Scenarios of the Romania's economic growth PhD Senior lecturer Nicolae Mihăilescu PhD Senior lecturer Claudia CăpăĠînă PhD Senior lecturer Cristina Burghelea “Hyperion” University - Bucharest

Abstract: The potential economic growth of a country is consistently a primary goal of existence and sustainable development, to ensure the livelihoods of all residents to increase living standards. To achieve this goal it is necessary to undertake complex studies to formulate a correct diagnosis and real of the economic status to substantiate, on this basis, the economic policy decisions and legislative decisions on short term or longer periods of time. In this context, this study presents an analysis of the dynamics of GDP as a synthetic macroeconomic indicator and its structural components by developing econometric models confirmed statistically as viable. Also, levels of forecast character as predictable scenarios are estimated, showing acceptable safety based on sufficiently small significance thresholds. Keywords: gross domestic product, final consumption, gross fixed capital formation, total gross value added, econometric model, trend equation, estimate, forecast. The importance of the "gross domestic product" (GDP) indicator to size the economic potential and economic performance in a territorial space for the State is well known and the approach of this indicator in economic and financial analysis and econometric presents a reasoned understanding through the significance and useful of conclusions offered to substantiate macroeconomic decisions. In the definition given to the concept of gross domestic product states that it is a representative indicator of macroeconomic nature that reflects the sum of the market value of all goods and services for final consumption produced in all branches of economy within a country for a year. It can also specify that GDP is the sum of consumption expenditure of households and private non-profit organizations, gross expenditures for investments, government spending, and investment for storage as export earnings minus the value of the imports. Gross domestic product as an expression of the economic potential of a state is simultaneously the indicator that summarizing the economic growth when its evolution is marked by positive growth rates and is a primary goal of existence and sustainable development. To achieve this goal it is necessary to undertake rigorous studies, complex, to formulate a correct diagnosis and real of the economic status for the economic policy decisions and legislative aimed short horizons but longer periods as well. In this context of the significance and importance of gross domestic product as synthetic macroeconomic indicator and its structural components is justified the realization of complex analysis of the dynamics through the developing of viable models and estimating, on this basis, of the predicted levels, statistically based, by applying of a rigorous methodologies on econometric modeling. The reasons set can provide support for a study to bring useful information to base macroeconomic decisions aimed at fostering real economic progress. The indicators that will be used to develop scenarios for economic growth are: - Gross domestic product - Final consumption - Gross fixed capital formation - Total gross value added From the methodological point of view, the analysis of the econometric scenario of the evolution of an indicator has the following components: 1. Define the econometric model 2. The calculation the econometric indicators 3. Interpretation of the results and the model validation 4. The estimation of the forecast levels The statistical data to develop scenarios proposed are presented in Appendix 1.

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A. Scenario of economical growth on GDP 1. Define the econometric model On the basis of Fig. 1 it is estimated to be sufficient reasons to believe that the gross domestic product in the period 2004-2013 has a development based on the linear tendency equation as mathematically model: y = a + bt. The parameters estimation of the tendency equation chosen is a procedural operation menus by the application of the method of least squares, and the system of equations used for this purpose is: ­ na  b Ȉ t ° Ȉy ° ® °Ȉ yt a Ȉt  bȈt 2 ¯° The estimated values of the parameters "a" and "b" are given in the synoptic picture of the results (Table 1) and define the following mathematical form of GDP trend: y 230 .8467  41 .87697 ˜ t Graphical representation of the gross domestic product of Romania (2004-2013) 700

SER01

600

500

400

300

200 0

1

2

3

4

5

6

7

8

9

10

11

SER02

Figure no. 1 Note: In the Figure no. 1 SER01 is the range of real values of the gross domestic product, and SER02 (t) is the time variable which has conventional values, as follows: 1,2,3,4,5,6,7,8,9,10.

2. The calculation and the graphic representation of the econometric indicators The development and support of the viability of the model is based on a system of indicators of econometric representation which are exposed both in tabular form (Table 2 and Table 3) and the graphics (Fig. 2, Fig. 3 and Fig. 4). The graphic exposing illustrates the comparative positioning of real and estimated levels of GDP in the period 2004-2013 and the disposal of the error term values (residues) in relation to the origin or estimation of the average error of the tendency equation (regression). Also, the interpretation hypotheses of the model quality of the parameters of tendency equation and residues are formulated and verified (the situation of autocorrelation of the residues variants, the normality of the residual variable distribution, the state of the residues homoscedasticity). Table no. 1 Synoptic picture of the results that characterize the econometric linear model of the evolution of gross domestic product Dependent Variable: SER01: GDP Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Tendency equation: y = 230.8467 + 41.87697 t Variable Coefficient Std. Error t-Statistic Prob. SER02 41.87697 3.591212 11.66096 0.0000 C 230.8467 22.28289 10.35982 0.0000 R-squared 0.944436 Mean dependent var 461.1700

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Adjusted R-squared 0.937490 S.D. dependent var 130.4652 S.E. of regression 32.61881 Akaike info criterion 9.984512 Sum squared resid 8511.892 Schwarz criterion 10.04503 Log likelihood -47.92256 F-statistic 135.9779 Durbin-Watson stat 0.935816 Prob(F-statistic) 0.000003 Note: The indicators presented in synoptic picture of the results were obtained using Eviews software Graphical representation of the evolution of GDP: the real data (Actual), estimated data (Fitted) and values of residual term (Residual) 700 600 500 400

80

300 40

200

0

-40 04

05

06

07

08

Residual

09

10

Actual

11

12

13

Fitted

Figure no. 2 Table no. 2 Series of real levels of the estimated levels on GDP and the margin of residual term Actual Fitted Residual Plot Residual r Vˆ ˆ r 32.61881 .y y y yˆ u y  yˆ

obs

 Vˆ y . yˆ

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

247.400 289.000 344.700 416.000 514.700 501.100 523.700 557.300 586.700 631.100

272.724 314.601 356.478 398.355 440.232 482.108 523.985 565.862 607.739 649.616

-25.3236 -25.6006 -11.7776 17.6455 74.4685 18.9915 -0.28545 -8.56242 -21.0394 -18.5164

| | | | | | | | | |

0

 Vˆ y . yˆ

.* | . .* | . . *| . . | *. . | . . | *. . * . . *| . .* | . .* | .

| | | | *| | | | | |

Statistical description and the test for normality of the distribution of the residual variable in case of the trend expressed by the equation for GDP estimation 6 Series: Residuals Sample 2004 2013 Observations 10

5 4

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

3 2 1

Jarque-Bera Probability

0 -50

-25

0

25

50

-1.92E-14 -10.17000 74.46848 -25.60061 30.75331 1.507523 4.438660 4.650102 0.097778

75

Figure no. 3

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Table no. 3 The synoptic picture of the "White Heteroskedasticity Test" to verify the hypothesis of heteroscedasticity of residual variable in case of the linear model of GDP trend White Heteroskedasticity Test: F-statistic 0.381227 Probability 0.696381 Obs*R-squared 0.982232 Probability 0.611943 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C -183.9818 2107.097 -0.087315 0.9329 SER02 630.2295 880.0127 0.716160 0.4971 SER02^2 -63.14523 77.96582 -0.809909 0.4446 R-squared 0.098223 Mean dependent var 851.1892 Adjusted R-squared -0.159427 S.D. dependent var 1663.794 S.E. of regression 1791.518 Akaike info criterion 18.06284 Sum squared resid 22466760 Schwarz criterion 18.15361 Log likelihood -87.31420 F-statistic 0.381227 Durbin-Watson stat 2.443932 Prob(F-statistic) 0.696381

Graphical representation of the estimated gross domestic product (SER01F) based on linear tendency equation and the limits witch places them within of r2,306 estimations of the average error conditions of tendency equation (based on the Student distribution law with bilateral disposal of significance level) for a significance level of 5% and 8 degrees of freedom 800 Forecast: SER01F Actual: SER01 Forecast sample: 2004 2013 Included observations: 10

700 600

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

500 400 300 200

29.17515 22.22109 5.312196 0.030579 0.000000 0.014291 0.985709

100 04

05

06

07

08

09

10

11

12

13

SER01F

Figure no. 4

where r tq = 0.05; f = 10-2 = r 2.306, is the critical value or the probability factor. Note: In Fig. 4 the limits of the confidence interval which include the estimated levels of the GDP in terms of a limit error, or the maximum permitted by r2 .306 ˜ 32.61881 r75 .21897586 , are calculated as follows:

Upper limit: ls = yˆ  2 . 306 ˜ 32 . 61881 Lower limit: li = yˆ  2 . 306 ˜ 32 . 61881 where the probability factor (the critical value), r tq = 0.05; f = 10-2 = r 2.306, is extracted from the table with the values of the Student distribution law, for a significance level of 5% and 8 degrees of freedom.

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3. Interpretation of the results and the model validation The calculations allow us to retain the linear model of gross domestic product trend of Romania in the period 2004-2013 with a certificate of viability acceptable. In support of this assessment are the following results: 1 - Under the "Criterion t" the parameters of trend equation have significantly different sizes from zero because the null hypothesis verification of each parameter is estimated by significance level below of 5%. It states that through the null hypothesis verification was refuted the insignificant nature of the difference between the estimated value of each parameter in the trend equation and the size zero (Table 1). It identifies, for each parameter, the following inequality, tstatistic > ttabelar, where ttabelar = tq; f = n-k = tq = 0,05; f = 10-2 = 2.306, corresponding to a minimum probability of 95% (the significance level: q = 0.05 is willing bilateral) and 8 degrees of freedom under the law of Student distribution. By this finding is concluded that the model was specified correctly, identified and estimated, the parameters of trend equation show a good efficiency if the linear model is used for the evolution extrapolating to calculate the expected estimation of the gross domestic product for the next time segments. 2 – The test of normality of the residual variable distribution (Jarque-Bera test) refutes the hypothesis of the existence of a significant similarities between the empirical distribution and the theoretical normal distribution (Gauss-Laplace), because to the statistical coefficient J-B = 4.650102 a probability of 9.7778 % is assigned, based on the law of distribution hi square with 2 degrees of freedom (Fig. 3). This statistical finding induces a specific vulnerability of the linear model of the GDP evolution which could be eliminated by increasing the number of observations. 3 - "The statistical coefficient - Durbin - Watson" through its size, DW = 0.935816, (shown in Table 1) reveal the existence of the autocorrelation phenomenon of the error term variants and thereby the risk of correct interpretation of the significance of the estimated values of the trend equation parameters of linear model. If we use "Durbin-Watson distribution table" with significance level q = 0.05, for n = 10 úi k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: 1.320 > (DW = 0.935816) < 4 – 1.320 = 2.680 4 - The relative expression of standard error estimation of the equation of linear trend compared to the GDP average value is 7.07%, a convenient size, positioned below a limit of 10%, to consider the linear model as viable. There is the statistical opportunity to consider that the modeling of GDP dynamic series in the period 2004-2013, through a linear model may present practical use to estimate future levels of the gross domestic product of Romania. 5 - "The coefficient of irregularity (inequality) of Theil" (Fig. 4) reconfirms by its size, Th = 3.0579%, the conclusion offered by the relative form of standard error estimation of the trend equation. The linear model of trend equation is considered as viable and can be considered that there are statistically reasons to consider that acceptable formalizes the GDP evolution and trend. 6 – The White test (Table 3) confirms the stationary of dynamic series (the series is homoscedastic), both in terms of Criterion F and hi square Criterion which supports the linear model sustainability. In light of the results and the conclusions drawn is obtain the statistical motivation to calculate the sustainable estimates of GDP levels which will be recorded in the future time segments.

4. The estimation of the forecast levels The probable levels of GDP in 2014 and 2015 shall be estimated by calculating confidence intervals taking into account a limited error corresponding to a probability of 95%. The probability factor (critical value) "t" is, in this case of r2.306 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: r t q 0.05; f n  k 10  2 8 ˜ ıˆ y; yˆ r 2.306 ˜ 32.61881 75.21895 billion lei The punctual value of GDP estimation for 2014:

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Y2014

230.8467  41.87697 ˜ 11 691.49337 billion lei Lower limit: li

691.49337 - 75.21895

616.27442 billion lei

Upper limit: l s 691.49337  75.21895 766.71232 billion lei The punctual value of GDP estimation for 2015: Y2015

230.8467  41.87697 ˜ 12

733.37034 billion lei

Lower limit: li

733.37034 - 75.21895

Upper limit: l s

733.37034  75.21895 808.58929 billion lei

658.15139 billion lei

B. Scenario of economical growth on the final consumption

1. Define the econometric model The graphical representation of Fig. 5, through the arrangement of waypoints offers the opportunity to appreciate that it is sufficient reason to believe that the final consumption growth in the period 2004-2013 has as mathematically model the linear trend equation: y = a + bt. The parameter values of the selected trend equation are estimated by the method of the least squares (the values are presented in synoptic picture of the results - Table 4). The system of equations used for this purpose is: ­ na  b Ȉ t ° Ȉy ° ® °Ȉ yt a Ȉt  bȈt 2 ¯° and the model which formalizing mathematical and summarizes the statistical lawfulness of the final consumption trend is: y 210 .3533  29 .65758 ˜ t Graphical representation of the final consumption of Romania (2004-2013) 500 450

SER01

400 350 300 250 200 0

1

2

3

4

5

6

7

8

9

10

11

SER02

Figure no. 5 Note: In the Figure no. 5 SER01 is the range of real values of the final consumption, and SER02 (t) is the time variable which has conventional values, as follows: 1,2,3,4,5,6,7,8,9,10.

2. The calculation and the graphic representation of the econometric indicators The viability of the linear model of final consumption is based on a system of econometric indicators which are presented as a systematization table (Table 4, Table 5 and Table 6) and by graphical representations (Fig. 6, Fig. 7 and Fig. 8). The graphic exposures offer the opportunity to state its comparative position of the real levels and estimated of the final consumption during the period 20042013 and the layout of the error term values (residues) with respect to the origin or average error estimation of the tendency equation (regression). Also in the context of these statistical determinations are formulated and tested the hypotheses of quality model interpretation, of tendency equation

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parameters and residues (autocorrelation phenomenon of the variants of residues, the normality of the residual variable distribution, the state of residues homoscedasticity). Table no. 4 Synoptic picture of the results that characterize the econometric linear model of the final consumption trend Dependent Variable: SER01: Consumul final Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Tendency equation: y = 210.3533 + 29.65758 t Variable Coefficient Std. Error t-Statistic Prob. SER02(variabila timp) 29.65758 3.082971 9.619805 0.0000 C 210.3533 19.12933 10.99638 0.0000 R-squared 0.920430 Mean dependent var 373.4700 Adjusted R-squared 0.910484 S.D. dependent var 93.59355 S.E. of regression 28.00247 Akaike info criterion 9.679319 Sum squared resid 6273.108 Schwarz criterion 9.739836 Log likelihood -46.39660 F-statistic 92.54064 Durbin-Watson stat 0.859339 Prob(F-statistic) 0.000011 Note: The indicators presented in synoptic picture of the results were obtained using Eviews software Graphical representation of the final consumption trend: the real data (Actual), estimated data (Fitted) and values of residual term (Residual) 600 500 400

80 60

300

40 200

20 0 -20 -40 04

05

06

07

08

Residual

09 Actual

10

11

12

13

Fitted

Figure no. 6 Table no. 5 Series of real levels of the estimated levels on final consumption and the margin of residual term obs

Actual

Fitted

y

yˆ

Residual u

y  yˆ

r Vˆ

Residual Plot

r 28.00247

y . yˆ

 Vˆ y . yˆ 2004 2005 2006 2007 2008 2009 2010

84

211.100 251.000 294.900 344.900 420.900 404.300 419.800

240.011 269.668 299.326 328.984 358.641 388.299 417.956

-28.9109 -18.6685 -4.42606 15.9164 62.2588 16.0012 1.84364

| | | | | | |

0

 Vˆ y . yˆ

*. | . .* | . . *| . . | *. . | . . | *. . * .

| | | | *| | |

Romanian Statistical Review - Supplement nr. 3 / 2015

2011 2012 2013

437.400 461.900 488.500

447.614 477.272 506.929

-10.2139 -15.3715 -18.4291

| | |

. *| . .* | . .* | .

| | |

Statistical description and the test for normality of the distribution of the residual variable in case of the trend expressed by the equation for final consumption estimation 6 Series: Residuals Sample 2004 2013 Observations 10

5

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

4 3 2 1

Jarque-Bera Probability

0 -50

-25

0

25

50

-4.69E-14 -7.320000 62.25879 -28.91091 26.40098 1.322232 4.105743 3.423275 0.180570

75

Figure no. 7 Table no. 6 The synoptic picture of the "White Heteroskedasticity Test" to verify the hypothesis of heteroscedasticity of residual variable in case of the linear model of the final consumption trend White Heteroskedasticity Test: F-statistic 0.277438 Probability 0.765680 Obs*R-squared 0.734461 Probability 0.692650 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C 167.1965 1495.944 0.111767 0.9141 SER02 327.6088 624.7692 0.524368 0.6162 SER02^2 -34.85023 55.35220 -0.629609 0.5489 R-squared 0.073446 Mean dependent var 627.3108 Adjusted R-squared -0.191284 S.D. dependent var 1165.317 S.E. of regression 1271.897 Akaike info criterion 17.37773 Sum squared resid 11324049 Schwarz criterion 17.46851 Log likelihood -83.88866 F-statistic 0.277438 Durbin-Watson stat 2.379141 Prob(F-statistic) 0.765680

Graphical representation of the estimated final consumption (SER01F) based on linear tendency equation and the limits witch places them within of r2,306 estimations of the average error conditions of tendency equation (based on the Student distribution law with bilateral disposal of significance level) for a significance level of 5% and 8 degrees of freedom

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600 Forecast: SER01F Actual: SER01 Forecast sample: 2004 2013 Included observations: 10

500

400

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

300

200

25.04617 19.20400 5.587303 0.032657 0.000000 0.020726 0.979274

100 04

05

06

07

08

09

10

11

12

13

SER01F

Figure no. 8

Note: In Fig. 8 the limits of the confidence interval which include the estimated levels of the final consumption in terms of a limit error, or the maximum permitted by are calculated as follows: Upper limit: ls = yˆ  2 . 306 ˜ 28 . 00247 Lower limit: li = yˆ  2 . 306 ˜ 28 . 00247 where r tq = 0.05; f = 10-2 = r 2.306 is the critical value or the probability factor.

3. Interpretation of the results and the model validation The calculations allow us to retain the linear model of final consumption trend of Romania in the period 2004-2013 with a certificate of viability acceptable. In support of this assessment are the following results: 1 - Under the "Criterion t" the parameters of trend equation have significantly different sizes from zero because the null hypothesis verification of each parameter is estimated by significance level below of 5%. It states that through the null hypothesis verification was refuted the insignificant nature of the difference between the estimated value of each parameter in the trend equation and the size zero (Table 4). It identifies, for each parameter, the following inequality, tstatistic > ttabelar, where ttabelar = tq; f = n-k = tq = 0,05; f = 10-2 = 2.306, corresponding to a minimum probability of 95% (the significance level: q = 0.05 is willing bilateral) in accordance with the law of Student distribution. By this finding is concluded that the model was specified correctly, identified and estimated, the parameters of trend equation show a good efficiency if the linear model is used for the evolution extrapolating to calculate the expected estimation of the final consumption for the next time segments. 2 – The test of normality of the residual variable distribution (Jarque-Bera test) refutes the hypothesis of the existence of a significant similarities between the empirical distribution and the theoretical normal distribution (Gauss-Laplace), because to the statistical coefficient J-B = 3.423275 a probability of 18.057% is assigned, based on the law of distribution hi square with 2 degrees of freedom. This statistical finding induces a specific vulnerability of the linear model of the final consumption evolution (Fig. 7). 3 - "The statistical coefficient - Durbin - Watson" through its size, DW = 0.859339, (shown in Table 4) reveal the existence of the autocorrelation phenomenon of the error term variants and thereby the risk of correct interpretation of the significance of the estimated values of the trend equation parameters of linear model. If we use "Durbin-Watson distribution table" with significance level q = 0.05, for n = 10 úi k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: 1.320 > (DW = 0.859339) < 4 – 1.320 = 2.680

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4 - The relative expression of standard error estimation of the equation of linear trend compared to the final consumption average value is 7.4979%, a convenient size, positioned below a limit of 10%, to consider the linear model as viable. There is the statistical opportunity to consider that the modeling of final consumption dynamic series in the period 2004-2013, through a linear model may present practical use to estimate future levels of the final consumption of Romania. 5 - "The coefficient of irregularity (inequality) of Theil" (Fig. 8) reconfirms by its size, Th = 3.2657%, the conclusion offered by the relative form of standard error estimation of the trend equation. The linear model of trend equation is considered as viable and formalizes acceptable the final consumption evolution and trend. 6 – The White test (Table 6) offers the possibility of statistical appreciation that the dynamic series of final consumption is characterized by a stationarity (the series is homoscedastic), both in terms of Criterion F and hi square Criterion which supports the linear model sustainability. In light of the results and the conclusions drawn is obtain the statistical support to calculate the sustainable estimates of final consumption levels which will be recorded in the future time segments.

4. The estimation of the forecast levels The probable levels of final consumption in 2014 and 2015 shall be estimated by calculating confidence intervals taking into account a limited error corresponding to a probability of 95%. The probability factor (critical value) "t" is, in this case of r2.306 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error:

rtq

0.05; f n  k 10  2 8

˜ ıˆ y; yˆ

r 2.306 ˜ 28.00247

64.5736958 billion lei

The punctual value of final consumption estimation for 2014: Y2014 210.3533  29.65758 ˜ 11 536.58668 billion lei Lower limit: li

536.58668 - 64.5736958 472.0129842 billion lei

Upper limit: l s 536.58668  64.5736958 601.1603758 billion lei The punctual value of final consumption estimation for 2015: Y2015

210.3533  29 . 65758 ˜ 12

566.24426 billion lei

Lower limit: li

566.24426 - 64.5736958 501.6705642 billion lei

Upper limit: l s

566.24426  64.5736958

630.8179558 billion lei

C. Scenario of economical growth on the gross fixed capital formation

1. Define the econometric model The graphical representation of Fig. 9 offers the opportunity to appreciate that it is sufficient reason to believe that the gross fixed capital formation growth in the period 2004-2013 has as mathematically model the linear trend equation: y = a + bt. The parameter values of the selected trend equation are estimated by the method of the least squares (the values are presented in synoptic picture of the results - Table 7). The system of equations used for this purpose is: ­ na  b Ȉ t ° Ȉy ° ® °Ȉ yt a Ȉt  bȈt 2 °¯ and the model which formalizing mathematical and summarizes the statistical lawfulness of the gross fixed capital formation trend is:

y

63 .97333  10 .12121 ˜ t

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Graphical representation of the dynamics of gross fixed capital formation of Romania (2004-2013) 180 160

SER01

140 120 100 80 60 40 0

1

2

3

4

5

6

7

8

9

10

11

SER02

Figure no. 9 Note: In the Figure no. 9 SER01 is the range of real values of the gross fixed capital formation, and SER02 (t) is the time variable which has conventional values, as follows: 1,2,3,4,5,6,7,8,9,10.

The graphics offer the possibility to be observed the comparative position of real and estimated levels of gross fixed capital formation during the period 2004-2013 and layout the error term values (residues) with respect to the origin or the average error estimation of trend equation (regression). Also in the context of these statistical determinations hypotheses of quality model interpretation, trend equation parameters and residues (autocorrelation phenomenon of residues variants, normality of the residual variable distribution, and homoscedasticity of residues) are formulated and tested.

2. The calculation and the graphic representation of the econometric indicators The linear model of gross fixed capital formation is subject to viability analysis based on a system of econometric representation indicators which are presented as a systematization table (Table 7, Table 8 and Table 9) and the graphics (Fig. 10, Fig. 11 and Fig. 12). The graphic features can be observed visually comparative position of actual and projected levels of gross fixed capital formation during the period 2004-2013 and layout error values (residues) with respect to the origin or the average error estimation equation trend (regression). Also in the context of these determinations statistical hypotheses are formulated and tested quality interpretation model, trend equation parameters and residues (autocorrelation phenomenon variants situation residues, normality distribution of the residual variable, state homoscedasticitate residues). Table no. 7 Synoptic picture of the results that characterize the econometric linear model of the gross fixed capital formation trend Dependent Variable: SER01: Formarea brută de capital fix Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Tendency equation: y = 63.97333 + 10.12121 t Variable Coefficient Std. Error t-Statistic Prob. SER02 (variabila timp) 10.12121 2.484373 4.073950 0.0036 C 63.97333 15.41513 4.150036 0.0032 R-squared 0.674758 Mean dependent var 119.6400 Adjusted R-squared 0.634103 S.D. dependent var 37.30476 S.E. of regression 22.56544 Akaike info criterion 9.247572 Sum squared resid 4073.592 Schwarz criterion 9.308089 Log likelihood -44.23786 F-statistic 16.59707 Durbin-Watson stat 1.182069 Prob(F-statistic) 0.003564 Note: The indicators presented in synoptic picture of the results were obtained using Eviews software

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Graphical representation of the gross fixed capital formation trend: the real data (Actual), estimated data (Fitted) and values of residual term (Residual) 200 160 60

120

40

80

20

40

0 -20 -40 04

05

06

07

08

09

Residual

10

Actual

11

12

13

Fitted

Figure no. 10

obs

Table no. 8 Series of real levels of the estimated levels on gross fixed capital formation and the margin of residual term Actual Fitted Residual Residual Plot y yˆ u y  yˆ r Vˆ ˆ r 22.56544 y. y

 Vˆ y . yˆ 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

53.9000 68.5000 88.3000 125.600 164.300 122.400 129.400 145.200 154.300 144.500

74.0945 84.2158 94.3370 104.458 114.579 124.701 134.822 144.943 155.064 165.185

-20.1945 -15.7158 -6.03697 21.1418 49.7206 -2.30061 -5.42182 0.25697 -0.76424 -20.6855

| | | | | | | | | |

0

* | .* | . *| . | . | . *| . *| . * . * * |

 Vˆ y . yˆ . . . * . . . . . .

| | | | *| | | | | |

Statistical description and the test for normality of the distribution of the residual variable in case of the trend expressed by the equation for the gross fixed capital formation trend 5 Series: Residuals Sample 2004 2013 Observations 10

4

3

2

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

4.26E-15 -3.861212 49.72061 -20.68545 21.27490 1.350142 4.051961

Jarque-Bera Probability

3.499229 0.173841

1

0 -30

-20

-10

0

10

20

30

40

50

Figure no. 11

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Table no. 9 The synoptic picture of the "White Heteroskedasticity Test" to verify the hypothesis of heteroscedasticity of residual variable in case of the linear model of the gross fixed capital formation trend White Heteroskedasticity Test: F-statistic 0.260272 Probability 0.777984 Obs*R-squared 0.692162 Probability 0.707455 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C 100.0508 965.1744 0.103661 0.9203 SER02 211.4113 403.0975 0.524467 0.6161 SER02^2 -22.21958 35.71292 -0.622172 0.5535 R-squared 0.069216 Mean dependent var 407.3592 Adjusted R-squared -0.196722 S.D. dependent var 750.1459 S.E. of regression 820.6205 Akaike info criterion 16.50132 Sum squared resid 4713926. Schwarz criterion 16.59210 Log likelihood -79.50662 F-statistic 0.260272 Durbin-Watson stat 2.280120 Prob(F-statistic) 0.777984

Graphical representation of the estimated gross fixed capital formation (SER01F) based on linear tendency equation and the limits witch places them within of r2,306 estimations of the average error conditions of tendency equation (based on the Student distribution law with bilateral disposal of significance level) for a significance level of 5% and 8 degrees of freedom 240 Forecast: SER01F Actual: SER01 Forecast sample: 2004 2013 Included observations: 10

200 160

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

120 80 40

20.18314 14.22388 13.53980 0.081421 0.000000 0.098034 0.901966

0 04

05

06

07

08

09

10

11

12

13

SER01F

Figure no. 12

Note: In Fig. 12 the limits of the confidence interval which include the estimated levels of the gross fixed capital formation in terms of a limit error, or the maximum permitted by r 2.306 ˜ 22.56544 52 .03590464 , are calculated as follows: Upper limit: ls = yˆ  2 . 306 ˜ 22.56544 Lower limit: li = yˆ  2 . 306 ˜ 22.56544 where r tq = 0.05; f = 10-2 = r 2.306, is the critical value or the probability factor.

3. Interpretation of the results and the model validation The calculations allow us to retain the linear model of gross fixed capital formation trend of Romania in the period 2004-2013 with a certificate of relative viability, but acceptable. In support of this assessment are the following results: 1 - Under the "Criterion t" the parameters of trend equation have significantly different sizes from zero because the null hypothesis verification of each parameter is estimated by significance level

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below of 5%. It states that through the null hypothesis verification was refuted the insignificant nature of the difference between the estimated value of each parameter in the trend equation and the size zero (Table 7). It identifies, for each parameter, the following inequality, tstatistic > ttabelar, where ttabelar = tq; f = n-k = tq = 0,05; f = 10-2 = 2.306, corresponding to a minimum probability of 95% (the significance level: q = 0.05 is willing bilateral) in accordance with the law of Student distribution. By this finding is concluded that the model was specified correctly, identified and estimated, the parameters of trend equation show a good efficiency if the linear model is used for the evolution extrapolating to calculate the expected estimation of the gross fixed capital formation for the next time segments. 2 – The test of normality of the residual variable distribution (Jarque-Bera test) refutes the hypothesis of the existence of a significant similarities between the empirical distribution and the theoretical normal distribution (Gauss-Laplace), because to the statistical coefficient J-B = 3.499229 a probability of 17.3841% is assigned, based on the law of distribution hi square with 2 degrees of freedom (Fig. 11). This statistical finding induces a specific vulnerability of the linear model of the gross fixed capital formation evolution. 3 - "The statistical coefficient - Durbin - Watson" through its size, DW = 1.182069, (shown in Table 7) reveal the existence of the autocorrelation phenomenon of the error term variants and thereby the risk of correct interpretation of the significance of the estimated values of the trend equation parameters of linear model. If we use "Durbin-Watson distribution table" with significance level q = 0.05, for n = 10 úi k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: 1.320 > (DW = 1.182069) < 4 – 1.320 = 2.680 4 - The relative expression of standard error estimation of the equation of linear trend compared to the gross fixed capital formation average value is 18.861%, an inconvenient size, positioned below a limit of 10%, to consider the linear model fully viable. For statistical expression of the dynamic series of gross fixed capital formation of Romania in the period 2004-2013, through a linear model allows us to see that the relative form of the standard error estimation of the trend equation has a size which is positioned at a level that motivates us to consider that the model may show some weaknesses when is used to estimate future levels of gross fixed capital formation of Romania. 5 - "The coefficient of irregularity (inequality) of Theil" (Fig. 12) reconfirms by its size, Th = 8.1421%, the conclusion offered by the relative form of standard error estimation of the trend equation. The linear model of trend equation is affected by a reduced econometric viability if is used in calculating the expected levels of gross fixed capital formation in future time segments. A solution to improve this result can be considered only if the number of observations will be increased. 6 – The White test (Table 9) offers the possibility of statistical appreciation that the dynamic series of gross fixed capital formation is characterized by a stationarity (the series is homoscedastic), both in terms of Criterion F and hi square Criterion which supports the linear model sustainability. In light of the results and the conclusions drawn is obtain the statistical support necessary to calculate the sustainable estimates of the predicted levels on gross fixed capital formation which will be recorded in the future time segments.

4. The estimation of the forecast levels The probable levels of gross fixed capital formation in 2014 and 2015 shall be estimated by calculating confidence intervals taking into account a limited error corresponding to a probability of 95%. The probability factor (critical value) "t" is, in this case of r2.306 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error:

r t q 0.05; f n  k 10  2 8 ˜ ıˆ y; yˆ

r 2.306 ˜ 22.56544

52.0359046 billion lei

The punctual value of gross fixed capital formation estimation for 2014: Y2014 63.9733  10.12121 ˜ 11 175.30661 billion lei

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Lower limit: li

175.30661 - 52.0359046 123.2707054 billion lei

Upper limit: l s 175.30661  52.0359046 227.3425146 billion lei The punctual value of gross fixed capital formation estimation for 2015: Y2015 63.9733  10.12121 ˜ 12 185.42782 billion lei Lower limit: li

185.42782 - 52.0359046 133.3919154 billion lei

Upper limit: l s

185.42782  52.0359046

237.4637246 billion lei

D. Scenario of economical growth on the total gross value added

1. Define the econometric model

The graphical representation of Fig. 13 offers the opportunity to appreciate that it is sufficient reason to believe that the total gross value added growth in the period 2004-2013 has as mathematically model the linear trend equation: y = a + bt. The parameter values of the selected trend equation are estimated by the method of the least squares (the values are presented in synoptic picture of the results - Table 10). The system of equations used for this purpose is: ­ na  b Ȉ t ° Ȉy ° ® °Ȉ yt a Ȉt  bȈt 2 ¯° and the model which formalizing mathematical and summarizes the statistical lawfulness of the total gross value added trend is: y 207 .8200  36 .37273 ˜ t Graphical representation of the total gross value added of Romania (2004-2013) 560 520 480

SER01

440 400 360 320 280 240 200 0

1

2

3

4

5

6

7

8

9

10

11

SER02

Figure no. 13 Note: In the Figure no. 13 SER01 is the range of real values of the total gross value added, and SER02 (t) is the time variable which has conventional values, as follows: 1,2,3,4,5,6,7,8,9,10.

2. The calculation and the graphic representation of the econometric indicators The linear model of the total gross value added is subjected to further analysis of viability which is based on a system of indicators of econometric representation which are presented as a systematization table (Table 10, Table 11 and Table 12) and by graphic representation (Fig. 14, Fig. 15 and Fig. 16). There is undeniably the practical utility of the graphic that offers the opportunity to visually the comparative position of real and estimated levels of total gross value added in the period 2004-2013 and the arrangement of the values of the error term (residue) related to the origin or with the average

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error estimation of the tendency equation (regression). Also in the context of these statistical determinations are formulated and verified the hypotheses of interpretation of the econometric model quality, of the tendency equation parameters and residues (the autocorrelation phenomenon of residues variants, the normality of the residual variable distribution, the state of residues homoscedasticity). Table no. 10 Synoptic picture of the results that characterize the econometric linear model of the total gross value added trend Dependent Variable: SER01: Valoarea adăugată brută totală Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Tendency equation: y = 207.8200 + 36.37273 t Variable Coefficient Std. Error t-Statistic Prob. SER02 (variabila timp) 36.37273 3.460517 10.51078 0.0000 C 207.8200 21.47195 9.678675 0.0000 R-squared 0.932476 Mean dependent var 407.8700 Adjusted R-squared 0.924036 S.D. dependent var 114.0415 S.E. of regression 31.43171 Akaike info criterion 9.910368 Sum squared resid 7903.620 Schwarz criterion 9.970885 Log likelihood -47.55184 F-statistic 110.4764 Durbin-Watson stat 0.833758 Prob(F-statistic) 0.000006 Note: The indicators presented in synoptic picture of the results were obtained using Eviews software

Graphical representation of the total gross value added trend: the real data (Actual), estimated data (Fitted) and values of residual term (Residual) 600 500 400

80 60

300

40 200

20 0 -20 -40 04

05

06

07

Residual

08

09 Actual

10

11

12

13

Fitted

Figure no. 14

obs

Table no. 11 Series of real levels of the estimated levels on total gross value added and the margin of residual term Actual Fitted Residual Residual Plot y yˆ u y  yˆ r Vˆ ˆ r 31.43171 y. y

 Vˆ y . yˆ 2004 2005 2006 2007 2008 2009

220.900 255.200 304.300 368.400 458.500 451.000

244.193 280.565 316.938 353.311 389.684 426.056

-23.2927 -25.3655 -12.6382 15.0891 68.8164 24.9436

| | | | | |

0

 Vˆ y . yˆ

.* | . .* | . . *| . . | *. . | . . | *.

Revista Română de Statistică - Supliment nr. 3 / 2015

| | | | *| |

93

2010 2011 2012 2013

466.400 487.700 512.100 554.200

462.429 498.802 535.175 571.547

3.97091 -11.1018 -23.0745 -17.3473

| | | |

. |* . *| .* | .* |

. . . .

| | | |

Statistical description and the test for normality of the distribution of the residual variable in case of the trend expressed by the equation for the total gross value added trend 6 Series: Residuals Sample 2004 2013 Observations 10

5 4

Mean Median Maximum Minimum Std. Dev. Skewness Kurtosis

3 2 1

Jarque-Bera Probability

0 -50

-25

0

25

50

-1.42E-14 -11.87000 68.81636 -25.36545 29.63410 1.327918 3.840265 3.233131 0.198580

75

Figure no. 15 Table no. 12 The synoptic picture of the "White Heteroskedasticity Test" to verify the hypothesis of heteroscedasticity of residual variable in case of the linear model of the total gross value added trend White Heteroskedasticity Test: F-statistic 0.419810 Probability 0.672683 Obs*R-squared 1.070996 Probability 0.585378 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: 2004 – 2013; Included observations: 10 Variable Coefficient Std. Error t-Statistic Prob. C -199.5600 1769.381 -0.112785 0.9134 SER02 578.5688 738.9681 0.782942 0.4593 SER02^2 -56.94042 65.46979 -0.869721 0.4133 R-squared 0.107100 Mean dependent var 790.3620 Adjusted R-squared -0.148015 S.D. dependent var 1404.055 S.E. of regression 1504.381 Akaike info criterion 17.71348 Sum squared resid 15842142 Schwarz criterion 17.80425 Log likelihood -85.56738 F-statistic 0.419810 Durbin-Watson stat 2.400444 Prob(F-statistic) 0.672683

Graphical representation of the estimated total gross value added (SER01F) based on linear tendency equation and the limits witch places them within of r2,306 estimations of the average error conditions of tendency equation (based on the Student distribution law with bilateral disposal of significance level) for a significance level of 5% and 8 degrees of freedom.

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700 Forecast: SER01F Actual: SER01 Forecast sample: 2004 2013 Included observations: 10

600 500

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

400 300 200

28.11338 22.56400 6.003648 0.033349 0.000000 0.017476 0.982524

100 04

05

06

07

08

09

10

11

12

13

SER01F

Figure no. 16

Notă: Note: In Fig. 16 the limits of the confidence interval which include the estimated levels of the total gross value added in terms of a limit error, or the maximum permitted by r 2.306 ˜ 31.43171 72 .48152326 , are calculated as follows: Upper limit: ls = yˆ  2 . 306 ˜ 31.43171 Lower limit: li = yˆ  2 . 306 ˜ 31.43171

where r tq = 0.05; f = 10-2 = r 2.306, is the critical value or the probability factor. 3. Interpretation of the results and the model validation The calculations allow us to retain the linear model of total gross value added trend of Romania in the period 2004-2013 with a certificate of viability acceptable. In support of this assessment are the following results: 1 - Under the "Criterion t" the parameters of trend equation have significantly different sizes from zero because the null hypothesis verification of each parameter is estimated by significance level below of 5%. It states that through the null hypothesis verification was refuted the insignificant nature of the difference between the estimated value of each parameter in the trend equation and the size zero (Table 10). It identifies, for each parameter, the following inequality, tstatistic > ttabelar, where ttabelar = tq; f = n-k = tq = 0,05; f = 10-2 = 2.306, corresponding to a minimum probability of 95% (the significance level: q = 0.05 is willing bilateral) in accordance with the law of Student distribution. By this finding is concluded that the model was specified correctly, identified and estimated, the parameters of trend equation show a good efficiency if the linear model is used for the evolution extrapolating to calculate the expected estimation of the total gross value added for the next time segments. 2 – The test of normality of the residual variable distribution (Jarque-Bera test) refutes the hypothesis of the existence of a significant similarities between the empirical distribution and the theoretical normal distribution (Gauss-Laplace), because to the statistical coefficient J-B = 3.233131 a probability of 19.858% is assigned, based on the law of distribution hi square with 2 degrees of freedom (Fig. 15). This statistical finding induces a specific vulnerability of the linear model of the total gross value added evolution. It is conceivable, however, that there is a sustainable solution to improve the outcome of this test if more observations will be incorporated into the model respectively to increase the period of history subject to modeling to 15-20 years. 3 - "The statistical coefficient - Durbin - Watson" through its size, DW = 0.833758, (shown in Table 10) reveal the existence of the autocorrelation phenomenon of the error term variants and thereby the risk of correct interpretation of the significance of the estimated values of the trend equation parameters of linear model. If we use "Durbin-Watson distribution table" with significance level q = 0.05, for n = 10 úi k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: 1.320 > (DW = 0.833758) < 4 – 1.320 = 2.680

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95

4 - The relative expression of standard error estimation of the equation of linear trend compared to the total gross value added average value is 7.7063%, a convenient size, positioned below a limit of 10%, to consider the linear model as viable. Statistical modeling of dynamic series of total gross value added of Romania in the period 2004-2013, with a linear model allows us notice that the relative expression of standard error estimate of trend equation has a size which is positioned at a level that we reasons to consider that the model may have practical utility to estimate future levels of total gross value added of Romania. 5 - "The coefficient of irregularity (inequality) of Theil" (Fig. 16) reconfirms by its size, Th = 3.3349%, the conclusion offered by the relative form of standard error estimation of the trend equation. The linear model of trend equation is considered as viable and formalizes acceptable the total gross value added evolution and trend. 6 – The White test (Table 12) confirms the stationary dynamic series (the series is homoscedastic), both in terms of of Criterion F and hi square Criterion which maintains the viability of the total gross value added liniar model. In light of the results and the conclusions drawn is obtain the statistical support necessary to calculate sustainable estimates of the predictable levels of total gross value added which will be recorded in the future time segments.

4. The estimation of the forecast levels The probable levels of total gross value added in 2014 and 2015 shall be estimated by calculating confidence intervals taking into account a limited error corresponding to a probability of 95%. The probability factor (critical value) "t" is, in this case of r2.306 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: r tq 0.05; f n  k 10  2 8 ˜ ıˆ y; yˆ r 2.306 ˜ 31.43171 72.481523 mld. lei The punctual value of total gross value added estimation for 2014: Y2014 207.8200  36.37273 ˜ 11 607.92003 billion lei Lower limit: l i

607.92003 - 72.481523

535 . 438507 billion lei

680 . 401553 billion lei Upper limit: l s 607.92003  72.481523 The punctual value of total gross value added estimation for 2015: Y2015

207.8200  36 . 37273 ˜ 12

644.29276

billion lei

Lower limit: l i

644.29276 - 72.481523

Upper limit: l s

644.29276

571 . 811237 billion lei

 72.481523

716.774283

billion lei

Note: In calculating the estimated values of the estimation indicators limits it was used the estimation of the trend equation average error (SE of regression) exposed in the synoptic picture of the results that characterize each econometric model as a value that can provide statistical support needed.

An alternative calculation may be based on the estimate of average error of trend equation in corrected shaped (expected) ( ıˆ yˆ ; t ) , that will produce a sensible extension of the limits of the v v

confidence interval associated to prognosis and the possibility of practical confirmation possibility is increased. When the time horizon of the forecast is farthest the estimate size of this error is larger. The calculation of this estimate is as follows:

Vˆ yˆ , t

96

§

v

¨ Vˆ y2 , yˆ ¨ 1  1  ¨ ©

n

(t

v





t ) 2 ·¸

Ȉ ti  t

2 ¸¸¹

where ti is time variable.

Romanian Statistical Review - Supplement nr. 3 / 2015

Conclusions

The econometric models which summarizing the evolution of macroeconomic indicators in the period 2004-2013 are represented by the following trend equations: - for the gross domestic product: y = 230.8467 + 41.87697 t - for the final consumption: y = 210.3533 + 29.65758 t - for the gross fixed capital formation: y = 63.97333 + 10.12121 t - for the total gross value added: y = 207.8200 + 36.37273 t Analysis of the dynamics of indicators offers the opportunity to specify through the size of the regression coefficient, the average annual growth recorded during the 10 years, as follows: - GDP increased on average from one year to another with 41.87697 billion lei; - the final consumption increased with 29.65758 billion lei; - the gross fixed capital formation increased with 10.12121 billion lei; - the total gross value added increased with 36.37273 billion lei. The models identified by linear regression equations allow the appreciating and the existence of the following structural contributions: - 70.82% of the average growth of gross domestic product is explained by average growth of final consumption; - 24.17% from the average growth of the gross domestic product is explained by the average growth of the gross fixed capital formation.

Note: It is noted that these results are related to the trend expressed by the tendency equation and in these circumstances the error term is eliminated from the calculation. The four econometric models have the statistical support to justify the general acceptance of their viability, with some vulnerability indicated by the Jarque-Bera criterion and the Durbin - Watson criterion. It can be appreciated that the increasing of the representativeness of the models developed can be obtained if the number of observations increases. Given the results presented, the models developed have an acceptable support to be used as a basis to forecast levels or confidence intervals, guaranteed with a probability of 95%, based on the Student distribution law. The analysis and projection of the total gross value added structure on branches of the national economy by use of the Markov chains Method

The methodology for calculating of the predicted structure of total gross value added involves determining a number of n-1 transitional matrices (10-1 = 9). The data of statistical information necessary for the application the Markov chains method are shown in the following table: The structure of the total gross value added on branches of the national economy (%) in the period 2004-2013 Year

2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

The total gross value added

100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00%

in which: in agriculture, forestry and fishing 14.08 9.52 8.84 6.52 7.44 7.16 6.41 7.44 5.59 6.35

in the industry

in construction

in servicies

27.88 28.10 27.80 27.45 25.78 26,75 31.85 32.93 32.36 34.13

6.61 7.40 8.38 10.29 12.24 11.71 10.25 9.23 9.82 9.02

51.43 54.98 54.98 55.74 54.54 54.38 51.49 50.40 52.23 50.50

Source: National Institute of Statistics

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a) Calculate the transition matrix (1) expressing the changing of the structure of total gross value added on branches of the national economy in 2005 compared to 2004: The transition matrix 1 (2004-2005) a b a 9.52 0.22 b 27.88 c d Year 2005 9.52 28.10 Increases 0.22

c 0.79 6.61 7.40 0.79

d 3.55 51.43 54.98 3.55

Year 2004 14.08 27.88 6.61 51.43 100.00

Decreases 4.56

4.56

Note: To facilitate the tabular writing of the n-1 transitional matrices we use the following notations: a = Agriculture, forestry and fishing b = Industry c = Construction d = Servicies

The transition matrix 1 provides information that the proportion of industry, construction and services in total gross value added increased by 0.22, with 0.79 and 3.55 percentage points in 2005 compared to 2004, on account of lower proportion of activities contribution in agriculture, forestry and fishing with 4.56 percentage points. b) Calculate the transition matrix (2) expressing the changing of the structure of total gross value added on branches of the national economy in 2006 compared to 2005: The transition matrix 2 (2005-2006) a b a 8.84 b 27.80 c d Year 2006 8.84 27.80 Increases

c 0.68 0.30 7.40 8.38 0.98

d 54.98 54.98

Year 2005 9.52 28.10 7.40 54.98 100.00

Decreases 0.68 0.30

0.98

The transition matrix 2 allows us to see that the proportion of construction increased by 0.98 percentage points in 2006 compared to 2005, due to lower proportion of activities contribution in agriculture, forestry and fishing with 0.68 percentage points respectively in industry with 0.30 percentage points. c) Calculate the transition matrix (3) expressing the changing of the structure of total gross value added on branches of the national economy in 2007 compared to 2006: The transition matrix 3 (2006-2007) a b a 6.52 b 27.45 c d Year 2007 6.52 27.45 Increases

c 1.56 0.35 8.38 10.29 1.91

d 0.76 54.98 55.74 0.76

Year 2006 8.84 27.80 8.38 54.98 100.00

Decreases 2.32 0.35

2.67

The transition matrix 3 shows that the proportion of construction and services increased by 1.91 percentage points and 0.76 percentage points in 2007 compared to 2006, due to lower proportion of activities contribution in agriculture, forestry and fishing with 2.32 percentage points respectively in industry with 0.35 percentage points.

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d) Calculate the transition matrix (4) expressing the changing of the structure of total gross value added on branches of the national economy in 2008 compared to 2007: The transition matrix 4 (2007-2008) a b a 6.52 b 0.92 25.78 c d Year 2008 7.44 25.78 Increases 0.92

c 0.75 10.29 1.20 12.24 1.95

d 54.54 54.54

Year 2007 6.52 27.45 10.29 55.74 100.00

Decreases 1.67 1.20 2.87

The transition matrix 4 highlights that the share of agriculture, forestry and fisheries and construction increased by 0.92 percentage points and 1.95 percentage points in 2008 compared to 2007, due to lower share of industry contribution with 1.67 percentage points and in services with 1.20 percentage points. e) Calculate the transition matrix (5) expressing the changing of the structure of total gross value added on branches of the national economy in 2009 compared to 2008: The transition matrix 5 (2008-2009) a b a 7.16 0.28 b 25.78 c 0.53 d 0.16 Year 2009 7.16 26.75 Increases 0.97

c 11.71 11.71

d 54.38 54.38

Year 2008 7.44 25.78 12.24 54.54 100.00

Decreases 0.28 0.53 0.16 0.97

The transition matrix 5 allows us to see that the share of industry increased by 0.97 percentage points in 2009 compared to 2008, due to lower share of activities contribution in agriculture, forestry and fishing with 0.28, in construction with 0.53 and in services with 0.16 percentage points. f) Calculate the transition matrix (6) expressing the changing of the structure of total gross value added on branches of the national economy in 2010 compared to 2009: The transition matrix 6 (2009-2010) a b a 6.41 0.75 b 26.75 c 1.46 d 2.89 Year 2010 6.41 31.85 Increases 5.10

c 10.25 10.25

d 51.49 51.49

Year 2009 7.16 26.75 11.71 54.38 100.00

Decreases 0.75 1.46 2.89 5.10

The transition matrix 6 allows us to see that the share of industry increased by 5.10 percentage points in 2010 compared to 2009, due to lower share of activities contribution in agriculture, forestry and fishing with 0.75, in construction with 1.46 and in services with 2.89 percentage points. g) Calculate the transition matrix (7) expressing the changing of the structure of total gross value added on branches of the national economy in 2011 compared to 2010:

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The transition matrix 7 (2010-2011) a b a 6.41 b 31.85 c 1.02 d 0.01 1.08 Year 2011 7.44 32.93 Increases 1.03 1.08

c 9.23 9.23

d 50.40 50.40

Year 2010 6.41 31.85 10.25 51.49 100.00

Decreases

1.02 1.09 1.11

The transition matrix 7 allows us to see that the share of agriculture, forestry and fisheries and industry increased by 1.03 percentage points and 1.08 percentage points respectively in 2011 compared to 2010, due to lower share of activities contribution in construction with 1.02 and respectively in services with 1.09 percentage points. h) Calculate the transition matrix (8) expressing the changing of the structure of total gross value added on branches of the national economy in 2012 compared to 2011: The transition matrix 8 (2011-2012) a b a 5.59 b 32.36 c d Year 2012 5.59 32.36 Increases

c 0.02 0.57 9.23 9.82 0.59

d 1.83 50.40 52.23 1.83

Year 2011 7.44 32.93 9.23 50.40 100.00

Decreases 1.85 0.57

2.42

The transition matrix 8 highlights that the share of construction and services increased by 0.59 percentage points and respectively 1.83 percentage points in 2012 compared to 2011, due to lower share of the contribution of agriculture, forestry and fisheries with 1.85 percentage points respectively of the industry with 0.57 percentage points. i) Calculate the transition matrix (9) expressing the changing of the structure of total gross value added on branches of the national economy in 2013 compared to 2012: The transition matrix 9 (2012-2013) a b a 5.59 b 32.36 c 0.76 0.04 d 1.73 Year 2013 6.35 34.13 Increases 0.76 1.77

c 9.02 9.02

d 50.50 50.50

Year 2012 5.59 32.36 9.82 52.23 100.00

Decreases

0.80 1.73 2.53

The transition matrix 9 allows us to see that the share of agriculture, forestry and fisheries and industry increased by 0.76 percentage points and respectively 1.77 percentage points in 2013 compared to 2012, due to lower share of activities contribution from construction with 0.80 and in services with 1.73 percentage points. The calculations and results that are exposed by the transitional matrices highlight changes in the relative sizes of structure on the total gross value added, which varies from year to year, but generally do not exceed 3 percentage points. In particular most significant changes are recorded in the period 2004-2005 in the services level (increase of 3.55 percentage points) and in agriculture, forestry and fisheries (decrease of 4.56 percentage points) and in 2009-2010 when an increase of 5.10 percentage points of the industry contribution it was revealed.

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The total transition matrix (2004-2013) a b a 62.56 1.25 b 0.92 258.01 c 1.78 2.03 d 0.01 5.86 Total 65.27 267.15

The transitional probability matrix a a 0.856986 b 0.003526 c 0.020715 d 0.000021

b 0.017123 0.988923 0.023624 0.012204

c 3.05 1.97 82.12 1.20 88.34

d 6.14 473.10 479.24

c 0.041781 0.007551 0.955661 0.002499

Total 73.00 260.90 85.93 480.17 900.00

d 0.084110 0.000000 0.000000 0.985276

The Projection of the structure of the total gross value added on branches of the national economy for 2014 (The product of the transposition of the transitional probability matrix with the last vector of the relative sizes of the structure for the considered period - 2013):

§ 0.856986 ¨ ¨ 0 .017123 ¨ ¨ 0 .041781 ¨ 0 .084110 ©

0 .003526

0 .020715

0 .988923 0 .007551 0 .000000

0 .023624 0 .955661 0 .000000

0 .000021 · § 6 .35 · ¸ ¸ ¨ ¸ ¨ 34 .13 ¸ ˜ ¸ ¸ ¨ ¸ ¨ 9 .02 ¸ ¸ ¨ 50 .50 ¸ ¹ ¹ ©

0 .012204 0 .002499 0 .985276

§ 5 .75 · ¨ ¸ ¨ 34 .69 ¸ ¨ ¸ ¨ 9 .27 ¸ ¨ 50 .29 ¸ © ¹

The Projection of the structure of the total gross value added on branches of the national economy for 2014, based on the average probability of change of the relative sizes of structure, from one year to another, recorded during the period 2004-2013, allowed to estimate the following proportions: - Agriculture, forestry and fishing = 5.75% - Industry = 34.69% - Construction = 9.27% - Servicies = 50.29%

References:

[1] Andrei T. - Statistics and Econometrics, Economic Publishing House, Bucharest, 2003; [2] Andrei T., Bourbonnais R. - Econometrics, Economic Publishing House, Bucharest, 2008; [3] Baron T., Biji Elena, Tövissi L., Wagner P., Isaic-Maniu Al., Korka M., Porojan D. - Theoretical Statistics and economic, Didactic and Pedagogic Publishing House, Bucharest, 1996; [4] Burghelea Cristina - Macroeconomics, Transversal Publisher, Targoviste, 2014; [5] Isaic-Maniu Al., Mitrut C., Voineagu V. - Statistics for Business Management, Economic Publishing House, Bucharest, 1995; [6] Mihailescu N. - Statistics and statistical bases of econometrics, Targoviste Publisher, 2014.

Revista Română de Statistică - Supliment nr. 3 / 2015

101

Annex no. 1 Gross domestic product and its main components

- billion lei (current prices) Year

GDP

Final consumpt ion

Gross fixed capital formation

Exports of goods and services

Imports of goods and services

The total gross value added 220.9 100.00% 255.2 100.00% 304.3 100.00% 368.4 100.00% 458.5 100.00% 451.0 100.00% 466.4 100.00% 487.7 100.00% 512.1 100.00% 554.2 100.00%

2004

247.4

211.1

53.9

88.6

110.9

2005

289.0

251.0

68.5

95.6

125.0

2006

344.7

294.9

88.3

111.3

152.7

2007

416.0

344.9

125.6

121.9

179.7

2008

514.7

420.9

164.3

156.6

223.7

2009

501.1

404.3

122.4

153.4

183.6

2010

523.7

419.8

129.4

185.5

215.5

2011

557.3

437.4

145.2

222.9

252.6

2012

586.7

461.9

154.3

238.5

266.1

2013

631.1

488.5

144.5

264.9

268.5

in which: in agriculture, forestry and fishing 31.1 14.08% 24.3 9.52% 26.9 8.84% 24.0 6.52% 34.1 7.44% 32.3 7.16% 29.9 6.41% 36.3 7.44% 28.6 5.59% 35.2 6.35%

in the industry 61.6 27.88% 71.7 28.10% 84.6 27.80% 101.1 27.45% 118.2 25.78% 120.6 26,75% 148.6 31.85% 160.6 32.93% 165.7 32.36% 189.1 34.13%

in constructio n 14.6 6.61% 18.9 7.40% 25.5 8.38% 37.9 10.29% 56.1 12.24% 52.8 11.71% 47.8 10.25% 45.0 9.23% 50.3 9.82% 50.0 9.02%

in servicies 113.6 51.43% 140.3 54.98% 167.3 54.98% 205.3 55.74% 250.0 54.54% 245.2 54.38% 240.2 51.49% 245.8 50.40% 267.4 52.23% 279.8 50.50%

Source: National Institute of Statistics

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Romanian Statistical Review - Supplement nr. 3 / 2015