nonlinearities in regional economic growth and convergence: the role of entrepreneurship in the...

Ann Reg Sci (2012) 48:719–741DOI 10.1007/s00168-010-0419-z

ORIGINAL PAPER

Nonlinearities in regional economic growthand convergence: the role of entrepreneurshipin the European union regions

Georgios Fotopoulos

Received: 13 March 2010 / Accepted: 23 November 2010 / Published online: 10 December 2010© Springer-Verlag 2010

Abstract Nonlinearities have been identified in recent literature on growth andconvergence at the cross-country level and they have been associated with a numberof variables of interest such as initial conditions and human capital accumulation.This research takes the analysis at the regional level within a European context whilefocusing on entrepreneurship and, using semiparametric regression techniques, pro-vides evidence for nonlinear effects of the base-year income per capita on growthsuggesting that convergence may be a phenomenon restricted to particular incomebands. Entrepreneurship has a positive effect on regional growth and no serious depar-tures from linearity are detected, while evidence for an almost L-shaped relationshipbetween income per capita levels and self-employment rates was produced. A qual-ity-adjusted proxy for human capital stock was found to be a positive and significantdeterminant of economic growth across European regions but, again, no departuresfor linearity were detected for this effect.

JEL Classification O40 · R11 · C14 · L26

1 Introduction

The aim of this research is to explore the possibility of nonlinearities in the effectof variables considered in the literature as determinants of regional economic growthwhile paying some particular attention to the role of entrepreneurship.

There have been two points of departure for such a research endeavour. One stemsfrom the literature on economic growth (Azariadis and Drazen 1990; Hansen 2000;Durlauf and Johnson 1995; Liu and Stengos 1999; Kalaitzidakis et al. 2001) providing

G. Fotopoulos (B)Department of Economics, University of Peloponnese, Tripolis, Greecee-mail: [email protected]

123

720 G. Fotopoulos

theoretical reasoning but also empirical evidence suggesting the existence of multi-ple equilibria, club convergence and nonlinearities in the determinants of economicgrowth. These notions confront the neoclassical notions of unconditional and condi-tional convergence, depending on whether differences in the steady states betweencountries have been assumed. Club convergence or polarization (Durlauf and Quah1999) implies convergence amongst similar economies but no convergence betweengroups of such economies. Azariadis and Drazen (1990) propose a model where mul-tiple equilibria arise due to the presence of externalities that yield increasing returnsto scale and kick in once a threshold level of human capital is reached. Quah (1996),on the other hand, suggests a model of growth where, under certain conditions, imper-fect capital mobility across multiple economies can lead to polarization and clubconvergence. Models of endogenous growth with localized spillovers (Grossman andHelpman 1991) can explain not only why some countries may have a higher growthrate of per capita income, but also why these differences may persist over time leadingto polarization.

Bernard and Durlauf (1996) maintain that the evidence found in favour of con-vergence by Mankiw et al. (1992) owes to a misspecified linear model where theoverall evidence of convergence is essentially inherited from a group (but not all) ofcountries converging to a common steady state. Liu and Stengos (1999), employinga semiparametric modelling strategy, find evidence suggesting that the convergencehypothesis applies only to countries of the middle and upper income range. Morerecently, research by Flaschi and Lavezzi (2003) suggest the existence of multipleequilibria and nonlinearities in the growth process in a cross country context. Evi-dence for nonlinearities for the effect of human capital on economic growth has beenprovided at country-level analysis by Liu and Stengos (1999) and Kalaitzidakis et al.(2001).

In another strand of economic literature focusing on entrepreneurship, Carree et al.(2002) and Van Stel and Caree (2004) develop a model in which there is an equilib-rium level of self-employment rate in economy and deviations for that level have anegative effect on economic growth. This suggests that there may be too many or toofew self-employed in an economy and there is thus a nonlinear relationship betweenthe business ownership rate and economic growth. Evidence is also provided for aU-shaped relationship between business ownership and economic development,although it is carefully noted that U-shaped functions cannot be easily distinguishedfrom L-shaped ones in a statistical sense (for an up-to-date review and critical discus-sion of this relationship, see Wennekers et al. 2010). Earlier studies such as Yamada(1996) and Schultz (1990) have provided (although the latter in a somewhat indirectmanner) some evidence for a negative relationship between economic developmentand the self-employment rate. Indeed, Iyigun and Owen (1999) identify that “in econ-omies with higher per capita income, fewer individuals are employers compared to thenumber of individuals who work for others” (ibid. p. 216) may be one of the motives fordeveloping a theoretical model where entrepreneurial human capital plays a relativelymore important role in intermediate economies. As an economy grows, individualschoose to invest more time accumulating professional skills—through education—rather than accumulating entrepreneurial human capital as the opportunity cost of thelatter increases as the economy develops. This model also accounts for the possibility

123

Nonlinearities in regional economic growth and convergence 721

of poverty traps owing to too little entrepreneurial and/or professional human capital.For OECD countries Blanchflower (2000) provides some evidence suggesting thatincreases in the proportion of self-employed lead to lower and not higher GDP.

The importance of entrepreneurship in economic growth has been recognized inthe literature. Baumol (1968) notes that studies relying on capital accumulation andlabour force expansions to account for historical growth in production leave muchunexplained, and suggests a turn to entrepreneurial initiative in order for this gap tobe filled. Leff (1979) maintains that “entrepreneurship is so important for economicdevelopment that it has sometimes been conceptualized as a ‘fourth’ factor of produc-tion” (ibid. p. 47). Indeed, Audretsch and Keilbach (2004a,b) expand the traditionalproduction function to further include ‘entrepreneurship capital’. Leibenstein (1968,p. 75) attributes the following four traits to the entrepreneur: “he connects differentmarkets, he is capable of making up for market deficiencies (gap filling), he is an‘input completer’, and he creates or expands time-binding input-transforming entities(i.e. firms)”. Audretsch and Keilbach (2004b) explain that the role of entrepreneur-ship capital facilitates the spillover of knowledge and transforms general knowledge toeconomic knowledge, the latter being of use in the production process of the economy.The authors further point out the difficulties in measuring entrepreneurship capital andresort to new firm formation rates at the regional levels to proxy it. Acs et al. (2005)suggest that within an endogenous growth context, entrepreneurship may serve as aconduit for the spillover of knowledge contributing to economic growth. Audretschand Keilbach (2004a,b) use augmented production functions and provide evidencethat “entrepreneurship capital” is a significant and positive determinant of regionaloutput and labour productivity. In a somewhat different context, Braunerhjelm andBorgman (2004) find that entrepreneurship positively affects regional labour produc-tivity. Carree and Thurik (2005) offer a thorough account of the literature on the impactof entrepreneurship on economic growth.

The role of entrepreneurship on regional employment growth should also be addedto the effects of entrepreneurship on regional output and productivity. In regionalanalysis there has been an early shift of interest from the determinants of interre-gional relocation of firms to the determinants of intraregional new firm formationor dissolution and their effects on regional employment growth (Mason 1983). Newfirm formation and incumbent firm dissolution have been deemed to be more impor-tant than industry-mix or firm migration in accounting for industrial development ofdecline (Fothergill and Gudgin 1982). In a recent wave of studies following the sem-inal work of Fritsch and Mueller (2004) and Van Stel and Storey (2004) the effectsof entrepreneurial activity on regional employment are analyzed in an econometricframework that allows time-lag structures in a panel data context. In such a researchframework, indirect (i.e. displacement and replacement of less competitive incumbentfirms) as well as direct employment effects are analyzed. This line of research suggestsa promising way forward in the understanding of some of the effects of entrepreneur-ship at the regional level. Fritsch (2008), however, carefully notes that we still lackan adequate understanding of the ways by which new firm formation determines eco-nomic development as well as the time that is needed for effects of new firm formationto show up in empirical data.

123

722 G. Fotopoulos

While there are a number of studies testing for convergence among Europeanregions (Barro and Sala-i-Martin 1991; Armstrong 1995; Cheshire and Carbonaro1995; Dewhurst and Mutis-Gaitan 1995; Sala-i-Martin 1996; Lopez-Bazo et al. 1999;Cheshire and Magrini 2000; Martin 2001; Cuadrado-Roura 2001; Badinger et al.2004—to offer a representative albeit limited account of published research in thiscontext)1 covering a variety of periods and differing in terms of spatial coverage andtechniques, there have been only a couple of studies (Basile and Gress 2005; Basile2008) that investigate the possibility of nonlinearities in a regional-growth regressioncontext. This also seems to be the case for regional analyses that have included entre-preneurship among possible determinants of regional economic growth (Audretschand Keilbach 2004a,b; Braunerhjelm and Borgman 2004). In view of this, some scopeexists for the examination of the possibility of nonlinearities in the growth and conver-gence process in the European regional context while paying some particular atten-tion to the role of entrepreneurship in regional economic growth. This special focuson entrepreneurship is one of the main distinguishing features between the presentresearch and the only two other studies that use semiparametric econometric methodsfor analyzing nonlinearities in regional economic growth.

The paper is organized as follows. In the next section an account is provided of theempirical and econometric methodology used along with the definition of variables andtheir sources. In Sect. 3 the results of estimations are presented and placed within con-text of the existing literature, whereas, in the last section, some conclusions are drawn.

2 Methodology and data

In a seminal paper, Mankiw et al. (1992) extended Solow’s (1956) basic model byincorporating human capital stock in a standard production function. In particular,these authors suggested a production function of the form:

Yt = K at HCβ

t (At Lt )1−a−β

where Y stands for output, K for physical capital, L for labour, A for exogenous labouraugmenting technology and HC for human capital stock. Letting y = Y/AL, k =K/AL and hc = HC/AL be the variables of interest in per-effective-labour (AL)terms, Mankiw et al. (1992, p. 416) demonstrate that the evolution of the economy isdetermined by changes over time in the capital stock per effective labour as well asby changes in the human capital stock per effective labour. Denoted as sk the fractionof income invested in physical capital and shc the corresponding fraction invested inhuman capital, changes in physical and human capital stock, both per effective labour,are given by:

kt = sk yt − (n + g + δ) kt

1 This limited account only refers to studies that employ a particular analytical framework for the testingof convergence. Magrini (2004) provides a thorough discussion of theoretical and empirical issues involvedas well as evidence produced.

123


and

hc = shc yt − (n + g + d) hct

where n is the rate of growth of labour force, g is the rate of technological change andd the depreciation rate that applies to both physical and human capital.

Mankiw et al. (1992, p.417) derive two equations showing how income per capitadepends on population growth and the accumulation of physical and human capital

ln (Yt/Lt ) = ln A0 + gt − a + β

1 − a − βln (n + g + d)+ a

1 − a − βln (sk)

+ β

1 − a − βln (shchc)

or alternatively (ibid. p. 418)

ln (Yt/Lt ) = ln A0 + gt − a

1 − aln (n + g + d)+ a

1 − aln (sk)+ β

1 − aln (hc)

As the authors note, the above equations suggest two possible ways to model the effectof human capital depending on whether available data on human capital better corre-spond to human capital accumulation or to human capital stock. This also bears someimplications for the estimable equation whereby growth rather than the level of percapita income becomes the variable of interest. Kalaitzidakis et al. (2001) also makethis point and suggest the following equation when analysing economic growth.

ln (Yt/Lt )−ln (Y0/L0) = gt + (1 − eλt) (ln A0 + g (t − 0))− (

1 − eλt) ln (Y0/L0)

+ (1 − eλt)

(a

1 − aln (n + g + d)+ a

1 − aln (sk)+ β

1−aln (hc)

)

This has been the basic formulation used for the estimation in this research. However,as an empirical extension, a variable accounting for entrepreneurship has been addedto the basic formulation in the present research context.2 Recently Braunerhjelm et al.(2010) suggested a modification of the endogenous growth model where the role ofentrepreneurship is derived than assumed, as the growth in the model is dependenton knowledge accumulation and its diffusion through entrepreneurial activities. Thiswork takes a significant step in bridging economic growth modelling and empiricalentrepreneurship research within the same context. The authors provide evidence for arobust positive effect of entrepreneurship on economic growth in OECD countries forthe 1981–2002 period as well as producing test results that suggest that causality runsfrom entrepreneurship to growth and not vice versa. In a different and more indirectfashion, Gries and Naudé (2008) propose a model where regional economic growth is

2 This empirical extension is motivated by Leff’s (1979) theorization of entrepreneurship as the ‘fourth’factor of production and Audretsch and Keilbach (2004a,b) theorizations and empirical applications.

123

724 G. Fotopoulos

driven by an expansion of new firm start-ups in the intermediate goods and servicessectors.

Following Acs et al. (2005) and Braunerhjelm et al. (2010), self-employment rateshave been used as a proxy of entrepreneurship. The definition of the term ‘entrepre-neur’ remains an unresolved matter (Bruyat and Julien 2001), as “the entrepreneur isat the same time one of the most intriguing and one of the most elusive characters inthe cast that constitutes the subject of economic analysis” (Baumol 1968). Audretschet al. (2006, p. 7) draw attention to the difficulties in obtaining an operational def-inition of entrepreneurship and to the variety of entrepreneurship proxies that havebeen used in the empirical work. These encompass self-employment rates, businessownership rates, new firm start-ups, and concepts of business demography such asfirm turnover and net entry. According to these authors (ibid. p. 8) self-employmentbased measures of entrepreneurship “reflect change that is occurring for individualsstarting a new business. [However] Because very little of this change is projectedonto the larger industry, nation, or global economy, self-employment as a measure ofentrepreneurial activity has been criticized. What is new and different for the indi-vidual may not be so different for the industry or the global economy”. However,self-employment has been often used to proxy entrepreneurship, especially by laboureconomists, as it fulfills the entrepreneurial function of being a risk-bearing residualclaimant (Parker 2004 p. 5). An account of the difficulties of using self-employment asan entrepreneurship proxy may be found in Parker (2004, pp. 5–8). Carree and Thurik(2005, p. 441) point out that entrepreneurship is not restricted to individuals startingor operating new firms and such theorizations exclude entrepreneurship taking placein large firms (intrapreneurs or corporate entrepreneurs). This said, the association ofentrepreneurship with self-employment choice and the set-up of new business can betraced back to Knight (1921) who suggested that an individual moves across threestates—unemployment, paid employment and self-employment. What determines thetransition between employment and the set-up of a new firm depends on a comparisonbetween the expected utility of the wage earned when working for someone else andthe future entrepreneurial income. These ideas have been formalized by Kihlstromand Laffont (1979) who further introduced a risk element based on the assumptionthat, when individuals choose between wage income and running their own busi-ness, they are both uncertain about the prevailing demand and cost conditions as wellas their own entrepreneurial ability. Jovanovic (1982) assumes that individuals areunsure about their abilities, but can gradually learn and ultimately change their behav-iour over time. Lucas (1978) recognizes that individuals differ in their entrepreneurialabilities and equilibrium in an economy is achieved through an allocation of individ-uals across managerial and working roles. Brock and Evans (1989) add that there isindustry-specific human capital, which does not restrict individuals to switch betweenentrepreneurial activity and working for someone else, but might be restrictive in thesense that in doing so individuals are often confined to the same industry. A secondimportant consideration in the literature has been that of switching between beingunemployed and self-employed. Oxenfeldt (1943) proposed that individuals facedwith unemployment and little alternative prospect of obtaining work as an employeewould be more inclined to set up their own business than those in employment. Evansand Leighton (1989) explore some empirical aspects of entrepreneurship and suggest

123


that people becoming self-employed tend to be those who were receiving low wages,who have changed jobs frequently and who have had long unemployment intervalsin their professional life. Blau (1987) develops a model to account for rising self-employment that allows for heterogeneity of workers in terms of managerial ability.An account of the determinants of self-employment can be found in Aronson (1991)and Parker (2004), whereas a critical review of empirical studies on self-employmentin Le (1999).

As in Acs et al. (2005), self-employment rates (SE/E) are sought to exclude theagricultural sector. Although self-employment data are reported by Eurostat in theirLabour-Force-Survey (LFS) commencing in 1999, these are not detailed by sector.Nevertheless, in the Statistical Yearbook of Regions (2005) some figures for self-employment shares in the agricultural sector are provided for some European regions.This research relies on unpublished Eurostat data on self-employment by 1-digit NACEsectors for the year 2004 for adjusting the data for self-employment in agriculture.3 Asthe study period covers the period 1999–2004 and 197 European regions (primarilyNUTS II),4 the share of self-employment in agriculture-hunting and forestry in totalemployment in 2004 was assumed to be the same for base year (1999) and was thusused to calculate the number of self-employed in all sectors but agriculture-huntingand forestry. This compromise was dictated by data availability but might be somewhatjustified in that the self-employment rates (including agriculture) are highly correlatedover the study years and the period itself is rather short. Data on output, populationand investment are taken from Cambridge Econometrics. The data on GDP per capitaare expressed in PPP adjustede. The investment-output ratio (INV/Y ) is defined as theannual average for the study period and the same applies to the population growth(n).Following Mankiw et al. (1992) there has been a standard practice in country-levelstudies to assume that (g + d) is 0.05 per annum for every country in the sample.However, in this study g is allowed to vary between regions belonging to differentcountries (but to be the same in regions of the same country) and is proxied as theannual average of total factor productivity growth (TFP, the amount of output growththat is not accounted for by production factors accumulation) over the study periodcalculated on TFP figures reported in ECOFIN’s AMECO database. The latter is alsothe data source used to calculate depreciation (d) as the difference between gross andnet investment over net capital stock in each of the study period years and which isthen averaged.5

In constructing a human capital stock proxy, a modification on a suggestion madeby Wössmann (2003) for constructing a quality-adjusted measure was used. In par-ticular, the following formulation HCQ

r = e∑

a ra Qi sa,r∈i was employed, where ra isthe OECD average rate of return to education at level a (see Psacharopoulos 1994,

3 Jonny Johansson of Eurostat is gratefully thanked for kindly providing these data.4 See Appendix Table A3 for a list of the regions used in this study.5 Restricting both the depreciation rate and the rate of technological growth to be invariant for the regionsbelonging to the same country is certainly a caveat. This will restrict the variability in the final compositevariable, however it seems unavoidable due to data availability problems.

123

726 G. Fotopoulos

p. 1328),6 sa,r∈i is average years of schooling at education level a in region r thatbelongs in country i (r ∈ i), and Qi is a quality of education index at the countrylevel. The latter is taken from Hanushek and Kimko (2000) and is based on informa-tion from the National Assessments of Educational Progress (NAEP) and additionalinformation for scores on six voluntary international tests of student achievement inmathematics and science that were conducted over the past three decades. The indexis expressed in relative to US performance terms. Such a quality adjusted of humancapital measure relates to the efforts of societies to improve the cognitive abilities oftheir populations or what Sternberg and Grigorenko (2001) call environmental effectson cognitive abilities.

To calculate average years of schooling at education level a in each region r(sa,r∈i )

data from LFS for employment by age and highest education level attained by NUTS IIwere used. As in Lopez-Rodriguez et al. (2007), age classes within the range of 25–64years were used along with the assumptions that, on average, primary education (loweducational attainment) consists an average of 8 years of education, secondary edu-cation (medium educational attainment) consists of 4 years of education, and tertiaryeducation (high educational attainment) consists of 4 years of education. The resultinghuman capital stock variable was calculated for each of the study period years andthen averaged. In Table A1 in the Appendix a correlation matrix of the explanatoryvariables along with some descriptive statistics are provided.

Following Liu and Stengos (1999) and Kalaitzidakis et al. (2001), partial linearmodel (PLM) estimation techniques were employed to search for possible nonlinear-ities in the effect of some of the determinants of regional economic growth. Yatchew(2003) provides an accessible presentation of PLM (ibid. 47–49) and the expositionherein of the basic features of the model takes after him. Let us consider the model

yn×1

= Xn×q

βq×1

+ψ (z)n×1

+ εn×1

where X is a matrix of variables that are assumed to be linearly related to the depen-dent variable y and ψ (z) is an unknown function of some variable z that is supposedto affect the dependent variable in a nonlinear manner. Both the coefficient vector βand the unknown functionψ (z) need to be estimated. Speckman (1988) and Robinson(1988) independently suggested a modelling approach for achieving this. In particular,

6 As reported by Psacharopoulos (1994, p. 1328) social returns to education for the OECD countries areon average 14.4 for primary education, 10.2 for secondary and 8.7 for higher. Using these OECD averagereturns to education instead of country level corresponding figures may be a source of concern. There wereno data for returns to education by level and European country available to the present study. As noted byMiddendorf (2008, p. 5) the returns on education data presented in the collected volume edited by Harmonet al. (2001) “are not per se comparable across countries” (see also Wössmann 2003 for a critical reviewof the data presented in this volume). Furthermore, data on returns to education by level are not providedfor all countries covered therein. In contrast Heinrich and Hilderbrand (2005) produce estimates for returnsto education by level for each of the EU-countries. However, as they separate the primary from the firststage of secondary education (ibid. p. 15), their levels of education do not correspond exactly to those ofEurostat’s regional employment by age and highest educational level attained.

123


they suggested that the model be transformed in the following way:

y − E ( y| z) = (x − E (x| z)) β + ε

The transformed model can be then estimated by Ordinary Least Squares to obtain β.This “double-residual” estimator (Yatchew 2003, p. 47) relies on estimating the con-ditional expectations E ( y| z) and E (x| z). These conditional expectations require anon-parametric regression of y on z and non-parametric regression of each columnof x on z. Yatchew (2003, p. 49) notes that these non-parametric regressions canbe estimated using spline, local polynomial or other non-parametric smoothers. Letm yz = E(y|z) and mxz = E(x|z) be the non-parametric estimates of the correspond-ing conditional and then transform the model by taking the resulting residual terms foreach of these estimations, that is y −m yz and x−mxz . The “double residual” estimatoris then given by β = ((x − mxz)

′(x − mxz))−1((x − mxz)

′(y − m yz)). Expressionsfor the residual variance of this estimator as well as for the covariance matrix of βcan be found in Yatchew (2003, p. 49). Once β has been obtained then ψ(z) can bederived by the means of a non-parametric regression of y − xβ on z.

The non-parametric regression techniques used here for the estimation of the con-ditional expectations are primarily the Nadaraya–Watson estimator and the local poly-nomial regression. The first estimator can be demonstrated to be a special case of thesecond (for polynomial of degree 0). The local polynomial regression estimator (seeHärdle et al. 2004, pp. 94–95) of m p(x) (of a non-parametric regression of, say, Y onX) is given by m(x) = (X′X)−1X′WY , note that the estimator varies with x , where

X =

⎛

⎜⎜⎜⎝

1 (X1 − x) (X1 − x)2 · · · (X1 − x)p

1 (X2 − x) (X2 − x)2 · · · (X2 − x)p

......

.... . .

...

1 (Xn − x) (Xn − x)2 · · · (Xn − x)p

⎞

⎟⎟⎟⎠

and

W =

⎛

⎜⎜⎜⎝

Kh (x − X1) 0 · · · 00 Kh (x − X2) · · · 0...

.... . .

...

0 0 0 Kh (x − Xn)

⎞

⎟⎟⎟⎠

The Nadaraya–Watson (or local constant) estimator corresponds to m0(x)

=∑n

i=1 Kh(x−Xi )Yi∑ni=1 Kh(x−X j )

, where hKh(x − Xi ) = Kh((x − Xi )/h)/h is a kernel function

and h is a bandwidth.7 The kernel function that has been used in this research is theGaussian one Kh(x) = 1√

2πexp(−0.5( x−Xi

h )2).

The local polynomial estimator is influenced less by outliers than the Nadaraya–Watson, it improves the function estimation in areas with sparse observations and

7 Unless otherwise stated bandwidths are selected using cross-validation (Härdle et al. 2004, pp. 113–118).

123

728 G. Fotopoulos

self-employment rate 1999 self-employment rate 2004 self-employment rate 2004 excluding sectors agriculture-forestry and fishing

(a) (b) (c)

Fig. 1 Empirical density estimates for self-employment rates

performs better near the boundaries (ibid. pp. 96–97). For these traits local polynomialfit has also been used along with standard Nadaraya–Watson. Pointwise approximateconfidence intervals can be constructed when a Gaussian kernel is used according tothe following relationship (see also Härdle et al. 2004, p. 119):

[

mh (x)− z1− a2

√(4π)−1/2 σ2 (x)

nh fh (x), mh (x)+ z1− a

2

√(4π)−1/2 σ2 (x)

nh fh (x)

]

where z1− a2

is the(1 − a

2

)quantile of the standard normal distribution and the esti-

mate of the variance σ 2 (x) is given by σ 2 (x) = 1n

∑ni=1 Whi (x) (ui )

2, with Whi the

weights from the Nadaraya–Watson estimator Whi = Kh(x−Xi )

n−1∑n

j=1 Kh(x−X j)and (ui )

2 =(Yi − mh (x)

)are non-parametric regression residuals. Had the function ψ (z) been a

function of more variables, say ψ (z1, z2), the estimation procedure would have usedmultivariate non-parametric regression and the effect of each of the variables involvedcould have been estimated by marginal integration of the joint distribution (Lintonand Nielsen 1995 or other methods suggested by Hastie and Tibshirani 1990).

3 Results

Empirical density estimation using a Gaussian kernel, f (x) = 1n

∑ni=1

1hx

√2π

e−0.5(xi −x

hx)2 , and bandwidth selected according to the criterion suggested by Sheather

and Jones (1991) were used to help depict the distribution of relative (to contempora-neous mean) self-employment rates in 1994 and 2004. For the year 2004, the relativeself-employment rate was also calculated by excluding self-employment in agricul-ture-forestry-fishing sectors and then its empirical density was estimated. The resultsof density estimation are presented in Fig. 1.

There is a considerable resemblance between the density estimates for 1999 (a)and 2004 (b) as both densities appear to be trimodal and in both cases most of the

123


Table 1 OLS and PLM estimation results for 197 EU-15 regions over the 1999–2004 period (standarderrors in parentheses)

(1) (2) (3) (4) (5) (6)

Constant 0.5404*** 0.5462*** 0.4183*** 0.6319***

(0.1392) (0.1449) (0.1278) (0.0948)

ln(Y/L)0 −0.0477∗∗∗ −0.0644∗∗∗ −0.0356∗∗∗ −0.0297∗∗ −0.0744∗∗∗(0.0143) (0.0145) (0.0132) (0.0138) (0.0092)

HCQ 0.0197*** 0.0307*** 0.0202*** 0.0345*** 0.0322***

(0.0055) (0.0050) (0.0066) (0.0056) (0.0051)

ln(INV/L) 0.0051 0.0196** 0.0068 0.01530 0.0259***

(0.0107) (0.0095) (0.0118) (0.01054) (0.0096)

ln(n + g + d) −0.0335∗∗ −0.0247∗ −0.0219 −0.0076 −0.0345∗∗(0.0173) (0.0152) (0.0223) (0.01841) (0.0153)

ln(SE/E)0 0.0667*** 0.0571***

(0.0086) (0.0128)

(SE/E)0 − (SE/E)∗0 0.0447***

(0.0102)

R2 0.04896 0.11063 0.31938 0.44465 0.37451 0.31854

Jn = 6.4450∗∗∗∗ (see Hsiao et al. 2007) rejects the null hypothesis that basic model (3) is linear at the0.1% level∗∗∗ Significant at 1% level; **significant at 5% level and *significant at 10% level

probability mass is concentrated in the area corresponding to self-employment ratesbelow the mean (the mean in both cases corresponds to about 15% of regional employ-ment). When the self-employment in agriculture is subtracted for the relative self-employment figures, the distribution has two pronounced modes. The first is locatedaround the 0.8 of the mean and the second about 1.8 times of the mean (in this casethe mean is about 12% of regional employment). In the non-adjusted for agricultureself-employment rates for 2004, above 1.5 times the mean can be found primarily inGreek, Italian and Portuguese regions, whereas Spanish regions closely follow. Whenthe self-employment rates are adjusted to exclude agriculture, rates above 1.5 timesthe mean can be found in Greek and Italian regions. The two self-employment ratesfor 2004 are highly correlated (0.91).

The results of econometric estimation are presented in Table 1. Column (1) of theresults accounts for the estimation of what is usually termed as “unconditional conver-gence”. The estimated coefficient of the logarithm income per capita is negative andstatistically significant implying an annual rate of convergence of about 0.9%.8 Theresults presented in column (2) correspond to the model suggested by Mankiw et al.(1992). All the variables have the theoretically correct signs and all but the coefficienton investment ratio are statistically significant at conventional levels. The convergencerate becomes 1.33% per annum, the coefficient of the human capital stock variable

8 The convergence rate is given as −λ = log(β + 1)/t where β is the estimated coefficient of ln(Y/L)0.

123

730 G. Fotopoulos

Fig. 2 Nonparametric estimation of the effect of initial conditions on regional growth

is positive whereas the coefficient on the ln(n + g + d) is negative as expected. Thefit of the model is rather low. The model is then empirically extended to include thepossible direct effects of cross regional differences in self-employment rates, whilethe latter is adjusted to exclude self-employment in agriculture-fishing and forestry.The fit of the model is considerably improved, all variables are now significant and thecoefficient of the logarithm of self-employment rate is positive. The implied annualconvergence rate, however, now becomes smaller—at about 0.77%. The positive effectof entrepreneurship on economic growth accords with the findings of Acs et al. (2005)for country-level analysis, and is in the same vein as those of Audretsch and Keilbach(2004a,b) for German regions, although the entrepreneurship definition used in thelatter studies does not rely on self-employment rates. On the other hand Braunerhjelmand Borgman (2004) also use self-employment and find a positive effect of labourproductivity changes in a dynamic setting.

Assuming that the effect of all variables considered (except for the base-year incomeper capita) is linear, the estimation then moves on to examine possible nonlinearitiesof the initial conditions on regional economic growth. This is facilitated by employinga PLM and the techniques described in the previous section. The results concerningthe linear part are presented in column (4). All variables retain their signs but onlythose of the quality adjustment human capital stock and the self-employment rate isnow statistically significant. The estimated nonlinear function for the “average” effectof initial conditions on growth is presented in Fig. 2.

The effect of initial conditions estimated by a Nadaraya–Watson estimator isdepicted along with 95% pointwise confidence intervals. The resulting curve slopes

123


downwards up to e19,930 (9.9 on the horizontal axis) indicating convergence asthe growth rate decreases as the level of development increases, but then slopesupwards suggesting divergence for per capita income range between e19,930 ande 32,860. Although there is some indication for convergence for income levels abovee32,860, this corresponds to an area whose estimation is far less reliable as can beseen by the widening confidence interval. Along with the Nadaraya–Watson estima-tor, Fig. 2 also depicts the result of local quadratic estimation (see previous section).This is indeed smoother at the edges and is contained within the pointwise confi-dence intervals of the Nadaraya–Watson estimation. In contrast, the benchmark linearparametric fit lies outside these intervals providing evidence for the existence of anonlinear structure that is not captured by the linear model. Thus, some evidence isproduced suggesting that convergence is neither linear nor does it apply to all incomeranges.

As the 197 regions used in this study belong to 15 EU member states it possibleto account for country effects by introducing country dummies or by appropriatelytransforming the data. This, in effect, will remove the between countries variationand leave only within country variation. Introducing country effects in our PLM isalso possible since the non-parametric regressions of the binary indicators on the var-iable(s) in the non-parametric part can be estimated using the kernel suggested byAitchison and Aitken (1976). Although the econometric estimation per se may notbe problem, there do remain some problems. First of all, introducing the dummiesor applying the “within” transformation may reduce possible bias as it accounts forcountry-level heterogeneity, however this comes at the expense of higher standarderrors at it relies entirely on within country variation (Durlauf et al. 2005). More,importantly there is always the argument that more attention should be paid in tryingto model heterogeneity rather than finding ways to eliminate its effects (ibid., see alsoTemple 1999). This country heterogeneity seems to have been important in the Euro-pean regional convergence as this had been governed by a sizeable country-specificcomponent (Magrini 2004). This research is interested in both between country andwithin country variation and convergence. For this reason, no country dummies wereintroduced.

It may, however be interesting to account for some heterogeneity not only betweenmember states but also between spatial regimes or spatial clubs. In a European regionalcontext such regimes have been identified by Baumont et al. (2003). Although theregional coverage of their data and consequently their resulting classification do notfully correspond to those used here, their regional spatial-club membership has beenused as a guideline. Earlier results by Neven and Gouyette (1995) suggest differen-tiated convergence experiences of the southern European regions when compared tothe northern ones (see also Paci 1997). Thereby, it would be interesting to examinewhether the nonlinear pattern revealed in Fig. 2 holds after accounting for two spatialregimes, namely north and south. The results of this exercise are presented in theappendix. Figure A1 presents the results of the estimation of the non-parametric part,whereas the results of the estimation of the parametric part are provided in Table A2.These results suggest that nonlinearities in the effect of initial conditions still existafter controlling for north–south spatial regimes (see Table A3 for a classification ofthe regions used in “North” and “South”).

123

732 G. Fotopoulos

Fig. 3 Nonparametric estimation of the effect of entrepreneurship on regional growth

The results presented in column (5) of Table 1 assume that the effect of all vari-ables—excluding that of entrepreneurship—is linear and presents the estimated coef-ficients for the linear part of the PLM. Although all variables retain their signs, onlythe coefficients of initial conditions and human capital are significant. The nonlineareffect of entrepreneurship is presented in Fig. 3.

In this case the estimated function has a positive slope for almost its entire lengthand the linear parametric fit is contained to a large extent (essentially all of the centralpart) within the Nadaraya–Watson pointwise confidence intervals suggesting that devi-ations from linearity may not be that important. Again these results offer corroboratingevidence for the positive effect of entrepreneurship on economic growth.

Overall, the results obtained show that regions with a higher quality of human capi-tal stock and higher rates of self-employment grow faster. Furthermore, although poorregions generally grow faster than their wealthier counterparts, there is evidence thatthe rate of growth also rises with income per capita after some level.

Basile and Gress (2005) propose semiparametric spatial autoregressive and spatialerror models for analyzing the growth behaviour of 156 European regions in the 1988–2000 period. In the spatial autoregressive model semiparametric model the spatial lagenters the parametric part whereas the non-parametric part is a seven dimensional one(6 variables plus an interaction term). The models were ultimately estimated as semi-parametric additive ones. That is, the variables that enter the non-parametric part areassumed to be additive unknown functions. The results obtained reveal nonlinearitiesfor the effects of both initial GDP per capita and the human capital proxy (averagepercentage of working-age population in secondary schools) on regional growth. It isimportant to note that these nonlinearities were obtained having controlled for spatial

123


Fig. 4 Nonparametric estimation of the effect of GDP per capita on self-employment rate

dependence. Basile (2008) estimates a semiparametric Spatial Durbin Model (bothspatial lags of the dependent and some of the independent variables coexist) for thesame period providing affirmative evidence for nonlinear effect of initial GDP/capitaland human capital on regional growth as well as for their interaction with the cor-responding spatial lag. Not accounting for inter-regional spatial inter-dependenciesmay be seen as a potential limitation of this study. While these spatial interdepen-dencies have been accounted for by Basile and Gress (2005) and Basile (2008), thenonlinearities still remained evident. It is thus possible that the nonlinearities revealedby the present research may not have been the result of unaccounted—for spatialinterdependencies.

So far the analysis has considered the effect of entrepreneurship in a direct man-ner, however, as explained in the introduction to this paper, there has been evidencesuggesting that there might be a U-shaped or L-shaped relationship between entrepre-neurship and the level of development and that there might be too much or too lowof self-employment in an economy (Carree et al. 2002; Van Stel and Caree 2004). Ifthis is true then deviations from some optimal rate must inhibit the growth process. Toinvestigate the relationship between self-employment rates (once self-employment inthe primary sector has been removed) and the level of economic development acrossEuropean regions, a non-parametric regression of self-employment rates on per capitaincome has been estimated for the year 1999. The results of this estimation are pre-sented in Fig. 4.

The non-parametric estimate suggests that there is a negative effect of the level ofdevelopment on self-employment rates. However, there is a plateau between 10 and

123

734 G. Fotopoulos

10.5 that is more discernible in the local quadratic fit and might allow some tentativesuggestion for an almost L-shaped effect. Having estimated this effect, as a next stepthe residuals of the non-parametric estimation were included as an additional regres-sor in the basic growth formulation (column 6 of Table 1). This variable measures theexistence of self-employment rates in excess of what the level of development wouldhave predicted for each region. The estimated coefficient of this variable is positiveand statistically significant. This seems to suggest that no evidence can be providedindicating that there might be too much self-employment. Trying to take the absoluteresiduals or the squared residuals yielded statistically insignificant estimates.

4 Conclusions

This research adds itself to the only other two existing studies (Basile and Gress 2005;Basile 2008) using semiparametric methods to explore possible sources of nonlin-earity within a regional growth regression context. In doing so, non-parametric andsemiparametric techniques were employed. The results obtained suggest that growthrates do not decrease as the income levels increases for the whole range of the latter,there is an income range where growth rates increase with base-year income per capitaindicating that divergence and not convergence sets in there. Some further researchmight be needed to delve into the nature of this result. This result might be seen to be inagreement with results of other studies employing different methods and approachessuch as Magrini (2004) and Pittau and Zelli (2006) that provide evidence for polariza-tion past and future in the regional distribution of per capita income in the EuropeanUnion.

As far as the effect of entrepreneurship on economic growth is concerned, this hasbeen found to be positive and its direct effect does not present pronounced devia-tions from linearity. The effect of income per capita levels on self-employment ratesat the regional level seems to suggest an almost L-shaped pattern. However, whenthe residuals of a non-parametric regression of self-employment rates on GDP percapita were included in the right hand side of the estimated growth regression, itseffect was positive. Thus, self-employment rates in excess of what the level of eco-nomic development would have predicted have positive effects on regional economicgrowth. Thereby, no evidence for penalty of having too much of self-employment hasbeen produced.

The results on the positive effect of entrepreneurship on regional growth accordwith those of earlier studies and vindicate the views of the European Commission’s(2003) Green Paper on entrepreneurship where it is stated that ‘The challenge for theEuropean Union is to identify the key factors for building a climate in which entre-preneurial initiative and business activities can thrive. Policy measures should seek toboost the Union’s levels of entrepreneurship, adopting the most appropriate approachfor producing more and getting more firms to grow’ (ibid. p. 9). At the regional level theneed to foster entrepreneurship is emphasized in a recent report of the Committee onRegional Development to the European Parliament (2007), whereas the OECD (2003,p. 4) recognizes that the facilitation of new firm formation is a necessary, though notnecessarily efficient, condition for regional development.

123


When it comes to the role of human capital, the quality-adjusted proxy for humancapital stocks that was used in this study suggests that human capital has a significantand positive effect in determining regional growth. The results, however, of preliminaryeconometric investigation have produced no evidence in favour of nonlinearity for thiseffect.

Appendix

See Tables A1, A2, A3 and Fig. A1.

Table A1 Correlation matrix of explanatory variables and descriptive statistics

HCQ ln (INV/L) ln (n + g + d) ln (SE/E)0

HCQ 1.0000 −0.5608 0.3356 −0.3343

ln (INV/L) −0.5608 1.0000 −0.0766 0.0322

ln (n + g + d) 0.3356 −0.0766 1.0000 −0.1866

ln (SE/E)0 −0.3343 0.0322 −0.1866 1.0000

Mean 2.247 −1.586 −2.844 −2.145

Standard deviation 0.247 0.416 0.227 0.418

Table A2 Estimation of PLM with North-South Spatial Regimes: estimation of the linear part (standarderrors in parentheses)

HCQ ln (INV/L) ln (n + g + d) ln (SE/E)0 North

0.0298 0.0129 −0.0312 0.0525 −0.0172

(0.0049) (0.0097) (0.0151) (0.0108) (0.0107) Jn = 5.8612∗∗∗∗

Jn test (Hsiao et al. 2007) rejects the null hypothesis that the corresponding model is linear at the 0.1%level. Estimation follows Li and Racine (2004) and uses the np package in R (see also Racine and Li 2004)

Table A3 Regions used in the analysis

at11 Burgenland (North) def0 Schleswig-Holstein (North)

at12 Niederösterreich (North) deg0 Thüringen (North)

at13 Wien(North) dk00 Denmark (North)

at21 Kärnten (North) es11 Galicia (South)

at22 Steiermark (North) es12 Principado de Asturias (South)

at31 Oberösterreich (North) es13 Cantabria (South)

at32 Salzburg (North) es21 Pais Vasco (South)

at33 Tirol (North) es22 Comunidad Foral de Navarra (South)

at34 Vorarlberg (North) es23 La Rioja (South)

be10 Région de Bruxelles-Capitale/BrusselsHoofdstedelijk Gewest (North)

es24 Aragón (South)

be21 Prov. Antwerpen (North) es30 Comunidad de Madrid (South)

123

736 G. Fotopoulos

Table A3 continued

be22 Prov. Limburg (B) (North) es41 Castilla y León (South)

be23 Prov. Oost-Vlaanderen (North) es42 Castilla-la Mancha (South)

be24 Prov. Vlaams Brabant (North) es43 Extremadura (South)

be25 Prov. West-Vlaanderen (North) es51 Cataluña (South)

be31 Prov. Brabant Wallon (North) es52 Comunidad Valenciana (South)

be32 Prov. Hainaut (North) es53 Illes Balears (South)

be33 Prov. Liège (North) es61 Andalucia (South)

be34 Prov. Luxembourg (B) (North) es62 Región de Murcia (South)

be35 Prov. Namur (North) es70 Canarias (ES) (South)

de11 Stuttgart (North) fi13 Itä-Suomi (North)

de12 Karlsruhe (North) fi18 Etelä-Suomi (North)

de13 Freiburg (North) fi19 Länsi-Suomi (North)

de14 Tübingen (North) fi1a Pohjois-Suomi (North)

de21 Oberbayern (North) fr10 Île de France (North)

de22 Niederbayern (North) fr21 Champagne-Ardenne (North)

de23 Oberpfalz (North) fr22 Picardie (North)

de24 Oberfranken (North) fr23 Haute-Normandie (North)

de25 Mittelfranken (North) fr24 Centre (North)

de26 Unterfranken (North) fr25 Basse-Normandie (North)

de27 Schwaben (North) fr26 Bourgogne (North)

de30 Berlin (North) fr30 Nord - Pas-de-Calais (North)

de4 Brandenburg (North) fr41 Lorraine (North)

de50 Bremen (North) fr42 Alsace (North)

de60 Hamburg (North) fr43 Franche-Comté (North)

de71 Darmstadt (North) fr51 Pays de la Loire (North)

de72 Gießen (North) fr52 Bretagne (North)

de73 Kassel (North) fr53 Poitou-Charentes (North)

de80 Mecklenburg-Vorpommern (North) fr61 Aquitaine (North)

de91 Braunschweig (North) fr62 Midi-Pyrénées (North)

de92 Hannover (North) fr63 Limousin (North)

de93 Lüneburg (North) fr71 Rhône-Alpes (North)

de94 Weser-Ems (North) fr72 Auvergne (North)

dea1 Düsseldorf (North) fr81 Languedoc-Roussillon (North)

dea2 Köln (North) fr82 Provence-Alpes-Côte d’Azur (North)

dea3 Münster (North) fr83 Corse (North)

dea4 Detmold (North) gr11 Anatoliki Makedonia, Thraki (South)

dea5 Arnsberg (North) gr12 Kentriki Makedonia (South)

dec0 Saarland (North) gr13 Dytiki Makedonia (South)

dee1 Dessau (North) gr14 Thessalia (South)

dee2 Halle (North) gr21 Ipeiros (South)

dee3 Magdeburg (North) gr22 Ionia Nisia (South)

ukc1 Tees Valley and Durham (North) gr23 Dytiki Ellada (South)

123


Table A3 continued

ukc2 Northumberland, Tyne and Wear (North) gr24 Sterea Ellada (South)

ukd1 Cumbria (North) gr25 Peloponnisos (South)

ukd2 Cheshire (North) gr30 Attiki (South)

ukd3 Greater Manchester (North) gr41 Voreio Aigaio (South)

ukd4 Lancashire (North) gr42 Notio Aigaio (South)

ukd5 Merseyside (North) gr43 Kriti (South)

uke1 East Riding and North Lincolnshire (North) ie01 Border, Midlands and Western (North)

uke2 North Yorkshire (North) ie02 Southern and Eastern (North)

uke3 South Yorkshire (North) itc1 Piemonte (North)

uke4 West Yorkshire (North) itc2 Valle d’Aosta (North)

ukf1 Derbyshire and Nottinghamshire itc3 Liguria (North)

ukf2 Leicestershire, Rutland and Northants (North) itc4 Lombardia (North)

ukf3 Lincolnshire (North) itd3 Veneto (North)

ukg1 Herefordshire, Worcestershire and Warks (North) itd4 Friuli-Venezia Giulia (North)

ukg2 Shropshire and Staffordshire (North) itd5 Emilia-Romagna (North)

ukg3 West Midlands (North) ite1 Toscana (North)

ukh1 East Anglia (North) ite2 Umbria (South)

ukh2 Bedfordshire, Hertfordshire (North) ite3 Marche (South)

ukh3 Essex (North) ite4 Lazio (South)

uki1 Inner London (North) itf1 Abruzzo (South)

uki2 Outer London (North) itf2 Molise (South)

ukj1 Berkshire, Bucks and Oxfordshire (North) itf3 Campania (South)

ukj2 Surrey, East and West Sussex (North) itf4 Puglia (South)

ukj3 Hampshire and Isle of Wight (North) itf5 Basilicata (South)

ukj4 Kent (North) itf6 Calabria (South)

ukk1 Gloucestershire, Wiltshire and North Somerset (North) itg1 Sicilia (South)

ukk2 Dorset and Somerset (North) itg2 Sardegna (South)

ukk3 Cornwall and Isles of Scilly (North) lu00 Luxembourg (North)

ukk4 Devon (North) nl11 Groningen (North)

ukl1 West Wales and The Valleys (North) nl12 Friesland (North)

ukl2 East Wales (North) nl13 Drenthe (North)

ukm1 North Eastern Scotland (North) nl21 Overijssel (North)

ukm2 Eastern Scotland (North) nl22 Gelderland (North)

ukm3 South Western Scotland (North) nl23 Flevoland (North)

ukm4 Highlands and Islands (North) nl31 Utrecht (North)

ukn0 Northern Ireland (North) nl32 Noord-Holland (North)

se01 Stockholm (North) nl33 Zuid-Holland (North)

se02 Östra Mellansverige (North) nl34 Zeeland (North)

se04 Sydsverige (North) nl41 Noord-Brabant (North)

se06 Norra Mellansverige (North) nl42 Limburg (NL) (North)

se07 Mellersta Norrland (North) pt11 Norte

se08 Övre Norrland (North) pt15 Algarve

123

738 G. Fotopoulos

Table A3 continued

se09 Småland med öarna (North) pt16 Centro (PT)

se0a Västsverige (North) pt17 Lisboa

pt18 Alentejo

pt20 Região Autónoma dos Açores (PT)

pt30 Região Autónoma da Madeira (PT)

Fig. A1 Nonparametric estimation of the effect of initial conditions on regional growth when accountingfor “north” and “south” spatial regimes (bootstrap error bars)

References

Acs ZJ, Audretsch DB, Braunerhjelm P, Carlsson B (2005) Growth and entrepreneurship: an empiricalassessment. Discussion Paper 5409, CEPR

Aitchison IA, Aitken CGC (1976) Multivariate binary discrimination by the kernel method. Biometrica63:716–723

Armstrong HW (1995) An appraisal of the evidence from cross-sectional analysis of the regional growthprocess within the European Union. In: Armstrong HW, Vickerman RW (eds) Convergence and diver-gence among European regions. Pion, London

Aronson RL (1991) Self-employment: a labor market perspective. ILR Press, New YorkAudretsch DB, Keilbach MC, Lehman EE (2006) Entrepreneurship and economic growth. Oxford Univer-

sity Press, OxfordAudretsch DB, Keilbach M (2004a) Entrepreneurship capital and economic performance. Reg Stud 38:

949–959Audretsch DB, Keilbach M (2004b) Entrepreneurship and regional growth: an evolutionary interpretation.

J Evol Econ 14:605–616Azariadis C, Drazen A (1990) Threshold externalities in economic development. Q J Econ 105:501–526

123


Badinger H, Muller WG, Tondl G (2004) Regional convergence in the European Union, 1985–1999: aspatial dynamic panel analysis. Reg Stud 38:241–253

Barro RJ, Sala-i-Martin X (1991) Convergence across states and regions. Brookings Pap Econ Ac 1:107–182

Basile R (2008) Regional economic growth in Europe: a semiparametric spatial dependence approach. PapReg Sci 87:527–544

Basile R, Gress B (2005) Semiparametric spatial auto-covariance models of regional growth behaviour inEurope. Région Dével 21:93–118

Baumol WJ (1968) Entrepreneurship in economic Theory. Am Econ Rev 58:64–71Baumont C, Ertur C, Le Gallo J (2003) Spatial convergence clubs and the European regional growth process,

1980–1995. In: Fingleton B (ed) European regional growth. Springer, BerlinBernard AB, Durlauf SN (1996) Interpreting tests of the convergence hypothesis. J Econom 71:161–173Blanchflower DG (2000) Self-employment in OECD countries. Lab Econ 7:471–505Blau DM (1987) A time series analysis of self employment in the United States. J Polit Econ 95:445–467Braunerhjelm P, Borgman B (2004) Geographical concentration, entrepreneurship and regional growth:

evidence from regional data in Sweden, 1975–99. Reg Stud 38:929–949Braunerhjelm P, Acs ZJ, Audretsch DB, Carlsson B (2010) The missing link: knowledge diffusion and

entrepreneurship in endogenous growth. Small Bus Econ 34:105–125Brock WA, Evans DS (1989) The economics of small businesses: their role and regulation in the U.S.

economy. Holmes and Meier, New YorkBruyat CA, Julien PA (2001) Defining the field of research in entrepreneurship. J Bus Ventur 16:165–180Carree MA, Thurik R (2005) The impact of entrepreneurship on economic growth. In: Acs ZJ, Audretsch

DB (eds) Handbook of entrepreneurship research: an interdisciplinary survey and introduction.Springer, New York

Carree MA, Van Stel AJ, Thurik AR, Weenekers ARM (2002) Economic development and business own-ership: an analysis using data of 23 OECD countries in the period 1976–1996. Small Bus Econ19:271–290

Cheshire P, Carbonaro G (1995) Convergence-divergence in regional growth rates: an empty black-box?In: Armstrong HW, Vickerman RW (eds) Convergence and divergence among European regions.Pion, London

Cheshire P, and Magrini S (2000) Endogenous processes in European regional growth: convergence andpolicy. Growth Change 31:455–479

Cuadrado-Roura JR (2001) Regional convergence in the European Union: from hypothesis to the actualtrends. Ann Reg Sci 35:33–356

Dewhurst JHL, Mutis-Gaitan H (1995) Varying speeds of regional GDP per capita convergence in theEuropean Union, 1981–1991. In: Armstrong HW, Vickerman RW (eds) Convergence and divergenceamong European regions. Pion

Durlauf SN, Quah DT (1999) The new empirics of economic growth. In: Taylor JB, Woodford M (eds)Handbook of macroeconomics, vol IA. North-Holland, Amsterdam

Durlauf SN, Johnson PA, Temple J (2005) Growth econometrics. In: Aghion P, Durlauf SN (eds) Handbookof economic growth, vol 1A. North-Holland, Amsterdam, pp 555–677

Durlauf SN, Johnson PA (1995) Multiple regimes and cross country growth behavior. J Appl Econ 10:365–384

European Parliament (2007) On the effectiveness of cohesion policy in reducing disparities in the poorestregions of the EU. Committee on Regional Development Report, A6-0241/2007

European Commission (2003) Green paper: entrepreneurship in Europe Enterprise publicationsEvans DS, Leighton LS (1989) Some empirical aspects of entrepreneurship. Am Econ Rev 79:519–535Flaschi D, Lavezzi AM (2003) Distribution dynamics and nonlinear growth. J Econ Growth 8:379–401Fothergill S, Gudgin G (1982) Urban and regional employment change in the UK. Heinemann, LondonFritsch M (2008) How does new business formation affect regional development? Introduction to the special

issue. Small Bus Econ 30:1–14Fritsch M, Mueller P (2004) Effects of New Business Formation on Regional Development over Time. Reg

Stud 38:961–975Gries T, Naudé W (2008) Entrepreneurship and regional economic growth: towards a general theory of

start-ups. UNU-WIDER Research Paper No. 2008/70Grossman GM, Helpman E (1991) Innovation and growth in the global economy. MIT Press, CambridgeHansen B (2000) Sample splitting and threshold estimation. Econometrica 68:575–603

123

740 G. Fotopoulos

Hanushek EA, Kimko DD (2000) Schooling, labor-force, and the growth of nations. Am Econ Rev 90:1184–1208

Härdle W, Müller M, Sperlich S, Werwatz A (2004) Nonparametric and semiparametric models. Springer,Berlin

Harmon C, Walker I, Westergaard-Nielsen (2001) Education and earnings in Europe: a cross country anal-ysis of the returns to education. Edward Elgar, Cheltenham

Hastie TJ, Tibshirani RJ (1990) Generalized additive models. Chapman and Hall, LondonHeinrich G, Hilderbrand V (2005) Returns to education in the European Union: a reassessment from com-

parative data. Eur J Educ 40:13–34Hsiao C, Li Q, Racine JS (2007) A consistent model specification test with mixed discrete and continuous

data. J Econom 140:802–826Iyigun M, Owen A (1999) Entrepreneurs, professionals, and growth. J Econ Growth 4:213–232Jovanovic B (1982) Selection and evolution of industry. Econometrica 3:37Kalaitzidakis P, Mamuneas TP, Savvides A, Stengos T (2001) Measures of human capital and nonlinearities

in economic growth. J Econ Growth 6:229–254Kihlstrom R, Laffont J (1979) A general equilibrium entrepreneurial theory of firm formation based on risk

aversion. J Polit Econ 87:719–748Knight F (1921) Risk, uncertainty and profit. Houghton Mifflin, New YorkLe AT (1999) Empirical studies of self-employment. J Econ Surv 13:381–416Leff NH (1979) Entrepreneurship and economic development: the problem revisited. J Econ Lit 17:46–64Leibenstein H (1968) Entrepreneurship and development. Am Econ Rev 58:72–83Li Q, Racine J (2004) Cross-validated local linear nonparametric regression. Stat Sin 14:485–512Linton O, Nielsen JP (1995) A kernel method of estimating structured nonparametric regression based on

marginal integration. Biometrica 82:93–101Liu Z, Stengos T (1999) Non-linearities in cross-country growth regressions: a semiparametric approach.

J Appl Econ 14:527–538Lopez-Bazo E, Vaya E, Mora AJ, Surinach J (1999) Regional economic dynamics and convergence in the

European Union. Ann Reg Sci 33:343–370Lopez-Rodriguez J, Faina JA, Lopez-Rodriguez J (2007) Human capital accumulation and geography:

empirical evidence from the European Union. Reg Stud 41:217–234Lucas RE (1978) On the size distribution of business firms. Bell J Econ 9:508–523Magrini S (2004) Regional (di)convergence. In: Henderson JV, Thisse J-F (eds) Handbook of regional and

urban economics, vol 4. Elsevier, AmsterdamMankiw NG, Romer D, Weil DN (1992) A contribution to the empirics of economic growth. Q J Econ

107:407–437Martin R (2001) EMU versus the regions? Regional convergence and divergence in Euroland. J Econ Geogr

1:51–80Mason C (1983) Some definitional difficulties in new firms research. Area 15:53–60Middendorf T (2008) Returns to education in Europe-detailed results from a harmonized Survey. Ruhr

Economics Papers #65Neven D (1995) Regional convergence in the European community. J Common Market Stud 33:47–65OECD (2003) Entrepreneurship and local economic development: programme and policy recommenda-

tions. OECD, ParisOxenfeldt AR (1943) New firms and free enterprise: pre-war and post-war aspects. American Council on

Public Affairs, WashingtonPaci R (1997) More similar and less equal: economic growth in the European Union. Weltwirtsch Arch

133:609–634Parker SC (2004) The economics of self-employment and entrepreneurship. Cambridge University Press,

CambridgePittau M-G, Zelli R (2006) Empirical evidence of income dynamics across EU regions. J Appl Econ 21:605–

628Psacharopoulos G (1994) Returns to investment in education: a global update. World Dev 22:1324–1343Quah DT (1996) Convergence empirics across economics with (Some) capital mobility. J Econ Growth

1:95–124Racine J, Li Q (2004) Nonparametric estimation of regression functions with both categorical and contin-

uous data. J Econom 119:99–130Robinson PM (1988) Root n-consistent semiparametric regression. Econometrica 56:931–954

123


Sala-i-Martin X (1996) Regional cohesion: evidence and theories of regional growth and convergence. EurEcon Rev 40:1325–1352

Schultz PT (1990) Women’s changing participation in the labor force: a world perspective. Econ Dev CultChange 38:457–488

Sheather SJ, Jones CM (1991) A reliable data-based bandwidth selection method for kernel density esti-mation. J Roy Stat Soc B 53:683–690

Solow RM (1956) A contribution to the theory of economic growth. Q J Econ 70:65–94Speckman PE (1988) Regression analysis for partially linear models. J Roy Stat Soc B 50:413–436Sternberg RJ, Grigorenko EL (2001) Environmental effects on cognitive abilities. Lawrence Erlbaum Asso-

ciates, New JerseyTemple J (1999) Robustness tests of the augmented Solow model. J Appl Econ 4:361–375Van Stel A, Storey DJ (2004) Link between firm births and job creation: is there a Upas Tree effect?. Reg

Stud 38:893–909Van Stel AJ, Caree MA (2004) Business ownership and sectoral growth: an empirical analysis of 21 OECD

countries. Int Small Bus J 22:389–419Wennekers S, van Stel A, Carree M, Thurik R (2010) The relationship between entrepreneurship and

economic development: is it U-shaped?. Found Trends Entrepreneurship 6:167–237Wössmann L (2003) Specifying human capital. J Econ Surv 17:239–270Yamada G (1996) Urban informal employment and self-employment in developing countries: theory and

evidence. Econ Dev Cult Change 44:289–314Yatchew A (2003) Semiparametric regression for the applied econometrician. Cambridge University Press,

Cambridge

123

nonlinearities in regional economic growth and convergence: the role of entrepreneurship in the...

Documents