ПРОГНОЗИРОВАНИЕ ВВП БЕЛЬГИИ С ПОМОЩЬЮ ЭКОНОМЕТРИЧЕСКОЙ МОДЕЛИ

FORECASTING THE GDP IN BELGIUM USING THE ECONOMETRIC MODEL

Introduction

Belgium, a small and open economy of 11.4 million inhabitants, is located in the heart of Europe. The economy benefits from a strong communication infrastructure and a highly qualified workforce.

Real GDP Growth data in Belgium is updated quarterly. Belgium’s GDP expanded 0.4 percent on quarter in the three months to December 2018, the same as in the previous period and in line with preliminary estimates. Household consumption (0.5 percent vs 0.7 percent in Q4) and gross fixed capital formation (0.1 percent vs 0.4 percent) slowed while government expenditure rose faster (1.1 percent vs 0.5 percent). Also, foreign demand contributed negatively to growth, as exports rose 0.6 percent (vs -0.4 percent) and imports increased at a faster 0.9 percent (vs -0.3 percent). Year-on-year, the GDP advanced 1.2 percent, slowing from a 1.6 percent expansion in the previous period and also matching earlier estimates. It was the lowest annual GDP growth since Q2 2014. Considering 2018, the economy advanced 1.4 percent, the least since 2013 and below a 1.5 percent gain in 2017. So, the data reached an all-time high in 2018 and a record low in 2000 year.

 

Table 1 GDP – Belgium 2000-2018


Regression analysis

A correlation analysis was carried out of the relationship between the endogenous indicator, which is understood in this case as the GDP and exogenous indicators from 2001 to 2018.

 – the endogenous parameter (the GDP).

Year

GDP (current US$)

2000

284933,00

2001

296257,00

2002

312900,00

2003

320613,00

2004

333831,00

2005

347658,00

2006

371464,00

2007

390526,00

2008

405729,00

2009

407955,00

2010

434371,00

2011

451933,00

2012

469720,00

2013

487344,00

2014

503620,00

2015

521018,00

2016

550989,00

2017

577535,00

2018

597433,00

Figure 1 - The data for Y –the GDP in Belgium

 

We study the main factors (variables) that affect the indicator of GDP. There are two exogenous parameters in this model. GPD is the first to be taken with a lag. The lag is one year.

 – the lagged GDP.

 

 

 

 

Year

GDP (-1) (current US$)

2001

284933,00

2002

296257,00

2003

312900,00

2004

320613,00

2005

333831,00

2006

347658,00

2007

371464,00

2008

390526,00

2009

405729,00

2010

407955,00

2011

434371,00

2012

451933,00

2013

469720,00

2014

487344,00

2015

503620,00

2016

521018,00

2017

550989,00

2018

577535,00

Figure 2 - The data for X1 – lagged GDP

The second parameter for our model is the general government final consumption expenditure.

 – the general government final consumption expenditure.

Year

General government spending (current US$)

2001

12144,00

2002

11990,00

2003

12392,00

2004

12922,00

2005

12992,00

2006

13691,00

2007

17790,00

2008

19174,00

2009

20583,00

2010

21363,00

2011

22598,00

2012

23790,00

2013

24422,00

2014

24719,00

2015

24576,00

2016

25147,00

2017

25818,00

2018

26636,00

Figure 3 - The data for X2 – general government final consumption expenditure

So, let's create the linear equation, by using the linear regression function in Excel to calculate the coefficient for each exogenous parameter. In that case, it is possible to estimate the relevance of the model.

 

Results

Our estimated model is presented below.

Coefficient of determination (R2adj) equals 0,995647526340896. This means that around 99,7 % in changes of dependent variables are explained by changes in independent variables by linear regression models.

F-test checks non-randomness of R2 and equality of specification of a linear regression model. From calculations it was received, that Fcrit= 3,591530568 and F=1601,28084171368. So, the coefficient of determination is non-random and quality of specifications is high.

Then need to perform the T-test by comparing the T-statistics with the P-value. As can be seen from Table 1, in the absolute value, the T-statistic is higher than the P-value for all the considered coefficients. So, that is why our linear regression coefficients are significant.

Table 1 - The data for T-test

T-statistic

P-value

-0,709631617

0,489583798

15,78776858

2,580811178

-1,068406623

0,303413885

 

Let's check the three conditions of the Gauss-Markov.

The first condition of Gauss-Markov theorem is that average mean of residuals is equal to zero. In order to check that, the average mean of residuals should be calculated. As it can be seen from the residual table, the average mean of residuals is nearly equal to zero, henсe the first condition of Gauss-Markov theorem is satisfied. This means, that coefficients of the model are unbiased.

The Goldfeld-Quandt test can be used to check the second Gauss-Markov condition. This test checks the homoscedasticity in regression analyses. As it can be seen from the table 2, Fcrit is higher than GQ and 1/GQ.

 

Table 2 - The Goldfeld-Quandt test calculation

GQ

1,817679422

1/GQ

0,550152017

FcritGQ

6,094210926

 

In order to verify the third Gauss-Markov condition, it is necessary to conduct the Durbin-Watson Test. Based on the test results, it can be noted that the Darbin-Watson value lies in the yellow zone between dl and du. Based on it, we can conclude that there is no information about autocorrelation.

The adequacy of the model is checked throughout the construction of the confidence interval. Based on the data from Table 3, we can conclude that the real value lies between Y^- and Y^+, so, that is why the model is adequate.

 

Table 3 - The Goldfeld-Quandt test calculation

Y^2018=

605937,08

Y^-2018=

592826,65

Y^+2018=

605973,54

Y2018=

597433,00

 

Finally, the average approximation variance is equal 1,42%, mistake of approximation is more than 25% that means that our model is inaccurate, so this model is relevance for using.

 

 

 

 

References

 

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