30 Why is N is a steady state ( a resting point) of the economy? imagine that the economy is in a situation where N < N, what happens to N? similarly what if N > N? What does g ( z f ( L N )) N have to look like for there to be a steady state?

31 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 land per capita there is: ( ) c c = y c = z f (l ) l = f 1 Since we know how much total land there is, i.e. we know L, this gives us the level of population: z l = L N N = L l

32 Or to show it in some graphs:

33 to find the equilibrium per capita consumption, c, we need to solve the equation: g(c ) = 1 this implies that the long-run standard of living (per capita consumption) is entirely determined by the function g( ) so improvements in the production technology (increase in z), or the acquisition of more land (increase in L) lead to higher aggregate labor, and higher aggregate consumption, but do not lead to a change in the long-run standard of living

34 An increase in productivity, z

35 Transitional dynamics - productivity increase the economy does not jump to the new steady state, as it takes time for the population to adjust transitional dynamics: the description of the path of the different endogenous variables of the model as the economy adjusts to the new steady state So what happens if z increases, say from z a to z b? Starting from the old steady state with N = N a, the transitional dynamics caused by a higher z are: 1. y increases immediately (from production function), so c increases immediately (from market clearing condition) 2. N 2 will be larger than N a (from population growth function), but probably smaller than N b 3. y 2 is still above y b = y, so c 2 > c b = c 4. N 3 is probably still below N b, so 5. y 3 > y and c 3 > c, so N 3 > N b... and N keeps growing until c n = c

36 Transitional dynamics - productivity increase

37 Population control Malthus s proposal to increase the standards of living was population control if the state would limit the number of children families can have, that would reduce population growth for each level of consumption per capita the function g(c) would shift down the effects of such a policy in the Malthusian model is indeed that in the long run per capita consumption increases, i.e. living standards rise

38 Population control

39 Summary of the Malthusian model the model provides a good explanation for the pre industrial revolution growth facts GDP per capita is roughly constant stagnation population growth is higher when living standards rise mainly agricultural production this model does not explain the patterns after the industrial revolution there is sustained growth in GDP per capita modern economic growth there is a demographic transition: decline in the growth rate of the population there is a structural transformation: from agricultural production to industries and to services

40 What is missing from the Malthusian model? Malthus did not consider the role of capital accumulation capital fundamentally different from land: land is in limited supply capital is reproducable, it can be accumulated Malthus did not predict the effects of economic forces on fertility: it is true that a higher standard of living reduces death rates, but it also reduces birth rates the opportunity cost of raising a large family the role of human capital: quantity vs quality trade-off

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