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).

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.

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.

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 (R²_adj) 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 F_crit= 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

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, F_crit is higher than GQ and 1/GQ.

Table 2 - The Goldfeld-Quandt test calculation

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 d_l and d_u. 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

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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