The Spatial Distribution of Human and Physical Capital in Integrated Economic Systems:

Theory and Implications

Sascha Sardadvar

St. Petersburg, 3 December 2015

2

Presentation outline

Economic geography and neoclassical growth theory

Presentation of two papersSardadvar, S. (2013): Does the neoclassical growth model predict interregional convergence? On the impact of free factor movement and the implications for the European Union, Economics and Business Letters 2(4), 161-168Sardadvar, S. (2016): Regional economic growth and steady states with free factor movement: theory and evidence from Europe, Région et Développement 43

Conclusions and outlook

3

Economic geography

“By ‘economic geography’ I mean ‘the location of production in space’; that is, that branch of economics that worries where things happen in relation to one another.”(Krugman 1991, pp. 1)

“Economic geography seeks to explain the riddle of unequal spatial development.”(Combes, Mayer and Thisse 2008, pp. xiii)

“Economic geography explicitly integrates the mobility of factors (capital and/or labor).”(Combes, Mayer and Thisse 2008, pp. xiv)

4

Core-periphery relations

Myrdal (1957):Investment flows to advanced regions.Well educated workers migrate from the periphery to the core.

Krugman (1991): Economic integration increases or triggers regional disparities.

The location of firms (physical capital) and workers (labour) becomes endogenous.

5

Neoclassical growth theory

Assumptions of standard neoclassical models:Closed economiesHomogeneous labourNo mobility costs

Convergence hypothesisConvergence between regions is likely due to similarity (Barro and Sala-i-Martin 1995, López-Bazo 2003).Labour migration accelerates convergence between regions (Barro and Sala-i-Martin 2004).

6

Human capital

Plays a paramount importance in accounting for regional differences in development (Gennaioli et al., 2013).

Can result in a major spatial reallocation of factors (Faggian and McCann, 2009).

A city’s or a region’s stock of human capital is often the main determinant of its economic and social future (Prager and Thisse, 2012).

7

Features of the models

Adopting economic geography’s perspectives to a neoclassical setting:

Microeconomic decisions shape macroeconomic outcomes.The present allocation of physical and human capital is decisive on future allocations.The mobility of factors is bounded by distance.In the long run, disparities with respect to factor allocation prevail.

Model I: two-region growth relationship with investment flows and labour migration (Sardadvar 2013)

Model II: long-run steady state spatial factor allocation for a system of regions (Sardadvar 2016)

8

Contributions to theory

Production functions

Q total outputK total physical capital stockH total human capital stockL total labour supplya, b, c output elasticities

, 0, 0, 0a b cQ K H L a b c

1 1 0a b cQ KabK H L

H

1 1 1 ln 0, 1a b cQ K HaK H L b H H

b

Model I: Physical capital accumulation

k physical capital stock per workeri, j region indexessK physical capital investment rate (saving rate)

r additional investments (subsidies)λ integration parameter (speed of relocations)q output per workerδ depreciation rate

,, ,, , , ,

, ,

j ti t i tK i i t i t i t

i t j t

qdk qs q r k

dt k k

Physical capital investments flow to where expected profits are higher:

Human capital accumulation

v human capital wageL total labour stockh human capital stock per workersH human capital investment rate (educational spending rate)

,, , , , ,

i tH i i t i t j t i t

dhs q v v h

dt

Human capital suppliers follow wages, not marginal productivity:

The compensation for human capital is received by workers in addition to their compensation for raw labour:

, ,, ,

, , ,

i t i ti t i t

i t i t i t

Q Q bv q c

L H h

Growth under constant returns

, , , 2, , , , ,2

, , , , ,

1t i t j ti t j t i t j t

i

jj t

t i t j t i t j t

dq dt q qb a h h bk k b ch

h k k h h

…expression is negative if:

, 1j th b c

The interplay of factors in both regions determines one region’s growth:

12

, , ,

, , ,

, ,, ,

, , , , ,

0

00 00

1 1 11 1

t i t j tj

t j t j t

j t i ti j i t j t i j i j j i i

i t i t j t j t i t

i

j

dQ dt q qb

H h L

L Lc c L L b c a a b c b

h k k h h

Expression depends on interplay of elasticities and factor endowments:

Growth under varying returns

Model II: Factor allocation in N regions

, , ,, , ,

, ,

ijwN

i t i t i tK K t i t i t

i j j t j t

dk q ks q k

dt q k

, ,, , ,

,

ijwN

i t i tH H t i t i t

i j j t

dh vs q h

dt v

, , ,( )i t i t i tv q x c b

Evolution of physical capital stocks:

Evolution of human capital stocks:

w connectivity between regionsμ variable of total flows within the systemx share of workers who supply human capital

,,

1,, ,, , ,

2 2, , , , ,

, ,

1( )

01 1 1 1

iji

i

iji

wN

j ti tK i

i j j ti t i ti t i t i t

wNi t i t i t i i t i i t

Hi ji t j t

kqas

qk hq q qb

h h v b c h b chs

b ch v

Human capital’s within-region effect

Human capital increases within one region affect its growth positively:

1

N

i iji

w

2, 1 (1 ) 1 1i t i ih b b c b

Human capital’s neighbourhood effect

, , , ,

11,, , ,, , ,

,2, ,

,

,, , ,

( )00

1 1

ijij

ij

ij

ij

ww b Ni t j t j t j t

K wa bj i j ti t j t j ti t i t i t

ij i jwNj t j t

j tH w

j i j ti t j t j t

q k h kas

qk k hq q qb w w

h h b c b hs

vh b ch v

Human capital increases in neighbouring regions affect its growth unambiguously negatively:

Long-run output steady-states

1

1** * *

* *( )

( )

iij

i

a aa b N a wiK

i j jai jH H i

hsq q b ch

s b ch

1

1** ** *

* * * *1

( )( )

10

( )

0

iij

ij

i i ij

a aa wa b N a wij ji iKj ja a w

i jj i H H i j

ij

a w b chq hsq b ch

q a s b ch q

w

Long-run steady-state levels (as marked by asterisks) of output are similar across neighbouring regions:

17

Empirics

Variance of GRP per inhabitant (logs), 250 EU regions

18

Growth regression

Spatial lag of X model (LeSage and Pace, 2009):

19

1 1 2 2T T 0 0 0 0 0q q = ι q + h + Wq + Wh + u

T number of periods

α intercept

β, γ regression coefficients

ι (N,1) identity vector

q (N,1) vector of observations on initial output per labour input

h (N,1) vector of observations on human capital endowment

W (N, N) spatial weight matrix

u (N,1) vector of residuals

Growth regression, 250 EU regions

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without dummy including NMS dummy

  2000-2013 2000-2008 2008-2013 2000-2013 2000-2008 2008-2013

α 0.275 (0.000) 0.428 (0.000) -0.006 (0.817) 0.195 (0.000) 0.370 (0.000) -0.116 (0.018)

β1 -0.032 (0.000) -0.046 (0.000) -0.015 (0.000) -0.024 (0.000) -0.040 (0.000) -0.004 (0.420)

γ1 0.022 (0.000) 0.022 (0.000) 0.020 (0.000) 0.019 (0.000) 0.020 (0.001) 0.020 (0.000)

β2 0.015 (0.000) 0.018 (0.000) 0.020 (0.000) 0.013 (0.000) 0.017 (0.000) 0.018 (0.000)

γ2 -0.047 (0.000) -0.059 (0.000) -0.025 (0.000) -0.041 (0.000) -0.055 (0.000) -0.023 (0.001)

NMS ― ― ― 0.018 (0.015) 0.013 (0.306) 0.019 (0.002)

σ2 0.012 0.017 0.019 0.011 0.017 0.019

R² 0.768 0.785 0.131 0.786 0.788 0.175

LIK 761.77 659.36 636.82 772.70 661.82 643.90

AIC -1,511.54 -1,306.71 -1,261.63 -1,531.39 -1,309.65 -1,273.81

Steady state regression

Spatial Durbin model (LeSage and Pace, 2009):

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1 2 t t t tq = Wq ι h + Wh + u

ρ spatial auto-correlation coefficientμ standard regression coefficient

α intercept

ι (N,1) identity vector

q (N,1) vector of observations on initial output per labour input

h (N,1) vector of observations on human capital endowment

W (N, N) spatial weight matrix

u (N,1) vector of residuals

Steady state regression, 250 EU regions

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  2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

α 0.767 (0.000)

-0.050 (0.872)

0.085 (0.788)

0.026 (0.935)

-0.059 (0.858)

0.108 (0.747)

0.114 (0.748)

0.385 (0.286)

0.641 (0.095)

0.623 (0.104)

0.605 (0.116)

0.583 (0.127)

0.510 (0.199)

0.582 (0.146)

μ1

0.647 (0.000)

0.629 (0.000)

0.656 (0.000)

0.676 (0.000)

0.706 (0.000)

0.762 (0.000)

0.729 (0.000)

0.752 (0.000)

0.794 (0.000)

0.807 (0.000)

0.847 (0.000)

0.889 (0.000)

0.901 (0.000)

0.909 (0.000)

μ1

-0.458 (0.000)

-0.462 (0.000)

-0.502 (0.000)

-0.527 (0.000)

-0.543 (0.000)

-0.611 (0.000)

-0.560 (0.000)

-0.600 (0.000)

-0.655 (0.000)

-0.686 (0.000)

-0.722 (0.000)

-0.773 (0.000)

-0.762 (0.000)

-0.783 (0.000)

Direct 0.713 (0.000)

0.691 (0.000)

0.701 (0.000)

0.726 (0.000)

0.763 (0.000)

0.802 (0.000)

0.771 (0.000)

0.775 (0.000)

0.797 (0.000)

0.804 (0.000)

0.842 (0.000)

0.878 (0.000)

0.896 (0.000)

0.900 (0.000)

Indirect 0.663 (0.019)

0.643 (0.030)

0.477 (0.118)

0.510 (0.127)

0.588 (0.063)

0.374 (0.211)

0.418 (0.167)

0.209 (0.435)

0.013 (0.960)

-0.021 (0.941)

-0.056 (0.834)

-0.101 (0.727)

-0.031 (0.913)

-0.092 (0.752)

Total 1.376 (0.000)

1.335 (0.000)

1.178 (0.001)

1.235 (0.001)

1.351 (0.000)

1.176 (0.001)

1.189 (0.001)

0.983 (0.001)

0.810 (0.005)

0.783 (0.016)

0.785 (0.011)

0.777 (0.019)

0.865 (0.008)

0.808 (0.016)

ρ 0.862 (0.003)

0.874 (0.000)

0.871 (0.000)

0.880 (0.000)

0.878 (0.000)

0.870 (0.000)

0.856 (0.000)

0.843 (0.000)

0.827 (0.000)

0.842 (0.000)

0.841 (0.000)

0.850 (0.000)

0.839 (0.000)

0.842 (0.000)

σ2 0.077 0.066 0.064 0.056 0.054 0.052 0.053 0.053 0.055 0.054 0.052 0.049 0.050 0.048

LIK -71.97 -54.99 -50.25 -35.33 -28.85 -22.86 -23.27 -22.77 -23.40 -24.35 -20.03 -13.11 -14.72 -10.43

BP 11.914 (0.003)

8.947 (0.011)

7.291 (0.026)

4.501 (0.105)

3.471 (0.176)

1.769 (0.413)

1.648 (0.439)

1.789 (0.409)

3.544 (0.170)

4.616 (0.162)

3.636 (0.162)

2.414 (0.299)

2.718 (0.257)

0.362 (0.835)

Wald 1887.6 (0.000)

2286.8 (0.000)

2164.9 (0.000)

2536.0 (0.000)

2446.1 (0.000)

2145.7 (0.000)

1741.5 (0.000)

1434.4 (0.000)

1165.2 (0.000)

1407.5 (0.000)

1403.1 (0.000)

1580.6 (0.000)

1358.6 (0.000)

1413.3 (0.000)

Human capital determines a region’s attractiveness for mobile factors, which includes human capital.

Regions with initially high factor endowments benefit from economic integration.

Instruments to support convergence:altering the level of economic integration,

compensating disadvantaged regions by subsidies,

benefitting from increasing returns (e.g. metropolitan regions),

increasing investments and educational spending.

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Summary of results

24

Conclusions and outlook

The spatial distribution of human capital is both cause and effect of factor relocations.

Under free market forces, factor relocations lead to spatial inequality of factor distribution.

Without state intervention, disparities will prevail in the long run.

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ReferencesBarro, R.J., Mankiw, G., Sala-i-Martin, X.X. (1995): Capital mobility in neoclassical models of growth, American Economic Review 85(1), 103-115

Barro, R.J., Sala-i-Martin, X.X. (2004): Economic Growth [2nd edition]. New York, McGraw-Hill

Combes, P.-P., Mayer, T., Thisse, J.-F. (2008): Economic Geography – The Integration of Regions and Nations. Princeton, Princeton University Press

Faggian, A., McCann, P. (2009): Human capital and regional development, in Capello, R., Nijkamp, P. (eds.): Handbook of Regional Growth and Development Theories. Cheltenham and Northampton [MA], Edward Elgar, 133-151

Gennaioli, N., La Porta, R., Lopez-de-Silanes, F., Shleifer, A. (2013): Human capital and regional development, The Quarterly Journal of Economics 128(1), 105-164

Krugman, P. (1991): Geography and Trade [reprint 1992]. Leuven and Cambridge [MA], Leuven University Press

LeSage, J., Pace, R.K., (2009): Introduction to Spatial Econometrics. Boca Raton, London and New York, CRC Press

López-Bazo, E. (2003): Growth and convergence across economies: the experience of the European regions, in Fingleton, B., Eraydin, A., Paci, R. (eds.): Regional Economic Growth, SMEs and the Wider Europe. Aldershot and Burlington, Ashgate, 49-74

Myrdal, G. (1957): Economic Theory and Under-Developed Regions [German edition 1974]. Frankfurt/Main, Fischer Taschenbuch Verlag

Prager, J.C., Thisse, J.F. (2012): Economic Geography and the Unequal Development of Regions. Abingdon and New York, Routledge

Sardadvar, S. (2013): Does the neoclassical growth model predict interregional convergence? On the impact of free factor movement and the implications for the European Union, Economics and Business Letters 2(4), 161-168

Sardadvar, S. (2016): Regional economic growth and steady states with free factor movement: theory and evidence from Europe, Région et Développement 43

Model simulation

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12 regions: A, B, …, L,a = 0.3, b = 0.2, δ = 0.05, sK = 0.25, sH = 0.15, λ = 0.1

0 1 0 1 0 0 1 0 0 1 0 0 9

1 0 1 1 0 1 0 0 0 0 0 3

0 1 0 0 1 1 1 0 0 0 0 0 5

1 1 0 0 1 0 0 0 1 1 0 0 8

0 1 1 1 0 1 0 0 0 1 0 0 9

0 0 1 0 1 0 1 0 0 0 0 0 7.5

1 1 1 0 0 1 0 1 0 0 0 0

0 0 0 0 0 0 1 0 1 0 0 0

1 0 0 1 0 0 0 1 0 1 1 0

0 0 0 1 1 0 0 0 1 0 1 0

0 0 0 0 0 0 0 0 1 1 0 1

0 0 0 0 0 0 0 0 0 0 1 0

1

0W k

5

6

5 2.24

4.5 2.52

5.5 2.72

4 2.42

8.5 5 2.62

7 3.5 2.3

8 5 2.57

7.5 4 2.42

8 3 2.02

4 1.5 1.64

2.67

1.99

0 0h q

Long-run human capital distributionH

uman

cap

ital (

logs

)

Periods

27

Regions:

Simulation: output distributionO

utpu

t (lo

gs)

Periods

Regions:

28

Simulation: physical capital distributionPh

ysic

al c

apita

l (lo

gs)

Periods

regions:29