Economic Convergence. Parametric Methods

Regional Economic Policy
Prof.ssa Cristina Brasili
A. Y. 2015-2016
Economic Convergence.
Parametric Methods
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Economic Convergence. Parametric Methods - Cristina Brasili
1. Cohesion, integration and
convergence
2. Theoretical model of convergence
and divergence
3. Convergence measures
4. Beta and sigma convergence
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Economic Convergence. Parametric Methods - Cristina Brasili
1. Cohesion, integration and convergence
Cohesion is a political object supported by the
integration and convergence process and it
stimulates the objectives of convergence and
integration
Cohesion
CONVERGENCE
INTEGRATION
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Economic Convergence. Parametric Methods - Cristina Brasili
1. Cohesion, integration and convergence
Cohesion is at the base of
the first social (and second in the EU)
policy of European Union
Cohesion without convergence remains
a theoretical concept
The institutional cohesion has to be
high to lead and to improve the
cohesion
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Economic Convergence. Parametric Methods - Cristina Brasili
1. Cohesion, integration and convergence
The convergence is the process utilized
to measure the cohesion
It will be convergence when there is a
significant reduction among regions and
countries in the disparities
of social and economic development
We could speak of convergence only in
the case of increasing development and
wellbeing for all the regions/countries
nor reducing the richness for the most
developed regions.
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Economic Convergence. Parametric Methods - Cristina Brasili
2. Theoretical model of convergence and divergence
The theory of convergence showing the
pattern towards the cohesion
The regional/national economies converge
if the less development economies growth
at the higher rate than the more developed
ones because of market mechanism and/or
public policies
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Economic Convergence. Parametric Methods - Cristina Brasili
2. Theoretical model of convergence and divergence
Convergence scenarios
-Fordism’s industrialization (Hoffmann 1958,
Hamilton 1986)
-«Light» industrialization (SMES’s
enterprises) (Garofoli 1991, Piore e Sabel
1984, Putnam, Leonardi e Nanetti 1993)
-Development’s poles and relevance of
public sector (Perroux 1959, Carrello 1989,
Saraceno 1977)
-at the opposite the liberalization of the
markets (Olson 1982, Hirsch 1976)
-Fundamental role of the endogenous factors
for the development by the local
governments (Garofoli 1992, Nanetti 1987) 7
Economic Convergence. Parametric Methods - Cristina Brasili
2. Theoretical model of convergence and divergence
Divergence scenarios
-The regions could have some spillovers
however it prevails the difficulties to have
the convergence and it is born a vicious
circle (by the economist Myrdal who studied
the “cumulative circular causality”, 1957)
- The Marxist economists support the
hypothesis that in the capitalistic economies
it is impossible to reach the convergence
(Frank 1974, Holland 1976).
-divergence model center-pherifery (Rokkan
e Urwin 1982 e 1983, Tarrow 1977)
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical model
How we can measure the convergence
process?
Theory of growth is the base of the
measure of the economic convergence
Neo-classical theory and endogenous
theory are the theoretical frameworks for
analysis of convergence
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 1.
Neo-classical theory essentially argues that
across regions with similar preferences and
access to similar technologies, poorer
regions will catch up wealthier regions
and the marginal return from capital in the
latter begins to diminish.
Poorer regions, since they have less capital
will attract mobile investment because of
the relatively higher returns that they offer.
Labour will migrate from regions where
wages are low to those where wages are
higher pushing up wages in the former and
reducing them in the latter
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 2.
The standard neo-classical model of
economic growth was formulated in
1956 by Solow and independently by
Swan.
The Solow-Swan model (1956)
predicts that countries or regions with
the same preferences and technology
will converge to identical levels of per
capita income reaching a steady state
equilibrium.
Constant marginal returns is one of
the hypothesis
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Neo-classical approach 3.
.
The basic structure of the neo-classical
model
Aggregate production function:
Yt =F(Kt ,Lt )
•where Yt : output, Kt : capital stock, Lt :
labour force
•One sector
•Homogeneous output
•Infinitive mixture of the productive factors
•Interest rate does not condition the saving
but it changes the ratio capital/output
• Initially there isn’t technological
progress
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Neo-classical approach 4
The Solow-Swan model (1956) predicts
that countries or regions with the same
structural parameters: saving rate,
population growth rate
(and then
technology) will converge to the same
steady state equilibrium.
From that point the economies will growth
at the same rate
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 5.
The Solow-Swan model starting from a generic
production function Y=F(L,K)
It has to satisfy the three properties:
Positive and diminishing marginal returns of
factor inputs
a. positive and diminishing marginal returns of
capital
2

F
F
0
0
2
K
K
and positive diminishing marginal returns of
labour
F
0
L
 2F
L
2
0
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 6.
F(•) has constant returns to scale
b.
F ( K ,  L )    F (K , L )
0
for every
c. Inada conditions;
lim (FK )  lim (FL )  
k 0
L0
lim (FK )  lim (FL )  0
k 
L
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 6.
THE NEOCLASSICAL SOLOW-SWAN
GROWTH MODEL by Sarantis Kalyvitis
Pp. 4-6
For the methodological details to derive the
The law of motion for the
capital stock in per capita terms becomes:

k  s  f (k )  (n   )  k
(FUNDAMENTAL DIFFERENTIAL
EQUATION FOR CAPITAL STOCK
ACCUMULATION IN THE SIMPLE
NEOCLASSICAL SOLOW-SWAN
MODEL)
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 6.
Steady-State Equilibrium
At the steady  state the rate growth
is constant k  0

k  s  f (k )  (n   )  k
k  k
s  f (k  )  (n   )  k 
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Neo-classical approach 7.
Absolute Convergence
Growth Rate> 0
n 
Growth Rate< 0
s*f(k)/k
K(0) poors
k*
K(0)richs
Catching Up
Absolute convergence, which can be
defined as a process in which economies
with lower capital per worker grow
faster than economies with higher capital
per worker.
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Steady-State with technology parameter
Robinson (1938) and Uzawa (1961) also
include A(t) a technological index
Y  F K , L  A(t )
labor augmenting: output growths as the
labour stock
k and A(t) growth at the same rate x,
kˆ  k A(t )  K /( L  A(t ))
LA(t) is the effective quantity of labour
(labour per its efficiency)
dove x è il tasso di crescita del progresso
tecnologico
•Equation at steady state
s  f ( kˆ )  ( x  n   )  kˆ
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Conditional Convergence
n 
srichs*f(k)/k
spoors*f(k)/k
k*poors
K(0)
poors
k*richs
K(0)richs
However, when we take into account
empirical observations, the hypothesis of
absolute convergence is in breach of reality
for the high capital per worker economies
also achieve faster GDP growth per worker.
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Beta convergence
log yˆ (t)  et  log yˆ (0)  (1  et )  log( yˆ  )
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Economic Convergence. Parametric Methods - Cristina Brasili
3. Convergence measures
Beta convergence
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5. Sigma convergenza
The concept of σ-convergence Dalgaard and
Vastrup (2001), Lucke (2008), Miller and
Upadhyay (2002) also comes from neoclassical
growth theory.
The σ-convergence is defined as lowering
of variance of real GDP per capita
logarithm among economies in time.
2  (1 N)
ln yit  
t Tt
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Convergence measures:
Beta and Sigma convergence
Sigma Versus Beta-convergence in EU28: do
they lead to different results? KATEŘINA
DVOROKOVÁ, Mathematical Methods in
Finance and Business Administration
Button K. , Pentecost E.,
Regional
Economic
Performance
within
the
European Union Edward Elgar, 1999 da pag
84 a pag 100
Convergence issues in the EU ed. by W.
Meeusen J. Villaverde da pag 62 a pag 82
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Economic convergence - Cristina Brasili
References
• Sigma Versus Beta-convergence in EU28: do
they lead to different results? KATEŘINA
DVOROKOVÁ, Mathematical Methods in Finance
and Business Administration
• Button K. , Pentecost E., Regional Economic
Performance within the European Union
Edward Elgar, 1999 da pag 84 a pag 100
• Convergence issues in the EU ed. by W. Meeusen
J. Villaverde da pag 62 a pag 82
To deepen
• THE NEOCLASSICAL SOLOW-SWAN
GROWTH MODEL Sarantis Kalyvitis
Italian
• L’approccio parametrico alla convergenza
economica, Maria Sassi da pag. 31 a pag. 45 in
Cambiamenti strutturali e convergenza
economica nelle regioni dell’Unione europea a
cura di Cristina Brasili, Clueb Bologna, 2005