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## The International Conference GLOBAL ECONOMY & GOVERNANCE – GEG 2014

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**The International Conference GLOBAL ECONOMY & GOVERNANCE –**GEG 2014 10-12 September 2014, Bucharest, Romania A non-linear model to estimate the long run economic growth in EU and in South-East Asia Lucian-Liviu ALBU Institute 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. 2**A. Real convergence in EU**Spatial distribution of macroeconomic variables in EU Trends in real convergence. How crisis affected convergence in EU Differences between EU-15 and EU-10 Structural convergence in EU B. A non-linear model to simulate an optimal convergence in EU Empirical evidences in EU compared to the theory A non-linear model to simulate the convergence Applications in case of EU Application in case of Romania C. A model to simulate an optimal convergence in South-East Asia Empirical evidences in South-EastAsia Applications of the simulation model in case of South-EastAsia 3**A. Real convergence in EU**Spatial distribution of macroeconomic variables in EU Trends in real convergence. How crisis affected convergence in EU Differences between EU-15 and EU-10 Structural convergence in EU**Spatial distribution of GDP per capita in EU (Malta and**Cyprus excluded), 2012(in PPS, Purchasing Power Standard; UE28=100) A1. Spatial distributionof macroeconomic variables in EU**Spatial distributionin UE ofthe export percapita (in**thousand euro PPS), 2011**Spatial distributionin UE ofthe import percapita (in**thousand euro PPS), 2011**Spatial distributionin EU of the ratio export/GDP (in %),**2011**Spatial distribution in EU of the ratio import/GDP (in %),**2011**Spatial distributionin EU of FDI percapita (in thousand**USD), 2010**Correlation between FDI per capita (y) and GDP per capita**(x) in EU, 2010**A2. Trends in real convergence. How crisis affected**convergence in EU Dinamics of GDP per capita in UE-26, excluding Luxembourg (average level of EU=100), 2000-2011**Convergence indicators:1. Variation coefficient2. Gini I**coefficient, Ga (based on Lorenz curve, by estimating econometrically parametersfor acontinuous function, ye(x), which best approximates Lorenz curve, and its integration onthe 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.**where i = 1, 2,..., n (n=27) areEU countries, and t = 1,**2,..., T (T=12) areyears of theperiod 2000-2011. Coefficient of variation sy = S Vy P / Y where unde sy is coefficient of variation in case of GDP per capita, y, Vy isvariance (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, sy_y are as follows:**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)**Gini coefficient Gb**Other method less precise to estimate Gini coefficient based on Lorentz curve is as follows: 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.**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%)**Values of estimatedconvergence indicators in EU and GDP**percapita, 2000-2011 EU-27 – CONVERGENCE**Dinamicsof convergence indicators andGDP per capitain EU,**2000-2011 EU-27 – CONVERGENCE**UE-27**- CONVERGENCEin period 2000-2009 - STOPING CONVERGENCE in crisis**Dinamicsof GDP per capita in EU10 andEU15 (% against average**EU27 level), 2000-2012 EU10 – 44.5% in 2000 and 62.6% in 2012 EU15 – 115.5% in 2000 and 109.5% in 2012**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: where x = ln (y), y as GDP per capita; m = ln (ym), ym asweighed mean of GDP per capita in EU; and s dispersion**Lognormal distribution of population in EU by the level of**GDP per capita, 2000-2012**Normalised distribution of population in EU by the level of**GDP per capita, 2000-2012**A3. Differences between EU15 and EU10**EU10 - CONVERGENCEin period 2000-2008 - STOPING CONVERGENCE in crisis**EU15**- STAGNATION in period 2000-2009 - DIVERGENCEîn crisis**Values of variation coefficient andunemployment rate in EU,**2000-2011 (%) EU-27 – DIVERGENCE EU-10 – CONVERGENCE EU-15 – DIVERGENCE 31**Lorenz curve in case of the export percapita in EU,in 2000**and in 2011**Values of variation coefficientand export percapita in EU-10**andin EU-15, 2000-2011 EU-10 – CONVERGENCE EU-15 – DIVERGENCE**Values of variation coefficientand ratio export/GDP in EU,**2000-2011 (%) EU-27 – DIVERGENCE EU-10 – CONVERGENCE EU-15 – DIVERGENCE 34**Values of variation coefficientand ratio import/GDP in EU,**2000-2011 (%) EU-27 – DIVERGENCE EU-10 – CONVERGENCE EU-15 – DIVERGENCE 35**A4. Structural Convergencein EU**Structural changes in EU (EU26, Luxemburg excluded), 2000-2011 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 - +0.816 y-na - -0.699 y-ni - -0.580 36**Share of agriculture in labour force(%) in EU (271 regions),**2010 37**Share of industry in labour force(%) in EU (271 regions),**2010 38**Share of services in labour force(%) in EU (271 regions),**2010 39**Estimated values ofconvergence indicators in EUandthe share**of services sector in employment, 2000-2011 (%) EU-27 – CONVERGENCE**Values of variation coefficientand share of services sector**in employment in EU-10 and EU-15, 2000-2011 (%) EU-10 – CONVERGENCE EU-15 – CONVERGENCE**Values of variation coefficientand share of industrial**sector in employmentin UE, 2000-2011 (%) EU-27 – DIVERGENCE EU-10 – CONVERGENCE EU-15 – DIVERGENCE**Values of variation coefficientand share of agricultural**sector in employmentin UE, 2000-2011 (%) EU-27 – CONVERGENCE EU-10 – DIVERGENCE EU-15 – CONVERGENCE**B. A non-linear model to simulate optimal convergence in EU**Empirical evidences in EU compared to the theory A non-linear model to simulate the convergence Applications in case of EU 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),m(the value of correlation coefficient was -0.219 incase 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**Correlation between GDP per capita and annual growth rate in**EU26, 2000-2012 Correlation between GDP per capita and the ratio h in EU26, 2000-2012 46**For EU27, the values of correlation coefficient between y**andmand respectively between h and m, for the period 2000-2012 are shown in the following Table (fory andhdata are referring to years from the period 2000-2011, and formthey signify the growth indices for years from the period 2001-2012 against previous year, mbeing 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 -mand respectively plus for the second correlation,h-m. 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**Correlation coefficient (in %) in case of EU, during the**period 2000-2012**Useful could be the graphical representation of correlation**among the three variable used as a rule when the convergence process is analysed, y - h-m, 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 convergenceprocess, because higher growth rates, m, 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, m, 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