Basic facts of growth. Solow growth model a quick reminder

Transcription

1 Joanna Siwińska-Gorzelak Basic facts of growth. Solow growth model a quick reminder Advanced Macroeconomics

2 Most graphs in these slides are from Acemoglu: Introduction do Modern Economic Growth See:

3 The distribution of countries according to GDP per capita

4 Small differences in growth rates have great implications Source: T.Picketty;

5 Population weighted distribution of countries

6 PKB per capita w roku 1960 i 2000

7 GDP per capita, in 1990 prices Maddison A. ;

8 GDP per capita since 1000 AD

9 GDP per capita

10 GDP per capita and quality of life

11 Distribution of world GDP, 2012 Source: T.Picketty;

12 Poverty in the world

13 Poverty While poverty rates have declined in all regions, progress has been uneven: The reduction in extreme poverty was mainly driven by East Asia and Pacific: China & India. Half of the extreme poor live in Sub-Saharan Africa. A vast majority of the global poor live in rural areas and are poorly educated, mostly employed in the agricultural sector.

14 Source: T.Picketty;

15 The Solow model The Solow model is remarkable for its simplicity The Solow model is a good starting point and a springboard for further models At the centre of the model is the neoclassical production function We will analyze it in continuous time (i.e. we make the time units - the difference between t and t+1 - as small as possible From now on, a dot over a variable means the change of this variable over time: dx dt t x t

16 Neoclassical production function Y t =F(K t, A t N t Where K denotes capital, A technology; N labour force (population Neoclassical production function is characterised by 1. Constant returns to scale 2. Positive and diminishing marginal products of capital and labour 3. Inada conditions

17 Neoclassical production function 1. cy F( ck; cna c 0 2. dy MPK 0 dmpk 0 dk dk dy MPN 0 dmpn 0 dl dn 3. lim K lim N MPK MPN 0 0 limmpk K 0 limmpn N 0 1. Constant returns to scale 2. Marginal product of K & N positive and diminishing 3. Inada conditions (what happens at extremes

18 Further assumptions of the Solow model Y=C+I, so that G=0 and NX=0 The produced good is homogenous and it can change from consumption into investment good at no cost The rate of saving is constant and is equal to s, so that S=sY. Since Y=C+I, hence sy=i The depreciation rate of capital is constant and is equal to d The rate of population growth is n and the rate of technological progress is g N N n A A g

19 The Solow model If we define: y Y AN k K AN A A g Then we can express the production function as: y N N n y t f ( k t

20 Capital accumulation The increase in capital stock depends on (among others investment Note, however that we are more interested in the bahaviour of capital per effective worker K t1 I 1 dk t K t sy 1 dk t K t K t sy 1 dk t

21 Capital accumulation k g n d sy k k g n AN dk sy AN A N A N K AN AN K dt AN K d k t t ( ( ( ( ( / ( 2 2

22 The Solow Diagram: Steady State n g k ŷ y k * ŷ ss sy sk sk n g * * k k * k

23 The steady-state In the steady-state: g A A y y ya A y y y N K k N Y y Define y k 0 * ( 0 0

24 Cobb-Douglas production function an example 1 1 1` 0 ( ( g n d s k s g n d k k k g n d sk k k g n d sy k

25 Modifications A famous modification is due to Mankiw, Romer, Weil: A Contribution to the Empirics of Economic Growth, QJE, 1992 (MRW, who have stressed the role of human capital Human capital accumulation is a very similar process to the accumulation of k h k y AN H K Y ( 1 h g n d y s h H (

26 Empirics ( 1 ln( 1 ln( 1 ln( ln ( 1 ln( 1 ln( ln ( 1 ln( 1 ln( ln * 1 1 g n d s s A y g n d s A y g n d s A y g n d s A y H K t This approach has been followed by MRW

27 Empirics - convergence Note that Solow model predicts convergence a very important phenomenon, which we will discuss later

28 MRW

29 What have we learnt from the Solow model? We have a simple framework that allows us to study implications of capital accumulation and technological progress This framework is already quite useful in thinking about the world But on the other hand, we have not learn that much Technological progress is a black box; so is the saving rate Solow model is good at laying out the questions We need to dig deeper in order to answer them That s our job for the next 4 weeks.

30 What are the fundamentals of growth Culture Climate Institutions Luck Acemolgu: institutions! Institutions: are the rules of the game in a society or are the humanly devised constraints that shape human interactions

31 Institutions Acemoglu argues: North and South Korea The colonization of many countries by Europeans after 1492 (large scale natural experiment Europeans transformed the institutions of all the conquered nations Historical evidence shows that there has been a remarkable reversal of fortune in economic prosperity within former European colonies Aztecs, Incas, societies of India were among the richest in the world; now the nations that exist in these boundaries are among the poorest

32 Institutions and GDP per capita

33 Acemoglu, Johnson & Robinson (2001

34 Acemoglu, Johnson & Robinson (2001

35 Conclusions Countries are richer if the save more Sustained GDP per capita growth rate is due to technological progress What factors make people save more? What factors make people invent? Acemoglu says: institutions.