ESTAT- NTTS, Brussels, Feb.18-20, 2009
Spatial effects of regional
income disparities and growth in
the EU countries and regions
Tiiu Paas
University of Tartu, Estonia
Faculty of Economics and Business Administration
Friso Schlitte
HWWI, PhD student of Hamburg University, Germany
The main focus of the paper
How to measure spatial effects of regional income
convergence.
May ignored spatial effects lead to biased and/or
inefficient OLS estimates.
The empiricalt part of the presentation bases on the paper written together with
the PhD student Friso Schlitte from Hamburg University, Germany. The
extended version of the paper is published in Italian Journal of Regional
Science, Vol.7. N02, 2008
Empirics
Data
GDP (PPS) of the EU-25 at the NUTS-3 (Nomenclature of
Statistical Territorial Units of EUROSTAT) level during the
period 1995-2004 distinguishing two groups of countries: EU-15
and EU-10. Database REGIO.
Spatial weights (W)
Inverse of travel time of freight vehicles between the centers of
regions (Thanks go to Carsten Schürmann (Dortmund))
Dataset and regional system
• Regional aggregation, mainly NUTS-3 regions:
Number
of
regions
EU-25
NMS
EU-15
861
122
739
– distinguishing two groups of countries: EU-15 and the
new member states (NMS) that joined in May 2004
Data: GDP per capita (PPP), 1995 - 2003, taken from Eurostat
database
Weight matrix
• The weight matrix is based on the travel time of
freight vehicles between the centers of regions. An
element wij of distance matrix W is calculated as
follows:
•
1
wij  w ji 
1 2 (timeij  time ji )
• We like to thank Carsten Schürmann (Dortmund University,
Germany) for the generous provision of the travel time data.
What says economic theory?
• Neoclassical growth theory (Solow 1956): poor countries grow
faster (“law of diminishing returns”) - convergence optimism.
• Endogenous growth theory (Romer 1990): due to involvement of
human capital and knowledge the “law of diminishing returns” might
not be valid - convergence pessimism.
• New Economic Geography (Krugman 1990): due to impact of
different conditions and factors (eg transport costs) regional
disparities could increase or decrease - no clear support to
convergence optimism or pessimism.
• Evolutionary economics (Dosi, et al 1988; Freeman, 1994): the
relationships are not linear, there are spillover effects, “social filters” ,
changing conditions etc.
In sum: Clear theoretical framework explaining regional disparities
has not yet fully developed.
The results of previous empirical
studies vary
The results of empirical studies depend on
•
time period;
•
data (cross-sections, panel data, time series; quality of data);
•
estimation techniques (non-spatial, spatial, etc); the level of
aggregation (MAUP – Modifable Areal Unit Problem);
•
etc…
In sum: Regional disparities follow a pro-cyclical character;
developed regions ordinarily grow faster in periods of
expansion.
Decomposition of regional income inequality
Theil index
• T
=
overall
 Ni 
 Ni   Ni / N 
  Twithin  Tbetween
  Ti     ln 
i  N 
i  N   Yi / Y 
where
Yij – the income of the region j in the country i,
Y – the total income of all regions,
Nij – the population of the the region j in the country i,
N - the total income of all regions
Nij
Ni / Ni
) ln(
)
Ti   (
Yij / Yi
j Ni
Decomposition of regional income
inequality in EU-25
0.10
between
within
0.08
0.06
0.04
0.02
0.00
1995
1996
1997
1998
1999
2000
2001
2002
2003
Decomposition of regional income inequality
Theil’s index decomposed into within-country and betweencountry inequality, 1995 – 2003 (NUTS3 data)
EU-15
0.06
and
NMS
0.10
between within
between within
0.08
0.04
0.06
0.04
0.02
0.02
0.00
0.00
1995
1995
1996
1997
1998
1999
2000
2001
2002
2003
1996
1997
1998
1999
2000
2001
2002
2003
Convergence
• Convergence is a concept that generally describes
catching up of poor with rich ones; the process of
diminishing disprarities.
• Absolute convergence bases on assumption that
economies (countries, regions) converge towards the
same steady state equilibrium.
• Conditional convergence assumes that regions
converge towards different steady-state income
levels; it will occur if some structural characteristics
(eg demographic situation, government policy, employment, etc)
have an impact on economic growth.
• Absolute beta-convergence model:
yiT
ln(
)     ln( yi 0 )   i
yi 0
where
•

yit 
income level in region i in year t
Conditional beta-convergence:
y
• ln( iT )     ln( yi 0 )   ( factors)   i
yi 0
Regression analysis
• The convergence rate measures how fast
economies converge towards the steady state:
s   ln( 1   ) / T
where T is the number of periods.
• The half-life is defined as the time which is
necessary for half of the initial income inequalities
to vanish
   ln( 2) / ln( 1   / T )
Classical assumption
• Assumption for the correct OLS estimators:
the non-systematic component  i is
2

 independently of ln y0i
0
,

normally distributed
• This assumption is not always valid; the
residuals of nearby regions are often
correlated, there may be spillovers between
regions; there may be spatial effects.
• Ignored spatial effects may lead to biased or
inefficient OLS estimates
– Biased if direct regional interaction (substantive
form)
– Inefficient if spatial effects are only in error term
(nuisance form).
Spatial effects are ordinarily taken into account by choosing
a proper model class and spatial weight matrix W.
Spatial effects
• There are two types of spatial effects (see also Anselin 1988).
– Observations from adjacent regions can be correlated
(spatial autocorrelation; substantive form of spatial
dependence). Spatial Lag Models (SLM) or Spatial
Autoregressive Models (SAR) a proper model class to work
with.
– A functional relationship can vary across regions; threre are
measurement errors (spatial heterogeneity; nuisance
dependence). Spatial Error Models (SER) a proper model
class to work with.
Regression analysis
• SLM - suitable model for the
substantive form:

yiT
yT 
ln(
)     W  ln( )   ln( yi 0 )   i
yi 0
y0  i

• SEM - suitable model for the nuisance
form:
yiT
ln(
)     ln( yi 0 )   i
yi 0
where
 i   W   i  ui
Model Estimation and Selection
1. Models:
–
–
with/without country dummies
with/without NMS dummies
2. OLS. Test for spatial effects (Moran I,
Robust LM(error), Robust LM(lag),
3. Spatial models (SEM, SLM), selection
based LM tests.
Moran I- statistic
• As a measure of spatial clustering of
income levels and growth:
N
N
N  xi, t xj, t wi, j
It 
i 1 j 1
N
N b  xi,2 t
i 1
where
x i,t = variable in question in region i and in year t (in deviations from the mean)
Nb

N = number of regions
= 
sum of all weights (since we use row-standardised weights N is equal
to N)
Regression analysis
Moran’s I-test for spatial autocorrelation
Moran coefficient I (Standardised z-value)
y

ln  i 2003 
 yi1995 
ln( yi1995 )
ln( yi 2003)
100
0.46 (18.24)**
0.76 (30.15)**
0.67 (26.53)**
200
0.44 (25.09)**
0.75 (42.60)**
0.66 (37.55)**
300
0.41 (26.81)**
0.72 (47.57)**
0.64 (41.90)**
400
0.38 (27.09)**
0.70 (49.98)**
0.62 (43.97)**
500
0.36 (27.29)**
0.68 (51.11)**
0.60 (44.96)**
600
0.35 (27.13)**
0.66 (51.08)**
0.58 (44.93)**
700
0.34 (27.09)**
0.64 (50.93)**
0.56 (44.80)**
800
0.33 (26.91)**
0.62 (50.52)**
0.55 (44.47)**
900
0.32 (26.69)**
0.61 (50.05)**
0.53 (44.07)**
1000
0.32 (26.49)**
0.59 (49.56)**
0.52 (43.66)**
2000
0.29 (25.39)**
0.53 (46.89)**
0.47 (41.41)**
Critical cut-off
distance (km)
**significant at the 0.01 level
– Significant spatial clustering in all cases
– Spatial clustering slightly less pronounced in 2003
– Spatial dependence of surrounding regions becomes insignificant when distance is
larger than 500 km, hence critical cut-off is 500 km.
Regression analysis
• Distance based weight matrix:
w ij  0
if i  j

2
W  w ij  1 dij if dij  D

if dij  D
w ij  0

– d= distance between centroids of regions, as the crow flies
– Weighted by the inverse of squared distance
– Using critical distance cut-off point D
• Results might be sensitive to the functional form of the weight matrix.
• But we do not have a priori information about nature of spatial dependence.
EU-25
Country dummies
EU-15
NMS
EU-25
no
EU-15
NMS
yes
OLS-model
Convergence speed
Half-life
AIC
2.0**
1.8**
1.4*
0.3
0.9**
-1.5**
35
38
50
240
81
-
-1371.4
-1230.1
-151.1
-1721.3
-1483.3
-190.2
Spatial Error Model
Convergence speed
0.6**
0.7**
-0.2
0.2
0.7**
-1.0*
Spatial lag coeff.
116
0.840**
105
0.809**
0.830**
283
0.495**
99
0.592**
0.540**
AIC
-1636.1
-1467.4
-185.5
-1764.8
-1568.7
-199.0
Half-life
Spatial Lag Model
Convergence speed
0.6**
0.7**
0.3
0.2
0.6**
-1.4**
Spatial error coeff.
110
0.780**
103
0.782**
253
0.604**
344
0.410**
113
0.535**
0.508**
AIC
-1640.1
-1473.2
-174.9
-1755.0
-1558.2
-197.8
Half-life
**significant at the 0.01 level, *significant at the 0.05 level
Note: Direct comparison of convergence speed between OLS- and spatial models not possible.
Regression analysis
Testing: Substantive versus nuisance
form
(Anselin and Florax, 1995)
– If LM test for spatial lag is more significant than LM test for
spatial error, and robust LM test for spatial lag is significant but
robust LM test for spatial error is not, then the appropriate model
is the spatial lag model.
– Conversely, if LM test for spatial error is more significant than LM
test for spatial lag and robust LM test for spatial error is
significant but robust LM test for spatial lag is not, then the
appropriate specification is the spatial error model.
– LM-test ; the test may be unreliable in the presence of nonnormality
Which is a proper model class?
In the case of absolute convergece:
– SLM for EU-15 and SER for NMS
In the case of conditional convergence
(national effects are considered):
- SEM for EU-15, no clear results for NMS
.
Empirical results (1)
• Absolute convergence across EU regions (OLS; spatial
effects are not taken into account): the rate of convergence
was around 2% in EU-25; 1.8% in EU-15 and 1.4% in
NMS (half-lifes 35, 38 and 50 years).
• The model-fits of the conditional convergence
estimations are better than those in absolute
convergence models - national factors matter.
• Conditional convergence (OLS): the rate of
convergence is 0.9% in EU-15 (half life 81 years);
• -1.5% (divergence) in NMS.
Empirical results (2)
• There are spatial effects in economic growth
between NUTS 3 level regions of EU-25.
Neighborhood matter!
• The rate of conditional convergence is by taking
spatial effects into account is around 0.6%-0.7% in
EU-15 and there is divergence in NMS.
• Spatial spillovers seems to stop at national borders!
National macroeconomic factors are more influential
on regional growth than spatial spillovers.
Conclusion
• There are spatial effects spatial effects of regional income
convergence.
• National factors play a more important role in determining growth than
cross-border spillovers do. The cross-border cooperation is still weak in
EU.
• There is a trade off between convergence on the national and regional
within-country convergence, particularly in NMS. Thus, some policy
measures that support economic and social cohesion are necessary.
•
There are still plenty of un-solved statistical problems in order to take
spatial effects properly into account (e.g non-normality; how to test
sensitivity to the weight matrix; additional covariates (conditional
convergence), fill missing data etc).
Policy implications
• Lowering regional income disparities is should be mainly
responsibility of the member states’ regional policy.
• On the country level it is possible to better specify
whether the increase of regional income inequality in the
conditions of quick economic growth is a normal selfbalancing process or it may lower the country’s
competitiveness in the long run.
• Regional policy measures should improve labour
flexibility and absorptive ability of the poorer regions to
take over innovations created in richer regions.
Thank You!
Your comments and discussions are welcome!
[email protected]; www.mtk.ut.ee