ESTAT- NTTS, Brussels, Feb.18-20, 2009

Spatial effects of regional income disparities and growth in

the EU countries and regions

Tiiu PaasUniversity of Tartu, Estonia

Faculty of Economics and Business Administration

Friso SchlitteHWWI, 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))

• Regional aggregation, mainly NUTS-3 regions:

– 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

Dataset and regional system

EU-25 NMS EU-15Number of regions

861 122 739

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:

•

• We like to thank Carsten Schürmann (Dortmund University, Germany) for the generous provision of the travel time data.

)(21

1

jiijjiij timetime

ww

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

• Toverall=betweenwithin

i i

iii

i

i TTYY

NN

N

NT

N

N

/

/ln

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

)/

/ln()(

iij

ii

j i

ijT YY

NN

N

Ni

Decomposition of regional income inequality in EU-25

0.00

0.02

0.04

0.06

0.08

0.10

1995 1996 1997 1998 1999 2000 2001 2002 2003

between within

Decomposition of regional income inequality

Theil’s index decomposed into within-country and between-country inequality, 1995 – 2003 (NUTS3 data)

EU-15 and NMS

0.00

0.02

0.04

0.06

1995 1996 1997 1998 1999 2000 2001 2002 2003

between within

0.00

0.02

0.04

0.06

0.08

0.10

1995 1996 1997 1998 1999 2000 2001 2002 2003

between within

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:

•

iii

iT yy

y )ln()ln( 00

iii

iT factorsyy

y )()ln()ln( 00

• Conditional beta-convergence:

where income level in region i in year t

y it

• The convergence rate measures how fast economies converge towards the steady state:

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

Ts /)1ln(

)/1ln(/)2ln( T

Regression analysis

Classical assumption

• Assumption for the correct OLS estimators: the non-systematic component is normally distributed independently of

• 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.

i 2,0

iy0ln

• 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.

• SLM - suitable model for the substantive form:

• SEM - suitable model for the nuisance form:

where

ii

i

T

i

iT yy

yW

y

y

)ln()ln()ln( 0

00

iii

iT yy

y )ln()ln( 00

iii uW

Regression analysis

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:

where = variable in question in region i and in year t (in deviations from the mean)

N = number of regions

= sum of all weights (since we use row-standardised weights N is equal

to N)

I t N xi, txj, twi, j

j1

N

i1

N

Nb xi, t2

i1

N

x i,t

Nb

Moran coefficient I (Standardised z-value)

Critical cut-off

distance (km)

1995

2003lni

i

y

y )ln( 1995iy )ln( 2003iy

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)**

**significant at the 0.01 level

Moran’s I-test for spatial autocorrelation

– 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:

– 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.

W

wij 0 if i j

wij 1 dij2 if dij D

wij 0 if dij D

Regression analysis

EU-25 EU-15 NMS EU-25 EU-15 NMS

Country dummies no yes

OLS-model

Convergence speed 2.0** 1.8** 1.4* 0.3 0.9** -1.5**

Half-life 35 38 50 240 81 -

AIC -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*

Half-life 116 105 - 283 99 -

Spatial lag coeff. 0.840** 0.809** 0.830** 0.495** 0.592** 0.540**

AIC -1636.1 -1467.4 -185.5 -1764.8 -1568.7 -199.0

Spatial Lag Model

Convergence speed 0.6** 0.7** 0.3 0.2 0.6** -1.4**

Half-life 110 103 253 344 113 -

Spatial error coeff. 0.780** 0.782** 0.604** 0.410** 0.535** 0.508**

AIC -1640.1 -1473.2 -174.9 -1755.0 -1558.2 -197.8 **significant at the 0.01 level, *significant at the 0.05 levelNote: Direct comparison of convergence speed between OLS- and spatial models not possible.

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 non-normality

Regression analysis

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 self-balancing 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!Tiiu.paas@mtk.ut.ee; www.mtk.ut.ee