Scenarios of the Romania's economic growth

Transcription

1 Scenarios of the Romania's economic growth PhD Senior lecturer Nicolae Mihilescu PhD Senior lecturer Claudia Cpîn 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. 78

2 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 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: y na bt 2 yt at bt 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 t Graphical representation of the gross domestic product of Romania ( ) SER 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, 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 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: ; Included observations: 10 Tendency equation: y = t Variable Coefficient Std. Error t-statistic Prob. SER C R-squared Mean dependent var Revista Română de Statistică - Supliment nr. 3 /

3 Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 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) obs Residual Actual 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 Residual Plot y ŷ u y yˆ ˆ y. yˆ ˆ y. yˆ 0 ˆ 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 Series: Residuals Sample Observations 10 Mean -1.92E-14 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Figure no. 3 80

4 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 Probability Obs*R-squared Probability Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: ; Included observations: 10 Variable Coefficient Std. Error t-statistic Prob. C SER SER02^ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Graphical representation of the estimated gross domestic product (SER01F) based on linear tendency equation and the limits witch places them within of 2, 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 Forecast: SER01F Actual: SER01 Forecast sample: Included observations: 10 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion SER01F Figure no. 4 where t q = 0.05; f = 10-2 = 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 , are calculated as follows: Upper limit: ls = y ˆ Lower limit: li = y ˆ where the probability factor (the critical value), t q = 0.05; f = 10-2 = 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. Revista Română de Statistică - Supliment nr. 3 /

5 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 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, t statistic > t tabelar, where t tabelar = t q; f = n-k = t q = 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 = a probability of % 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 = , (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 i k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: > (DW = ) < = 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 , 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 = %, 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 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: t q0.05; f nk ˆ y; yˆ billion lei The punctual value of GDP estimation for 2014: 82

6 Y billion lei Lower limit: l i Upper limit: l s The punctual value of GDP estimation for 2015: Y billion lei 2015 Lower limit: Upper limit: l i l s billion lei billion lei billion lei 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 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: y na bt 2 yt at bt and the model which formalizing mathematical and summarizes the statistical lawfulness of the final consumption trend is: y t Graphical representation of the final consumption of Romania ( ) SER 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, 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 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 Revista Română de Statistică - Supliment nr. 3 /

7 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: ; Included observations: 10 Tendency equation: y = t Variable Coefficient Std. Error t-statistic Prob. SER02(variabila timp) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 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) Residual Actual Fitted obs Figure no. 6 Table no. 5 Series of real levels of the estimated levels on final consumption and the margin of residual term Actual y Fitted ŷ Residual u y yˆ Residual Plot ˆ y. yˆ ˆ y. yˆ 0 ˆ y. yˆ * * * * * * *. 84

8 * * *. 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 Series: Residuals Sample Observations 10 Mean -4.69E-14 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability 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 Probability Obs*R-squared Probability Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: ; Included observations: 10 Variable Coefficient Std. Error t-statistic Prob. C SER SER02^ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Graphical representation of the estimated final consumption (SER01F) based on linear tendency equation and the limits witch places them within of 2, 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 Revista Română de Statistică - Supliment nr. 3 /

9 Forecast: SER01F Actual: SER01 Forecast sample: Included observations: 10 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion 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 = y ˆ Lower limit: li = y ˆ where t q = 0.05; f = 10-2 = 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 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, t statistic > t tabelar, where t tabelar = t q; f = n-k = t q = 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 = a probability of % 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 = , (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 i k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: > (DW = ) < =

10 4 - The relative expression of standard error estimation of the equation of linear trend compared to the final consumption average value is %, 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 , 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 = %, 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 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: t q0.05; f nk 1028 ˆ y; yˆ The punctual value of final consumption estimation for 2014: Y billion lei Lower limit: l i billion lei Upper limit: l s billion lei The punctual value of final consumption estimation for 2015: Y billion lei Lower limit: l i billion lei Upper limit: l s billion lei 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 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: y na bt 2 yt at bt and the model which formalizing mathematical and summarizes the statistical lawfulness of the gross fixed capital formation trend is: y t Revista Română de Statistică - Supliment nr. 3 /

11 Graphical representation of the dynamics of gross fixed capital formation of Romania ( ) SER 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 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 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 brut de capital fix Method: Least Squares Sample: ; Included observations: 10 Tendency equation: y = t Variable Coefficient Std. Error t-statistic Prob. SER02 (variabila timp) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Note: The indicators presented in synoptic picture of the results were obtained using Eviews software 88

12 Graphical representation of the gross fixed capital formation trend: the real data (Actual), estimated data (Fitted) and values of residual term (Residual) obs Residual Actual Fitted Figure no. 10 Table no. 8 Series of real levels of the estimated levels on gross fixed capital formation and the margin of residual term Actual y Fitted ŷ Residual u y yˆ Residual Plot ˆ y. yˆ ˆ y. yˆ 0 ˆ 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 Series: Residuals Sample Observations 10 Mean 4.26E-15 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability Figure no. 11 Revista Română de Statistică - Supliment nr. 3 /

13 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 Probability Obs*R-squared Probability Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: ; Included observations: 10 Variable Coefficient Std. Error t-statistic Prob. C SER SER02^ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Graphical representation of the estimated gross fixed capital formation (SER01F) based on linear tendency equation and the limits witch places them within of 2, 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 Forecast: SER01F Actual: SER01 Forecast sample: Included observations: 10 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion 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 , are calculated as follows: Upper limit: ls = y ˆ Lower limit: li = y ˆ where t q = 0.05; f = 10-2 = 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 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 90

14 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, t statistic > t tabelar, where t tabelar = t q; f = n-k = t q = 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 = a probability of % 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 = , (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 i k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: > (DW = ) < = The relative expression of standard error estimation of the equation of linear trend compared to the gross fixed capital formation average value is %, 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 , 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 = %, 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 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: t q0.05; f nk ˆ y; yˆ The punctual value of gross fixed capital formation estimation for 2014: Y billion lei billion lei Revista Română de Statistică - Supliment nr. 3 /

15 Lower limit: Upper limit: l i l s billion lei billion lei The punctual value of gross fixed capital formation estimation for 2015: Y billion lei Lower limit: billion lei Upper limit: l i l s 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 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: y na bt 2 yt at bt and the model which formalizing mathematical and summarizes the statistical lawfulness of the total gross value added trend is: y t Graphical representation of the total gross value added of Romania ( ) SER 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, 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 and the arrangement of the values of the error term (residue) related to the origin or with the average 92

16 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 adugat brut total Method: Least Squares Sample: ; Included observations: 10 Tendency equation: y = t Variable Coefficient Std. Error t-statistic Prob. SER02 (variabila timp) C R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) 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 obs Residual Actual Fitted Figure no. 14 Table no. 11 Series of real levels of the estimated levels on total gross value added and the margin of residual term Actual y Fitted ŷ Residual u y yˆ Residual Plot ˆ y. yˆ ˆ y. yˆ 0 ˆ y. yˆ * * * * * *. Revista Română de Statistică - Supliment nr. 3 /

17 * * * *. 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 Series: Residuals Sample Observations 10 Mean -1.42E-14 Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability 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 Probability Obs*R-squared Probability Test Equation: Dependent Variable: RESID^2 Method: Least Squares Sample: ; Included observations: 10 Variable Coefficient Std. Error t-statistic Prob. C SER SER02^ R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Graphical representation of the estimated total gross value added (SER01F) based on linear tendency equation and the limits witch places them within of 2, 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. 94

18 Forecast: SER01F Actual: SER01 Forecast sample: Included observations: 10 Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion SER01F Figure no. 16 Not: 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 , are calculated as follows: Upper limit: ls = y ˆ Lower limit: li = y ˆ where t q = 0.05; f = 10-2 = 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 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, t statistic > t tabelar, where t tabelar = t q; f = n-k = t q = 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 = a probability of % 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 years. 3 - "The statistical coefficient - Durbin - Watson" through its size, DW = , (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 i k'=1, the statistical significance of the information provided by DW coefficient is confirmed by the inequality: > (DW = ) < = Revista Română de Statistică - Supliment nr. 3 /

19 4 - The relative expression of standard error estimation of the equation of linear trend compared to the total gross value added average value is %, 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 , 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 = %, 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 under the law of Student distribution (bilateral disposition of significance level q = 0.05 and f = 8 degrees of freedom). The limit error: t ˆ mld. lei q0.05; f nk 1028 y; yˆ The punctual value of total gross value added estimation for 2014: Y billion lei Lower limit: l i billion lei Upper limit: l s billion lei The punctual value of total gross value added estimation for 2015: Y billion lei 2015 Lower limit: l i billion lei Upper limit: l s 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) ( ˆ 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: ˆ yˆ, t v ( t t ) ˆ 1 v, ˆ n 2 t t where t i is time variable. y y i 96