PREDICTIONS AGGREGATION BY COUNTRY TO IMPROVE THE ACCURACY OF EUROPEAN UNION GDP RATE FORECASTS? Mihaela Simionescu *

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1 PREDICTIONS AGGREGATION BY COUNTRY TO IMPROVE THE ACCURACY OF EUROPEAN UNION GDP RATE FORECASTS? Mihaela Simionescu * Address for corespondence: Institute for Economic Forecasting of the Romanian Academy 13, Calea 13 Septembrie, District 5, Bucharest mihaela_mb1@yahoo.com, mihaela.simionescu@ipe.ro Biographical Note Mihaela Simionescu is Scientific Researcher at the Institute for Economic Forecasting of the Romanian Academy. She has a PhD in Economics for the domain Cybernetics and Statistics. She is member in some national and international associations: Romanian Society of Econometrics, Romanian Association of Regional Sciences, General Association of Economists from Romania, International Regional Science Association, International Association of Scientific Innovation and Research. She is in the Editorial Board of many national and international journals. Her research interests concerns Econometrics and forecasting, economic convergence and macroeconomics. Abstract The GDP forecasting is a prior concern for each country, but also for an entire region composed by more countries with specific and different evolutions of GDP. The GDP predictions for the 7 European Union are based on two econometric techniques. It was proved, using accuracy indicators like U1 and U Theil s coefficients and statistical tests (Morgan-Granger-Newbold test, Harvey-Leybourne-Newbold test and Diebold-Mariano test) that the aggregation of forecasts made for each country in the EU on horizon provided better forecasts than the use of a single semi-logarithmic model for the entire region. However, the naïve forecasts gave more accurate results than the proposed models, this conclusion being in accordance with the recent results in literature regarding GDP forecasting. For 013 the ex-ante evaluation of forecasts was made, considering that the actual value is the one registered in 01. It is anticipated an underestimation of the GDP rate according to the aggregation technique if the benchmark is the indicator s value in 01. Keywords: forecasts accuracy, naïve forecasts, predictions, GDP rate, econometric model JEL Classification: E7, C51, C53 87

2 1. Introduction The prediction of GDP in each economy is a real concern that determined more and more researchers to find the most suitable forecasting method that generates the less prediction errors. Most of the specialists concluded that the simple econometric models tend to be the best solution. A particular situation is given by the predictions made for regions composed by more countries with specific evolutions of GDP. The regional approach was also analyzed by Goschin (007), who explained the relation between productivity and wages by regions. The purpose of this study is to make predictions of the real between gross domestic product (GDP) in the European Union using two techniques: the aggregation of the predictions made for each state of the 7 European Union using a linear regression model and the prediction of overall real GDP using a single model. The accuracy of these forecasts made for is assessed using U1 and U Theil s statistics and some accuracy tests.. Literature The predictions made for GDP are based on different forecasting methods, the quantitative ones being the most utilized. Another goal of the researchers is the search of the best method to generate the most accurate predictions. Most international organizations like World Bank, OECD (Organisation for Economic Co-operation and Development), European Commission, SPF (Survey of professional Forecasters), IMF (International Monetary Fund) and others provide the own predictions regarding the future evolution of GDP or inflation in the next years. The predictions for these variables are really important in establishing the government policy. Marcellino (007) showed that corrected specified linear models for GDP outperform the non-linear ones in terms of predictions based on these methods. However, in certain cases, complicated models are better than the linear ones. Previously, Stock and Watson (1999) and Marcellino (004) came to the same conclusion, showing the average linear models superiority for GDP in USA and Euro Area in most of the cases. In predicting the GDP growth, Stck and Watson (003) analysed in detailed the role of the financial time series in improving the forecasts accuracy. 88

3 Allan (01) observed a suitable accuracy for the predictions provided by OECD which combined the outturn values of GDP growth for G7 countries ( ). There are two categories of accuracy methods: qualitative methods and quantitative statistics. Dovern and Weisser (011) analyzed the predictions performance (accuracy, bias and efficiency), resulting consistent differences between countries and for a country regarding different variables. Most of the predictions are biased and only few GDP predictions are unbiased. Deschamps and Bianchi (01) observed important differences for macroeconomic predictions for China in what concern the accuracy indicators for variables like inflation rate and GDP, respectively consumption and investment. The data are inefficiently used, the forecasts being biased due to the mild adjustment to structural shocks. Ruth (008) improved the forecasts accuracy for European macroeconomic variables using as strategy the combination of specific sub-groups forecasts compared to forecasts that used a single model for the entire European Union. Gorr (009) recommended the univariate method for forecasting in normal conditions using conventional accuracy indicators. However, the multivariate methods are suitable for predicting in exceptional conditions, the ROC curve being the suitable accuracy indicator in this case. 3. GDP predictions for 7 EU using two types of econometric models. The forecasts accuracy For the entire European Union we proposed a semi-logarithmic model. The GDP data series is provided by the European Commission. We start from the following relationship: GDP t = GDP 0 (1 + r) t (1) t- time variable GDP t - GDP at time t GDP t - GDP at initial moment r- GDP rate Applying the logarithm, we will have: ln _GDP t = a + bt + u t a,b- the parameters to be estimated ln _GDP t - natural logarithm of GDP u t - error term 89

4 ln _GDP t = t Because the data series is too short ( ), we estimate the parameters by bootstrapping with replications of the residuals values. All the coefficients are significant for a level of significance of R-squared is and Breusch-Godfrey tests puts in evidence the errors independence for a lag of 1. According to White test, the errors are homoscedastic while Jarque-Bera test application makes us to do not have reasons for rejecting the normality distribution of the errors. Moreover, the normality problem is solved by the high number of replications ( replications). The tests applied for checking the regression model assumptions are presented in Appendix 1. This model will be used to make predictions on horizon Transformations are made in order to get the forecasts for the real GDP rate. We determined then the connection between gross domestic product (GDP), net exports and public consumption for the 7 European Union countries for the year 010. The data s source is Eurostat, the official site of the European Commission. The GDP represents the monetary value of finished goods and services that are produced inside a country in a specific period, usually a year. This indicator is composed by government outlays, private and public consumption, investments and net export (exports less imports). GDP = G +C+ I + NX () "C"- private consumption in the country economy "G"- government spending "I"- sum of all businesses spending on capital "NX" - exports minus imports. The GDP measurement is complex, being 3 methods for determining it: - income approach: by summing up what someone earned in a year - expenditure method: summing up what someone spent in a year - production approach: supposes the computation of intermediate consumption. All the methods should conduct us to the same result. A map of Europe was realized in GeoDa software with 4 groups of countries based on the levels of GDP in 013. The groups are denoted from 1 to 4, from the darkest nuance to the light one. The unit of measurement is thousand Euro. 90

5 Group 1- [0; 8538] Group - [8578; 3.908e+004] Group 3- [4.494e+004;.76e+005] Group 4- [.896e+005;.356e+006] Figure 1. Groups of European countries according to GDP level in 013 Economic growth has a large impact on the economy of any country. For example, when we have a healthy economy, there is an important clue that the unemployment level is low and the salary grows because the demand on the labour market increases. A high change in GDP (increase or decrease) has an important effect on the stock market. The significance is relevant; a bad economy supposes lower profits for firms, this fact meaning mean small stock prices. The investors worry about decrease GDP growth that is one of the important elements to compute if an economy is in recession. The relationship between the three variables chosen will be studied using a simple regression between GDP and public consumption, a multiple regression involving all the three variables where the GDP represents the dependent variable. The multiple regression model has the following form: Y i = β 0 + β 1 X i1 + β X i + e i (3) 91

6 β 0 -the intercept β 1 -the coefficient of government expenditure β -the coefficient of net exports e i -the error The multiple regression was generated as well from Data Analysis in Excel using all the three variables. The regression equation is: Y i = 4958, , X 1 + 4, X + e i, where β 0 =-4958,009698, β 1 = 1, , β =4, From the economic point of view, the intercept, β 0, has no significance. It only means that in the absence of the influence of net exports and public consumption, the value of the GDP would be 4958,009 US$. Similarly with the simple regression, in the case of the multiple one positive slopes (β 1,β ) indicate a direct relationship between net exports and public consumption on one side and GDP on the other. Each additional dollar of net exports leads to an increase in average of 1,498 US$ in the values of GDP. When public consumption increases by 1 US$ the value of GDP increase in average by 4,43 US$. A coefficient of determination, R, of % indicates that the variations of net exports and public consumption, considered together, explain 94.31% of the variation in GDP. The ANOVA table contains information about the sum of squared deviations (the SS column) and the degrees of freedom (d f ). The last concept refers to the number of independent pieces of information present in the deviations that are used to compute the corresponding SS. MS (the variance estimate) is computed by dividing each SS to their correspondingd f. The p-value of the coefficients should be smaller than 0.05 in order to have a significant coefficient. As noticed in the table above, the intercept is the only coefficient whose p-value is larger than the level mentioned. The Significance F has to be as well below a threshold in order to have a valid model. In the case of this analysis, its value is very close to zero, much lower than 5 %, which indicates the validity of the model. 9

7 The following data is found as well in the ANOVA table and the equality can be checked: SST (the total sum of square) = SSR (Sum of square Regression) + SSE (Sum of square Residual). The ANOVA table is presented in Appendix. The parameters significance is checked using the t-student test. 1. Stating the null and the alternative hypothesis H 0 β 1 = 0β = 0 H 1 β 1 0β 0. Choosing the distribution t-student distribution, t-test (since the number of observations, 7, is not larger than 30) 3. Choosing the significance level α = 5% 4. Defining the acceptance and rejection region: t comp < t t => do not rejecth 0 t comp > t t =>rejecth 0 5. Computing the test t th =,06 t b1 = -0,306 <,06 t b =,999 >,06 t b3 = 45,91 >,06 6. Making the statistical decision and interpreting the results Parameter β 0 is not statistically significant, but its significance is not important for the model s validity. Parameters β 1 and β are statistically significant. t 1 > t t => The null hypothesis is rejected in favor of the alternative one; consequently the parameters β 1, β are statistically different from 0. F test is also used to test the model validity. 1. Stating the null and the alternative hypothesis H 0 : The model is not statistically valid 93

8 H 1 : The model is statistically valid. Choosing the type of test F-test is used =>Fα,k,n k 1 3. Choosing the significance level α = 5% 4. Defining the acceptance and rejection region: If F calc < F => do not rejecth 0 If F calc > F t => rejecth 0 5. Computing the test MS Regression = SSRegr = (y i y) = 1,07934E+13 = 5,39668E+1 dfreg k is valid. MS Residual = SSRes dfres F comp = MS Regression MS Residual = (y i Y i ) n k 1 = 5,04145E+1 6. Making the statistical decision E+11 =1,14435 = F calc > F t - The null hypothesis is rejected in favor of the alternative one 7. Interpreting the results The regression model explains much of the variation in GDP, consequently the model In order to analyse the homoscedasticity, the data is sorted from smallest to largest by the independent variable (public consumption) and then dived into three categories approximately equal. Then, regression analyses for the first and for the last group are performed. Afterwards, the ratio SSE/SSE1 is computed. 1. Stating the null and alternative hypothesis H 0 : There is no heteroscedasticity H 1 : There is heteroscedasticity. Choosing the test Fisher test F α,k,n k F 0.05,,5 3. Choosing the level of significance α=5% 94

9 4. Defining the acceptance and rejection region: If F calc < F => do not rejecth 0 If F calc > F t => rejecth 0 5. Calculating the test F comp = SSE ,5 = = SSE1 1,50151 E+11 F th = 3,38 6. Making the statistical decision F calc < F t The null hypothesis is accepted in favour of the alternative one. 7. Interpreting the results There is homoscedasticity in the errors data series. The White test is also applied and the LM statistic is lower than the critical value. This implies that H0 can t be rejected, the errors homoscedasticity being checked. Durbin-Watson test is applied to check the first order errors auto-correlation. The following steps are performed: 1) Stating the null and alternative hypothesis H 0 No errors autocorrelation H 1 Errors autocorrelation ) Computing DW statistic DW = (l i l i 1 ) e i (4) 3) Making the decision 0 < DW < D 1 =>negative correlation D 1 < DW<D = > indecision D < DW < 4 D => no correlation 4 D < DW < 4 D 1 =>indecision 4 D 1 < DW < 4 1 =>positive correlation D 1 =1.16 D = D <DW=,70147 <4-D 1 From the Durbin-Watson test, there is no autocorrelation between model s errors. 95

10 To conclude, the analysis proved that there was a very strong relationship between net exports, GDP and public consumption in 010 for the countries selected. Moreover the variation of net exports and public consumption highly influenced the value of the GDP since the coefficient of determination was close to Forecasts accuracy assessment The predictions of GDP in 7 EU are made under some assumptions: - We consider the public consumption and the net exports registered in the previous year and we make one-step-ahead predictions for each country; - The predictions for each country in a year are aggregated by summing of the forecasted GDP; - The real GDP rates are computed starting from the real GDP. Table 1. Predictions of the real GDP rate (%) in 7 EU using the two econometric techniques Year Technique 1 Technique Source: own computations The following notations are used: a- the registered results f- the forecasted results t- reference time e- the error (e=a-p) n- number of time periods U 1 n t 1 n t 1 a ( a f ) t t t n t 1 f t According to Bratu (01), if U 1 is closer to one, the forecast accuracy is higher. (5) 96

11 U n 1 t 1 n 1 t 1 f ( t 1 a ( t 1 at 1 ) at at ) a t (6) If U =1=> no differences in terms of accuracy between the two forecasts to compare If U <1=> the forecast to compare has a higher degree of accuracy than the naive one If U >1=> the forecast to compare has a lower degree of accuracy than the naive one The ex-ante error for 013 is computed under the assumption of keeping in 013 the same value of GDP rate as in 01. Table. The accuracy of real GDP rate (%) forecasts in 7 EU (horizon: ) Accuracy measure Technique 1 Technique U1* U* Ex-ante error *horizon: Source: own computations The U1 coefficient values show the superiority of predictions based on the countries forecasts aggregation compared to the technique that uses a single econometric model for the entire 7 EU. However, the random walk generated better forecasts for According to the first technique, on overestimation of the GDP rate is anticipated for 013 and an underestimation if the GDP is aggregated. The GDP overestimation shows clearly that the semi-logarithmic model did not take into account the shocks that appears in the economy. Morgan-Granger-Newbold (MGN) test supposes the calculation of differences between the corresponding errors and the sum of errors for the same unit. The sum and the difference of the errors are actually two data series corresponding to variables X, respectively Z. The correlation between these two variables is computed by the use of Spearman s coefficient of correlation, the calculation being made in the program Vassar Stats, which is available online at 97

12 X i = e T1i + e Ti Z i = e T1i + e Ti (7) The Spearman s coefficient of correlation between the two variables has the value is The computed t statistic is -9.87, its absolute value being greater than the critical value. The associated p-value is almost 0, which is less than the level of significance (0.05). Therefore, we can conclude that the differences between the forecasts based on the two techniques are significant on the horizon In conclusion, the second technique generated more accurate forecasts. This test was changed by Harvey, Leybourne and Newbold (1997) who built a simple linear regression model based on the two variables (X and Z which were defined above, where X is the endogenous variable): X t = α Z t + u t (8) The significance of the parameter α is checked using t test. The p-value is less than So, the parameter is significant and the differences between the forecasts based on the two techniques are significant. The Diebold and Mariano (1995) test (DM test) is built under the assumption that there are not significant differences between predictions from the point of view of accuracy. This test supposes the following stages: S1: The difference between squared errors of the two forecasts is computed- (e )- squared errors of the forecasts based on the first technique and (e ) -squared errors of the predictions based on the second technique: S: The model for which the parameter is estimated is: d t,t = e t,t (e t,t ) (9) d t,t = α + ε t (10) S3: The significance of the intercept is checked using t test. A non-significant intercept implies differences between the predictions based on the two techniques. The p-value is 0.044, which is less than Therefore, for a 5% significance level, there are significant differences between the two types of predictions in terms of accuracy. 98

13 All in all, the statistical tests (Morgan-Granger-Newbold test, Harvey-Leybourne- Newbold test and Diebold-Mariano test) conducted us to the same conclusion as the evaluation of U Theil s coefficients used in making comparisons between forecasts accuracy. 5. Conclusions The results of this research are in accordance with the conclusions drawn in literature. It seems that the aggregation of the predictions made for each country in the European Union is a better strategy of getting more accurate forecasts compared to the use of a single econometric model. The model used to describe the relationship between GDP and public consumption and net export in 010 was used to make predictions for each country in 011, 01 and 013. The aggregation of the predictions provided slightly superior predictions. For 013 it is anticipated a better prediction using the aggregation technique, but the naïve forecast will be probably the best solution. Indeed, the last researches in literature put in evidence the necessity to come back to non-linear models for making prediction in crisis period. This research could be extended by proposing a non-linear model that could provide more accurate predictions even better than the naïve forecasts. References Allan, G. (01), Evaluating the usefulness of forecasts of relative growth, Strathclyde Discussion Papers in Economics, Vol. 1, No. 1-14, pp Bratu, M. (01), Strategies to Improve the Accuracy of Macroeconomic Forecasts in USA, LAP LAMBERT Academic Publishing, Munich. Deschamps, B. and Bianchi, P. (01), An evaluation of Chinese macroeconomic forecasts, Journal of Chinese Economics and Business Studies, Vol. 10, No. 3, pp Diebold, F.X. and Mariano, R.S. (00), Comparing Predictive Accuracy, Journal of Business & Economic Statistics, Vol. 0, No. 3, pp Dovern, J. and Weisser, J. (011), Accuracy, unbiasedness and efficiency of professional macroeconomic forecasts: An empirical comparison for the G7, International Journal of Forecasting, Vol. 7, No., pp

14 Gorr, W.L. (009), Forecast accuracy measures for exception reporting using receiver operating characteristic curves, International Journal of Forecasting, Vol. 5, No. 1, pp Goschin, Z. (007), Spatial and sectoral analysis of productivity-wage dissimilarities in Romania, Romanian Journal of Regional Science, Vol. 1, No. 1, pp Harvey, D., Leybourne, S.J. and Newbold, P. (1998), Tests for Forecast Encompassing, Journal of Business & Economic Statistics, Vol. 16, No. 3, pp Marcellino, M. (004), Forecasting EMU macroeconomic variables, International Journal of Forecasting, Vol. 0, No. 1, pp Marcellino, M. (007), A comparison of time series models for forecasting GDP growth and inflation, Ruth, K. (008), Macroeconomic forecasting in the EMU: Does disaggregate modeling improve forecast accuracy?, Journal of Policy Modeling, Vol. 30, No. 3, pp Stock, J.H. and Watson, M.W. (1999), A comparison of linear and nonlinear univariate models for forecasting macroeconomic time series, Oxford University Press, Oxford. Stock, JH and Watson, M.W. (003), Forecasting Output and Inflation: The Role of Asset Prices, (with James H. Stock), Journal of Economic Literature, Vol. 41, No. 3, pp APPENDICES APPENDIX 1 Estimation and tests for checking the homoscedasticity, the independence and the normal distribution of the errors Dependent variable: LN_GDP Method: Least Squares Included observations: 10 Bootstrapped coefficient estimates and standard errors (10000 repetitions) 100

15 Variable Coefficient Std. Error t-statistic Prob. C T 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 Hannan-Quinn criter F-statistic Durbin-Watson stat Breusch-Godfrey Serial Correlation LM Test: F-statistic Prob. F(1,7) Obs*R-squared Prob. Chi-Square(1) Heteroskedasticity Test: White F-statistic Prob. F(,7) Obs*R-squared Prob. Chi-Square() Scaled explained SS Prob. Chi-Square() Series: Residuals Sample Observations 10 Mean -1.06e-15 Median Maximum Minimum Std. Dev Skew ness Kurtosis Jarque-Bera Probability

16 APPENDIX The estimation of the multiple regression model SUMMARY OUTPUT Regression Statistics 0, Multiple R 9 0, R Square 4 Adjusted R 0, Square 7 Standard Error 69051,743 9 Observations 7 ANOVA df SS MS F 1,07934E+1 Regression 3 1,14435E+1 Residual ,09078E+1 Total 6 3 Significanc e F 5,39668E ,8 1,78E-4 Intercept X Variable 1 X Variable Coefficient s ,0097 1, , Standard Error t Stat P-value Lower 95% Upper 95% 16195,9073 0, , ,7 8468,7 0, , ,0061, , , , ,71E- 4, ,