$$\begin{equation}Hierarch{y_{EU}} = \frac{{German\,GDP}}{{Sum\,of\;remaining\;EU\;member\;states'GDPs}}\end{equation}$$(4.1)

$$\begin{equation}d = \sqrt {{{\left( {{X_a} - {X_b}} \right)}^2} + {{\left( {{Y_a} - {Y_b}} \right)}^2}}\end{equation}$$(4.2)

$$\begin{equation}VcGe{r_{Ger,j}} = \sqrt {{{\left( {{X_{Ger}} - {X_j}} \right)}^2} + {{\left( {{Y_{Ger}} - {Y_j}} \right)}^2}}\end{equation}$$(4.3)

$$\begin{equation}\left( {Model\,1} \right):\quad IA{S_{1980 - 2021}} = V{C_{Ger}} + Trus{t_{EC{\rm{\_}}normal}} + Hie{r_{Ger}}\end{equation}$$(4.4)

$$\begin{equation} \left( {Model2} \right):\,IA{S_{1980 - 2021}} = V{C_{Ger}} + Trus{t_{EC\_low}} + Hie{r_{Ger}}\end{equation}$$(4.5)

$$\begin{equation} \left( {Model\,3} \right):\quad IA{S_{1980 - 2021}} = V{C_{Ger}} + Trus{t_{EC{\rm{\_}}high}} + Hie{r_{Ger}}\end{equation}$$(4.6)

$$ $$ IAS = \frac{{\sum \nolimits_6^{i = 1}{C_i}}}{6}$$ $$

$$ $$ Hierarchy = \frac{{GMY}}{{E{U_{rest}}\left( {from\,\,the\;date\;they\;joined} \right)}}$$ $$

$$ $$ Value\,Convergenc{e_{a,b}} = \sqrt {{{\left( {{X_a} - {X_b}} \right)}^2} + {{\left( {{Y_a} - {Y_b}} \right)}^2}} $$ $$

$$ $$ VcGe{r_{Ger,j}} = \sqrt {{{\left( {{X_{Ger}} - {X_j}} \right)}^2} + {{\left( {{Y_{Ger}} - {Y_j}} \right)}^2}} $$ $$