Info-Metrics: Theory and Applications
Department of Economics - American University Campus
Washington DC, September 24-25 2010
GME ESTIMATION WITH NON-LINEARITIES AND SPATIAL DEPENDENCE IN CLUB
CONVERGENCE ACROSS OECD COUNTRIES
Rossella Bernardini Papalia*, Silvia Bertarelli^
*Department of Statistics, University of Bologna, Italy, [email protected]
^Department of Economics, University of Ferrara, Italy, [email protected]
1
MOTIVATIONS
 Empirical evidence on regional convergence suggests that regions and countries are not homogenous and
not independent units.
 It is necessary to incorporate heterogeneity by making a further distinction between the concepts of
absolute location (spatial heterogeneity) and relative location (spatial dependence)
1. Absolute location refers to the impact of being located at a particular point in space.
2. Relative location considers relevant the position of a region relative to other regions.
 From a theoretical perspective as suggested by Masanjala and Papageorgiou (2004) heterogeneity is strictly
connected with non linearities.
 Spatial externalities may be introduced in theoretical growth models yielding convergence equations with
spatial autocorrelation.
2
ESTIMATION PROBLEMS
 Estimation of models incorporating spatial heterogeneity poses both identification and collinearity problems
(omitted variable bias; correlation between unobserved heterogeneity -individual specific effects- and
explanatory variables).
 In the presence of residual regional heterogeneity, estimation of convergence models poses -SPECIFIC
PROBLEMS:
1. identification problems;
2. endogeneity/collinearity problems;
3. omitted variables related to initial conditions;
4. simultaneity
5. incidental parameter problem, short panels, spatial and time period fixed effects.
 As a consequence: the standard estimation procedures employed in many studies can produce biased
estimates (and/or with large variances) of the convergence rate.
ML-based estimation techniques (Anselin, 1988)
Groups and a nonparametric covariance estimation technique, GMM (Driscoll at al., 1998),
Feasible GLS procedures, two stages procedures; estimated GLS (EGLS) (Baltagi, 2006;
Kelejian and Prucha, 1998, 1999),
MCMC methods (Kakamu et al., 2006)
introduction of prior restrictions on the parameters to reduce the dimensionality of the
problem.
3
OBJECTIVES
‐ to develop a two stage strategy to estimate a spatial club convergence model which introduces:
(i)
(ii)
(iii)
non linearities;
information on clustering schemes identified by a mapping analysis;
a GME estimation procedure
AT THE FIRST STAGE:
 We introduce spatial heterogeneity (absolute location effects)
 The spatial dependence is incorporated into the model by specifying a dynamic spatial model
 In spatial process models, one proceeds by specifying the spatial process and by choosing an appropriate
spatial weights matrix that must not contain any of the exogenous or endogenous variables used in the
growth regression.
 We assume
1. non linearities
2. different TFPs
3. statial autocorrelation
 Clubs are identified by means of a mapping analysis.
4
AT THE SECOND STEP
 The objective is to incorporate spatial effects and/or externalities into the regimes specification.
 The growth analysis is extended to take account of relative location effects by explicitly modeling spatial
dependence (residual heterogeneity) within clubs.
 We specify a multi-club spatial convergence model, with clubs corresponding to subsets of regions, which
are identified at the first stage of the analysis.
APPLICATION
The proposed strategy is applied to assess the existence of club convergence across OECD countries over the
period 1965-2004.
The case of OECD countries gives us the possibility to contribute to a debate on the identification of clubs across
a small sample of countries whose results are still ambiguous.
5
ECONOMIC BACKGROUND (1)
GROWTH MODELS WITH HETEROGENEOUS PARAMETERS
Heterogeneity is strictly connected with non linearities.
 From a theoretical perspective non linearities may be connected with the internal sources of factor
accumulation (Peretto, 1999), could be the result of different adoption speeds of technological spillovers
(Parente and Prescott 1994), the evolution of one economy might be path dependent so that different initial
conditions induce the choice of different technologies (Ciccone and Matsuyama, 1996; Galor and Zeira,
1993) or technology is CES (Masanjala and Papageorgiou, 2004).
 Non linear growth processes imply multiple steady states. Multiple equilibria may be generated by the
presence of threshold externalities of accumulated factors (Azariadis and Drazen, 1990) and cross country
differences in the level of financial development (Acemoglu and Zilibotti, 1997).
 From an empirical perspective, the pioneering work of Durlauf and Johnson (1995) has empirically studied
multiple development clubs and growth regimes, accounting for parameter heterogeneity and implying that
different countries obey different linear growth processes. Several subsequent papers have shown
significant non linearities for a variety of variables (Mamuneas et al., 2006; Ketteni et al., 2007).
6
ECONOMIC BACKGROUND (2)
GROWTH MODELS WITH SPATIAL CORRELATION
Spatial externalities may be introduced in theoretical growth models yielding convergence equations with spatial
autocorrelation
From a theoretical perspective, models of endogenous growth often emphasize the importance of technological,
physical and human capital spillovers. Such spillovers are connected to i) human capital and institutional
differentials ii) bilateral channels such as trade and foreign direct investment (Coe et al., 1995; Keller, 1998).
The magnitude of these spillovers depends on the patterns of spatial interdependence among regions
Growth models with spillovers arising from geographical proximity have been derived by Lopez-Bazo et al.
(2004), Ertur and Koch (2007).
The interest in location and economic growth issues has led the economists of the New Economic Geography to
include explicit mechanism of geographical agglomeration in endogenous growth models (Martin and Ottaviano
2001, Fujita and Thisse 2002).
From an empirical perspective, the empirical evaluation of spatial dependence in convergence processes has
been implemented at regional level by Ertur et al. (2006) and Ertur and Koch (2007) among others.
7
STEP I – PROCEDURE: IDENTIFICATION OF CONVERGENCE CLUBS BY A MAPPING
STRUCTURE
 A mapping structure is introduced in the dynamic optimization problem to investigate unobserved
heterogeneity.
 The approach aims at investigating regional spatial heterogeneity by also capturing the contribution of
omitted variables such as the unobserved quality of institutions, and the unobserved determinants of
regional technological and structural characteristics.
Advantages:
1. to allow for an endogenous selection of regional clusters
2. to facilitate the interpretation of the cluster outcomes, providing a measure of the role (weight) of
different unobserved dimensions.
8
THE LOCATION MAP OF UNOBSERVED VARIABLES
As in the choice map, the position of the unobserved variables on the M-dimensional map and the weights for
these dimensions are derived.
The resulting location map can be obtained by using a two stage process:
 First, the parameters of the growth model are estimated and the covariance matrix of unobserved
components  i ’s is computed.
 Then this matrix is used as an input in multidimensional scaling to obtain their locations in a multi-attribute
space.
We assume that the time-invariant effect,  i , is a linear function of the country’s time invariant attributes which
lie within a two-dimension map, such as:
i  s1l1  s2l2  i
(s1 , s2) are parameters modeled as a function of country’s characteristics;
(l1 , l2) are the coordinates representing the location of the unobserved effect on the
map (to be estimated);
i
is a random error with zero mean.
This procedure endogenously identifies the determinants of TFP differences.
The interpretation of the dimensions of the map (l1i, l2i) is driven by growth theory and may capture the
contribution of national unobserved variables such as the quality of institutions, and the distance matrix.
9
MODEL SPECIFICATION
We start by specifying a dynamic panel model with country fixed effects as follows:
ln y   ln y
 'D
  t  u
(1)
it
it 1
it 1
i
it
5-year average data: all data are expressed in logs and are calculated as 5-year averages to eliminate the business
cycle component.
 ln yit-1 refers to the endogenous lagged per capita GDP level,
 Time effects control for the presence of a time trend component and of a common stochastic trend (the
common component of technology).
 Individual effects capture total factor productivity (TFP) differences, and other time-invariant omitted
variables (correspond to initial conditions for technological characteristics and institutions and strongly
influence the formation of clubs).
 Explanatory variables suggested by theory to approximate the steady state output are (in logs):
the vector Dit-1 of country-specific explanatory variables includes skit-1 the investment rate in physical capital,
ndxit-1 the sum of the population growth rate, the exogenous technological growth rate, and the depreciation
rate (gives the determinants of the steady state output and consists of a set of country-specific explanatory
variables suggested by the theory).
 Additional country-specific control variables that influence both the steady state output and total factor
productivity (TFP) levels: variables capturing technological and geographical spillovers.
10
Fixed effects in Dynamic spatial panel models:
Panel models give us the advantage of introducing and estimating fixed effects in the conditional convergence
model to identify convergence clubs and to allow for spatial unobserved heterogeneity among spatial units.
Spatial dependence effects capture pecuniary and technological spillovers since they are connected to
geographical distance between country pairs.
The Dynamic models for Spatial Panel models exhibiting both dependence in the dependent variable and the
error structure
y    I W  y  X  u
N
 T
u  W u  
N
E  '   2 I
NT
with y as a NT×1 vector, X as a NT×K matrix and
parameter, and the other notation is as before.

as a NT×1 vector,  is the scalar spatial autoregressive
The set of k explanatory variables X is enlarged to include the spatial lagged dependent variables lnyit-1 and
country and time fixed effects ( X  ln yiy 1 T  I N I T   N  );  is the Kronecker product operator, T and  N are T×1
and N×1 vectors of all unity elements respectively, and IN and IT are identity matrices of dimension N and T,
respectively.
11
 When the spatial autocorrelation is modeled by a spatial autoregressive process in the error terms we refer
to SPATIAL ERROR MODEL -SEM MODEL
 is the parameter associated to the spatially lagged error term
1. it is observed how a random shock in a region affects growth rates in that region and additionally
impacts all the other regions through the spatial transformation
2. the presence of global externalities are associated solely with random shocks (they measure the
joint effect of misspecification, omitted variables, and spatial autocorrelation).
 When the spatial autocorrelation is modeled by a SPATIAL LAG MODEL, SPATIAL
AUTOREGRESSIVE MODEL – SAR MODEL we have:
 is the parameter associated to the spatially lagged dependent variable WY
the spatial interaction effect indicate the degree to which the growth rate of per-capita GDP in one region
is determined by the growth rates of its neighboring regions.
1. all spatial dependence effects are captured by the lagged term.
2. It is observed how the performance of the dependent variable impacts all the other (neighbor)
regions through the spatial transformation
3. the presence of global spillovers is associated to GDP growth rates.
 One proceeds by testing the null hypotheses (ML and LM based tests, Anselin, 1992):
H0: =0; SEM
H0: ρ =0; SAR
12
 Spatial weights are derived from the location and spatial arrangements of observation by means of a
geographic information system.
 Regions are defined ‘neighbors’ when they are within a given distance of each other, i.e. wij =1 for d ij  
and ij, where dij is the great circle distance between the capital cities of region i and j,
 is a critical cut-off value (distance-based contiguity), above which all interactions are assumed to be
negligible.
 More specifically, a spatial weights matrix W* is defined as follow:
0 if

w  1 if
0 if

*
ij
i j
d ij   ,i  j .
dij   , i  j
 The elements of the row-standardized spatial weights matrix W (with elements of a row sum to one) result:
wij 
wij*
N
w
j 1
13
*
ij
,
i, j  1,.., N .
ESTIMATION_GME
We introduce a GME formulation which produces consistent parameter estimates of a conditional convergence
model in presence of collinearity and endogeneity of lagged dependent variable, spatial lag variables, and some
explanatory variables such as fiscal policy and openness.
This technique is here suggested with the aim of correcting for biases: (i) connected to model specification
problems (omitted variable bias), (ii) arising from simultaneity, miss-specified dynamics and/or measurement
errors.
It is suggested:
(i) in presence of small samples, when the number of time periods, T, is not sufficiently large,
(ii) when the number of regions N is greater than the number of time periods, T (N>T);
(iii) in presence of collinearity and/or endogeneity of explanatory variables.
14
The coefficients are all Re-Parameterized as expected values of discrete random variable with M fixed points for
the coefficients and J for the errors. The Re-Parameterized coefficients are defined as follows == Z =  p  ;
= Z  p   ; = Z  p   ; u= V u r u  ; = V  r   .  is enlarged to include time and fixed effects.
The matrices (Z, Z, Z) and (Vu, Vε) define the support fixed points for the re-parameterization of the
coefficients and the error terms.
The coefficients and the error terms are estimated by recovering the probability distribution of the discrete
random variables set.
The vectors p=vec(p p pρ) and r=vec(ru, r ) are vectors of proper probability distributions for parameters and
errors, respectively, while p, p, p, rε, ru, are calculated by the maximization the traditional entropy function
subjected to the following consistency and adding-up constraints.
The consistency constraint represents the information about the data expressed by the reformulated model in the
equation:


Y   Z  p   I W Y  X  Z  p     Z  p  W V u r u   V  r  ;
N

 T
 N
 

The adding-up constraints impose that the sum of each coefficients and the error terms probability vector have to
be equal to 1.
15
STEP II - PROCEDURE: SPECIFICATION OF THE SPATIAL MULTIPLE REGIMES MODEL
 Clubs correspond to subsets of regions identified by means of the mapping analysis. Each club may be
represented by a cross-sectional equation.
 Spillovers connected to geographical distance are modelled in terms of spatial dependence effects.
 We consider a system of two equations, one for each regime, the two-club growth model can be modelled
assuming a LAG functional form or SEM functional form.
 Consistent and asymptotically normal estimates may be obtained by using the generalized maximum
entropy (GME) estimation approach.
16
CLUB CONVERGENCE, THRESHOLD EXTERNALITIES AND SPATIAL DEPENDENCE
ANALYSIS FOR OECD COUNTRIES
Step I procedure: identification of clubs
‐ Pooled OLS estimates display spatial heterogeneity, heteroskedasticity, non normality and collinearity
(TABLE 1)
‐ Having proved the existence of endogeneity for ln yit-1 and shit-1, as well as collinearity, the generalized
maximum entropy approach has been employed.
‐
parameter estimates for a mixed model with both spatial lag and spatial error components
‐ Multi dimensional scaling of time invariant country specific effects, used to measure initial TFP levels
Results:
2 clubs of OECD countries emerge in accordance with Canova (2004)
Country groupings are different from Canova (2004). Club 1 comprises 15 countries, while Australia, Italy,
Korea, Mexico, Portugal, Spain, Switzerland and Turkey join club 2 (table 2)
Determinants of TFP levels (scatter plot analysis): good institutions and high quality human capital are positively
correlated with one dimension.
17
Step II procedure: differences in growth determinants across clubs
‐ GME estimates of a system of two convergence equations, for both spatial SEM and spatial LAG models
‐ The Wald test on the homogeneity of the parameters across equations points out to the superiority of a
specification with heterogeneous slope coefficients.
‐ Since the LM Lag test value exceeds the LM Error test value, the two tests point to the presence of spatial
lag dependence rather than spatial error autocorrelation.
Results:
With reference to spatial dependence, per capita GDP in a country is positively affected by neighboring
countries’ GDP within each club. In addition, these complementarity effects are different across regimes
(stronger in club 2 countries than in club 1 ones).
With reference to interaction terms (threshold externalities), the non-monotonic pattern of convergence is
strongly influenced by human capital stocks. In club 1, significant non linear effects of primary and secondary
attainment emerge. In club 2, primary and tertiary attainment levels show significant coefficients with opposite
signs.
With reference to club convergence determinants, a link between stages of development and returns to physical
capital and levels of education emerges: club 2 shows the highest returns of physical capital and primary average
years of schooling, while the highest return on secondary average years of schooling is related to club 1. Tertiary
school attainment shows negative effects in club 2, while club 1 coefficient is not significant.
18
RESULTS
• Our results strongly support the presence of TFP heterogeneity across OECD COUNTRIES in the 19652004 period.
• The key role of both technology spillovers through human capital accumulation and non linearities
(interaction terms, threshold externalities )has been confirmed by our results.
• First step results:
1. two clubs are identified
2. presence of mixed spatial correlation and non linearities.
• Second step results:
1. Our analysis, while confirming the convergence club hypothesis across OECD COUNTRIES in the
1965-2004 period, has shown the presence of spatial lag dependence. The global externalities are not
associated with random shocks, but neighbors’ growth rates tend to positively influence the
economic performance of a region (LAG model).
2. Results consistent with analyses based on a large sample of countries (72 countries, with all OECD
countries) We find four clubs: OECD countries are in clubs 1 and 2 (only Turkey is in club 3). Club
1 in the OECD sample coincides with club 1 in the large sample, with the exception of Italy,
Australia (reported in club 2 in the OECD sample analysis and in club 1 in the large sample one) and
Greece (reported in club 1 in the OECD sample analysis and in club 2 in the large sample one). With
reference to growth determinants, our OECD results are confirmed. The convergence process is
different across regimes, threshold externalities are important and different returns on factor
accumulation emerge.
19
FURTHER INVESTIGATION
should be done in order to:
 to compute TFP levels without imposing stationarity
FURTHER RESEARH
 Spatial weights Matrix: Economic distance, semi-parametric, entropy based estimation;
 Computational vs statistical efficiency
 Spatial panels: separability vs non-stationarity
20
Table 1: Pooled OLS estimates
Tests (p-values)
Tests for heteroskedasticity:
Variables
ln yit-1
Estimation results
0.784***
ndxit-1
-0.078
1) Breusch-Pagan test
skit-1
0.060**
2) White test°°
Education primary
-0.370
Tests for normality:
1) Skewness and kurtosis of
residuals°
2) Information Matrix test
Education secondary
Education tertiary
-0.400
0.266
Financial development
0.371**
- Skewness°°
Openness
Fiscal expenditure
Inflation
0.024*
-0.022
0.524***
- Kurtosis°°
Rate of convergence
Adj. R2
RMSE
21
1.02
(0.386)
32.32
(0.029)
6.38
(0.012)
Autocorrelation of residuals°°°
0.214***
- Lag 2
0.041
0.042
-0.020
- Lag 3
3.76
(0.0002)
1.31
(0.192)
0.11
(0.909)
AIC
BIC
N. obs.
-392.71
-334.17
138
- Lag 1
Edu tert * Fin dev
Lagged dep var * edu
prim
Lagged dep var * edu sec
Lagged dep var * edu tert
8.59
(0.003)
138
(0.46)
VARIABLE
0.9845
0.0546
Table 2: Step I GME estimates
Variables
ln yit-1
ndxit-1
skit-1
Education primary
Education secondary
Education tertiary
Financial development
Openness
Fiscal expenditure
Inflation
Edu tert * Fin dev
Lagged dep var * edu prim
Lagged dep var * edu sec
Lagged dep var * edu tert
Spatial dep. variable
Spatial error
Rate of convergence
Adj. R2
RMSE
22
Std.
Coefficient Error
0.825
0.000002
-0.008
0.00003
0.004
0.00004
0.167
0.0016
0.026
0.0028
-0.002
0.0009
-0.007
0.0008
0.004
0.0001
0.016
0.0001
0.001
0.0002
0.004
0.0008
0.018
0.002
-0.0004
0.103
0.00003
0.0002
0.0003
0.0001
0.0006
0.00001
VARIABLE
0.9639
N. obs.
0.0684
P-value
<.0001
<.0001
<.0001
<.0001
<.0001
0.012
<.0001
<.0001
<.0001
0.002
<.0001
<.0001
<.0001
0.000
<.0001
<.0001
138
Table 3: OECD country groupings
Club
Club AUS
1
2
Australia
AUT Austria
CHE
BEL Belgium
Switzerland
CAN Canada
ESP Spain
DNK Denmark
ITA Italy
FIN Finland
KOR Korea
MEX
FRA France
Mexico
PRT
Portugal
GBR Great Britain
TUR
GER Germany
Turkey
GRC Greece
IRL Ireland
JPN Japan
NLD Netherlands
NOR Norway
SWE Sweden
USA United States of
America
23
Table 4: Step II GME estimates, OECD countries (1965-2004)
Club 1
Club 2
Std.
PStd.
Variables
Coefficient Error value Coefficient Error
ln yit-1
0.964
0.0008 <.0001
0.855
0.0008
ndxit-1
-0.021
0.0003 <.0001 -0.040
0.0002
skit-1
0.002
0.00002 <.0001
0.020
0.0001
Education primary
0.059
0.001 <.0001 0.314
0.001
Education secondary
0.015
0.004 0.000
0.006
0.003
Education tertiary
-0.003
0.003 0.340
-0.019
0.001
Financial
development
-0.002
0.0002 <.0001 -0.055
0.007
Openness
0.001
0.00004 <.0001
0.009
0.00003
Fiscal expenditure
0.010
0.0001 <.0001
0.009
0.0001
Inflation
0.0004
0.0001 0.002
0.001
0.0001
Edu tert * Fin dev
0.0004
0.001 0.572
0.032
0.005
Lagged dep var *
edu prim
0.008
0.0002 <.0001
0.026
0.0003
Lagged dep var *
edu sec
0.001
0.0003 0.005 -0.000001 0.0002
Lagged dep var *
edu tert
-0.0004 0.0002 0.089
-0.001 0.00004
Spatial dep. variable
0.004
0.0001 <.0001
0.007
0.00004
24
Pvalue
<.0001
<.0001
<.0001
<.0001
0.033
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
0.997
<.0001
<.0001
Table 5: Country groupings, Durlauf and Johnson (1995) sample
Club
Club
Club
Club
1
2
3
4
AUS
AUT
BEL
CAN
DNK
FIN
FRA
GBR
GER
IRL
ISR
ITA
JPN
NLD
NOR
SWE
USA
25
Australia
Austria
Belgio
Canada
Denmark
Finland
France
United
Germany
Ireland
Israel
Italy
Japan
Netherlands
Norway
Sweden
United
ARG
CHE
CHL
CRI
ECU
EGY
ESP
GRC
KOR
MEX
PAN
PHL
PRT
URY
VEN
Argentina
Switzerland
Chile
Costa Rica
Ecuador
Egypt
Spain
Greece
Korea
Mexico
Panama
Philippines
Portugal
Uruguay
Venezuela
BGD
BOL
BRA
COL
DZA
GTM
HND
IDN
IND
JAM
JOR
LKA
MAR
MUS
MYS
PAK
PER
PRY
SLV
THA
TUN
TUR
Bangladesh
Bolivia
Brazil
Colombia
Algeria
Guatemala
Honduras
Indonesia
India
Jamaica
Jordan
Sri Lanka
Morocco
Mauritius
Malaysia
Pakistan
Peru
Paraguay
El
Thailand
Tunisia
Turkey
CIV
CMR
ETH
GHA
HTI
KEN
MDG
MLI
MWI
NGA
RWA
SDN
SEN
SGP
SLE
UGA
ZAR
ZMB
ZWE
Cote
Cameroon
Ethiopia
Ghana
Haiti
Kenya
Madagascar
Mali
Malawi
Nigeria
Rwanda
Sudan
Senegal
Singapore
Sierra
Uganda
Congo
Zambia
Zimbabwe
Table 6: Step II GME estimates, Durlauf and Johnson (1995) sample
Club 1
Club 2
Std.
PStd.
PVariables
Coefficient Error value Coefficient Error value
ln yit-1
0.899
0.001 <.0001
0.801
0.001 <.0001
ndxit-1
-0.007
0.00001 <.0001 -0.101
0.0002 <.0001
skit-1
0.002
0.00001 <.0001
0.001
0.000003 <.0001
Education primary
0.174
0.001 <.0001
0.357
0.002 <.0001
Education secondary
0.036
0.002 <.0001 -0.003
0.002 0.072
Education tertiary
-0.003
0.0005 <.0001 -0.023
0.001 <.0001
Financial
development
-0.003
0.0002 <.0001 -0.005
0.0001 <.0001
Openness
0.001
0.000004 <.0001
0.001
0.000003 <.0001
Fiscal expenditure
0.013
0.0001 <.0001
0.008
0.00003 <.0001
Inflation
0.0001
0.00001 <.0001
0.000
0.00001 <.0001
Edu tert * Fin dev
0.001
0.0003 <.0001
0.002
0.0001 <.0001
Lagged dep var * edu
prim
0.013
0.00002 <.0001
0.035
0.0002 <.0001
Lagged dep var * edu
sec
0.002
0.0002 <.0001 -0.001
0.0002 <.0001
Lagged dep var * edu
tert
-0.0003 0.00004 <.0001 -0.003
0.0001 <.0001
Spatial dep. variable
0.004
0.00001 <.0001
0.009
0.00002 <.0001
26
Table 6 (continue): Step II GME estimates, Durlauf and Johnson (1995) sample
Club 3
Club 4
Std.
PStd.
PVariables
Coefficient Error value Coefficient Error value
ln yit-1
0.917
0.001 <.0001
0.949
0.001 <.0001
ndxit-1
-0.040
0.00006 <.0001 -0.005
0.00001 <.0001
skit-1
0.005
0.00001 <.0001
0.001
0.000002 <.0001
Education primary
0.027
0.0004 <.0001
0.016
0.0004 <.0001
Education secondary
-0.004
0.001 <.0001 -0.015
0.001 <.0001
Education tertiary
-0.010
0.0002 <.0001 -0.007
0.0001 <.0001
Financial
development
-0.002
0.00003 <.0001 -0.004
0.00004 <.0001
Openness
0.001
0.000002 <.0001
0.004
0.00001 <.0001
Fiscal expenditure
0.004
0.00001 <.0001
0.002
0.00001 <.0001
Inflation
-0.001
0.00001 <.0001
0.000
0.000003 <.0001
Edu tert * Fin dev
0.002
0.0001 <.0001
0.001
0.00001 <.0001
Lagged dep var * edu
prim
0.002
0.00005 <.0001
0.001
0.00004 <.0001
Lagged dep var * edu
sec
-0.001
0.0001 <.0001 -0.003
0.0001 <.0001
Lagged dep var * edu
tert
-0.002
0.00004 <.0001 -0.002
0.00002 <.0001
Spatial dep. variable
0.012
0.00003 <.0001
0.010
0.00002 <.0001
27
The case of OECD countries gives us the possibility to contribute to a debate on the identification of clubs across
a small sample of countries whose results are still ambiguous. Results of previous studies of convergence for
OECD countries indicate some potential puzzles:
- Early studies (Barro, 1991; Mankiw et al., 1992; among others) have found evidence of absolute convergence
for OECD countries.
- Within the time series approach, Bernard and Durlauf (1995) reject convergence hypothesis of OECD countries
using standard univariate and multivariate time series techniques and find more than one common long run
factor. Andres and Bosca 2000) identify two different groups within the OECD, with significantly different
technologies. Nahar and Inder (2002) find evidence of convergence of OECD countries towards USA per capita
GDP, regarded as the closest proxy of steady state output.
- Canova (2004) applies a Bayesian technique to find two clubs for OECD countries using initial income as a
mean to order and group countries.
For a large sample of countries (OECD included)
- Durlauf and Johnson (1995) have empirically studied multiple development clubs and growth regimes,
accounting for parameter heterogeneity and implying that different countries obey different linear growth
processes. They use initial income per capita to identify clubs and then estimate a (linear) conditional
convergence equation for each club
- Several subsequent papers have shown significant non linearities for a variety of variables (Mamuneas et al.,
2006; Ketteni et al., 2007). In addition, Tan (2009) has used information on the interactions between covariates,
to account for threshold externalities such as the model of Azariadis and Drazen (1990).
28