1

The International Conference GLOBAL ECONOMY & GOVERNANCE – GEG 201410-12 September 2014, Bucharest, Romania

A non-linear model to estimate the long run economic growth in EU and in South-East Asia

Lucian-Liviu ALBUInstitute for Economic Forecasting

Romanian Academy

Bucharest, September 10, 2014

Acknowledgement:

Partially this presentation is based on work done in Institute for Economic Forecasting, Romanian Academy, under an EU project (“IDEAS” project: Non-linear modeling of relations between financial market and macroeconomic variables). The research project is supported by a grant of the Ministry of National Education, CNCS – UEFISCDI, project number PN-II-ID-PCE-2012-4-0631.

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A. Real convergence in EU1. Spatial distribution of macroeconomic variables in EU

2. Trends in real convergence. How crisis affected convergence in EU

3. Differences between EU-15 and EU-10

4. Structural convergence in EU

B. A non-linear model to simulate an optimal convergence in EU1. Empirical evidences in EU compared to the theory

2. A non-linear model to simulate the convergence

3. Applications in case of EU

4. Application in case of Romania

C. A model to simulate an optimal convergence in South-East Asia1. Empirical evidences in South-East Asia

2. Applications of the simulation model in case of South-East Asia

3

A. Real convergence in EU1. Spatial distribution of macroeconomic variables in EU

2. Trends in real convergence. How crisis affected convergence in EU

3. Differences between EU-15 and EU-10

4. Structural convergence in EU

4

Spatial distribution of GDP per capita in EU (Malta and Cyprus excluded), 2012 (in PPS, Purchasing Power Standard; UE28=100)

0 10 20

40

50

60

196.391

182.69 168.989155.287

155.287

141.586

141.586

141.586

127.884

127.884

127.884

127.884

127.884

114.183

114.183

114.183

114.183

114.183

100.482

100.482

100.482

100.482

100.482

86.78

86.78

73.079

73.079

73.079 59.377

,,LO LA yPPS

A1. Spatial distribution of macroeconomic variables in EU

GDP Growth in EU, 2012 (%)

0 10 20

40

50

60

4.262

3.548

2.833

2.119

2.119

1.405

1.405

1.4051.405

0.69

0.69

0.69

0.69

0.69

0.69

0.024

0.024 0.024

0.024 0.024

0.024

0.024

0.739

0.739

0.739

0.739

0.739

1.453

1.453 1.453

2.168

2.168

2.882

2.882 3.596 3.596 4.311 5.025

,,LO LA rY2012

Unemployment (%) in EU (October 2013)

0 10 20

40

50

60

23.01321.58721.587 20.162

20.162

18.73618.736

17.311

17.311

17.311

15.886

15.886

15.88614.46

14.46

14.4613.035

13.035

13.035

13.035

11.609

11.609

11.609

11.609

11.609

10.184

10.184

10.184

10.184

10.184

10.184

8.758

8.758

8.758

8.758

8.758

8.758

8.7588.758

7.333

7.333

7.333

7.333

5.907

5.907

,,LO LA u%

Inflation (%) in EU, 2012 (annual average)

0 10 20

40

50

60

5.325.0244.727

4.43

4.134

4.134

3.837

3.837

3.543.54

3.54

3.244

3.244

3.244

2.947

2.947

2.947

2.947

2.65

2.65

2.65

2.65

2.65

2.65

2.65

2.65

2.65

2.354

2.354

2.354

2.354

2.3542.354

2.354

2.3542.354

2.0572.057

2.057

2.057

1.761.761.76

1.76

1.464

1.4641.464

1.1671.167

1.167

,,LO LA %

Spatial distribution in UE of the export per capita (in thousand euro PPS), 2011

0

10

20

010

2030

102030

,,LO LA exPPS0 10 20

40

50

60

35

30

3025

25

25

20

20

20

20

15

15

15

15

1515

15

10

1010

10

10

10

,,LO LA exPPS

9

Spatial distribution in UE of the import per capita (in thousand euro PPS), 2011

0

10

20

010

2030

1020

,,LO LA imPPS0 10 20

40

50

60

25

25

20

20

20 1515

15 15

15

15

15

15

10

10

101010

10

10

10

,,LO LA imPPS

10

Spatial distribution in EU of the ratio export/GDP (in %), 2011

0

10

20

010

2030

406080100

,,LO LA ex%

0 10 20

40

50

60

105 100

95

90

90

90

85

85

85

80

80

80 80

80

8075

75

75

75

75

75 70

70

70

7070

65

65

65

65

65

65

60

60

60

60

60

60

6055

55

55

5555

55

55

5550

50

50

50

50

50

5050

50

45

45

45

45

45

40

40

40

40

40

35

3535 30

3025

,,LO LA ex%

11

Spatial distribution in EU of the ratio import/GDP (in %), 2011

0

10

20

010

2030

406080

,,LO LA im%

0 10 20

40

50

60

85

85

80

8080

75

75

75 75

75

7570

70

70 70

70

70

65 65

65 65

65

65

60

60

60

60

60

60

60

55

5555

55

55

55

55 50

50

5050

50 50

50

50

50

45

45

45

45

45

45

45

45

40

40

40

3535

35

3530

30

,,LO LA im%

12

Spatial distribution in EU of FDI per capita (in thousand USD), 2010

0

10

20

010

2030

204060

,,LO LA isdUSD

0 10 20

40

50

60

55

55

50

50

45

45

4540

40

40

35

35

35

35

30

30

30

30

30

25

25

25

25

2020 20

20

20

15

15

15

15

10

10

10

10

5

5

5

,,LO LA isdUSD

13

Correlation between FDI per capita (y) and GDP per capita (x) in EU, 2010

0 10 20 30 40 50 60 7010

20

30

yi

yEi

xi

14

15

Dinamics of GDP per capita in UE-26, excluding Luxembourg (average level of EU=100), 2000-2011

01

23

45

67

89

1011

1213

1415

1617

1819

2021

2223

2425

0 1 2 3 4 5 6 7 8 9 10 110102030405060708090100110120130140150

yPPS%

A2. Trends in real convergence. How crisis affected convergence in EU

Convergence indicators:

1. Variation coefficient

2. Gini I coefficient, Ga (based on Lorenz curve, by estimating econometrically parameters for a continuous function, ye(x), which best approximates Lorenz curve, and its integration on the interval [0, 1])

3. Gini II coefficient, Gb (based on Lorenz curve, by an interpolation method, the so-called method of trapezoids)

4. Coeficientul RH (estimated on the Lorenz curve base)

…and many others.

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Coefficient of variation

y = Vy P / Y

where unde y is coefficient of variation in case of GDP per capita, y, Vy is variance (deviation from the mean), P is number of population, and Y is total GDP.

Computing relations for weighted mean, ym, variance at the EU level, Vy, and variation coefficient at EU level, y_y are as follows:

ymt

= 1

n

i

.y ,i t P ,i t

= 1

n

i

P ,i t

_yt.= 1

n

i

.Vy ,i t P ,i t

.

= 1

n

i

P ,i t ymt

100

where i = 1, 2,..., n (n=27) are EU countries, and t = 1, 2,..., T (T=12) are years of the period 2000-2011.

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Lorentz curve (EU - 2000, and EU - 2011)

0 10 20 30 40 50 60 70 80 901000

10

20

30

40

50

60

70

80

90

100

Yc%,i 0

Pc%,i 0

Pc%,i 0

0 10 20 30 40 50 60 70 80 901000

10

20

30

40

50

60

70

80

90

100

Yc%,i 11

Pc%,i 11

Pc%,i 11

19

Gini coefficient Ga

Ga = A / (A + B) or Ga = 2 A

where A is area between Lorentz curve and the diagonal of the square unit and B is area under the Lorentz curve.

For practical applications, we can use various methods to estimate the Gini coefficients, which usually involve a large amount of computation. One of the methods we use are based on econometric estimates of the parameters of a continuous function, ye (x) that best approximates Lorentz curve; then we can apply the integration on the interval [0, 1] to calculate area B, as in the following

relationship, where ye(x) = x / (a x + b) B d

0

1

xye( )x

20

Gini coefficient Gb

Other method less precise to estimate Gini coefficient based on Lorentz curve is as follows:

G 1

= 1

n

i

.Xi Xi 1

100

Yi Yi 1

100

where, in case of GDP in UE, X=Pc% and Y=Yp%. First one means the cumulated share in total number of population in EU and the second is the cumulated share in total GDP of EU.

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RH coefficient

Other method based on Lorentz curve is the maximum vertical distance between this curve and the line of perfect equality (the diagonal line of the unit square). This could be interpreted as the share in total income that should be transferred from rich people (countries) to poor people (countries) in order to obtain the perfect equality. This is the reason that sometimes it is called the Robin Hood coefficient.

RH = max (Pc% - Yc%)

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YearVariation

Coefficient ()

Gini I Coefficient (Ga)

Gini II Coefficient (Gb)

Robin Hood Coefficient (RH)

GDP per capita(in PPS)

- in % -

2000 26.208 18.006 15.794 12.960 19356

2001 25.458 17.508 15.314 12.549 20072

2002 24.208 16.820 14.954 11.943 20736

2003 22.970 16.590 14.584 11.439 21032

2004 22.179 15.980 14.482 11.005 22001

2005 21.622 15.399 14.175 10.740 22855

2006 20.831 15.087 13.605 10.343 24053

2007 19.774 14.780 12.891 9.826 25393

2008 18.506 13.874 12.223 9.205 25426

2009 17.680 13.197 11.718 8.794 23878

2010 18.135 13.605 12.322 8.814 24875

2011 17.998 13.045 12.161 8.679 25544

Values of estimated convergence indicators in EU and GDP per capita, 2000-2011

EU-27 – CONVERGENCE

Dinamics of convergence indicators and GDP per capita in EU, 2000-2011

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 20115

10

15

20

25

30

_yt

Gat

Gbt

RHt

ymt

t

23

EU-27 – CONVERGENCE

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 201217

18

19

20

21

22

23

24

25

26

27

_yPPSt

yPPSmt

t

UE-27- CONVERGENCE in period 2000-2009- STOPING CONVERGENCE in crisis

25

Dinamics of GDP per capita in EU10 and EU15 (% against average EU27 level), 2000-2012

EU10 – 44.5% in 2000 and 62.6% in 2012EU15 – 115.5% in 2000 and 109.5% in 2012

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012404550556065707580859095

100105110115120

yUE10%t

yUE15%t

t

26

Lognormal distribution

Finally, to assess the EU convergence process, we used the assumption of a lognormal distribution function of GDP per capita in the EU, as is otherwise commonly used in literature to study income distribution profile. Thus, to study the distribution of EU GDP in the period 2000-2011, we used the following form of the lognormal function, f, the discrete version:

f ,i t.1

..x ,i t.2 t

e

.1

2

x ,i t t2

t2

t

= 1

n

i

.x ,i t t2

p ,i t

where x = ln (y), y as GDP per capita; = ln (ym), ym as weighed mean of GDP per capita in EU; and dispersion

Lognormal distribution of population in EU by the level of GDP per capita, 2000-2012

0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

f,i 1

f,i 2

f,i 3

f,i 4

f,i 5

f,i 6

f,i 7

f,i 8

f,i 9

f,i 10

f,i 11

f,i 12

,,,,,,,,,,,y,i 1

y,i 2

y,i 3

y,i 4

y,i 5

y,i 6

y,i 7

y,i 8

y,i 9

y,i 10

y,i 11

y,i 12

27

28

Normalised distribution of population in EU by the level of GDP per capita, 2000-2012

1.5 2 2.5 3 3.5 4 4.50

0.1

0.2

0.3

0.4

0.5

f,i 1

f,i 2

f,i 3

f,i 4

f,i 5

f,i 6

f,i 7

f,i 8

f,i 9

f,i 10

f,i 11

f,i 12

,,,,,,,,,,,x,i 1

x,i 2

x,i 3

x,i 4

x,i 5

x,i 6

x,i 7

x,i 8

x,i 9

x,i 10

x,i 11

x,i 12

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 201289

1011121314151617181920212223242526

_yPPSt

yPPSmt

t

EU10- CONVERGENCE in period 2000-2008- STOPING CONVERGENCE in crisis

A3. Differences between EU15 and EU10

EU15- STAGNATION in period 2000-2009- DIVERGENCE în crisis

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 201218

19

20

21

22

23

24

25

26

27

28

29

._yPPSt 3

yPPSmt

t

31

Values of variation coefficient and unemployment rate in EU, 2000-2011 (%)

EU-27 – DIVERGENCEEU-10 – CONVERGENCEEU-15 – DIVERGENCE

YearVariation Coefficient () Unemployment rate

EU-27 EU-10 EU-15 EU-27 EU-10 EU-15

2000 33.556 26.962 34.635 8.110 10.437 7.4812001 33.813 38.268 29.693 7.712 11.151 6.7852002 30.358 37.291 24.419 7.921 11.156 7.0852003 25.223 41.448 19.667 7.937 9.997 7.4262004 19.880 34.864 14.401 7.984 9.869 7.5182005 15.204 38.193 8.538 8.131 8.842 7.9592006 16.718 28.158 13.838 7.583 7.519 7.6052007 17.805 23.111 16.606 6.853 5.699 7.1402008 24.996 15.226 24.377 7.003 5.141 7.4642009 31.011 13.655 30.900 8.799 6.828 9.2872010 30.392 15.943 32.419 9.068 7.739 9.4012011 34.872 14.778 38.616 9.212 7.872 9.543

32

Lorenz curve in case of the export per capita in EU, in 2000 and in 2011

0 10 20 30 40 50 60 70 80 901000

10

20

30

40

50

60

70

80

90

100

EXc%,i 0

Pc%,i 0

Pc%,i 0

0 10 20 30 40 50 60 70 80 901000

10

20

30

40

50

60

70

80

90

100

EXc%,i 11

Pc%,i 11

Pc%,i 11

33

Values of variation coefficient and export per capita in EU-10 and in EU-15, 2000-2011

EU-10 – CONVERGENCEEU-15 – DIVERGENCE

Year

Variation Coefficient (%) Export per capita(in PPS)

UE-10 UE-15 UE-10 UE-15

2000 57.306 31.289 3865 78742001 58.467 29.896 4143 81172002 52.794 31.785 4301 81792003 48.344 33.028 4747 80062004 44.510 35.826 5446 86302005 48.690 37.452 5785 92902006 47.366 38.530 6822 103342007 47.655 40.948 7515 109952008 45.276 41.601 7722 112072009 39.796 41.240 6945 93012010 40.121 42.896 8165 107072011 39.679 43.077 9358 11699

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Values of variation coefficient and ratio export/GDP in EU, 2000-2011 (%)

EU-27 – DIVERGENCEEU-10 – CONVERGENCEEU-15 – DIVERGENCE

YearVariation Coefficient () Ratio export/GDP

EU-27 EU-10 EU-15 EU-27 EU-10 EU-15

2000 30.329 38.424 27.462 36.230 44.886 35.235

2001 29.879 38.262 26.757 36.217 45.441 35.1502002 29.422 32.428 28.354 35.469 44.345 34.418

2003 29.801 27.949 29.250 34.791 46.333 33.4082004 31.796 25.544 31.675 36.178 49.049 34.594

2005 32.970 29.181 33.096 37.471 49.091 36.0152006 34.265 30.344 34.065 39.941 53.466 38.207

2007 35.790 31.963 35.771 40.504 53.261 38.7912008 35.622 31.795 35.840 41.286 52.213 39.748

2009 35.446 27.462 35.746 36.951 48.760 35.2572010 35.511 29.291 35.823 40.977 54.796 38.994

2011 34.816 30.858 34.816 43.972 59.308 41.710

35

Values of variation coefficient and ratio import/GDP in EU, 2000-2011 (%)

EU-27 – DIVERGENCEEU-10 – CONVERGENCEEU-15 – DIVERGENCE

YearVariation Coefficient () Ratio import/GDP

EU-27 EU-10 EU-15 EU-27 EU-10 EU-15

2000 26.689 31.782 23.295 36.434 49.745 34.9372001 27.117 33.738 22.989 35.876 49.530 34.327

2002 26.500 29.049 22.631 34.480 48.104 32.8962003 26.451 25.297 21.540 34.113 50.240 32.199

2004 27.221 22.767 22.123 35.505 52.937 33.3702005 25.683 25.473 22.774 37.098 52.376 35.191

2006 25.610 26.593 23.357 39.936 57.792 37.6532007 26.474 26.301 24.244 40.367 58.212 37.979

2008 26.418 25.447 25.048 41.544 57.619 39.2842009 27.370 23.685 26.423 36.214 49.133 34.350

2010 27.112 24.875 25.845 40.242 55.158 38.0932011 27.661 26.221 26.472 42.972 59.104 40.591

na (y) = (k1*y + k2) / (k3*y + k4)ns (y) = k5*y / (k6 + y)ni (y) = 1 – {[(k1*y + k2) / (k3*y + k4)] + [k5*y / (k6 + y)]} where k1,..., k6 are parameters

Correlation coefficients:y-ns - +0.816y-na - -0.699y-ni - -0.580

Structural changes in EU (EU26, Luxemburg excluded), 2000-2011

5 10 15 20 25 30 350

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

na%_Ei

ni%_Ei

ns%_Ei

na%i

ni%i

ns%i

yi

36

A4. Structural Convergence in EU

37

Share of agriculture in labour force (%) in EU (271 regions), 2010

=min( )na% 0.0

=max( )na% 48.7

10 20 30 40 50 60 70 800

10

20

30

40

50

na%i

na_Ei

na_Li

na_Ui

yPPSi

38

=min( )ni% 7.5

=max( )ni% 46.5

10 20 30 40 50 60 70 800

20

40

60

ni%i

ni_Ei

ni_Li

ni_Ui

yPPSi

Share of industry in labour force (%) in EU (271 regions), 2010

39

10 20 30 40 50 60 70 80

40

60

80

ns%i

ns_Ei

ns_Li

ns_Ui

yPPSi

=min( )ns% 29.4=max( )ns% 92.5

Share of services in labour force (%) in EU (271 regions), 2010

40

Estimated values of convergence indicators in EU and the share of services sector in employment, 2000-2011 (%)

EU-27 – CONVERGENCE

YearVariation

Coefficient ()Gini I

Coefficient (Ga)Gini II

Coefficient (Gb)Robin Hood

Coefficient (RH)Share of services sector

2000 13.961 9.506 9.725 6.981 65.3962001 13.095 9.022 9.210 6.548 66.2092002 12.210 8.369 8.502 6.105 67.2982003 12.030 8.171 8.399 6.015 67.8952004 11.736 7.927 8.164 5.868 68.4952005 11.591 7.814 8.054 5.795 68.8882006 11.239 7.672 7.833 5.619 69.3282007 11.085 7.496 7.777 5.543 69.5262008 10.839 7.432 7.681 5.420 69.8962009 10.612 7.097 7.339 5.306 70.8392010 10.442 7.024 7.197 5.221 71.5092011 10.504 7.123 7.298 5.252 71.798

41

Values of variation coefficient and share of services sector in employment in EU-10 and EU-15, 2000-2011 (%)

EU-10 – CONVERGENCEEU-15 – CONVERGENCE

YearVariation Coefficient () Share of services sector EU-10 EU-15 EU-10 EU-15

2000 18.057 6.896 45.582 70.644

2001 18.916 6.791 47.331 71.088

2002 14.577 6.736 49.694 71.680

2003 15.186 6.698 50.259 72.198

2004 13.078 6.561 51.126 72.722

2005 12.712 6.438 51.642 73.080

2006 11.926 6.275 52.564 73.433

2007 11.923 6.217 52.893 73.634

2008 11.482 5.966 53.175 74.060

2009 11.857 5.500 54.504 74.914

2010 12.471 5.263 55.275 75.539

2011 12.580 5.203 55.122 75.932

42

Values of variation coefficient and share of industrial sector in employment in UE, 2000-2011 (%)

EU-27 – DIVERGENCEEU-10 – CONVERGENCEEU-15 – DIVERGENCE

YearVariation Coefficient () Share of industrial sector

EU-27 EU-10 EU-15 EU-27 EU-10 EU-15

2000 14.662 13.772 15.798 26.082 28.547 25.4322001 15.376 11.272 15.649 26.147 30.060 25.1392002 15.765 8.770 16.018 25.866 30.727 24.6602003 16.130 9.191 16.344 25.432 30.423 24.2182004 16.915 8.024 16.741 25.212 30.960 23.8172005 17.224 7.650 16.937 24.980 30.975 23.5272006 17.499 6.445 16.874 24.886 31.411 23.2912007 17.692 5.832 16.849 24.893 31.838 23.1822008 17.692 5.469 16.418 24.677 32.110 22.8302009 17.934 4.992 15.595 23.744 30.855 21.9732010 18.506 6.196 15.894 23.054 29.833 21.3752011 19.863 6.261 17.327 22.841 30.029 21.064

43

Values of variation coefficient and share of agricultural sector in employment in UE, 2000-2011 (%)

EU-27 – CONVERGENCEEU-10 – DIVERGENCEEU-15 – CONVERGENCE

YearVariation Coefficient () Share of agicultural sector

EU-27 EU-10 EU-15 EU-27 EU-10 EU-15

2000 94.364 43.960 53.286 8.503 25.875 3.8992001 90.241 52.152 54.187 7.638 22.639 3.7572002 85.250 40.906 52.845 6.836 19.577 3.6602003 85.685 45.753 52.004 6.667 19.286 3.5842004 82.575 41.904 49.800 6.304 17.915 3.4742005 82.310 43.678 48.199 6.127 17.393 3.3852006 81.455 43.930 49.207 5.755 16.025 3.2372007 80.409 46.561 47.692 5.568 15.267 3.1702008 79.854 48.143 46.618 5.433 14.731 3.1142009 79.957 49.947 47.219 5.419 14.652 3.1122010 80.745 54.277 48.319 5.467 14.890 3.1232011 82.186 55.113 48.920 5.365 14.868 3.005

B. A non-linear model to simulate optimal convergence in EU1. Empirical evidences in EU compared to the theory

2. A non-linear model to simulate the convergence

3. Applications in case of EU

4. Applications in case of Romania

Taking into account one of the consequences of the standard convergence theory (which states simply that in the long run as income per capita increases its growth rate decreases) and using actual existing data, we are trying to estimate a theoretical (hypothetical) trend optimally with respect to certain rational criteria. Specifically, we impose to the simulation model, which is operating for each constituent entity of a group, the requirement that the total estimated revenue in the last year of a period to be equal to the total actual recorded income in that year or the total estimated income of the group for the whole considered period to be equal to the total actual income of the group for the same period. In this way, the simulation model used to estimate parameters will be subject to actual statistics. After the description of a non-linear theoretical model, we estimate its basic indicators by a recursive procedure, both in case of two groups of countries in EU and in case of Romanian economy composed by eight regions. Moreover, study is extended to focuss on the analyses of the gap between real convergence (divergence) and the optimal trend of convergence.

44

B1. Empirical evidences in EU compared to the theory

For the period 2000-2012, conforming to the grafical representation in the first next Figure, we can see in case of EU a significant negative correlation between GDP per capita (in thousand euro PPS), y, and annual GDP growth rate (computed again on the base of euro PPS), (the value of correlation coefficient was -0.219 in case of EU27 and respectively -0.373 for EU26, by excluding Luxemburg).

Evidently, there is also a strong negative correlation between the individual level of GDP per inhabitant, y, and the ratio between the average level of GDP per capita in EU and the individual level of GDP per capita, h (the value of the correlation coefficient was -0.785 for EU27 and respectively -0.896 for EU26), as is reflected by the graphical representation in the following second Figure.

45

46

Correlation between GDP per capita and annual growth rate in EU26, 2000-2012

5 10 15 20 25 30 35 400.8

1

1.2

1,i t

y,i t

Correlation between GDP per capita and the ratio h in EU26, 2000-2012

5 10 15 20 25 30 35 400

1

2

3

4

1

h,i t

y,i t

For EU27, the values of correlation coefficient between y and and respectively between h and, for the period 2000-2012 are shown in the following Table (for y and h data are referring to years from the period 2000-2011, and for they signify the growth indices for years from the period 2001-2012 against previous year, being equal to the ratio between two consecutive years, Yt / Yt-1).

Derived from correlations in terms of GDP per capita, in terms of GDP growth, the expected signs, according to the “convergence theory” are minus for the first correlation, y - and respectively plus for the second correlation, h- .

We can see how since 2008, beginning of crisis, the above mentioned correlations have some signs non-conforming to the theory (for years 2009 and 2011 in case of the first correlation and for 2009/2008, 2010/2009 and 2012/2011, in case of the second correlation).

47

48

Correlation coefficient (in %) in case of EU, during the period 2000-2012

Year 

Correlation y - Correlation h -

2000(1) -59.260 57.960

2001(2) -36.991 50.573

2002(3) -42.979 61.938

2003(4) -25.714 52.680

2004(5) -41.193 55.971

2005(6) -7.955 48.177

2006(7) -34.473 60.232

2007(8) -34.356 58.920

2008(9) -3.845 -4.798

2009(10) 30.160 -17.510

2010(11) -9.378 37.439

2011(12) 29.595 -26.959

Useful could be the graphical representation of correlation among the three variable used as a rule when the convergence process is analysed, y - h - , which we are presenting at the EU level for years 2000 and 20011 in next Figure.

First graphical representation (left side of Figure) represents a typical convergence process, because higher growth rates, , correspond to lower GDP per capita levels, y, and also to higher values of h.

Controversially, the second graphical representation (right side of Figure) represents a typical divergence process, because higher growth rates, , correspond to higher GDP per capita levels, y, but to lower values of h.

By applying the same methodology, in case of splitting EU in two group of countries resulted as conclusion: a convergence process in the group of less developed countries in EU and a divergence process in the group of advanced countries in EU.

49

50

Correlation y - h - in EU27, for 2000 and 2011

0 10 20 30 40 50

1

2

3

4

1.09

1.08

1.08

1.081.07

1.07

1.06

1.06

1.06

1.06

1.05

1.05

1.05

1.04

1.04

1.04

1.04

1.03

1.03 1.02

,,y2000 h2000 200020 40 60

1

2

1.02

1.02

1.015

1.015

1.011.01

1.01

1.01

1.01

1.005

1.005

1.005

1

1

1

1

0.995

0.995 0.99

0.99

0.99

,,y2011 h2011 2011

B2. A non-linear model to simulate the convergence

Based on main hypotheses of the convergence theory, according to on long run a process of diminishing differences among countries in matter of GDP per capita should exist, and on some empirical evidences, we conceived a non-linear model of simulation.Basic hypothesis of proposed model is referring to the inverse correlation between the growth index, , for a region in a country or a country in a group of countries and its level of income (or GDP) per capita, y. In the same time it is referring to the inverse correlation between the growth index, , for a region in a country or a country in a group of countries and the ratio, g, between its income per capita and average income per capita in country or in group of countries. share its level of income (or GDP) per capita.

Generically, the income (or GDP) index function of two variables can be expressed as follows:  e(ye, ge) = [a/(ye*ge)] + 1 (1)

ore(ye, he) = (a*he/ye) + 1 (2)

where e is the estimated index of income growth, a – a parameter (to be estimated), ye – the estimated level (by the model) of the average income, ge – relative proportion of individual income in average income of the country or of the group of countries, and he=1/ge is the ratio between the average level of income per capita and individual level of income per capita. Note that, based on real data, the values of annual growth index of total income, Y, for each country (region), can be computed, contrary to those estimated above, e, by the following definition relation: = Yt / Yt-1 (3)

from where annual growth rate, r, can be obtained as r = - 1 = (Yt / Yt-1) - 1 (4)

The estimated annual growth rate isre = e - 1 = (Yet / Yet-1) - 1 (5)

where t-1 and t are two consecutive years. 

On real published data the relative gap between the individual income per person in a country (region), y, and average level of it at the level of group of countries (regions), yM, can be expressed by the following ratio

g = y / yM (6)but in case of our model the estimated relative gap, ge, is done by relation

ge = ye / yMe (7)where yMe is the average value a group of countries (regions).

In case of real data, the value of the ratio between the average level at the group of countries (regions) and its individual level for a certain country (region) can be expressed as 

h = yM / y (8) but in case of our simulation model it is done by 

he = yMe / ye (9)

In long run, based on simulation model the resulted dynamics, in line with “Convergence Theory”, shows that at the limit (for very high values of GDP per capita), the values of basic variables for the convergence process demonstrate the following tendencies:tends to 1, decreasing in case of countries (regions) for which y > yM and increasing in case of those countries (regions) for which y < yM;

r tends to 0, decreasing where y > yM and increasing where y < yM;

h tends to 1, increasing in case of countries (regions) for which y > yM and decreasing in case of those for which y < yM;

g will tend also to 1, but increasing where y < yM and decreasing where y > yM.

Based on definition relations for derivate variables (indicators) involved in model and on equation (1), already confirmed by empirical data, using a recurrence process we issued to obtain the following fundamental relation describing the GDP dynamics (or income) for each country (region) inside of its group. Thus, in case of GDP, Y, its dynamics, estimated by proposed simulation model, is done by the following recurrence relation:

Ye,i t

.Ye,i t 1

..aP

,i t 12

Ye,i t 1

2

= 1

n

i

Ye,i t 1

= 1

n

i

P,i t 1

1

(10)

where Ye is estimated GDP, P – total number of population, i – country (region), n – total number of countries (regions), and t is time (years of analysed period or time horizon for simulation). For applications in this study, the base year was considered 2000 for which all values of variables (indicators) are the same as in case of real data.

Finally, based on real registered, by simulation of the model we estimated an optimum value for parameter a. In order to apply the numerical optimisation procedure we take into account two criteria: First imposes that the value of total estimated GDP at the level of the group of countries (regions) for the entire considered period to be equal to that real registered, thus Ye = Y;

Second presumes that the total estimated GDP at the level of the entire group of countries (regions) for the last year of the considered period to be equal to that effectively registered in that year, thus Ye = Y.

B3. Applications in case of EU

Applying our model in case of the group EU27 we obtained following optimal values for parameter a: 0.6610822 in case of first criterion and 0.5850933 in case of second criterion. Few results in case of first criterion are presented as graphical representations in the following Figure (where %y and %ye are variation coefficients, in %, conforming to real data and respectively to estimated data, and years in the period 2000-2012 are denoted on horizontal axe from 0=2000 to 12=2012).

Moreover, we applied the model separately in case of EU10 group and in case of EU15 group. In case of EU10 the estimated optimal values of parameter a are 0.6075593 for the first criterion and respectively 0.5888520 for the second criterion. In case of EU15, the estimated optimal values of parameter a are 0.73976385 for the first criterion and respectively 0.6257640 for the second criterion. Without presenting detailed simulating results, we note here that the proposed model can facilitate achievement of some refined analyses of the economic dynamics, eventually permitting to build a better base for economic policies in EU in order to accelerate the convergence process.

We can see a higher speed of convergence in case of simulating model, reflected by the gap between the two curves representing in Figure the trajectories of variation coefficients for real data and respectively simulated data (the gap between %y - %ye).

We consider useful to compare the real process of convergence within EU10 to those simulated by the model, conforming to the graphical representations in following Figure, where y1% to y10% mean the real ratios (as %) between GDP per capita for each country in the group and the average level of GDP per capita for the entire group, and ye1% to ye10% are the corresponding estimated ratios in case of simulation in order to fulfil the first optimal considered criterion (countries in EU10 are denoted as following:

1 – Bulgaria, 2 – Czech Rep., 3 – Estonia, 4 – Latvia, 5 – Lithuania, 6 – Hungary, 7 – Poland, 8 – România, 9 – Slovenia, and 10 – Slovakia.

Simulation results in case of the first criterion for EU15, 2000-2012 (divergence)

2 3 4 5 6 7 8 9 10 11 12 130

5

10

%yt

%yEt

%Et

t

2 3 4 5 6 7 8 9 10 11 12 1320

25

30

yMt

yMet

t

Simulation results in case of the first criterion for EU10, 2000-2012 (convergence)

2 3 4 5 6 7 8 9 10 11 12 135

10

15

20

yMt

yMet

t

2 3 4 5 6 7 8 9 10 11 12 130

10

20

30

%yt

%yEt

%Et

t

0 1 2 3 4 5 6 7 8 9 10 11 1240

60

80

100

120

140

160

180

y1%t

y2%t

y3%t

y4%t

y5%t

y6%t

y7%t

y8%t

y9%t

y10%t

t0 1 2 3 4 5 6 7 8 9 10 11 12

40

60

80

100

120

140

160

180

ye1%t

ye2%t

ye3%t

ye4%t

ye5%t

ye6%t

ye7%t

ye8%t

ye9%t

ye10%t

t

Real dynamics and simulated dynamics of GDP per capita in EU10 countries, 2000-2012

Simulation results in case of the first criterion for Romania, 2000-2011

B4. Applications in case of Romania

There are 8 regions in Romania. A typical process of divergence

2 3 4 5 6 7 8 9 10 11 120

10

20

30

yMt

yMet

t

2 3 4 5 6 7 8 9 10 11 120

20

40

%yt

%yEt

%Et

t

0 1 2 3 4 5 6 7 8 9 10 1150

100

150

200

250

y1%t

y2%t

y3%t

y4%t

y5%t

y6%t

y7%t

y8%t

t

0 1 2 3 4 5 6 7 8 9 10 1150

100

150

200

ye1%t

ye2%t

ye3%t

ye4%t

ye5%t

ye6%t

ye7%t

ye8%t

t

Real dynamics and simulated dynamics of income per capita in Romania (8 regions), 2000-2011

C. A non-linear model to simulate an optimal convergence in East-Asia1. Empirical evidences in East-Asia

2. Applications in case of East-Asia

3. Conclusions

Similary to the case of EU, we are trying to estimate a theoretical (hypothetical) trend optimally with respect to certain rational criteria in case of South-East Asia. Specifically, we impose to the simulation model, which is operating for each constituent entity of a group, the requirement that the total estimated revenue in the last year of a period to be equal to the total actual recorded income in that year or the total estimated income of the group for the whole considered period to be equal to the total actual income of the group for the same period. In this way, the simulation model used to estimate parameters will be subject to actual statistics. Study is also extended to focuss on the analyses of the gap between real convergence (divergence) and the optimal trend of convergence.

64

C1. Empirical evidences

For the period 1980-2017, conforming to the real published data and IMF forecasts the grafical representation in the first next Figure, we can see the impressive progress of China against all other countries registering a higher share in the Word economy in the first year of this period;

Among selected countries, for China the share in world economy increased by 16.1 percentage points (from 2.2% in 1980 to more than 18% expected in 2017). For all other selected countries (excepting India with +4.3 pp) their share decreased;

Today the average level of GDP per capita in China is close to the average world level and comparable to Eastern countries in EU (between 15-25 thousand PPP dollars per capita);

Among many other factors, we can suggest: structure by age of population (predominant active young population); a huge and continuous effort of saving and investment together with an impressive openness in matter of international trade and international movement of capital; modernisation of economic structure, etc.

65

Dinamics of China’s share in World economy against other major countries, 2000-2017 (%)

66

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

5

10

15

20

25

30

EUt

USt

CHINAt

BRASILt

CANADAt

INDIAt

JAPAN t

MEXICOt

RUSSIAt

t

=EU0 31.250 =EU37 17.160 =EU 14.090

=US0 24.610 =US37 17.740 =US 6.870

=CHINA0 2.186 =CHINA37 18.310 =CHINA 16.124

=BRASIL0 3.936 =BRASIL37 2.854 =BRASIL 1.082

=CANADA0 2.401 =CANADA37 1.578 =CANADA 0.823

=INDIA0 2.526 =INDIA37 6.818 =INDIA 4.292

=JAPAN0 8.797 =JAPAN37 4.793 =JAPAN 4.004

=MEXICO0 2.971 =MEXICO37 2.019 =MEXICO 0.952

=RUSSIA0 5.764 =RUSSIA37 2.966 =RUSSIA 2.798

Distinctive characteristics of China’s economy: A different structure by age of the population especially

against the situation in other developed countries, like EU, but also at the world level (see next Figure);

A large reserve of labour force coming from rural population (close to 50% of population is in rural areas);

High share of agriculture in GDP (10%) and especially in employment (33.6%), as comparing to western countries;

High rate of saving and investment (as average for long period between 40-50%), comparing to 15-25% in EU (2013: 19.2% saving rate and 17.9% investment rate) and to only 10-20% in US (2013: 13.5% saving rate and 15.3% investment rate);

Differences among sectors in matter of labour productivity, comparing to western countries

68

Population Pyramid in China against World economy and EU, 2014

69

Characteristics of China’s economy:

Share in GDP (2013): USA: agriculture – 1.1%; industry – 19.5%; services – 79.4% EU: agriculture – 1.8%; industry – 25.3%; services – 72.9% China: agriculture – 10.0%; industry – 43.9%; services – 46.1%

Share in Labour Force (2013): USA: agriculture – 0.7%; industry – 20.3%; services – 79.0% EU: agriculture – 5.1%; industry – 22.7%; services – 72.2% China: agriculture – 33.6%; industry – 30.3%; services – 36.1%

70

Characteristics of China’s economy:

Share in GDP (2013): USA: household consumption: 68.6%; government consumption: 18.6%;

investment in fixed capital: 15.3%; investment in inventories: 0.4%;

exports (goods&services): 13.4%; imports (goods&services): -16.3% EU: household consumption: 56.9%; government consumption: 21.6%;

investment in fixed capital: 17.9%; investment in inventories: 0.1%;

exports of goods and services: 44.9%; imports of goods and services: -42.9%

China: household consumption: 36.3%; government consumption: 13.7%;

investment in fixed capital: 46%; investment in inventories: 1.2%;

exports of goods and services: 25.1%; imports of goods and services: -22.2%

71

Expected future trends in economic development of China

According to the economic theory and historic empirical evidences, perhaps for China few major trends could be expected in future period, as follows:

Structural changes in economy by decreasing of rural population and of the share of agriculture both in employment and in GDP;

Increasing of household and government consumption in GDP, and as consequence a diminished share of saving and investment in GDP;

Continuing high GDP growth rate (but perhaps to limited rates between 5-8% per year) mainly on the base of rising the general level of productivity and technical progress (TFP);

A high speed in convergence to the global economy in matter of GDP per capita and in living standard for population;

Higher preoccupation for social assurance, conservation of environment and live quality followed by measures to redistribute incomes (and to decrease so-called Gini index).

72

C2. Applications in case of South-East Asia

Applying our model in case of the South-East Asia group of countries, 22 countries (Bangladesh, Bhutan, Brunei, Cambodia, China, Hong Kong, India, Indonesia, Japan, Korea, Lao, Malaysia, Maldives, Mongolia, Myanmar, Nepal, Philippines, Singapore, Sri Lanka, Taiwan, Thailand, and Vietnam), we obtained as optimal value for parameter a 0.280917 in case of first criterion. Few results in case of first criterion are presented as graphical representations in the following Figure (where %y and %yE are variation coefficients, in %, conforming to real data and respectively to estimated data, and years in the period 2000-2012 are denoted on horizontal axe from 0=2000 to 12=2012).

Moreover, we applied the model separately in case of SEA11, group of major countries in region. As example, in case of SEA11 the estimated optimal value of parameter a is 0.301848 for the first criterion. We can see a higher speed of convergence in case of simulating model, reflected by the gap between the two curves representing in Figure the trajectories of variation coefficients for real data and respectively simulated data (the gap between %y - %yE).

Simulation results in case of the first criterion for SEA22, 2000-2012 (convergence)

2 3 4 5 6 7 8 9 10 11 12 132

4

6

8

yMt

yMet

t

2 3 4 5 6 7 8 9 10 11 12 130

50

100

%yt

%yEt

%Et

t

We consider useful to compare the real process of convergence within SEA11 to those simulated by the model, conforming to the graphical representations in following Figure, where y1% to y11% mean the real ratios (as %) between GDP per capita for each country in the group and the average level of GDP per capita for the entire group, and ye1% to ye10% are the corresponding estimated ratios in case of simulation in order to fulfil the first optimal considered criterion (countries in SEA11 are denoted as following:

1 – China, 2 – India, 3 – Indonesia, 4 – Japan, 5 – Korea, 6 – Malaysia, 7 –Philippines, 8 – Singapore, 9 – Taiwan, 10 – Thailand, and 11 – Vietnam.

Simulation results in case of the first criterion for SEA11, 2000-2012 (convergence)

2 3 4 5 6 7 8 9 10 11 12 132

4

6

8

10

yMt

yMet

t

2 3 4 5 6 7 8 9 10 11 12 130

50

100

%yt

%yEt

%Et

t

Real dynamics and simulated dynamics of GDP per capita in SEA11, 2000-2012

0 1 2 3 4 5 6 7 8 9 10 11 120

200

400

600

800

1000

y1%t

y2%t

y3%t

y4%t

y5%t

y6%t

y7%t

y8%t

y9%t

y10%t

y11%t

t

0 1 2 3 4 5 6 7 8 9 10 11 120

200

400

600

800

1000

ye1%t

ye2%t

ye3%t

ye4%t

ye5%t

ye6%t

ye7%t

ye8%t

ye9%t

ye10%t

ye11%t

t

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