Analysis of the quarterly and annual GDP of Belgium for the period from 1995 to 2023 with the assumption of the economic downturns

Description of the Belgian economic downturns and undertaken policy measures:

Among the European countries Belgium has strong economic performance. In accordance with the Index of Economic Freedom (2024) it is placed 46th out of 184 countries with the overall score of 65.6, which gives it the status of? “Moderately free economy”. In addition, “OECD Economic Surveys: Belgium” (2020) specifies that the country economy behaves in a strong manner within a range of sectors and areas, but on the other hand there are still possibilities of сertain risks. Those risks mainly taking their origins from the economic downturns, which economy has experienced.

For the purpose of this academic paper, based on the analysis of the GDP of Belgium, the data was selected in a time period from 1995 till 2023 for both quarterly and annual time frequency in millions of euro. ?

To figure out what was the most influential shocks in the economy, in terms of the selected country and time dimension for the analysis, the graphs of the quarterly and annual GDP must be considered.

Figure 1 and Figure 2 illustrate the behavior of GDP over time. An analysis of the graphs clearly can highlight two massive deteriorations in 2009-2010 and 2019-2020. First one is Global Financial Crisis and second one is Covid-19 Pandemic Crisis. To understand their importance for the analysis and how the consequences were managed by the country government and Central Bank, the detailed, accurate characterisation of them is presented below.

Global Financial Crisis in 2008-2009:

The first significant economic crisis, which affected Belgian economy in the period from 1995 to 2023 was Global Financial Crisis in 2008-2009. Other countries of Benelux and in general the whole world was targeted with the consequences of the the U.S. Housing Bubble, subprime mortgage crisis and the failure of the Lehman Brothers along with American Insurance Group. In the context of Belgium, the economic crisis was supported with the political one at the same time. In accordance with “Sustainable Governance Indicators 2011: Belgium Report” by M. Castanheira, B. Rihoux and N.C. Bandelow, there was a pressure atmosphere in the govermental apparatus. Additionally, S. Troupin, J. Stroobants and T. Steen in the “Paper for Conference on the impact of the Fiscal Crisis on Public Administration” (2013) stated that during the financial crisis the office was helded by no less than four different governments, two different coalitions and three Prime Minesters. Due to that the sittuation in the country was pretty heated.

The Prime Minester Yves Leterme attempted to influence judicial processes in terms of the bankruptcy of Fortis Bank.

Fortis Bank as Lehman Brothers was suffering from solvency problems. Simply bank was not able to meet long term obligations. Same was with the Dexita Bank.

The main action implemented by the government and Central Bank was a bailout.

S. Troupin and others concluded that Belgium nationalized Fortis Bank with the cost of 4.7 billion euros and 75% of shares was sold to BNP Paribas. Along with the support of the Fortis Bank, government had recapitalized such financial institutions as Ethias and KBC with the injection of 4 billion euros. Overall, federal government of Belgium invested about 5% of GDP to rescue financial institutons. In the monetary equivalent it was about 20 billion euros.

Besides the bailout, recovery measures were implemented witht the so called “anti-crisis package”, which introduced VAT reduction in the real-estate sector and measures related to the unemployment.

Additionaly, it must be mentioned what J. Stroobants, S. Troupin and T. Steen discussed in “WP 7: The global fiancial crisis in the public sector as an emerging coordination challenge: Short Country report for Belgium” (2013). They have payed an attention to the fact that historically Belgium had public debt more than 100% of GDP. Right before the financial crisis government managed to decrease its level to 84%. Hovewer, from 2008 it went back to 100%, as government was trying to secure banking sector.

Covid-19 Pandemic in 2019-2022:

In 2019 world was hitted by terrible Covid-19 Pandemic. Since the virus does not respect borders, it appeared in Belgium as well and influenced its economy. In accordance with ???????V. Pattyn, J. Matthys, S.V. Hecke and their article “High-stakes crisis management in the Low Countries: Comparing government responses to Covid-19” (2021), in response to pandemic Belgium performed both immidiatelly and in a harsh way with the usage of “intelligent lockdown” and shelter-in-place approach.

The authors of the “The Covid-19 crisis and policy responses by continental European welfare stares” (2021),? B. Cantillon, M. Seeleib-Kaiser, R. Veen discussed policy responces measures implemented to save economic stability in the perios of the pandemic. They highlited that on 18 March 2020, the National Labour Council (NAR) signed an agreement to increase the system of unemployment for economic reasons. Due to the extention of unemployment measures Belgian citizens was identifyed as ones, who benefited the most among other countries as Germany and Nitherlands. Moreover, government took care for self-employed people with the extension of benefits for medical care, monthly appartment rent-paymens, social contributions. All mentioned measures helped to more than 400,000 self-employed people to overcome Covid times.

International Monetary Found (IMF) in “Policy Responces to Covid-19” (2021) concluded that in terms of the fiscal response to fight with pandemic, government introduced a package on March 2021 with approximate budget impact of 22.3 and 10.8 billions of euro (i.e. 5.0 and 2.3 % of GDP). Main measures was insuaring the boost of healthcare expenditures (health control and purchase of the vaccines), liquidity support, “below-the-line” measures, assistance with the issue of solvency.

In terms of monetary and macro-financial actions, IMF mentioned that Belgian government reduced so called “counter-cyclical bank capital buffer” to 0 percent.

Unit root tests and estimation of the models with interpretations:

In order to accept or reject the presence of the unit-root in the Belgian GDP from 1995 to 2023 for both quarterly and annual observations, the three types of non-stationarity were estimated starting from the largest one (i.e. random walk with drift and trend, random walk with drift, random walk) with the usage of econometric software Gretl and the Ordinary Least Squares (OLS) estimator and Augmented Dickey-Fuller (ADF) test to compare the obtained results. Estimated models can be presented in the following way:

Where ?Yt states for the first difference of the GDP, ?t ?for the drift component (constant, intercept), ? (“rho-value”; = ??-1, where ?? “delta”) for the coefficient of the one period lag GDP (Yt-1 ), β t for time trend and εt for the error term. Subscript “t” identifies model as a time series.

For the analysis of quarterly and annual data, all three equations can be written as:

?

The decisions of the presence of the unit root for the mentioned models in the OLS estimations can be concluded with the usage of the hypothesises:

To obtain an apptopriate results the one period lag were added to the regressor variables GDPQ (GDPQ_1) and GDPA (GDPA_1), and time trend was added as well. Than model was modified several times by the removal of the time trend to obtain random walk with drift and lastly constant was removed to get random walk model.

Right after the OLS estimations ADF test of both GDPQ and GDPA was conducted to finally approve or reject stationarity or non-stationarity processes within the specified models. ADF test can be considered as more advanced tool for the estimations. The main reason for it is that ADF test allows to regress more complex models with the more than one lag, as it is presented in usual OLS. Since OLS estimation is observed with one period lag (relatively simple model) it commonly results with the stationarity. To understand the results and make final decisions of the ADF test, the following hypothesis must be considered:

OLS estimations concluded the next results for quarterly data:

From the presented results above it is clearly visible that for the quarterly data non-stationarity (unit root) presents only in the last model. This desission comes from the following factors:

-?????? Model 1 (random walk with drift and trend) shows that all the values are significant at 1% level in accordance with p-values (different from 0 at 1% significance level); value of ?=-0.546610, ?t = 25415.6, β t = 413.117. Since the condition of ?=0 (insignificant) is not met, the decision rool concludes the rejection of Ho and acceptance of the H1. Model 1 bahaves as stationary.

Model 2 (random walk with drift) presents the insignificance of the coefficients. Due to that?tand?can be treated as not different from zero. The condition of the insignificance of ? is met, but to accept non-stationarity for this model ?t must not be equal to 0. Overall Model 2 accepts the H1 (stationarity).

-?????? Model 3 (random walk) illustrates that the value of ? is statistically insignificant in acordance with p-value (not different from 0), meaning that ?=0 (??=1) and based on the stated hypothesis Model 3 behaves as a random walk (non-stationary model).

ADF unit root test for quarterly data:

Since ADF test adds more than one lag into the testing of the model the following results appeared:

-?????? Model with constant and trend including 11 lags (random walk with drift and trend) has resulted in the way that p-value=99.98%. Accept of the Ho (non-stationary model). In comparison with OLS random walk with drift, ADF test resulted in the same way.

-?????? Model with constant along with 12 lags (random walk with drift) showed the???????????????? p-value=99.98% (acceptance of the Ho, non-stationarity). However, in the OLS results it was stated that model is stationary. From that factors it can be concluded that the second model can be trusted and observes non-stationarity right after the introduction of the 12 period lags.

-?????? Model without constant and addition of 12 lags (random walk) presented the???????????? p-value=99.92% based on which model is considered to be non-stationary. The same conclusion was made right after the OLS estimation. In accordance with OLS it is enough to have one period lag to conclude the non-stationarity process. But ADF has suggested 12 period lag.

Overall, for quarterly GDP of Belgium OLS and ADF presented non-stationatity in the simplest model (?GDPQt = ?GDPQt-1 + εt) . One period lag is not enough for the random walk with drift and random walk with drift and trend to observe the unit root (non-stationarity), ADF test suggest for them to have at least 11 and 12 period lags.

OLS estimations for Annual data:?

OLS estimatins for annual data showed that with the usage of one period lag in all three models, the unit root can not be observed. And due to that, presented models can not be used in terms of the description of any significant flactuations in the values of Belgian GDP. Lets break down all models and give their interpretations to understand the stated information above.

-?????? Model 1 stands for random walk with drift and trend. It is viasible that p-values are statistically insignificant (not different from 0). Due to that all obtained coefficients can be considered as equal to 0 (?=?t =β t =0). In accordance with the hypothesis. To accept the presence of the unit root ?t and β t must be different from 0. That is why it can be concluded that in Model 1 there is no unit root (data is stationary).

-?????? Model 2 describes random walk with drift. OLS estimation presented the following information about the model: p-value of the constant is statistically insignificant, meaning ?t =0; p-value of the ? is statistically significant at 5% level, ? itself equals to 0.0569007. Since ?≠0 and ?t =0, H1 is accepted. Belgian changes GDP based on the annual data for the long-term period (from 1995 till 2023) can not be fully observed with the usage of the second model.

-?????? Model 3 resulted in the same way as previous two. Last model considered to be stationary due to the following outcome: p-value of ? is statistically significant at 5% level and equals to 0.0382588. Such result leads to the acceptance of the H1 .

ADF unit root test for annual data:

In order to check additionally the suitability of the models for the description of the Belgian annual GDP from 1995 to 2023, the ADF test was conducted.

-?????? Model with constant and trend (random walk with drift and trend) assumed 0 lags and provided the p-value=99.11 (non-stationary model since p-value>10%).

-?????? Model with constant (random walk with drift) as well assumed 0 period lags and showed the p-value=100% (non-stationary model as well).

-?????? Model without constant (random walk) also was tested with 0 lags and p-value=100% (non-stationary).

In terms of OLS for all three models, it presented stationarity with the introduction of one period lag for annual GDP.

Complemantary funcrion, assuming the trand stationary process as a correct model:

In accordance with the project description, the trend stationarity process was assumed as the correct model for the analysis of Belgian quarterly and annual GDP from 1995 to 2023.

Generally, GDP is considered as trend stationary process if ?≠0, ?≠0 and β≠0 and looks as the following equation:

In accordance with the stated identifications of quarterly and annual GDP complemantary functions can be expressed in the next ways:

Stated equations may help to understand the impact of the shocks in the economy. If a certain shock appears the value of A identifies how far economy is from the equilibrium and ??

?? = ?? +1 ?? (0;1) represents the adjustment parameter of how fast economy will get back to the equilibrium.

It must be clarified that the smaller value of ?? indicates a faster adjustment of the economy back to the equilibrium, and the main reason for such factor is that in each unit of the time (year or quarter) ?? presents the amount of the consequenses left from the shock. To fully catch and analyze ??, A can be setted to the value of 1.

For the purpose of the analysis several levels of the shocks were asssumed (0%, 10% and 50% of the shock). Their impacts to the economy are presented for each type of the data below.

Quarterly GDP complementary function:

The state of the economy after a certain shock, assuming quarterly deviation may be presented and described with the usage of Figure 12.

In accordance with the chart and the value of the ? from OLS estimation Model 1, complementary function starts from the value 0,45339.

Since the economic sence of ?? was already clarified, it can be councluded that for the period between 1995 and 2023 if a certaint economic downturn appeared in Belgium, economy was left with 50% of it only in approximate 3 quarters and ??≈0,22 , with 10% after 5th quarter (?? ≈0,05) and all in all nothing remained only after 11th quarter (??=0).

Annual GDP complementary function:

In terms of the annual data, the following Figure was obtained:

It is visible that complementary function starts from the value of 0,9492023 .

Assuming that some random shock appeared in Belgium from 1995 to 2023, and the annual economy adjustment, 50% of a downturn remained left in 14 years with the ??≈0,47 , and the 10% along with equilibrium condition can be reached only after 2023 (??=0).

Since ?= ??-1, ??=1+?. Quarterly OLS Model 1 presented ?=-0,546610, meaning that                                    ??=1+(-0,546610)=0,45339.
Since ?= ??-1, ??=1+?. Annual OLS Model 1 presented ?=-0,0507977, meaning that                                    ??=1+(-0,0507977)= =0,9492023.        

Conclusion:

All in all the analysis of the GDP of Belgium from 1995 till 2023 resulted in the way that quarterly data models with one period lag as random walk with drift and random walk with drift are stationary, random walk is non-stationary. ADF test for quaterly data showed non-stationarity for the models only with the introduction of 11 and 12 lags. In terms of the annual data OLS estimations with one period lag all models appeared to be stationary, and ADF test suggested non-stationariry with 0 period lags.

Complementary function provided such results that shows the faster adjustment from the some random shock in Belgium between 1995 and 2023 for the quarterly data, since the value of ??(quarterly)< ??(annual).

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