Neoclassical theory versus new economic geography: competing explanations of crossregional variation in economic development
ABSTRACT This paper uses data for 255 NUTS2 European regions over the period 1995–2003 to test the relative explanatory performance
of two important rival theories seeking to explain variations in the level of economic development across regions, namely
the neoclassical model originating from the work of Solow (Q J Econ 70:65–94, 1956) and the socalled Wage equation, which
is one of a set of simultaneous equations consistent with the shortrun equilibrium of new economic geography (NEG) theory,
as described by Fujita etal. (The spatial economy. Cities, regions, and international trade. The MIT Press, Cambridge, 1999).
The rivals are nonnested, so that testing is accomplished both by fitting the reduced form models individually and by simply
combining the two rivals to create a composite model in an attempt to identify the dominant theory. We use different estimators
for the resulting panel data model to account variously for interregional heterogeneity, endogeneity, and temporal and spatial
dependence, including maximum likelihood with and without fixed effects, two stage least squares and feasible generalised
spatial two stage least squares plus GMM; also most of these models embody a spatial autoregressive error process. These show
that the estimated NEG model parameters correspond to theoretical expectation, whereas the parameter estimates derived from
the neoclassical model reduced form are sometimes insignificant or take on counterintuitive signs. This casts doubt on the
appropriateness of neoclassical theory as a basis for explaining crossregional variation in economic development in Europe,
whereas NEG theory seems to hold in the face of competition from its rival.
JEL ClassificationC33O10

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Page 1
Electronic copy available at: http://ssrn.com/abstract=1111590
Neoclassical Theory versus New Economic Geography.
Competing explanations of crossregional variation in economic development
Bernard Fingleton
Department of Economics, University of Strathclyde
Scotland, UK
Manfred M. Fischer
Institute for Economic Geography and GIScience
Vienna University of Economics and BA, Vienna, Austria
Abstract. This paper uses data for 255 NUTS2 European regions over the period 19952003
to test the relative explanatory performance of two important rival theories seeking to explain
variations in the level of economic development across regions, namely the neoclassical
model originating from the work of Solow (1956) and the socalled Wage Equation, which is
one of a set of simultaneous equations consistent with the shortrun equilibrium of new
economic geography (NEG) theory, as described by Fujita, Krugman and Venables (1999).
The rivals are nonnested, so that testing is accomplished both by fitting the reduced form
models individually and by simply combining the two rivals to create a composite model in an
attempt to identify the dominant theory. We use different estimators for the resulting panel
data model to account variously for interregional heterogeneity, endogeneity, and temporal
and spatial dependence, including maximum likelihood with and without fixed effects, two
stage least squares and feasible generalised spatial two stage least squares plus GMM; also
most of these models embody a spatial autoregressive error process. These show that the
estimated NEG model parameters correspond to theoretical expectation, whereas the
parameter estimates derived from the neoclassical model reduced form are sometimes
insignificant or take on counterintuitive signs. This casts doubt on the appropriateness of
neoclassical theory as a basis for explaining crossregional variation in economic
development in Europe, whereas NEG theory seems to hold in the face of competition from
its rival.
Keywords: New economic geography, augmented Solow model, panel data model, spatially
correlated error components, spatial econometrics
JEL Classification: C33, O10
Page 2
Electronic copy available at: http://ssrn.com/abstract=1111590
1
1
Introduction
In recent years New Economic Geography (NEG) has rivalled neoclassical growth theory as a
way of explaining spatial variation in economic development. This new theory is particularly
appealing because increasing returns to scale are fundamental to a proper understanding of
spatial disparities in economic development, and several attempts have been made to
operationalise and test various versions of NEG theory with real world data (see for example
Fingleton 2005, 2007b). Much of this work focuses around the shortrun equilibrium wage
equation (see Roos 2001, Davis and Weinstein 2003, Mion 2004, Redding and Venables
2004, Head and Mayer 2006), which – although only one of the several simultaneous
equations that define a complete NEG model – is probably the most important and easily
tested relationship coming from the theory.
In the spirit of Fingleton (2007a), this paper aims to test whether the success of the NEG
Wage Equation is replicated in data on European regions, under the challenge of the
competing neoclassical conditional convergence (NCC) model. This paper provides some new
evidence using, for the first time, data extending to the whole of the EU, including the new
accession countries. We control for countryspecific heterogeneity relating to these new
accession countries throughout. Testing is accomplished by considering the rival models in
isolation followed by combining the two rival nonnested models within a composite spatial
panel data model, usually with a spatial error process to allow for omitted spatially correlated
variables or other unmodeled causes of spatial dependence. Unlike Fingleton (2007a), we
seek to include a price index in our measurement of market potential, which is the key
variable in the NEG model.
The paper is structured as follows. Section 2 introduces the two relevant theoretical models,
first, the neoclassical theory leading to the reduced form for the NCC model in Section 2.1,
and then the rival NEG model in Section 2.2, leading to the competing reduced form. Section
3 outlines the composite spatial panel data model in Section 3.1. Section 3.2 continues to
describe a procedure for estimating this nesting model. Section 4.1 describes the data, the
sample of regions and the construction of the market potential variable, while Section 4.2
presents the resulting estimates. Section 5 concludes the paper.
2 The theoretical models
Page 3
2
2.1 Neoclassical theory and the reduced model form
Neoclassical growth models are characterised by three central assumptions. First, the level of
technology is considered as given and thus exogenously determined, second the production
function shows constant returns to scale in the production factors for a given, constant level of
technology. Third, the production factors have diminishing marginal products. This
assumption of diminishing returns is central to neoclassical growth theory.
The theory used in this paper is based on a variation of Solow’s (1956) growth model that
contains elements of models by Mankiw, Romer and Weil (1992), and Jones (1997). We
suppose that output Y in a regional economy i=1, …, N at time t=1, …, T is produced by
combining physical capital K with skilled labour H according to a constantreturnstoscale
CobbDouglas production function
( , )( , ) [ ( , ) ( , )]
Y i tK i t A i t H i t
=
where A is the labouraugmenting technological (total factor productivity) shift parameter so
that ( , )( , )
A i t H i t may be thought of as the supply of efficiency units of labour in region i at
time t. The exponents ,
α 01
α<< , and (1)
α−
and effective labour, respectively. Skilled labour input is given1 by
( , )( , )( , )
H i th i t L i t
=
where L is raw labour input in region i, and h some regionspecific measure of labour
efficiency. Raw labour L and technology A are assumed to grow exogenously at rates n and
g. While technology growth g is supposed to be uniform in all regions2, the growth of labour
may differ from region to region. Thus, the number of effective units of labour, ( , )
grows at rate ( , )
n i tg
+ .
Letting lowercase letters denote variables normalised by the size of effective labour force,
then the regional production function may be rewritten in its intensive form as
( , )( )( , )
y i t f k k i t
≡=
1 Note that this way of modelling skilled labour guarantees constant returns to scale. The implication that factor
payments exhaust output is preserved by assuming that the human capital is embodied in labour (Jones 1997).
2 At some level this assumption appears to be reasonable. For example, if technological progress is viewed to be
the engine of growth, one might expect that technology transfer across space will keep regions away from
diverging infinitely, and one way of interpreting this statement is that growth rates of technology will
ultimately be the same across regions (Jones 1997). Note that we do not require the levels of technology to be
the same across regions.
1
αα−
(1)
are the output elasticities of physical capital
(2)
( , )
A i t H i t ,
α
(3)
Page 4
3
where y and k are regional output and capital per unit of effective labour, that is,
( , )( , )/[ ( , ) ( , )]
y i tY i tA i t H i t
=
and ( , ) ( , )/[ ( , )
k i t K i t
=
We can then examine how output reacts to an increase in capital, that is, we look at the
derivatives of output y with respect to k. Then
1
'( )( , )0, lim[ '( )]0 lim[ '( )]
kk
→∞→
( , )]
A i t H i t
.
0
f kk i tfk andfk
α
α
−
=>= = ∞ (4a)
2
''( )
k
(1),''( )
k
0.
fkf
α
α α
−
= −−<
(4b)
From Eqs. (4a) and (4b) we see that the first derivative is positive, but declines as capital goes
to infinity, and becomes very large if the amount of capital is infinitely small, features known
as Inada condition. This means that the marginal product of capital is positive, but it declines
with rising capital. Thus, all other factors equal, any additional amount of physical capital will
yield a decreasing rate of return in the production function. This assumption is central to the
neoclassical model of growth. Under this assumption capital accumulation does not make a
constant contribution to income growth. While accumulating capital, an additional unit of
capital makes a smaller contribution to output than the previous additional unit3.
The neoclassical model of growth postulates that a regional economy starting from a low level
of capital and low per effective worker income, accumulates capital and runs through a
growth process, where growth rates are initially higher, then decline, and finally approach
zero when the steady state per effective labour income is reached. The model predicts
conditional convergence in the sense that a lower value of income per effective labour unit
tends to generate a higher per effective labour growth rate, once we control for the
determinants of the steady state. The transition growth path of the single regional economy
can be transposed to the situation of N regional economies, which start from different levels.
If regional economies have the same steady state, the same transition dynamics will apply for
the whole crosssection of regions. Much of the crossregion difference in income per labour
force can be traced to differing determinants of the steady state in the neoclassical growth
model: population growth and accumulation of the physical capital.
3 Note that the assumption of diminishing returns has been challenged by new growth theory, which assumes
that constant or increasing returns can be an outcome of, for example, human capital accumulation or
knowledge spillovers.
Page 5
4
Physical capital per effective labour in region i evolves according to
( , )
k i t
where
technology growth and capital depreciation, respectively. The dot over k denotes
differentiation with respect to time5.
This differential equation is the fundamental equation of the growth model. It indicates how
the rate of change of the regional capital stock at any point in time is determined by the
amount of capital already in existence at that date. Together with this historically given stock
of physical capital, Eq. (5) determines the entire path of capital. In order to maintain a fixed
capital stock per effective labour unit, the region must invest an amount to replace the
depreciated capital,
( , )
k i t
δ
, and an amount to balance the growth of effective labour,
( , ).
n i tg
+
Due to the diminishing marginal product of capital, per effective labour output available for
investment will become smaller with additional capital. Thus, investment per effective labour
is nonlinear. It decreases with rising capital accumulation. Initially, investment exceeds the
term [ ( , )] ( , ),
n i tgk i t
δ++
and hence the capital share per effective labour increases. As the
capital share goes to infinity, investment becomes less than the term [ ( , )
Thus, there is a point k∗ where investment is just sufficient to balance the second term on the
right hand side of Eq. (5). At k∗ the amount of capital per effective labour unit is constant,
( , )0.
k i t
=
Thus, the steady state is given by the condition
( , ) ( , ) [ ( , )] ( , ).
i t k i t n i tg k i t
δ=++
It is then straightforward to solve for the value k∗
( , ) ( , ) [ ( , )
i t y i t
] ( , )
k i t
δ
K
sn i tg
•
=−++
(5)
K s is the investment rate4, n the rate of population growth, g and δ constant rates of
] ( , ).
k i t
δ
n i tg
++
•
K s
α
∗∗
(6)
1
α−
1
( , )
i t
+
( , )
( , )
n i t
K s
k i t
g
δ
∗
⎡
⎣
⎤
⎥
⎦
=⎢
+
. (7)
4 The economy is closed so that saving equals investment, and the only use of investment in this economy is to
accumulate physical capital. The assumption that investment equals saving may seem too simple, the more if
we consider open regional economies. But, as Feldstein and Horioka (1980) have shown, the coincidence of
investments and savings is empirically valid across a set of regions, including open regions.
5 Note that the term on the left hand side of Eq. (5) is the continuous version of k(i, t)–k(i, t–1), that is the
change in the physical capital stock in efficient labour unit terms per time period.
Page 6
5
Substituting Eq. (7) into the regional production function given by Eq. (3), and taking logs,
we find that steady state income per labour is
( , )
ln ln ( , )ln[ ( , ) ] ln ( , ) ln ( , )
( , )
L i t
11
Y i t
s i t n i tg A i th i t
α
α
−
α
α
−
δ=−++++
. (8)
Of course, neither A nor h are observed directly, but may be modelled as a loglinear
relationship so that
ln ( , ) ln ( , ) constantln ( , )
A i th i tS i tt
ββ+=++
12
( , )
i t
ξ+
(9)
where the level of regional technology,
region and timespecific measure of labour efficiency, ( , ),
workforce as given by the level of educational attainment of the population. The rationale for
this proxy is the widely recognised link between labour efficiency and schooling. ( , )
iid disturbance term with zero mean and constant variance, and
parameters.
Substituting Eq. (9) into Eq. (8) yields the following estimation equation:
( , )
ln constantln[ '( , ) ln ( , )]
( , )
L i t
( , )
A i t , is proxied by a deterministic trend, and the
h i t by the skills
( , )
S i t of the
i t
ξ
is an
1 β and
2
β are scalar
12
1
ln ( , )
S i t
( , )
i t
ε
Y i t
n i ts i tt
α
α
−
ββ
=−−+++
(10)
with '( , )
n i t
growth rate.
Most recently, Koch(2008) has formally extended the neoclassical model in order to capture
spillover effects. To save space we do not replicate his extended model structure in the current
paper, although account is taken of spatial effects in subsequent modelling.
2.2 NEG theory and the reduced model form
Whereas in the neoclassical model output per worker follows the longrun equilibrium path,
in the NEG framework we view output per worker [or equivalently nominal wages] as a short
( , )
n i tg
δ=++
and ln '( , ) ln ( , )
n i ts i t
−
referred to as the logadjusted population
Page 7
6
run equilibrium6 phenomenon. Only in the very longrun – which we do not consider here –
does factor mobility eliminate real wage differences.
The NEG theory used here is that set out by Fujita, Krugman and Venables (1999) which has
as a basis the DixitStiglitz model of monopolistic competition (Dixit and Stiglitz 1977), with
two sectors, N regions and transportation costs between these regions. Important components
of the model are the elasticity of substitution ( )
transportation costs of monopolistic competition goods from region i to region j.
Transportation costs – in terms of Samuelson’s iceberg form – are a basic element of the NEG
theory advanced by Fujita, Krugman and Venables (1999) since they determine the
attractiveness of production locations in terms of access to markets.
The traditional full general equilibrium model comprises two sectors: a perfectly competitive
sector (called Csector) that produces a single, homogeneous good under constant returns to
scale, whereas the other sector, termed the Msector, exhibits a monopolistically competitive
market structure and a large variety of differentiated goods. The production of each M variety
exhibits internal increasing returns to scale.
Preferences are of the CobbDouglas form with a constantelasticityofsubstitution (CES)
subutitility function for Mvarieties. Thus,
U
=
on Mgoods and ( 1)
θ −
that on the Cgood. The quantity of the composite Mgood is a
function of the
1,...,
xX
=
varieties ( )
m x , where X is the number of varieties so that
σ
σ
σ
σ
⎡⎤
=⎢
⎥
⎣⎦
σ between product varieties, and
1
M C
θθ
−
where θ is the share of expenditure
1
1
1
( )
X
x
Mm x
−
−
=
∑
. (11)
( )
m x denotes the consumption of each available variety x which at equilibrium is constant
across all varieties, and σ represents the elasticity of substitution between any two varieties.
There are internal increasing returns in production for each variety. In equilibrium, each
variety is produced by a single monopolistically competitive firm.
As σ becomes larger, differentiated goods become more substitutable, while as σ reduces,
the desire to consume a greater variety of Mgoods increases. Because M embodies a
preference for diversity, and there are increasingreturnstoscale, each firm produces a
distinct variety. Hence the number of varieties consumed is also the number of firms, and firm
6 Shortrun equilibrium in a Marshallian sense in which the allocation of labour among the regions is taken as
given.
Page 8
7
output equals demand for that variety. Choosing units of measurement in a way that shifts
attention from the number of firms and product prices to the number of workers and their
wage rates, Fujita, Krugman and Venables (1999, Chapter 4) introduce simplifying
normalizations so that θ is also equal to the equilibrium number of workers per firm and to
the equilibrium output per firm.
Five simultaneous nonlinear equations comprise the reduced model form of the basic NEG
model. Of particular interest for this paper is the wage equation that relates nominal wages,
( , )
w i t , in the monopolistically competitive sector M in region i to what is referred to as
market potential (or market access) for that sector in region i, ( , )
time:
( , ) ( , )
w i tP i t
=
M
P i t , and holds at all points in
1
σ
M
(12)
with
11
1
( , )
P i t
( , ) [
Y j t
( , )]
j t
[ ( , )]
i j
N
MM
j
GT
σσ−−
=
=∑
(13)
where the market potential given by Eq. (13) depends on transport costs of Mgoods from
region i to region j, ( , )
T i j , transport cost mediated price variations,
variations, ( , )
Y j t , across space. Regions that have a high income level and are close to
regions with high incomes, so that transport costs are low, will tend to posses high market
potential, and competition effects, that will be stronger within agglomerations, will also tend
to modify price levels and hence the market potential. In fact nominal wages will be increased
by a higher price index, ( , )
G j t , which indicates that there are less varieties sold in region j
at time t, since the price is inversely related to the number of varieties, and this means that if
region j has few varieties regioninternal competition is reduced.
The elasticity of substitution σ is a measure of product differentiation and indirectly a
measure of increasing returns in the Msector considered. The parameter σ appears in various
ways in the wage equation. It is both the (reciprocal of the) coefficient on P in the reduced
form (12), and it also determines P (see Eq. (13)), crucially controlling the magnitude of
transport cost mediated price variations. Since, by assumption, Cgoods are freely transported
and produced with a constantreturnstoscale technology, Cwages,
regions (that is, ( , ) ( , ) for , 1,...,
w j tw k t j k
==
Nominal income in region j at time t is given by
M
( , )
j t , and income
M
G
M
C
w , are constant across
).
CC
N
Page 9
8
Y j t
( , )( , )
j t w
( , ) (1
j t
)( , )
j t w
( , )
j t
MC
θ λ θ φ=+−
(14)
where θ is the expenditure share of Mgoods, λ and φ are the shares of total supply of M
and Cworkers in region j, while
w is the wage rate of workers in the competitive sector in j
at time t.
The Mprice index ( , )
Gj t for region j at time t is
⎧⎫
=⎨
⎬
⎩⎭
C
M
1
σ
−
1
1
1
( , )
j t
( , ) [
k t
λ
( , )
k t T
( , )]
k j
N
MMM
k
Gw
σ−
=
∑
(15)
where the number of varieties produced in region k is represented by ( , )
the share in region k of the total supply of Mworkers in region k.
We follow Fujita, Krugman and Venables (1999) in calling Eq. (12) the NEGWage Equation
that represents a shortrun equilibrium relationship based on the assumption that factor
mobility in response to real wage differences in the monopolistic competition sector is slow
compared with the instantaneous entry and exit of Mfirms so that profits are immediately
driven to zero. It is only in the very longrun that we would expect movement to a stable long
run equilibrium resulting from labour migration.
This wage equation is an exceptionally simple relationship. To add an extra injection of
realism we assume that wages, w(i, t), also depend on the efficiency level of the labour force,
( , ),
h i t so that
k t
λ
which is equal to
1
σ
( , )
w i t
( , )
P i t
( , )
h i t
=
. (16)
Taking logs and assuming that ( , )
Wage Equation
1
ln ( , ) ln ( , )
w i t P i t
σ
h i t may be proxied by ( , )
S i t yields the extended NEG
012
ln ( , )
S i t
( , )
i t
η
t
βββ=++++
(17)
where η is independently and identically distributed with zero mean and constant variance.
This equation is the counterpart to Eq. (10), but has a fundamentally different theoretical
provenience, and has somewhat different longrun implications. Note that the deterministic
time trend t is also introduced as an extra regressor, in order to control for the evolution of the
Page 10
9
level of regional technology. Otherwise this may be picked up by P and the significance of P
may be largely attributable to this rather than to true NEG processes.
3 Testing the nonnested rival models
Assessing the relative explanatory performance of the NEGWage Equation (17) and the
neoclassical model (10) is accomplished by setting up a composite spatial panel data model
within which both models are nested. The rival models are not special cases of each other, but
special cases of the data generating process (DGP) of the regressors in the composite model.
The problem of deciding between the competing models then amounts to considering whether
any one rival encompasses the DGP. By encompassing we mean that one model can explain
the results of another (Fingleton 2006).
Building on these ideas, we assume that in each time period t=1, …, T the data are generated
according to the following model
( )( )( )
ttt
=+
yXγu
(18)
where ( ) t
worker) in period t,
regressors including the NEGspecific market potential, the logadjusted population growth
rate, educational attainment as a proxy for labour efficiency, a time trend and a constant. All
variables, except the time trend, are expressed in logarithms. γ is the corresponding (K, 1)
vector of regression coefficients, and ( ) t
u
denotes the (N, 1) vector of disturbance terms.
When
reduces to the neoclassical conditional convergence model. Conversely, when
composite model reduces to the extended NEGWage Equation.
In most of the models we invoke a disturbance process in each time period, which follows a
first order spatial autoregressive (SAR) process
( ) ( )( )
ttt
ρ=+
u W u
ε ε
y
denotes the (N, 1) vector of observations on the dependent variable (i.e. output per
( ) t
X
denotes the (N, K) matrix of observations on the K=5 exogenous
1 γ , the coefficient associated with the market potential variable, is zero, the model
2
0
γ = , the
(19)
where W is an (N, N) matrix of nonstochastic spatial weights which define the error
interaction across the regions, ρ is a scalar autoregressive parameter with
a (N, 1) vector of the remainder disturbances. This assumption implies complex
interdependence between the regions so that a shock in region i is simultaneously transmitted
to all other (N–1) regions. The spatial matrix W is constructed in this study as follows: a
1
ρ < , and ( ) t
ε ε
is
Page 11
10
neighbouring region takes the value one, otherwise it is zero. The rows of this matrix are
normalised so that they sum to one.
Stacking the observations in Eqs. (18) and (19) we get
=+
yX γu (20)
with
=
u
1
()()
T NTT
ρρ
−
⊗+=−⊗
IW uIIW
ε ε ε ε (21)
where
and
Kronecker product.
4 Data description and estimation results
4.1 The sample data
The panel database that will be employed to estimate the rival models and the composite
model within which the two rival models are nested is composed of 255 NUTS2 regions,
over the period 19952003. The NUTS2 regions cover 25 European countries including
Austria (nine regions), Belgium (11 regions), Czech Republic (eight regions), Denmark (one
region), Estonia (one region), Finland (five regions), France (22 regions), Germany (40
regions), Greece (13 regions), Hungary (seven regions), Ireland (two regions), Italy (20
regions), Latvia (one region), Lithuania (one region), Luxembourg (one region), Netherlands
(12 regions), Norway (seven regions), Poland (16 regions), Portugal (five regions), Slovakia
(four regions), Slovenia (one region), Spain (16 regions), Sweden (eight regions), Switzerland
(seven regions), and UK (37 regions). The main data source is Eurostat’s Regio database. The
data for Norway and Switzerland were provided by Statistics Norway and the Swiss Office
Féderal de la Statistique, respectively.
Thus, the crosssection of the panel data is N=255, while the time dimension T=9. The time
dimension is relatively short due to a lack of reliable figures for the regions in Central and
Eastern Europe7 (see Fischer and Stirböck 2006). We use gross value added, gva, rather than
[ '(1),..., '( )]' ,
y
are identity matrices of dimension T and NT, respectively, while ⊗ denotes the
[ '(1),..., ' ( )]',
X y TX T
=
yX =
[ '(1),..., '( )]',
u
[ '(1),..., '( )]',
ε
u TT
ε=
u=
ε ε
TI
NT
I
7 This comes partly from the substantial change in accounting conventions from the Material Product Balance
System of the European System of Accounts 1995. But more importantly, even if estimates of the change in
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11
gross regional product (grp) at market prices as a proxy for regional output8. Gva is the net
result of output at basic prices less intermediate consumption valued at purchasers’ prices, and
measured in accordance with the European System of Accounts [ESA] 1995. The dependent
variable in the composite spatial panel data model is gva per worker. ( , )
rate of growth of the workingage population, where working age is defined as 15 to 64 years,
and the investment rate ( , )
s i t as the share of gross investments in gross regional product. We
assume that
0.05
g δ
+=
which is a fairly standard assumption in the literature (see, for
example, Bond, Hoeffler and Temple 2001), and use the level of educational attainment of the
population (15 years and older) with higher education defined by the ISCED 1997 classes 5
and 6 to proxy the variable ( , ).
S i t
One problem encountered in attempting to operationalise the NEGWage Equation is the
designation of M and Cactivities, given that the market structure for Mactivities is assumed
to be monopolistic competition, while Cactivities are competitive, lacking internal scale
economies. However we designate these sectors, they will impact market potential (see
Eq. (13)) via λ and φ , the shares of total supply of M and Cworkers, which are used in the
construction of the price index (14) and income (15). Therefore if we designate the sectors
inappropriately, then market potential will possess measurement error. However, market
potential is by definition endogenous involving twoway causation, and therefore
instrumentation is necessary to counter both these effects, either sector misspecification hence
measurement error, or twoway causation, or both. We therefore control for the assumptions
made regarding the M and C sectors using instrumental variables in some of our model
estimates. Note that the sectoral assumptions made do not have an effect on wage levels
because of the way we define these variables. We define the sector under monopolistic
competition (M) as NACEclasses G to K, which are broadly defined as services. The NACE
classes are given in the appendix. Firms in these subsectors can be characterised as being
small, highly differentiated varieties with easy entry and exit into the sector and minimal
strategic interaction, which is close to what is implied by monopolistic competition. All other
sectors are assumed to be competitive and are termed Cgoods. This is similar to the
definitions used by RiveraBatiz (1988) and AbdelRahman and Fujita (1990), and more
recently Redding and Venables (2004) have used a composite of manufacturing and service
activities.
n i t is measured as the
the volume of output did exist, these would be impossible to interpret meaningfully because of the
fundamental change of production from a planned to a market system.
8 Gva has the comparative advantage of being a direct outcome of variation in factors that determine regional
competitiveness (LeSage and Fischer 2009)
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12
Given these definitions, it is possible to measure the market potential variable ( , )
by Eq. (13). In order to quantify the variable, we have assumed that the parameter9 σ is equal
to 6.5, and calculated income, Mprices and transportation costs. Income is defined by
Eq. (14), and depends on the assumed M and Csector wage rates (
wmean gva
=
per Cworker, averaging across all 255 regions10), the share λ of the M
sector and the share φ of the Csector employment in each region, the share θ of the
European (total 255 NUTS2 regions) workforce that is employed in the monopolistic
competition sector M, and the share (1)
θ
−
of the total European workforce that is employed
in the competitive sector C .
Mprices are defined by Eq. (15), and these are quantified using again the Memployment
shares λ in each region, the assumed Mwage rate (equal to gva per Mworker) for each
region, and the transport costs from each region. We assume iceberg transport costs11 of the
form
exp[ ln ( , )] for
( , )
( )
for
ij
π
P i t defined
M
wgva
=
per Mworker,
C
2
3
ij
M
d i jdij
T i j
R i
τ
τ
⎧
⎪
⎪⎩
=≠
=⎨
=
(22)
with an areabased approximation of intraregional distances. ( )
in terms of square km, and ( , )
d i j denotes the great circle distance from region i to region j,
represented by their economic centres. The use of the natural logarithm of distance rather than
distance per se implies a power functional relationship between transport costs and distance.
For the (exogenous) distance multiplier τ we adopt the value
It is important to note that the iceberg transport cost function (22) maintains the constant
R i is region’s i area measured
2
τ =
throughout the analysis12.
9 There is no theoretical a priori basis for choosing
1
σ > under a monopolistic competition assumption (since
monopoly power, equal to one in the case of perfect competition). In fact, we use post hoc rationalisation to
justify this choice, since our preferred model estimates (see Table 2) imply a value not significantly different
from 6.5.
10 The rationale for this is that
( , )
w i t is the nominal wage rate in sector M and region i, which we approximate
by overall gva per worker. This undoubtedly leads to some measurement error which will be accommodated
by the model’s error term and by the use of instrumental variables for our market potential variable. In case of
( , )
w i t , this is constant across regions, and is approximated by the mean.
11 “Iceberg transport costs” imply that only a fraction of the shipped good reaches its destination.
12 Ideally, the parameter τ should be obtained from trade data, but these are not available at the NUTS2 level.
We assume
2
τ =
which implies that there are no economies of scale in distance transportation (
is a strong assumption that has been seen as somewhat unrealistic (McCann 2005, McCann and Fingleton
2007), and we could choose 01
τ
≤≤ although opting for
of the model which is the main focus of the paper.
6.5,
σ =
other than we expect the elasticity of substitution
/(1)
σμμ=−
where
μ > is the measure of
1
M
C
1).
τ ≥
This
2
τ =
does not diminish the relative performance
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13
elasticity of demand assumption that runs through the microeconomic theory underpinning the
NEGWage Equation.
4.2 Empirical results
The tables below show various panel regression estimates of the neoclassical growth model,
the rival NEG model, and the artificial nesting model which combines the variables from the
two theories under comparison. For each set of estimates, the dependent variable is the log of
gva per worker.
The neoclassical growth model
Table 1 presents the parameter estimates of the neoclassical growth model (10) using different
estimation procedures. The explanatory variables are the logadjusted population growth rate
ln '( , ) ln ( , )
n i t s i t
−
, log of share of residents with higher education (ln ( , ))
(1 to 9 for each of the years 1995 to 2003 inclusive), and dummy variables for each of the
new entrant countries (Poland, Hungary, Czech Republic, Slovakia, Slovenia, Estonia,
Lithuania and Latvia). Given that the growth rate of the working age population ( ')
share of investment in gross regional product ( ) s are lagged by one year, the adjusted log
population growth rate ln '( , ) ln ( , )
n i t s i t
−
is treated as an exogenous variable13. Since we are
setting the neoclassical model as the default model in this analysis, this is not an unreasonable
assumption since it means we avoid rejecting the default model too easily simply on account
of weak instruments. Following Mankiw, Romer and Weil (1992), we also relax the constraint
that the coefficients on ln '( , )
n i t and ln ( , )
s i t are equal in magnitude and opposite in sign,
leading to the unconstrained estimates given in the table (see columns 2, 4, 6 and 8).
Throughout, the variable ln ( , )
S i t is assumed to be dependent principally on background
policy and social variables rather than on contemporaneous gva per worker levels.
S i t
, the time trend
n and the
Table 1 about here
The pooled OLS estimates (Table 1, column 1) show that the adjusted log population growth
rate is significantly positively related to the dependent variable, and we also see an increasing
share of residents with higher education [ln ( , )]
S i t associated with a higher level of gva per
13 Note that for Halle, actual population growth for 19941995 means that '( , )
we cannot calculate ln ' n . To remedy this, population growth is set to the 19951996 rate of 0.0078
n i t is negative for t = 1995 so that
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14
worker. In addition there is a significant positive time trend effect, with gva per worker
increasing with time, reflecting an autonomously increasing level of technology. The country
dummy effects are all significantly negative, indicating that log gva per worker is
significantly reduced in the new entrant countries, by varying amounts, evidently due to
various institutional and structural differences, compared with the pre2005 EU countries.
The ML estimates (Table 1, column 3) allow an autoregressive error process (Elhorst 2003;
Baltagi 2001) based on a 255 by 255 W matrix of ones and zeros, according to whether or not
a pair of regions is contiguous14. This is standardised so that rows sum to one (and used
throughout). Although overall we see quite similar estimates to those from OLS estimation
(see column 3 in comparison to column 1), the presence of the highly significant
autoregressive parameter produces a similarly signed but smaller elasticity for
ln '( , ) ln ( , )
n i t s i t
−
. In addition, the FGS2SLS estimates (Kapoor, Kelejian and Prucha 2007;
Fingleton 2007a, 2008) are quite similar to the ML estimates (see column 5 in comparison to
column 3). Fingleton (2007a) uses FGS2SLS for estimating the spatial panel data model
extending15 the generalised moments procedure suggested in Kapoor, Kelejian and Prucha
(2007) to the case of endogenous righthandside variables, such as the market potential. In
this case the variables are used as instruments for themselves, in other words we initially
assume exogeneity. On the other hand, controlling for spatial heterogeneity via region
specific fixed effects eradicates the significance of ln '( , ) ln ( , )
high level of fit for this fixed effect panel data model reflects the impact of the unobserved
regionspecific effects, the autoregressive process and the time trend. Given the presence of
these variables, ln '( , ) ln ( , )
n i t s i t
−
and ln ( , )
S i t carry no additional explanatory information.
In particular the regionspecific effects represent catchalls probably for a range of factors,
including ln '( , ) ln ( , )
n i ts i t
−
and ln ( , )
S i t . This casts some doubt on the real significance of
these two variables, which could be simply picking up the effect of some of these factors
when the fixed effects are omitted.
Table 1 also gives estimates without the restriction on the coefficients on ln '( , )
ln ( , )
s i t (see columns 2, 4, 6 and 8). The principal feature of these estimates is the
counterintuitive signs on these two separate variables. With regard to ln '( , )
expect a negative sign (compare Mankiw, Romer and Weil 1992), and anticipate a positive
sign for ln ( , )
s i t . Instead, we see ln gva per worker increasing as ‘population’ growth
increases, and regions with high levels of the log of the investment to grp ratio (ln ( , ))
associated with low levels of ln gva per worker. This casts doubt on the neoclassical model as
an appropriate model for the EU regions.
n i t s i t
−
and ln ( , )
S i t . The very
n i t and
n i t , one would
s i t
are
14 For nine isolated regions it has been necessary to create artificial, contiguous neighbours.
15The method initially developed by Kapoor, Kelejian and Prucha (2007) was in the context of exogenous
regressors, but is it quite straightforward to extend this in order to allow for endogeneity.
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 Available from Bernard Fingleton · Jun 6, 2014
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