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Jesus Crespo Cuaresma and Gernot Doppelhofer and Florian Huber andPhilipp Piribauer

Human Capital Accumulation and Long-Term Income Growth Projections forEuropean Regions

Article (Accepted for Publication)(Refereed)

Original Citation:

Crespo Cuaresma, Jesus ORCID: https://orcid.org/0000-0003-3244-6560 and Doppelhofer, Gernotand Huber, Florian and Piribauer, Philipp

(2018)

Human Capital Accumulation and Long-Term Income Growth Projections for European Regions.

Journal of Regional Science, 58 (1).

pp. 81-99. ISSN 1467-9787

This version is available at: https://epub.wu.ac.at/5673/Available in ePubWU: August 2017

ePubWU, the institutional repository of the WU Vienna University of Economics and Business, isprovided by the University Library and the IT-Services. The aim is to enable open access to thescholarly output of the WU.

This document is the version accepted for publication and — in case of peer review — incorporatesreferee comments.

http://epub.wu.ac.at/

Human Capital Accumulation and Long-TermIncome Growth Projections for European

Regions∗

Jesus Crespo Cuaresmaa,c,d,e, Gernot Doppelhoferb, Florian Hubera, andPhilipp Piribauere

aVienna University of Economics and Business (WU)bNorwegian School of Economics (NHH)

cWittgenstein Centre for Demography and Human Capital (WIC)dInternational Institute for Applied Systems Analysis (IIASA)

eAustrian Institute of Economic Research (WIFO)

Abstract

We propose an econometric framework to construct projections for per capita incomegrowth and human capital for European regions. Using Bayesian methods, our ap-proach accounts for model uncertainty in terms of the choice of explanatory variables,the nature of spatial spillovers, as well as the potential endogeneity between outputgrowth and human capital accumulation. This method allows us to assess the po-tential contribution of future educational attainment to economic growth and incomeconvergence among European regions over the next decades. Our findings suggest thatincome convergence dynamics and human capital act as important drivers of incomegrowth for the decades to come.

Keywords: Income projections, model uncertainty, spatial Durbin model,European regions.

JEL Codes: C11, C15, C21, O52.

∗We would like to thank two anonymous referees, Samir KC, Geoff Hewings, participants of the 10thEUREAL Meeting at the University of Aberystwyth, the Nordic Macro Symposium as well as seminarsat Pablo de Olavide University, the Diplomatic Academy of Vienna and the first annual conference of theInternational Association for Applied Econometrics, Queen Mary University, London for helpful comments.We are grateful for financial support by the Austrian National Bank (Jubilaumsfonds) under Project No.15284. Email: jcrespo@wu.ac.at

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1 Introduction

Economic growth differentials in Europe over the last six decades have led to a substantivereduction of income per capita gaps across regions of the European Union (EU). In the lastfive years, however, the process of convergence of income per capita in the EU has deceleratedsignificantly as a consequence of the economic crisis in Europe. Understanding the futurechallenges facing regional policy in Europe requires the development of reliable quantitativetools (usually in the form of income projections) which are able to assess the reaction ofeconomic growth differences to economic policy at the national and regional level. The mainpurpose of this paper is to provide a methodological framework aimed at obtaining incomeprojections for European NUTS-2 regions which accounts for model uncertainty and can beused for policy analysis. We construct projections for growth of income per capita and humancapital accumulation based on model averaging and the (recursive) identifying assumptionthat income growth responds to human capital accumulation only with a lag. Our incomeprojections can provide useful information for the design of European regional policy andcontribute to integrated assessment models that require income projection scenarios, such asthe ones used by the Intergovernmental Panel on Climate Change (Kriegler et al., 2012). Byconcentrating on subnational units, the framework put forward here provides more detailedinformation than existing long-run income projection methods which are currently at use inglobal integrated assessment models (see, for example Crespo Cuaresma, 2015; Leimbach etal., 2015) .

A large literature has dealt empirically with the analysis of economic growth and incomeconvergence across European regions (see Sala-i-Martin 1996 for a seminal contribution).Several issues related to the econometric modelling of economic growth in sub-national unitshave dominated the modern empirical literature aimed at studying income dynamics at theregional level. First, spatial spillovers play a particularly important role as a determinant ofincome growth at the regional level (see, for example, Niebuhr 2001 or Fischer & Stirbock2006). In spite of the fact that many explanatory factors for regional economic performanceappear correlated in space, they do not tend to be sufficient to explain the economic growthclusters observed in European NUTS-2 regions. Even after controlling for economic growthdeterminants in cross-sectional regional datasets, residuals tend to present correlation struc-tures in space. Such a property of regional growth data requires the use of econometricmodels that account explicitly for spatially autocorrelated dependent variables and/or er-rors. These specifications have thus become the workhorse of econometricians dealing withthe analysis of growth patterns at the regional level. Boldrin & Canova (2001), Lopez-Bazoet al. (2004), Ertur & Koch (2006), Ertur et al. (2006), Fischer & Stirbock (2006), Ertur &Koch (2007) or Ertur et al. (2007), for instance, are some prominent examples of studies us-ing spatial econometric methods to model the growth and convergence process in Europeanregions.

When estimating economic growth regressions in a spatial econometric framework, one isconfronted with at least two dimensions of model uncertainty. One dimension is linked to thefact that the theoretical literature only offers limited guidance when it comes to the variablesthat should be included in the econometric model. Recently, the systematic assessment ofmodel uncertainty has featured prominently in the empirical analysis of economic growth re-

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gressions, both for assessing differences in income growth across countries and across regions.The contributions by Fernandez et al. (2001b) and Sala-i-Martin et al. (2004) gave rise to alarge number of studies that assess the robustness of economic growth determinants to modelspecification in terms of the set of variables that are controlled for in linear economic growthregression models. LeSage & Fischer (2008), Crespo Cuaresma & Feldkircher (2013), Cre-spo Cuaresma et al. (2014), or Piribauer & Fischer (2015) are recent studies which explicitlydeal with this issue for European regions and also address the uncertainty attached to theeconomic growth spillovers across regions. Econometric frameworks for spatially correlateddata typically requires a predefined spatial weight matrix, which defines the geographicallinks between the observations. As inference may be sensitive with respect to the structureof the spatial dependence, the choice of a particular spatial weight matrix is a crucial task(LeSage & Pace 2009). LeSage & Fischer (2008) account for both dimensions of uncertaintyusing Bayesian model averaging techniques for spatial autoregressive models put forward byLeSage & Parent (2007).

Our contribution builds on these developments in the field of econometric modelling undermodel uncertainty and spatial correlation of unknown form in order to obtain projections ofper capita income levels for European NUTS-2 regions for the period 2011-2100. The mostinnovative methodological aspect of our approach is the assessment of endogeneity in thiscontext. We account for potential endogeneity of human capital and income growth by mod-elling them in a system of equations. We propose a recursive identification of the model byassuming that output responds to human capital accumulation sluggishly. This new methodallows for the joint modelling of human capital and income dynamics in the presence of un-certainty about the determinants of both variables, as well as about the potential existenceof spatial spillovers. The projections obtained are based on Bayesian averaging of predictivedensities of spatial Durbin model specifications based on the estimation sample given bythe period 2001-2010. Our results confirm the importance of convergence forces and humancapital accumulation as a driver of income growth in Europe (see LeSage & Fischer 2008,Crespo Cuaresma & Feldkircher 2013, Crespo Cuaresma et al. 2014, or Piribauer 2015) oncethat we integrate away the uncertainty emanating from both the selection of covariates andof spatial linkage structures. By explicitly accounting for the simultaneous determination ofincome growth and human capital accumulation, we generalize the Bayesian model averag-ing applications put forward by LeSage & Fischer (2008), Crespo Cuaresma & Feldkircher(2013), or Crespo Cuaresma et al. (2014) and provide a new methodological framework to in-tegrate endogenous variables in the context of inference under model uncertainty and spatialcorrelation.

The paper is structured as follows. Section 2 describes the econometric framework, basedon Bayesian averaging of econometric specifications for spatially correlated data. Section3 discusses the results concerning the robust in-sample determinants of regional growth inEurope. Section 4 presents the results of the income projection exercise and Section 5concludes.

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2 Econometric framework

Due to the uncertainty surrounding the data generating process of income growth and humancapital accumulation at the regional level, we take a Bayesian stance and account for modeluncertainty by resorting to model averaging methods. While many econometric applicationsaimed at modelling income growth at the regional level tend to assume that human capital isexogenous to income growth, we take a more coherent approach and propose a model that iscapable of accounting for simultaneity in the relationship between human capital and outputgrowth. Given the importance of educational attainment as a robust determinant of regionaleconomic growth in Europe (see for instance the results in Crespo Cuaresma & Feldkircher,2013; Crespo Cuaresma et al., 2014), accounting for the simultaneous determination of hu-man capital accumulation and economic growth at the regional level in Europe appears asan important generalization of the Bayesian model averaging exercises carried out hithertoin the literature.

2.1 A spatial model of regional income growth and human capital in Europe

Consider a specification aimed at modelling the process of income growth and human capitalaccumulation for a cross section of regions indexed by i = 1, . . . , N , allowing for spatialspillovers,

yiτ = βy0 + ρyN∑j=1

wyijyjτ + νy0yit0 + µyhit0 + x′it0βy +

N∑j=1

wyijx′jt0ϑy + uyiτ (1)

hiτ = γyiτ + βh0 + ρhN∑j=1

whijhjτ + νh0 yit0 + µhhit0 + x′it0βh +

N∑j=1

whijx′jt0ϑh + uhiτ , (2)

where yiτ and hiτ denote the log-level of per capita gross value added (GVA) and tertiaryeducation attainment in region i at time τ , where τ denotes the final time point in ourestimation period (which in our dataset corresponds to the year 2010). The scalars βy0and βh0 denote the intercept parameters and γ denotes a parameter which establishes acontemporaneous relationship between yiτ and hiτ . Note that the model of equations (1)and (2) is recursive. While we assume that output yiτ enters the human capital equation(2), we assume that human capital does not influence output contemporaneously, but onlywith a lag. This identification assumption is predicated by the observation that outputusually reacts sluggishly to changes in human capital, leading to returns in terms of economicgrowth only after several years. Such an identification structure is analogous to the time-to-build assumption used to relate capital stock changes and output growth.1 The exogenousexplanatory variables are stored in a K×1 vector xit0 . The K-dimensional parameter vectorassociated with the exogenous variables xit0 is denoted by βl for l ∈ y, h, where t0 denotesthe initial year in the period considered (for our application, the year 2000). The vectorxit0 is composed by variables which are chosen from a set of potential predictors of botheconomic output and tertiary education attainment (see Table 1 for a list of variables). We

1Section 4.2 evaluates the robustness of our findings using an approach that is order-invariant.

4

allow for conditional convergence patterns in the data by including the initial value of eachone of the two variables as additional regressors in the model, where we treat them thesame way as the exogenous variables contained in xit0 . Once we control for initial conditionsand spatial spillovers, the error terms uyiτ and uhiτ are assumed to be contemporaneouslyuncorrelated and homoskedastic with variances λy and λh, respectively. Finally, wlij denotes

the ijth element of an N × N row-stochastic and non-negative spatial weight matrix W l.The spatial weight matrixW l summarizes the spatial linkages across regions and ρl ∈ (−1, 1)measures the degree of spatial autocorrelation. Specifically, wlij > 0 for i 6= j if region i andj are considered neighbors, and zero otherwise. By construction, we assume that wlii = 0.The parameters associated to the spatially lagged regressors are given by ϑy for the incomeequation and ϑh for the human capital equation.

Equations (1) and (2) constitute a flexible multivariate model akin to the well-known spa-tial Durbin model. The model accounts for spatial dependence in both the endogenous andexogenous variables and nests most models commonly employed in the spatial econometricsliterature (LeSage & Pace, 2009). This type of specification is employed to shed some lighton the complex relationship between human capital and output dynamics.

Defining a 2 × 1 vector ziτ = (yiτ , hiτ )′ and collecting all terms corresponding to time τ

on the left-hand side of equations (1) and (2) yields the structural form of the model (for thesake of simplifying notation, we include the variables measuring the initial values of incomeand human capital as part of the vector xit0),

Aziτ = β0 + Φz∗iτ +Bxit0 + Θx∗it0 + εiτ , (3)

with

A =

(1 0−γ 1

), β0 =

(βy0βh0

),Φ =

(ρy 00 ρh

)B =

(βy

βh

),Θ =

(ϑy

ϑh

). (4)

Information on the spatially lagged endogenous and exogenous variables for the ith ob-servation are stored in the vectors

z∗iτ =

(N∑j=1

wyijyjτ ,N∑j=1

whijhjτ

)′, (5)

x∗iτ =

(N∑j=1

wyijxjτ ,N∑j=1

whijxjτ

)′. (6)

Finally, εiτ = (uyiτ , uhiτ )′ ∼ N (0,Σ) is an error vector with variance-covariance matrix Σ

given by

Σ =

(λy 00 λh

). (7)

Equation (7) implies that the shocks are contemporaneously uncorrelated and homoskedas-tic. It is worth noting that the recursive structure of our model together with a diagonal

5

variance-covariance matrix of the structural form of the model given by equation (3) im-plies that we can treat the estimation problem as two separate problems, simplifying thecomputational burden required for posterior analysis enormously.

Since we are ultimately interested in producing a sequence of projections in the form ofconditional expectations, we start by writing the model in equation (3) in reduced form,

ziτ = µ+ Πz∗iτ + Λxit0 + Ψx∗iτ + eiτ . (8)

where µ = A−1β0, Π = A−1Φ, Λ = A−1B and Ψ = A−1Θ denote the reduced formcoefficient matrices. The reduced form innovations are denoted by eiτ = A−1εiτ ∼ N (0,Ω)with variance-covariance matrix given by Ω = (A−1)Σ(A−1)′,

Ω =

(λy γλy

γλy γ2λy + λh

). (9)

Equation (9) shows that Ω is a full matrix, which in turn implies that the reduced formshocks are contemporaneously correlated.

This framework explicitly deals with the complex relationship between income and humancapital in a flexible fashion which allows for Bayesian inference under model uncertaintyregarding covariate selection and spatial spillovers. In addition, since the right-hand side ofequation (8) comprises only variables evaluated in the initial year, it is possible to produceprojections conditional on xit0 for both the human capital and income variables.

2.2 Bayesian model averaging

Most empirical assessments of regional growth determinants carry out different model se-lection procedures to justify a particular choice of covariates and of the matrix W (see, forexample, LeSage & Pace 2009). In a similar fashion, predictions or projections are eventu-ally obtained using individual specifications, thus neglecting the uncertainty embodied by thechoice of a single model in the space of potential specifications, leading to an underestimationof the uncertainty of the quantities of interest (Raftery 1995).

To cope with such issues in a self-contained and coherent manner, we carry out inferenceand the projection exercise using Bayesian model averaging (BMA) techniques by elicitingsuitable prior distributions on the parameters of the model given by equation (3). Differentmodels in terms of included covariates are trivially obtained by setting the correspondingelements of B and/or Θ to zero. Alternative models are thus defined by selecting a givencombination of regressors (with and without spatial lags) and a spatial weighting matrix.

Assuming that the constant term is included in all potential specifications, with K po-tential explanatory variables (not including spatial lags of these) and R weight matrices, thecardinality of the model spaceMl isR 22K for each one of the two equations assessed. Poolingall parameters in the vector θl =

[βl0 ρl (βl)′ (ϑl)′ λl

]for l ∈ (y, h), the posterior distri-

bution of interest conditional on a particular model M lqr ∈Ml(q = 1, . . . , 22K ; r = 1, . . . , R)

6

is given by

p(θl|M lqr,D) =

p(D|θl,M lqr)p(θ

l|M lqr)

p(D|M lqr)

, (10)

with D denoting the available data. Since the marginal likelihood p(D|M lqr) does not involve

θl, the posterior for θl conditional on model M lqr is thus proportional to the likelihood

p(D|θl,M lqr) times the prior p(θl|M l

qr). The uncertainty regarding model choice can beintegrated out by carrying out inference on weighted averages of model-specific posteriorsusing posterior model probabilities p(M l

qr|D) as weights,

p(θl|D) =22K∑q=1

R∑r=1

p(M lqr|D)p(θl|M l

qr,D). (11)

The posterior model probabilities, in turn, are given by

p(Myqr|D) ∝ p(y|My

qr,D)p(Myqr), (12)

p(Mhqr|D) ∝ p(h|My

qr,D)p(Mhqr). (13)

For the parameters on the constant terms βl0 and the disturbance parameters λl, non-informative priors can be elicited. For the priors on the remaining slope parameters and theparameters corresponding to the eigenvectors we follow Fernandez et al. (2001b) and imposemultivariate normally distributed g-prior specification (see Zellner 1986):

[(βlqr)′ (ϑlqr)

′]′|λl,M lqr ∼ N (0, λl[g(Z l

qr)′(Z l

qr)]−1, (14)

where Z lqr is the matrix of explanatory and spatially lagged explanatory variables for model

M lqr. One virtue of the prior specification given in equation (14) is that the g-prior specifica-

tion yields closed-form solutions for the marginal likelihood. Moreover, only the scalar priorhyperparameter g has to be elicited. We follow the suggestions of Fernandez et al. (2001a)and set g = 1/max(N, (2K)2). In addition, we impose a uniform prior on ρl,

ρl ∼ U(−1, 1). (15)

This choice implies that we restrict the support of the posterior to the unit simplex andstay uninformative on the specific values of ρl. For the prior on the space of potential modelspecifications Ml, we elicit a uniform prior, so that

p(M lqr) ∝ 1. (16)

The posterior distributions of the quantities of interest can be evaluated using Markov chainMonte Carlo model composition (MC3) methods. Exact derivations and formulae for theposterior moments can be found in LeSage & Parent (2007).

For out-of-sample projections, the quantity of interest is the predictive density of futurevalues of the income and human capital variables (y and h, respectively), conditional on

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trajectories for other explanatory variables which are summarized in the matrix X. Thepredictive densities of y and h are given by

p(y|X,D) =22K∑q=1

R∑r=1

p(Myqr|D)p(y|X,My

qr,D) (17)

p(h|X,D) =22K∑q=1

R∑r=1

p(Mhqr|D)p(h|X,Mh

qr,D). (18)

The predictive densities are thus weighted averages of all model-specific predictive densities,where the weights are given by the corresponding posterior model probabilities. Given theidentification structure proposed, the predictive densities corresponding to one-step-ahead(i.e. ten-year ahead) projections can be used as starting values (that is, as part of X) toobtain two-step ahead (i.e. twenty-year ahead) projections and thus in this recursive mannerlong-run projections can be computed.

It should be noted that, in addition to assessing model uncertainty, the econometricframework put forward above deals with the potential contemporaneous effect of economicgrowth on education and thus allows for reduced-form errors which are correlated across theincome and human capital equation. In the setting presented, the initial level of humancapital plays the role of an instrumental variable if the specification is to be reinterpretedas a two-stage (or three-stage) least squares type of problem, and thus allows us to identifythe system of equations and estimate its parameters.

3 Determinants of regional economic growth in Europe

We start by applying BMA for the set of specifications described in the preceding sectionusing a cross-section of 273 European NUTS-2 regions.2 Our dependent variables are thegross value added per capita and the share of tertiary education attainment in the period2010.3

Table 1 presents the definition of the variables employed in the analysis, as well as theoriginal source of the data. All explanatory variables are measured in the year 2000, with theexception of the growth rate of population and the unemployment rate, which are averagesfor the period 1996-2000. Since the focus of our analysis is long term trends in income growth,we use a ten-year lag between the dependent and the explanatory variables to ensure thatour inference is not affected by business cycle dynamics.4 We use the same set of potentialcovariates (as well as their spatially lagged counterparts) for the income and human capitalequations. The variables proposed correspond to the standard type of factors used in other

2See the Appendix for the list of NUTS-2 regions included in the data.3To ensure that the projected tertiary educational attainment shares lie between 0 and 100%, the esti-

mations are run using the transformed series hit = log(

hit

1−hit

), where hit and hit denotes the transformed

and untransformed value of tertiary educational attainment for period t and region i, respectively.4In our analysis we therefore abstract from medium-run dynamics. Assessing business cycle movements

at the regional level would require a different set of potential covariates as those used in this piece.

8

studies dealing with model uncertainty in regional growth regressions. The literature ondeterminants of differences in human capital accumulation rates across economies in thepresence of model uncertainty is very limited. Crespo Cuaresma (2010) presents results fora cross-sectional country-level dataset including a large set of potential human accumulationdeterminants. The type of variables entertained in this study is partly similar to that inour work (initial educational levels, income, infrastructure variables, ...), although othercovariates such as credit access are not included in our analysis due to lack of informationat the regional level.5

The majority of the empirical growth literature includes the initial level of income as anexplanatory variable. As a proxy for human capital, we use tertiary education attainmentshares measured by means of the share of working age population with higher education(ISCED levels 5-6). To account for the industrial mix of the regions in the sample we more-over include the shares of employment in agriculture (NACE A and B), mining, manufactur-ing and energy (NACE C to E), construction services (NACE F) as well as employment inmarket services (NACE G to K) as additional explanatory variables. Our dataset moreovercontains information for several other potential control variables which summarize infor-mation about the accumulation of classical factors of production, degree of urbanization,population structure, infrastructure and geography.6

We consider 14 different spatial linkage matrices of three different classes: Queen contigu-ity matrices (first-order and second-order), k-nearest neighbour matrices (for k = 5, . . . , 14)and two matrices based on critical distance (where neighbours are defined as those regionswith a distance below a critical threshold, defined alternatively as the first or second quin-tile of the distribution of distances between pairs of regions). In all cases geodesic distancemeasures are used to construct the spatial linkage matrices.

Table 2 and Table 3 present the results of the in-sample model averaging exercise forthe income per capita and educational attainment equations of the reduced form model (8),respectively. The results are based on evaluating 100,000 models sampled using a MarkovChain Monte Carlo (MCMC) method after disregarding the first 10,000 steps of the Markovchain as initial burn-ins.7 We report the posterior inclusion probabilities in both equationsfor the explanatory variables (PIPx), as well as their spatially lagged counterparts (PIPwx).

5The results in Crespo Cuaresma (2010) indicate that the cross-country variation in education outcomesappears robustly related to differences in income and initial schooling measures (and to a lesser extent todemographic characteristics), variables which are in the pool of potential controls of our analysis.

6In spite of the fact that our model is a cross-sectional one, we also investigated the time series propertiesof the underlying yearly observations of our two variables of interest. We applied the Im-Pesaran-Shin unit-root test to the panel of yearly income per capita and tertiary educational attainment level using individualintercept and trends for the regions. The test statistics for GVA per capita and the education variableare −24.016 (p-value=0.000) and -17.924 (p-value=0.000), respectively, indicating that after controlling fordeterministic trends, the variables can be considered stationary.

7The standard statistics used to evaluate the convergence of the Markov chain indicate that convergencewas achieved. The correlation between simulated and analytical posterior model probabilities for the subsetof best models, for example, was above 0.99.

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Table 1: Explanatory variables: overview

Variable Description

Initial income Gross-value added divided by population, 2000. Source: Cambridge EconometricsPhysical capital investment Gross fixed capital formation, 2000. Source: Cambridge EconometricsInitial tertiary education attainment Share of population (aged 25 and over, 2000) with higher education (ISCED levels 1-2).

Source: EurostatEmployment agriculture Share of NACE A and B (agriculture) in total employment, 2000. Source: Cambridge

EconometricsEmployment energy and manufactur-ing

Share of NACE C to E (mining, manufacturing and energy) in total employment, 2000.Source: Cambridge Econometrics

Employment construction Share of NACE F (construction) in total employment, 2000. Source: Cambridge Economet-rics

Employment market services Share of NACE G to K (market services) in total employment, 2000. Source: CambridgeEconometrics

Population density Population per square km, 2000. Source: EurostatPopulation growth Average growth rate of the population for 1996-2000. Source: EurostatUnemployment rate Average unemployment rate for 1996-2000. Unemployment rate is defined as the share of

unemployed persons of the economically active population Source: EurostatLabor force participation rate Employed and unemployed persons as a share of total population, 2000. Source: EurostatChild dependency ratio The ratio of the number of people aged 0-14 to the number of people aged 15-64, 2000.

Source: EurostatOld-age dependency ratio The ratio of the number of people aged 65 and over to the number of people aged 15-64,

2000. Source: EurostatPeripheriality Measured in terms of distance to BrusselsAccessibility road Potential accessibility road, ESPON space=100. Source: ESPONAccessibility rail Potential accessibility rail, ESPON space=100. Source: ESPONSeaports Dummy variable, 1 denotes region with seaport, 0 otherwise. Source: ESPONAirports Dummy variable, 1 denotes region with airport, 0 otherwise. Source: ESPONCoastal region Dummy variable, 1 denotes region with coast, 0 otherwise. Source: ESPONLarge city Dummy variable, 1 denotes region with a city larger than 300, 000 inhabitants, 0 otherwise.

Source: ESPONRural region Dummy variable, 1 denotes region with a population density lower than 100 and without a

city larger than 125, 000 inhabitants, 0 otherwise. Source: ESPONBorder region Dummy variable, 1 denotes region with country borders, 0 otherwise. Source: ESPONPentagon region Dummy variable, 1 if in London-Paris-Munich-Milan-Hamburg pentagon. Source: ESPON

Posterior inclusion probabilities represent an alternative measure of the robustness of thepotential regressors as explanatory factors for the dependent variable and are defined asthe sum of posterior model probabilities of the specifications which include that particularvariable.

It is worth noting that for specifications with a spatial autoregressive component such asthose entertained in our exercise, the parameter estimates associated with the covariates donot represent marginal effects. LeSage & Pace (2009) show that due to the non-linear natureof such spatial specifications, a direct interpretation of the slope coefficients is inappropriate.Since spatial autoregressive processes usually exhibit non-zero cross-partial derivatives (i. e.a shock in a region’s explanatory variable typically also affects the dependent variable of otherregions), we follow LeSage & Pace (2009) and also report summary impact metrics labelled asaverage direct, indirect (spillover), and total effects. The tables thus also report the posteriormean estimates of the impact metrics along with posterior standard deviations. Such effectshave been obtained based on weighted averages of the corresponding model-specific direct,indirect and total effects.

Average direct impacts represent the average response of a region’s dependent variableto an own-region shock in a specific covariate. The interpretation of direct effects is thusreminiscent of slope coefficients in classical linear model specifications. Average indirect (orspillover) effects, on the other hand, refer to the average impact when changing a specificexplanatory variable in all other regions. While direct impacts measure own-region effects,

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average spillover impacts thus summarize cross-partial marginal effects. Average total im-pacts are given by the sum of average direct and spillover effects and are defined as theaverage response of a region’s dependent variable to a shock of a specific covariate in allregions.

The in-sample results in Table 2 confirm and complement recent contributions on economicgrowth determinants in pan-European regions (see, for example, LeSage & Fischer 2008,Crespo Cuaresma & Feldkircher 2013, or Crespo Cuaresma et al. 2014). With posteriorinclusion probabilities of unity both the initial per capita level of income and its spatiallylagged counterpart appear as extremely important drivers of economic growth. The posteriormean of its average direct impact is smaller than unity and positive implying (conditional)income convergence processes across regions.8 Interestingly, the coefficient associated with itsspatial lag is negative, leading to negative, however imprecise, spillover estimates. The initialshare of tertiary education attainment is also very robustly correlated with GVA per capitaafter accounting for model uncertainty, with an posterior inclusion probability near unity.A third variable which appears to have a considerable posterior probability of inclusionis the share of employment in the market services sector. The positive impact estimatessuggest that a larger share in the market services sector enhances economic growth. Theposterior mean for the spatial autoregressive parameter ρy amounts to 0.88 which highlightsthe importance to account for spatial dependence in the observations. This considerably largeestimate for ρy is attributable to the fact that the log-level of per capita output generallyexhibits a larger degree of spatial dependence as compared to growth rates.

The rest of the variables have a low posterior inclusion probability (below the prior inclu-sion probability of 0.5 implied by our uniform model prior) and their corresponding parame-ter and impact estimates have a low level of precision. The mean of the posterior distributionover model size is 5.9, with most of the posterior probability concentrated in models whichcontain 4 to 8 covariates as explanatory variables. The posterior results for the set of spa-tial weight matrices give strong support to distance-based nearest neighbour matrices. The11-nearest neighbour matrix yields the highest posterior probability of inclusion, 0.33. Al-ternative classes like contiguity-based or distance band matrices receive almost no supportof the data once that model uncertainty is integrated out.

Posterior results for the education equation presented in Table 3 emphasize the impor-tance of income and convergence dynamics as determinants of educational attainment differ-ences across European regions. The contemporaneous level of per capita income, the initialtertiary education attainment share, population growth as well as proxies measuring thesectoral structure appear to be very robustly related to the tertiary education attainmentshares. The posterior over model size in the human capital equation is centered around 7variables. The spatial autocorrelation parameter is positive and very precisely estimated.However, the degree of spatial autocorrelation in the tertiary education attainment equationis considerably smaller (ρh 0.45) than that of the GVA per capita equation. Concerninginference on the inclusion of spatial linkage matrices in the human capital equation, the

8Our income equation can be rewritten as a standard conditional convergence equation after substracting(logged) initial income on both sides. A coefficient of initial income below unity in our original specifica-tion implies a negative partial correlation between initial income and subsequent income growth and thus(conditional) convergence in income per capita across regions.

11

posterior mass appears very concentrated, with the first-order contiguity matrix achieving aposterior probability of inclusion of more than 0.99.

The posterior mean of the direct impact estimate for the initial tertiary education attain-ment covariate is positive and below unity, revealing (conditional) convergence processes alsoin the human capital equation. Interestingly, the average spillover effects are negative indi-cating some non-linearities in the convergence process in the tertiary education attainmentequation and an indication of substitutability of human capital across neighboring regions.Although the negative spillover estimate is precisely estimated, its posterior mean is rathersmall, translating into positive (and also precisely estimated) average total impacts. The pos-terior mean estimates for the contemporaneous and initial levels of per capita income showopposite signs. However, the positive and considerably larger effect of the contemporaneouslevel of income provides evidence that positive growth rates accelerate the accumulation ofhuman capital. Table 3 moreover provides evidence that population growth has some pos-itive effects on the accumulation of human capital, although the precision of the estimatedeffect is not particularly high. Furthermore, the share of employment in the agriculturalsector appears to exhibit positive spillover impacts to tertiary education attainment.

In order to assess the dynamic properties of the estimated specifications, we concentrateon the so-called median model (Barbieri & Berger, 2004) which is the specification containingas explanatory variables those covariates which have a posterior inclusion proability above0.5. Interpreting these model as a (one-period) dynamic spatial data model, the stabilitycondition would be given by the sum of the parameters on (a) the initial value of the de-pendent variable, (b) the spatial lag of the initial value of the variable and (c) the spatiallag of the dependent variable, being below unity (Lee & Yu, 2010). This is fulfilled in boththe GVA per capita and tertiary education equations for the estimates based on the meanof the posterior distribution of the parameters.

12

Table

2:

GV

Ap

erca

pit

aeq

uat

ion

Avg.

Dir

ect

Avg.

Spillo

ver

Avg.

Tot

alV

aria

ble

sP

IPx

PIP

wx

PM

PSD

PM

PSD

PM

PSD

Init

ial

inco

me

1.00

001.

0000

0.86

920.

0102

-0.1

170

0.10

080.

7504

0.10

31In

itia

lte

rtia

ryed

uca

tion

atta

inm

ent

0.96

460.

3695

0.05

640.

0158

0.18

260.

1588

0.23

990.

1530

Em

plo

ym

ent

mar

ket

serv

ices

0.73

210.

0832

0.00

230.

0014

0.01

230.

0091

0.01

460.

0102

Em

plo

ym

ent

const

ruct

ion

0.31

190.

0080

0.00

260.

0039

0.01

610.

0241

0.01

870.

0279

Old

-age

dep

enden

cyra

tio

0.26

040.

0004

-0.0

011

0.00

19-0

.006

80.

0116

-0.0

079

0.01

35P

opula

tion

den

sity

0.02

160.

0070

-0.0

003

0.00

19-0

.002

20.

0137

-0.0

025

0.01

55L

abor

forc

epar

tici

pat

ion

rate

0.02

150.

0020

0.00

010.

0004

0.00

040.

0025

0.00

040.

0029

Child

dep

enden

cyra

tio

0.01

840.

0027

-0.0

001

0.00

06-0

.000

50.

0038

-0.0

006

0.00

44E

mplo

ym

ent

agri

cult

ure

0.01

350.

0030

0.00

000.

0002

-0.0

001

0.00

17-0

.000

10.

0019

Em

plo

ym

ent

ener

gyan

dm

anufa

cturi

ng

0.01

000.

0088

0.00

000.

0002

0.00

020.

0019

0.00

030.

0021

Acc

essi

bilit

yra

il0.

0068

0.00

400.

0000

0.00

000.

0000

0.00

010.

0000

0.00

01R

ura

lre

gion

0.00

600.

0000

-0.0

001

0.00

16-0

.000

70.

0098

-0.0

008

0.01

14P

enta

gon

regi

on0.

0038

0.00

07-0

.000

10.

0010

-0.0

004

0.00

66-0

.000

50.

0076

Per

ipher

iality

0.00

370.

0053

0.00

000.

0003

0.00

040.

0052

0.00

050.

0054

Bor

der

regi

on0.

0027

0.00

020.

0000

0.00

050.

0002

0.00

550.

0002

0.00

58C

oast

alre

gion

0.00

270.

0001

0.00

000.

0002

0.00

000.

0023

0.00

000.

0025

Acc

essi

bilit

yro

ad0.

0020

0.00

790.

0000

0.00

000.

0000

0.00

010.

0000

0.00

01L

arge

city

0.00

180.

0085

0.00

000.

0014

-0.0

024

0.03

48-0

.002

50.

0359

Sea

por

ts0.

0016

0.00

140.

0000

0.00

02-0

.000

20.

0056

-0.0

002

0.00

58A

irp

orts

0.00

040.

0025

0.00

000.

0005

0.00

050.

0142

0.00

050.

0146

Unem

plo

ym

ent

rate

0.00

010.

0017

0.00

000.

0000

0.00

000.

0009

0.00

000.

0009

Physi

cal

capit

alin

vest

men

t0.

0001

0.00

140.

0000

0.00

01-0

.000

10.

0017

-0.0

001

0.00

18P

opula

tion

grow

th0.

0000

0.00

010.

0000

0.00

000.

0000

0.00

050.

0000

0.00

05

PM

PSD

ρy

0.88

530.

0020

λy

0.00

310.

0004

Colu

mn

sP

IPx

an

dP

IPw

xp

rese

nt

the

post

erio

rin

clu

sion

pro

bab

ilit

ies

of

the

core

spon

din

gvari

ab

lean

dit

ssp

ati

al

lag,

resp

ecti

vel

y.

PM

stan

ds

for

the

mea

nof

the

post

erio

rd

istr

ibu

tion

,P

SD

stan

ds

for

the

stan

dard

dev

iati

on

of

the

post

erio

rd

istr

ibu

tion

.

13

Table

3:

Ter

tiar

yed

uca

tion

atta

inm

ent

equat

ion

Avg.

Dir

ect

Avg.

Spillo

ver

Avg.

Tot

alV

aria

ble

sP

IPx

PIP

wx

PM

PSD

PM

PSD

PM

PSD

Init

ial

tert

iary

educa

tion

atta

inm

ent

1.00

001.

0000

0.74

530.

0122

-0.0

333

0.01

670.

7106

0.01

17In

com

e20

100.

9998

0.00

740.

3806

0.05

980.

2571

0.04

330.

6345

0.10

09In

itia

lin

com

e0.

9495

0.09

31-0

.245

70.

0593

-0.1

659

0.03

98-0

.412

00.

0978

Pop

ula

tion

grow

th0.

5555

0.06

460.

0328

0.02

830.

0288

0.02

980.

0616

0.04

89E

mplo

ym

ent

mar

ket

serv

ices

0.04

320.

0000

0.00

010.

0006

0.00

010.

0004

0.00

020.

0010

Em

plo

ym

ent

ener

gyan

dm

anufa

cturi

ng

0.03

850.

0000

-0.0

001

0.00

06-0

.000

10.

0004

-0.0

002

0.00

10P

opula

tion

den

sity

0.02

460.

0000

0.00

030.

0019

0.00

020.

0013

0.00

050.

0032

Per

ipher

iality

0.02

070.

0022

-0.0

011

0.00

75-0

.000

50.

0039

-0.0

016

0.01

13B

order

regi

on0.

0129

0.00

03-0

.000

30.

0025

-0.0

002

0.00

18-0

.000

50.

0043

Coa

stal

regi

on0.

0075

0.00

000.

0000

0.00

040.

0000

0.00

030.

0001

0.00

07A

cces

sibilit

yra

il0.

0074

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00L

arge

city

0.00

560.

0030

0.00

020.

0021

0.00

040.

0050

0.00

050.

0062

Pen

tago

nre

gion

0.00

250.

0198

-0.0

003

0.00

25-0

.003

00.

0211

-0.0

033

0.02

26E

mplo

ym

ent

agri

cult

ure

0.00

100.

9965

0.00

090.

0001

0.01

140.

0010

0.01

220.

0011

Old

-age

dep

enden

cyra

tio

0.00

100.

0026

0.00

000.

0001

0.00

000.

0004

0.00

000.

0005

Acc

essi

bilit

yro

ad0.

0002

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00Sea

por

ts0.

0001

0.00

000.

0000

0.00

020.

0000

0.00

010.

0000

0.00

03P

hysi

cal

capit

alin

vest

men

t0.

0000

0.03

500.

0000

0.00

030.

0006

0.00

320.

0007

0.00

35U

nem

plo

ym

ent

rate

0.00

000.

0002

0.00

000.

0000

0.00

000.

0001

0.00

000.

0001

Em

plo

ym

ent

const

ruct

ion

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Child

dep

enden

cyra

tio

0.00

000.

1047

0.00

010.

0001

0.00

070.

0020

0.00

070.

0021

Rura

lre

gion

0.00

000.

0002

0.00

000.

0001

0.00

000.

0014

0.00

000.

0015

Air

por

ts0.

0000

0.00

000.

0000

0.00

010.

0000

0.00

080.

0000

0.00

09L

abor

forc

epar

tici

pat

ion

rate

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

PM

PSD

ρh

0.44

500.

0033

λh

0.01

000.

0013

Colu

mn

sP

IPx

an

dP

IPw

xp

rese

nt

the

post

erio

rin

clu

sion

pro

bab

ilit

ies

of

the

core

spon

din

gvari

ab

lean

dit

ssp

ati

al

lag,

resp

ecti

vel

y.

PM

stan

ds

for

the

mea

nof

the

post

erio

rd

istr

ibu

tion

,P

SD

stan

ds

for

the

stan

dard

dev

iati

on

of

the

post

erio

rd

istr

ibu

tion

.

14

4 Income projections under model uncertainty: Human capital and the futureof economic growth in Europe

Using the Bayesian model averaging techniques described, we obtain the predictive densityof the income per capita and the tertiary education variables for all regions in our sampleas a weighted average of model-specific predictive densities as in equations (17) and (18),where the weights are given by the corresponding posterior model probabilities. Our methodallows us to simultaneously project educational attainment and income per capita and iteratethe process to obtain paths ranging over long prediction horizons. We provide benchmarkprojections that can be used for the assessment of future income trends in the continentby keeping all variables constant with the exception of the human capital variable and thelevel of income, thus calculating model-averaged predictions for all decades up to the year2100. Needless to say, these projections are of an exemplary nature and concentrate onmeasuring the potential effect of future human capital accumulation trends on income percapita differences across European regions. In this sense, they are not necessarily realisticaccounts of potential future socioeconomic trajectories in the continent, since the sectoralcomposition of output, for instance, is kept constant throughout the out-of-sample period.

4.1 Income and human capital projections

The expected value of the predictive density of income per capita growth, based on themodel-averaged conditional expectation of income per capita over the period 2010-2100 isshown in Figure 1, while Figure 2 presents the expected value of the predictive density ofthe growth rate of tertiary education attainment shares. The income growth projectionsimply a continuation of the cross-regional income convergence process in the continent overthe coming decades. In relative terms, the highest growth rates of income per capita tendto be concentrated in Central and Eastern European economies. This finding carries over tothe expected growth rate of the tertiary educational attainment variable. For human capitalwe find a broad pattern of convergence not only for regions located in Central and EasternEurope but also for regions located in the euro area periphery, most notably Portugal andto some extent Italy and Greece.

Figure 3 depicts the projected average growth rate of income per capita in the period2010-2100 against the (log) income per capita in 2010 for all NUTS-2 regions included inthe analysis. The same type of convergence plot over the projection period is shown inFigure 4 for the share of the labour force with tertiary education. The convergence trendsobserved in the available sample are projected to continue over the coming decades, with twoclearly discernible clusters of income growth across European regions depicted in Figure 3.These patterns imply that income convergence in Europe is expected to be mainly driven bybetween-country dynamics as opposed to within-country convergence. Such a developmentconstitutes a continuation of the relative income developments observed over the last decadesin Europe in terms of closing the gap in within-country versus between-country incomedifferentials (see for example the results in Crespo Cuaresma et al. 2014). Figure 4 providesinsights into the predicted convergence patterns across regions in terms of human capital.Regions that experienced high rates of tertiary education attainment in 2010 tend to present

15

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

3.2

3.4

Figure 1: Projected average annual growth of GVA per capita (2010 to 2100)

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Figure 2: Projected average annual growth of tertiary education attainment shares (2010to 2100)

16

8 9 10 11

1.5

2.0

2.5

3.0

Initial log(GVA)

Pro

ject

ed g

row

th r

ate

of G

VA

Figure 3: Projected average annual growth of GVA per capita (2010 to 2100) againstlog-level of GVA per capita, 2010

2.5 3.0 3.5 4.0

−1.

5−

0.5

0.5

1.5

Initial human capital

Pro

ject

ed g

row

th r

ate

of h

uman

cap

ital

Figure 4: Projected average annual growth of tertiary education attainment shares (2010to 2100) against tertiary education attainment share, 2010

17

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Figure 5: Projected average annual growth difference of per capita income between thebenchmark scenario and a hypothetical no-change scenario (2010 to 2100)

growth rates of this variable which are lower than those of regions with relatively low ratesof tertiary education attainment.

To quantify the output growth premium emanating from increasing human capital levelsacross regions we produce projections based on a no-change scenario. This scenario as-sumes that tertiary education levels remain at their 2010 levels, implying that convergenceis entirely driven by initial income dynamics. Figure 5 presents the differences of growthrates between both scenarios. For regions in Central and Eastern Europe the annual outputgrowth premium is between 0.40 and 0.70%. Regions in Portugal, Greece and southern Italyalso grow faster by around 0.45% under the human capital accumulation scenario. Our find-ings thus suggest that convergence in terms of income per capita is significantly affected byincreases in human capital in each respective regions, where the growth premium is especiallypronounced in regions with low initial income and human capital endowments.

These exemplary predicted income paths present a benchmark scenario which can be usedto downscale national income projections such as those used to inform integrated assessmentmodels for climate change simulations (see for example Crespo Cuaresma 2015). The focuson human capital dynamics as a driving force of income growth provides a suitable frameworkto combine the methods presented here with other population projections by age, sex andlevel of education such as those used in the context of the scenarios used recently by theIntergovernmental Panel for Climate Change in their fifth assessment report (see KC & Lutz2015). Our contribution offers thus a tool to expand the analysis provided by this input tointegrated assessment models to subnational units using a robust and internally coherentmethodological framework.

18

4.2 Robustness checks

A series of robustness checks were carried out to ensure that our results can be confidentlyused to construct projections of income and human capital over the next decades. Weobtained BMA results based on an alternative identification strategy where human capitalaccumulation is assumed to react with a lag to income changes, a reasonable assumptionif we take into account the duration of tertiary education cycles. The resulting projectionsand the in-sample results of basing inference on this alternative identification strategy arenot qualitatively different from those presented above, with the exception of the negativespillover effect of income per capita turning positive and the effect of human capital as adriver of income becoming relatively stronger.

Alternatively, we also repeated the exercise excluding the years corresponding to thefinancial crisis and subsequent recession, concentrating the analysis on the pre-crisis period2000-2007. The results were left practically unchanged, which implies that our inference isnot affected by potential structural changes in the relationships under scrutiny that mayhave been caused by the financial crisis.9 In terms of quantitative differences, neglectinginformation on the crisis only implies slightly higher growth rates of income per capita forthe regions in our sample.10

The final robustness check investigates whether the specific ordering of the variables inziτ exerts a significant impact on our findings. In principle, our estimation approach rests onthe notion that output growth reacts sluggishly with respect to movements in human capitalwhereas the latter is allowed to react immediately. This assumption simplifies the analysisand might be viewed skeptically because it induces a causal ordering on the endogenousvariables in the system. To estimate equation (8) directly we replace yiτ with uyiτ , implyingthat conditional on the coefficients of the first equation, the corresponding residuals are usedas a regressor in the second equation (see Carriero et al. 2015 for a similar approach appliedto VAR models). This approach, although computationally more involved since the problemdoes not have a structure that can be parallelized, yields draws from the joint posterior ofour system of equations. To see that this approach is order-invariant it is straightforward torewrite the full conditional posterior distribution of the regression coefficients (for simplicitydenoted by Ξ = (ξy, ξh)′, with ξy being the parameters of the output equation and ξh of thehuman capital equation) as

p(Ξ|•) = p(ξy|ξh, •)× p(ξh|•). (19)

Here, we let • be a generic notation that implies that we condition on all remaining pa-rameters of the model. This factorization allows us to draw Ξ by sampling sequentiallyfrom p(ξy|ξh, •) and p(ξh|•). Similar to our base algorithm, this method is also based on aCholesky decomposition of the variance-covariance matrix. Note that by the general product

9We abstract from explicitly modelling the effects that the crisis might have had on the human capitalstock of European regions beyond the particular shock correlation assumption built into our system ofequations. Assessing in depth the role that the crisis has played in education decisions of young Europeancohorts goes beyond the focus of our analysis.

10The detailed in-sample BMA results for the pre-crisis period are presented in the Appendix. Otherrobustness checks which have been carried out are available from the authors upon request.

19

rule it is also possible to write

p(Ξ|•) = p(ξh|ξy, •)× p(ξy|•). (20)

Thus, the joint posterior remains invariant with respect to the ordering of income and edu-cation.

Tables 4 and 5 display the reduced-form estimates obtained by using the order-invariantalgorithm outlined above. Comparing the posterior mean estimates and the correspondingPIPs suggests little differences between our approach that relies on a specific structuralidentification assumption and a situation where full system estimation is carried out.

Comparing the corresponding (reduced form) parameter estimates and the projected tra-jectories for human capital and income (not shown) suggests that both approaches yield verysimilar results, with correlations being particularly high, exceeding 0.9 for most income andhuman capital projections produced. However, we would like to stress that this approach isnot suitable for parallel computing since we have to condition on the errors of the first equa-tion based on a draw of ξj for j ∈ y, h. In practice, this increases the computation burdenconsiderably since the presence of the spatial autocorrelation parameter requires numericalmethods to simulate from the joint posterior distribution for each model sampled.

5 Conclusions

We present a framework to obtain projections of income per capita developments at the re-gional level in European countries. The projections build on recent development in Bayesianmodelling and explicitly allow for uncertainty over the importance of different growth deter-minants and the specification of spatial spillovers. We address possible endogeneity issuesby jointly modelling output and human capital in a system of equations. Using a samplespanning the period from 2000 to 2010, we asses the potential contribution of future edu-cational attainment to economic growth and income convergence among European regionsover the next decades.

Our results highlight the importance of income convergence dynamics and human capitalas driving forces for income growth in the continent, being consistent with the bulk of theliterature on growth determinants. Based on these estimates we design a projection exer-cise based on Bayesian averaging of predictive densities. We simultaneously project incomeand human capital, while keeping all other covariates at their 2010 levels. To disentanglethe growth premium caused by increases in human capital we also construct a hypotheti-cal no-change scenario, where all variables are held constant except for initial income. Ourbenchmark scenario shows significant income convergence effects leading to a further nar-rowing of the income differences between poor and rich regions in Europe over the comingdecades, fuelled by human capital investment. The relative return of improving educationalattainment levels in terms if economic growth appears particularly large in peripheral Euro-pean economies. Our results provide a new perspective on the possible importance humancapital has for future income convergence in the continent. While our empirical contribu-tion emphasizes the growth enhancing effect of human capital, it is worth noting that the

20

Table

4:

GV

Ap

erca

pit

aeq

uat

ion

Avg.

Dir

ect

Avg.

Spillo

ver

Avg.

Tot

alV

aria

ble

sP

IPx

PIP

wx

PM

PSD

PM

PSD

PM

PSD

Init

ial

inco

me

1.00

001.

0000

0.86

940.

0102

-0.1

359

0.09

530.

7299

0.09

63In

itia

lT

erti

ary

educa

tion

atta

inm

ent

0.93

110.

3446

0.05

300.

0180

0.18

180.

1615

0.23

490.

1582

Em

plo

ym

ent

mar

ket

serv

ices

0.85

600.

0808

0.00

270.

0012

0.01

540.

0085

0.01

820.

0092

Em

plo

ym

ent

const

ruct

ion

0.30

290.

0043

0.00

260.

0039

0.01

690.

0254

0.01

940.

0292

Old

-age

dep

enden

cyra

tio

0.19

290.

0019

-0.0

008

0.00

17-0

.005

00.

0104

-0.0

058

0.01

21L

abor

forc

epar

tici

pat

ion

rate

0.02

520.

0002

0.00

010.

0004

0.00

040.

0023

0.00

040.

0027

Child

dep

enden

cyra

tio

0.02

110.

0004

-0.0

001

0.00

06-0

.000

50.

0036

-0.0

006

0.00

42E

mplo

ym

ent

ener

gyan

dm

anufa

cturi

ng

0.01

640.

0082

0.00

000.

0002

0.00

030.

0027

0.00

040.

0028

Em

plo

ym

ent

agri

cult

ure

0.01

280.

0111

0.00

000.

0002

0.00

010.

0024

0.00

010.

0025

Acc

essi

bilit

yra

il0.

0071

0.00

130.

0000

0.00

000.

0000

0.00

010.

0000

0.00

01P

opula

tion

den

sity

0.00

540.

0001

-0.0

001

0.00

08-0

.000

40.

0050

-0.0

004

0.00

58B

order

regi

on0.

0049

0.00

970.

0001

0.00

070.

0014

0.01

790.

0014

0.01

85A

cces

sibilit

yro

ad0.

0044

0.00

240.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00P

enta

gon

regi

on0.

0044

0.00

02-0

.000

10.

0008

-0.0

003

0.00

58-0

.000

40.

0067

Coa

stal

regi

on0.

0037

0.00

020.

0000

0.00

02-0

.000

10.

0022

-0.0

001

0.00

24R

egio

nw

ith

ala

rge

city

0.00

180.

0058

-0.0

001

0.00

12-0

.002

50.

0353

-0.0

025

0.03

63R

egio

nw

ith

seap

orts

0.00

170.

0019

0.00

000.

0002

0.00

000.

0023

0.00

000.

0025

Dis

tance

toB

russ

els

0.00

110.

0015

0.00

000.

0002

0.00

010.

0024

0.00

010.

0026

Unem

plo

ym

ent

rate

0.00

090.

0007

0.00

000.

0001

0.00

000.

0008

0.00

000.

0008

Physi

cal

capit

alin

vest

men

t0.

0008

0.00

140.

0000

0.00

01-0

.000

10.

0036

-0.0

001

0.00

37P

opula

tion

grow

th0.

0000

0.00

160.

0000

0.00

02-0

.000

20.

0058

-0.0

002

0.00

59R

egio

nw

ith

anai

rpor

t0.

0000

0.00

080.

0000

0.00

040.

0004

0.01

330.

0004

0.01

36R

ura

lre

gion

0.00

000.

0080

0.00

010.

0008

0.00

260.

0297

0.00

270.

0305

ρy

0.89

030.

0030

λy

0.00

320.

0005

Colu

mn

sP

IPx

an

dP

IPw

xp

rese

nt

the

post

erio

rin

clu

sion

pro

bab

ilit

ies

of

the

core

spon

din

gvari

ab

lean

dit

ssp

ati

al

lag,

resp

ecti

vel

y.

PM

stan

ds

for

the

mea

nof

the

post

erio

rd

istr

ibu

tion

,P

SD

stan

ds

for

the

stan

dard

dev

iati

on

of

the

post

erio

rd

istr

ibu

tion

.

21

Table

5:

Ter

tiar

yed

uca

tion

atta

inm

ent

equat

ion

Avg.

Dir

ect

Avg.

Spillo

ver

Avg.

Tot

alV

aria

ble

sP

IPx

PIP

wx

PM

PSD

PM

PSD

PM

PSD

Ter

tiar

yed

uca

tion

atta

inm

ent

1.00

001.

0000

0.74

890.

0087

0.06

420.

0282

0.80

580.

0297

Err

ors

Inco

me

2010

1.00

000.

0065

0.32

380.

0196

0.24

420.

0391

0.57

130.

0332

Em

plo

ym

ent

mar

ket

serv

ices

0.99

970.

0179

0.00

700.

0006

0.00

520.

0014

0.01

230.

0016

Pop

ula

tion

grow

th0.

6570

0.04

480.

0406

0.02

880.

0359

0.03

000.

0769

0.05

25A

cces

sibilit

yro

ad0.

0838

0.08

10-0

.000

10.

0004

-0.0

002

0.00

07-0

.000

40.

0010

Init

ial

inco

me

0.08

310.

0000

0.00

440.

0147

0.00

360.

0119

0.00

800.

0266

Dis

tance

toB

russ

els

0.05

880.

0000

-0.0

036

0.01

46-0

.002

30.

0093

-0.0

059

0.02

39C

hild

dep

enden

cyra

tio

0.04

520.

0045

0.00

020.

0008

0.00

020.

0010

0.00

040.

0016

Acc

essi

bilit

yra

il0.

0378

0.01

830.

0001

0.00

030.

0001

0.00

060.

0002

0.00

08P

enta

gon

regi

on0.

0261

0.00

00-0

.000

80.

0048

-0.0

006

0.00

36-0

.001

40.

0084

Rura

lre

gion

0.01

980.

0000

0.00

020.

0018

0.00

020.

0014

0.00

040.

0032

Em

plo

ym

ent

agri

cult

ure

0.01

180.

9500

0.00

090.

0004

0.01

030.

0027

0.01

110.

0028

Em

plo

ym

ent

const

ruct

ion

0.00

090.

0000

0.00

000.

0001

0.00

000.

0001

0.00

000.

0001

Em

plo

ym

ent

ener

gyan

dm

anufa

cturi

ng

0.00

040.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0001

Unem

plo

ym

ent

rate

0.00

010.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Physi

cal

capit

alin

vest

men

t0.

0000

0.98

340.

0033

0.00

060.

0400

0.00

760.

0434

0.00

83O

ld-a

gedep

enden

cyra

tio

0.00

000.

0125

0.00

000.

0001

0.00

010.

0011

0.00

010.

0012

Bor

der

regi

on0.

0000

0.00

160.

0000

0.00

020.

0001

0.00

270.

0001

0.00

29C

oast

alre

gion

0.00

000.

0023

0.00

000.

0001

0.00

000.

0011

0.00

000.

0012

Reg

ion

wit

hse

apor

ts0.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00R

egio

nw

ith

ala

rge

city

0.00

000.

0000

0.00

000.

0000

0.00

000.

0002

0.00

000.

0002

Reg

ion

wit

han

airp

ort

0.00

000.

0000

0.00

000.

0000

0.00

000.

0003

0.00

000.

0003

Pop

ula

tion

den

sity

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Lab

orfo

rce

par

tici

pat

ion

rate

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

ρh

0.47

810.

0056

λh

0.01

890.

0017

Colu

mn

sP

IPx

an

dP

IPw

xp

rese

nt

the

post

erio

rin

clu

sion

pro

bab

ilit

ies

of

the

core

spon

din

gvari

ab

lean

dit

ssp

ati

al

lag,

resp

ecti

vel

y.

PM

stan

ds

for

the

mea

nof

the

post

erio

rd

istr

ibu

tion

,P

SD

stan

ds

for

the

stan

dard

dev

iati

on

of

the

post

erio

rd

istr

ibu

tion

.

22

scenario outlined above serves as a mere illustration of what is possible within our modellingframework. More complex scenarios that do not only assume that human capital is changingover time, but set other quantities under control of the policy maker, can be constructed ina straightforward fashion using the method outlined here.

The set of econometric methods presented in this paper can serve as a basic frameworkto obtain income projections and be expanded in a straightforward manner to include alter-native spatial structures, interaction terms or parameter heterogeneity across regions. It isworth noting that the proposed framework is linear and thus fails to account for temporalparameter heterogeneity. A possible avenue of further research would be to extend the exist-ing approach to allow for non-linearities over time. In particular, expanding the analysis topanel data would enable us to assess the relative importance of income growth and humancapital accumulation determinants in a more flexible manner, potentially allowing for modelweights that change over time.

23

References

Barbieri, M. M., & Berger, J. O. (2004). Optimal predictive model selection. Annals ofStatistics , 870–897.

Boldrin, M., & Canova, F. (2001). Inequality and convergence in Europe’s regions: Recon-sidering European regional policies. Economic Policy , 16 (32), 205-253.

Carriero, A., Clark, T. E., & Marcellino, M. (2015). Large vector autoregressions with asym-metric priors and time varying volatilities. Queen Mary, University of London WorkingPaper Series, 759 .

Crespo Cuaresma, J. (2010). Natural disasters and human capital accumulation. WorldBank Economic Review(24), 280-302.

Crespo Cuaresma, J., & Feldkircher, M. (2013). Spatial filtering, model uncertainty andthe speed of income convergence in Europe. Journal of Applied Econometrics , 28 (4),720-741.

Crespo Cuaresma, J. (2015). Income projections for climate change research: A frameworkbased on human capital dynamics. Global Environmental Change, forthcoming .

Crespo Cuaresma, J., Doppelhofer, G., & Feldkircher, M. (2014). The determinants ofeconomic growth in european regions. Regional Studies , 48 (1), 44–67.

Ertur, C., & Koch, W. (2006). Regional disparities in the European Union and the en-largement process: An exploratory spatial data analysis, 1995-2000. Annals of RegionalScience, 40(4), 723-765.

Ertur, C., & Koch, W. (2007). Growth, technological interdependence and spatial external-ities: theory and evidence. Journal of Applied Econometrics , 22 (6), 1033-1062.

Ertur, C., Le Gallo, J., & Baumont, C. (2006). The European regional convergence process,1980-1995: Do spatial regimes and spatial dependence matter? International RegionalScience Review , 29 (1), 3-34.

Ertur, C., Le Gallo, J., & LeSage, J. (2007). Local versus global convergence in Europe:A Bayesian spatial econometric approach. International Regional Science Review , 37 (1),82-108.

Fernandez, C., Ley, E., & Steel, M. F. (2001a). Benchmark priors for Bayesian modelaveraging. Journal of Econometrics , 100 (2), 381-427.

Fernandez, C., Ley, E., & Steel, M. F. (2001b). Model uncertainty in cross-country growthregressions. Journal of Applied Econometrics , 16 (5), 563-576.

Fischer, M. M., & Stirbock, C. (2006). Pan-European regional income growth and club-convergence. Insights from a spatial econometric perspective. Annals of Regional Science,40 (3), 1-29.

KC, S., & Lutz, W. (2015). The human core of the shared socioeconomic pathways: Pop-ulation scenarios by age, sex and level of education for all countries to 2100. GlobalEnvironmental Change(forthcoming).

Kriegler, E., O’Neill, B. C., Hallegatte, S., Kram, T., Lempert, R., Moss, R., & Wilbanks, T.(2012). The need for and use of socio-economic scenarios for climate change analysis: Anew approach based on shared socio-economic pathways. Global Environmental Change,22 (4), 807-822.

Lee, L.-f., & Yu, J. (2010). Some recent developments in spatial panel data models. RegionalScience and Urban Economics , 40 (5), 255–271.

Leimbach, M., Kriegler, E., Roming, N., & Schwanitzs, J. (2015). Future growth patterns

24

of world regions: a gdp scenario approach. Global Environmental Change, forthcoming .LeSage, J. P., & Fischer, M. M. (2008). Spatial growth regressions, model specification,

estimation, and interpretation. Spatial Economic Analysis , 3 (3), 275-304.LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. Boca Raton:

CRC Press.LeSage, J. P., & Parent, O. (2007). Bayesian model averaging for spatial econometric models.

Geographical Analysis , 39 (3), 241–267.Lopez-Bazo, E., Vaya, E., & Artıs, M. (2004). Regional externalities and growth: Evidence

from european regions. Journal of Regional Science, 44 (1), 43–73.Niebuhr, A. (2001). Convergence and the effects of spatial interaction. Jahrbuch fur Re-

gionalwissenschaft , 21 , 113-133.Piribauer, P. (2015). Heterogeneity in spatial growth clusters. Empirical Economics , doi:

10.1007/s00181-015-1023-y , 1–22.Piribauer, P., & Fischer, M. M. (2015). Model uncertainty in matrix exponential spatial

growth regression models. Geographical Analysis , 47 (3), 240–261.Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology ,

25 , 111-163.Sala-i-Martin, X. (1996). Regional cohesion: Evidence and theories of regional growth and

convergence. European Economic Review , 40 (6), 1325-52.Sala-i-Martin, X., Doppelhofer, G., & Miller, R. I. (2004). Determinants of long-term growth:

A Bayesian averaging of classical estimates (BACE) approach. American Economic Re-view , 94 (4), 813-835.

Zellner, A. (1986). Bayesian Inference and Decision Techniques: Essays in Honor of Brunode Finetti. In P. Goel & A. Zellner (Eds.), (chap. On Assessing Prior Distributions andBayesian Regression Analysis with g-Prior Distributions). North-Holland: Amsterdam.

25

Appendix

A List of regions

Country Region Region

Austria Burgenland SalzburgKarnten SteiermarkNiederosterreich TirolOberosterreich VorarlbergWien

Belgium Prov. Antwerpen Prov. LuxembourgProv. Brabant Wallon Prov. NamurProv. Hainaut Prov. Oost-VlaanderenProv. Liege Prov. Vlaams BrabantProv. Limburg Prov. West-VlaanderenRegion de Bruxelles-Capitale

Bulgaria Severen tsentralen YugoiztochenSeveroiztochen YugozapadenSeverozapaden Yuzhen tsentralen

Czech Republic Jihovychod SeverozapadJihozapad Strednı CechyMoravskoslezsko Stredne MoravaPraha Severovychod

Denmark Hovedstaden SjaellandMidjylland SyddanmarkNordjylland

Estonia Estonia

FinlandAland Lansi-SuomiEtela-Suomi Pohjois-SuomiIta-Suomi

France Alsace Ile de FranceAquitaine Languedoc-RoussillonAuvergne LimousinBasse-Normandie LorraineBourgogne Midi-PyreneesBretagne Nord - Pas-de-CalaisCentre Pays de la LoireChampagne-Ardenne PicardieCorse Poitou-CharentesFranche-Comte Provence-Alpes-Cote d’AzurHaute-Normandie Rhone-Alpes

Germany Arnsberg LeipzigBerlin Mecklenburg-VorpommernBrandenburg MittelfrankenBraunschweig MunsterBremen NiederbayernChemnitz OberbayernDarmstadt OberfrankenDetmold OberpfalzDresden Rheinhessen-PfalzDusseldorf SaarlandFreiburg Sachsen-AnhaltGiessen Schleswig-HolsteinHamburg SchwabenHannover StuttgartKarlsruhe ThuringenKassel TrierKoblenz TubingenKoln UnterfrankenLuneburg Weser-Ems

Greece Anatoliki Makedonia, Thraki KritiAttiki Notio AigaioDytiki Ellada PeloponnisosDytiki Makedonia Sterea ElladaIonia Nisia Thessalia

26

ctd.Ipeiros Voreio AigaioKentriki Makedonia

Hungary Del-Alfold Kozep-DunantulDel-Dunantul Kozep-Magyarorszag

Eszak-Alfold Nyugat-Dunantul

Eszak-MagyarorszagIreland Border, Midlands and Western

Southern and EasternItaly Abruzzo Molise

Basilicata PiemonteCalabria Bolzano-BozenCampania TrentoEmilia-Romagna PugliaFriuli-Venezia Giulia SardegnaLazio SiciliaLiguria ToscanaLombardia UmbriaMarche Valle d’AostaVeneto

Latvia LatviaLithuania LithuaniaLuxembourg Luxembourg (Grand-Duche)Netherlands Drenthe Noord-Brabant

Flevoland Noord-HollandFriesland OverijsselGelderland UtrechtGroningen ZeelandLimburg Zuid-Holland

Norway Agder og Rogaland Sr-stlandetHedmark og Oppland TrndelagNord-Norge VestlandetOslo og Akershus

Poland Dolnoslaskie PodkarpackieKujawsko-Pomorskie PodlaskieLodzkie PomorskieLubelskie SlaskieLubuskie SwietokrzyskieMalopolskie Warminsko-MazurskieMazowieckie WielkopolskieOpolskie Zachodniopomorskie

Portugal Alentejo LisboaAlgarve NorteCentro

Romania Bucuresti - Ilfov Sud - MunteniaCentru Sud-EstNord-Est Sud-Vest OlteniaNord-Vest Vest

Slovak Republic Bratislavsky kraj Vychodne SlovenskoStredne Slovensko Zapadne Slovensko

Slovenia Vzhodna Slovenija Zahodna SlovenijaSpain Andalucia Extremadura

Aragon GaliciaCantabria Illes BalearsCastilla y Leon La RiojaCastilla-la Mancha Pais VascoCataluna Principado de AsturiasComunidad de Madrid Region de MurciaComunidad Foral de Navarra Comunidad Valenciana

Sweden Mellersta Norrland Smaland med oarna

Norra Mellansverige Stockholm

Ostra Mellansverige Sydsverige

Ovre Norrland VastsverigeSwitzerland Central Switzerland Northwestern Switzerland

Eastern Switzerland TicinoEspace Mittelland ZurichLake Geneva

United Kingdom Bedfordshire, Hertfordshire KentBerkshire, Buckinghamshire and Oxfordshire Lancashire

27

ctd.Cheshire Leicestershire, Rutland and NorthamptonshireCornwall and Isles of Scilly LincolnshireCumbria MerseysideDerbyshire and Nottinghamshire North Eastern ScotlandDevon Northern IrelandDorset and Somerset Northumberland, Tyne and WearEast Anglia North YorkshireEast Yorkshire and Northern Lincolnshire Outer LondonEast Wales Shropshire and StaffordshireEastern Scotland South Western ScotlandEssex South YorkshireGloucestershire, Wiltshire and Bristol Surrey, East and West SussexGreater Manchester Tees Valley and DurhamHampshire and Isle of Wight West MidlandsHerefordshire, Worcestershire and Warks West Wales and The ValleysHighlands and Islands West YorkshireInner London

28

B BMA results: Pre-crisis period

29

Tab

le7:

GV

Ap

erca

pit

aeq

uat

ion:

Res

ult

sfo

rth

ep

erio

d20

00-2

007

Avg.

Dir

ect

Avg.

Spillo

ver

Avg.

Tot

alV

aria

ble

sP

IPx

PIP

wx

PM

PSD

PM

PSD

PM

PSD

Init

ial

inco

me

1.00

001.

0000

0.88

050.

0081

-0.1

624

0.04

560.

7194

0.04

75In

itia

lte

rtia

ryed

uca

tion

atta

inm

ent

0.88

030.

0002

0.04

320.

0164

0.28

720.

1092

0.33

020.

8803

Em

plo

ym

ent

mar

ket

serv

ices

0.19

500.

0000

0.00

040.

0009

0.00

300.

0064

0.00

340.

0073

Em

plo

ym

ent

agri

cult

ure

0.10

500.

0004

-0.0

002

0.00

06-0

.001

50.

0044

-0.0

017

0.00

50E

mplo

ym

ent

const

ruct

ion

0.07

770.

0000

0.00

040.

0014

0.00

280.

0098

0.00

320.

0112

Child

dep

enden

cyra

tio

0.06

910.

0008

-0.0

002

0.00

06-0

.001

00.

0041

-0.0

012

0.00

47A

irp

orts

0.02

800.

0000

-0.0

005

0.00

28-0

.003

40.

0201

-0.0

039

0.02

29O

ld-a

gedep

enden

cyra

tio

0.01

430.

0134

0.00

000.

0004

-0.0

003

0.00

28-0

.000

40.

0032

Em

plo

ym

ent

ener

gyan

dm

anufa

cturi

ng

0.00

320.

0000

0.00

000.

0001

0.00

000.

0008

0.00

010.

0010

Acc

essi

bilit

yra

il0.

0015

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00B

order

regi

on0.

0003

0.00

030.

0000

0.00

010.

0000

0.00

150.

0000

0.00

15L

abor

forc

epar

tici

pat

ion

rate

0.00

010.

0000

0.00

000.

0000

0.00

000.

0001

0.00

000.

0002

Physi

cal

capit

alin

vest

men

t0.

0000

0.00

000.

0000

0.00

010.

0000

0.00

050.

0000

0.00

05P

erip

her

iality

0.00

000.

0000

0.00

000.

0000

0.00

000.

0001

0.00

000.

0001

Coa

stal

regi

on0.

0000

0.00

000.

0000

0.00

000.

0000

0.00

010.

0000

0.00

01A

cces

sibilit

yro

ad0.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00P

opula

tion

den

sity

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Pen

tago

nre

gion

0.00

000.

0010

0.00

000.

0000

0.00

000.

0014

0.00

000.

0014

Sea

por

ts0.

0000

0.00

040.

0000

0.00

020.

0001

0.00

450.

0001

0.00

47L

arge

city

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Rura

lre

gion

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

Pop

ula

tion

grow

th0.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

00U

nem

plo

ym

ent

rate

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

0.00

000.

0000

PM

PSD

ρy

0.89

930.

0041

Colu

mn

sP

IPx

an

dP

IPw

xp

rese

nt

the

post

erio

rin

clu

sion

pro

bab

ilit

ies

of

the

core

spon

din

gvari

ab

lean

dit

ssp

ati

al

lag,

resp

ecti

vel

y.

PM

stan

ds

for

the

mea

nof

the

post

erio

rd

istr

ibu

tion

,P

SD

stan

ds

for

the

stan

dard

dev

iati

on

of

the

post

erio

rd

istr

ibu

tion

.

30

Table

8:

Ter

tiar

yed

uca

tion

atta

inm

ent

equat

ion:

Res

ult

sfo

rth

ep

erio

d20

00-2

007

Avg.

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31

C Median models: Estimates

Table 9: Median model for the GVA per capita equation

Variable Estimate Std. dev.

Constant 0.2843 0.0862Employment market services 0.0018 0.0008Initial income 0.8652 0.0173Initial tertiary education attainment 0.0469 0.0116W Initial income -0.7427 0.0180

ρy 0.8500 0.0479λy 0.0031 0.0005

Table 10: Median model for the tertiary education attainment equation

Variable Estimate Std. dev.

Constant -1.3487 0.2541Population growth 0.0552 0.0184Initial income -0.2543 0.0678Initial tertiary education attainment 0.7550 0.0225Income 2010 0.3794 0.0776W Employment agriculture 0.0069 0.0016W Initial tertiary education attainment -0.3506 0.0541

ρh 0.4260 0.0630λh 0.0189 0.0016

32