1. Macroeconomics: Economic Growth Master HDFS
Prof. PASQUALE TRIDICO
Università Roma Tre

2. Growth, Convergence and Technical Progress in neoclassical models

3. The 6° stylized facts of Kaldor
…there is NO significant evidence of convergence in growth rates of per capita income between the countries of the world and even in the long run
However, convergence in growth rates and income levels is one of the greatest conclusions in the exogenous growth theory (neoclassical/Solow)

4. Neoclassical Model (with/out TP same conclusions)
The growth rate tends to be equal to the rate of growth of the labor supply plus the growth of technical progress
These variables n and λ are generally constant, so the level of income stays along a "path of steady state," that is constantly growing, and when it is not on that path converges towards it

5. From the Cobb-Douglas
First degree omogeneous equation (constant return of scale)
Marginal productivity of each factor decreasing
Isoquants of K and L strictly convess towards the origin and apsyntothic to the axes
Elasticity of substitution constat (CES) and equal to 1
Shares of wL and rK constant and equal to  e a 1-. 

6. C-D function with Thecnical progress=A  (gA=0)
k = K/L

7. Since demand and supply of labour are equal and correspond to n (pop growth) the rate of growth of K/L=gK-n:

8. The function
Is a decreasing function of k as the exponent is negative, being α <1. This depends of course on the assumption of diminishing marginal productivity of the factors in the neoclassical production function. In the graphics function approaches asymptotically to 0.

9. IN K* instead: on the right on the left
gk is> when K / L is small, towards the left. At these levels the PMK is high because the K is scarce, and its accumulation is accelerated. After it slows down as the PMK decreases. gk is <when K / L is high to the right. At these levels the PMK is small because the K is abundant, and its accumulation decreases. gk will meet in a precise value, k * where gk-n = 0 with TP = 0
IN K*
instead:
on the right
on the left

10. Observation on A Remember in the previous case, A is 1 and gA=0
What about if A>1 and gA>0 ?
Long term effect on level of Y/Lwill be affected (higher Y/L)
No long term effect on growth of Y/L

11. Steady state
SS is then given by a level of K / L, and the Y/L (since y = ) which remains constant through time and is achieved automatically.
SS represents the growth path at a constant rate of product = n = with Full Employment

12. Convergence
At low levels of K, with K / L small the MPK is high, gk is larger but decreasing. Poor economy. If the economy is richer, will have more K, the MPK is lower, gk is smaller.
Then, if the country was so rich with abundant K, with MPK very low, its growth could not keep the growth of n, then K / L decrease until reaching K *

13. This is called also transition dynamics, and the results of course do not change also when considering depreciation

14. Convergence with technical progress
TP=>0
TP  Y as increasing L at a constant rate .
If K/Y is constant, labour productivity grows at the rate = 
The increase of L caused by  + the effective increase of L = “labour augmented in efficiecy unit LEU”
Income per labour in LEU
Capital per labour in LEU

15. x= k per labour in LEU

16. As usual to the capital accumulation sx one needs to subtract pop growth and TP  n+ ( labour growth in LEU terms)

17. In other words With A, k is no longer constant in the long run
The new SS is K/AL  k/A which is constant along the balanced growth because
gk=gA=g

18. Thecnology effect (on long run level of GDP/L, not on growth)

20. Transition with Technology

21. x* indicates a level of K/L
Now, line n+ is higher than n line (convergence is obtained at higher rate of growth)
x* indicates a level of K/L
in LEU which remains constant through time and it correponds to a level > of K/L in normal unit of labour because it is augmented now by TP

22. Observation
If n=0, that is L is not growing, but it only grows in terms of efficiency, driven by TP. In this case y must grow at the rate  otherwise, if it grew less,  U, since it would take less L with TP now in order to produce Y.
In other words as if TP increased number of L at rate .
In this model (with constantly increasing TP>0) y, per capital GDP, grows also in the long run, through a balanced path of growth

23. Consequences of TP as a free good
TP labour Augmenting (=K/Y):
The growth rate of the product per worker is g (y) = g (Y) -n  g (Y) = n + 
The growth rate is lower the higher the level of income per worker
The level of income per worker tends towards the path of SS associated with
These 3 propositions are the basis of the neoclassical theory of convergence

24. 2 growing economies along the SS path having all equal but s: s1>s2

25. =g of SS,  path of SS
Both economies converge toward the same growth rate BUT NOT towards the same path of SS. The economy 2, with s2 < s1, has a path of SS with K / L (and also with Y / L) lower than that of Economy 1.
=g of SS,  path of SS. The Economy 2 with s2 <s1 has a path of SS lower, and income per worker also lower
The richer and poorer economies converge towards the same level of Y / L only if they have the same s (conditional convergence)

26. Conditional and absolute convergence
The convergence in income levels per employee, in the neoclassical model, is therefore conditional to the propensity to save s.
The absolute convergence of growth rates of income per employee is instead always an obtained result in the neoclassical model.

27. determinants Hp PT=free good, no costs, accessable to all countries
MP of K e L decreasing
Otherwhise no:
TP= is a result of knowledge, competences, effort, invenstment, institutional framework, rules, state, etc
Specific national factors, institutions and models: ….. different path of growth: endogenous growth therry

28. Thecnological gap theory
1. leaders 2. Late comers  Followers
The Gap of technology is a delay but also an advantage.
When a leader replaces old K with the new, the old K is already quite modern.
This difference among followers is instead bigger.
However, the greater the gap the higher is the growth potential of Y and productivity among followers
(see f.i USA and Europe after 1945)

29. However costs are needed and institutions also for the theory of "TG"
Otherwise with an institutional system inefficient, lack of "social capability", and processing capacity and imitation, the gap is rooted  accumulation delayed of TP
Researches have shown that catching up is difficult, and the gap more than a potential advantage can be a trap. A part of society resists changes.
Socio-institutional factors Are needed ... etc (Kuznets1966; Rosowski and Ohkawa 1973; Gerschenkron)

30. Leader:USA
Consolidation advantage - Fordism, productivity growth and w - Accumulation of knowledge, technology and skills, virtuous process - The imitation was made difficult by the fact that even to imitate countries had to have certain organizations and institutions.
-Hence the delay in catching-up. Also massive invest. In R & D in private and public sector (especially in the military sector) have widened the gap.
Since 1950, instead, the followers improved institutional and social capacity  EU and Japan have recovered

31. AEs and LDEs
If there is some convergence between AE, this is not true for LDE
One can only speak of convergence among a groups "Club Convergence" and during the "Golden Age" ( ).
On average, poor countries do not grow faster than rich countries

32. Parametric estimation method
Cross country estimates of the country's income (y) i at time t
Average growth rate between 0 and t that estimates the HP of absolute convergence
= parameter of convergence. If  is significantly ≠ 0, then the average growth rate of poor countries is higher of the richer countries
But usually  is not significantly ≠ 0.
 absolute convergence unconfirmed

33. Beta-convergence
The existence of an economic convergence in which the poorest regions grow at rates greater than those initially richer (the so-called beta-convergence) is thus NOT confirmed.
In the long run this process should lead to equality in the levels of per capita wealth between the various economic systems.
The mechanism behind this process of "absolute” convergence, given the restrictive assumptions of the model, is found in the lower initial endowment capital of the poorest countries that guarantees them higher returns and growth over time.

34. Beta convergence
The -Convergence implies an inverse relationship between the rate of change of output per capita and the initial level of output per capita: this results in a greater expectation of growth in poorer countries than in rich ones. If there is no beta convergence can not be sigma convergence, necessary but not sufficient condition. Since the variance may increase or decrease depending on whether the country is above or below the steady state.
Paradoxically: “countries can diverge while converging”

35. Sigma-Convergence(1)
Parametrically, in addition to  another parameter that must be tested in a regression of convergence is . It indicates the dispersion within a group of countries, of their income level, measured for example by the standard deviation of the logarithm of GDP per capita in a group of states or regions. If this diminishes over time there is -convergence

36. Sigma-Convergence (2)
There is -convergence when the standard deviation of output per capita of the countries at the time t2 decreases with respect to time t1.
The -convergence implies a decline in the dispersion of the variable considered in all countries over time
This type of convergence is easily influenced by the presence of outliers from average.
The scattering cross-section can be measured as the variance of the logarithm of GDP per capita

37. Research Evolution of convergence
The TP does not allows for convergence  Endogenous growth theory
TP  Technological Gap theory a convergence/Cacthing up is possible among leader ad followers
Absolute convergence non confirmed ()
Conditional convergence (?)

38. Conditional Convergence
Unlike the absolute convergence the conditional one suggests the possibility for poorer economies to stay on a SS path < because of a <s and/or 
can be <because of a  s and 

39. Conditional Convergence(2)
C1 and C2 have the same K / Y in LEU initial X0 at time 0. C1: s1> s2. C1 will have a growth rate greater than n + , even when C2 has reached the growth rate of SS in X1,2. C1 converges at a higher speed towards the growth rate of SS for its path of SS with K / L = X1,1> X1,2

40. Conditional convergence: S = but production functions are # because of the . C1 and C2 have the same initial K (LEU) in t0. C1 has a> MPK that determines  1 while C2 is conditioned by circumstances that depress MPK2  PF lower.  2 <  1. C1 maintains this distance while C2 has already reached its level of growth of SS before. During the transition to the same level of growth of SS, but on another path, C1 maintains a higher distance and a bigger growth rate
xt1,1 X
n+,
g(x)t
n+
xt0
xt1,2

41. Combination of 2 different s and alpha
In reality it is possible that poorer countries are simultaneously with s and  parameters different.

42. Estimation of conditional convergence
Indicates one of the independent variables intended to capture the structural and institutional differences and  the corresponding factor.
If  is significantly ≠ 0 ( the relationship between initial income and growth is negative) there is conditional convergence effect of the variable S. The higher the growth rate is the lower its initial level, given that s is the same

43. Empirical results
Many critical and controversial results. However, empirical studies when testing the convergence with neoclassical assumptions, it remain linked not only to certain periods and groups of countries, but also to specific variables such as
Initial income (-)
I (+)
R&D (+)
Capital Accumulation (+)
Education and Human Capital (+)
Openess, Export and international trade (+)
INSTITUTIONS(+)

49. Countries with similar technology and human capital

50. Countries with different level of technology and human capital