# Methodological Annex

The index was created on the basis of data collected from knowledge databases of the World Bank, International Monetary Fund, International Energy Agency, Stockholm International Peace Research Institute (SIPRI), Forbes magazine, Standard & Poor’s, Moody’s and Fitch rating agencies and Shanghai Ranking Consultancy.

Group indicators and sub indicators of the State Power Index (the weights of the group and sub indicators are indicated in parenthesis)

Economic capital (40%)

• Size of GDP according to PPP (80%)
• Country rating (10%)
• Number of richest citizens (10%)

Militarisation (20%)

• Military expenditure (50%)
• Arms production and sales (30%)
• The number of uniformed officers (10%)
• Military expenditure as a percentage of the GDP (5%)
• Possession of nuclear weapons (5%)

Land (10%)

• Country’s surface area (100%)

Human resources (10%)

• Population (90%)
• Demographic burden of people 65+ (10%)

Culture (10%)

• Number of universities in the Shanghai ranking (100%)

Natural resources (5%)

• Amount of energy produced in the country (50%)
• Energy independence (50%)

Diplomacy (5%)

• Membership in the UN Security Council (60%)
• Membership in the most important international organisations (20%)
• Leadership positions in international organisations (20%)

Formulas for the partial and group indicators and the State Power Index

Formula to calculate the sub indicator is as follows:

$$z_{ijk} = \frac {x_{ijk}} {\sum_{i=1}^n x_{ijk}} \times w_{ijk},$$ $$z_{ijk} \in [0,100],$$

where:
$$x_{ijk}$$ – value of variable $$j$$ in country $$i$$ in year $$k$$,
$$w_{ijk}$$ – value of weight $$j$$ in country $$i$$ in year $$k$$,
$$z_{ijk}$$ – calculated value of variable $$j$$ in country $$i$$ in year $$k$$.

Formula to calculate the group indicator is the following:

$$g_{ikl} = \frac {\sum_{i=1}^n (z_{ijk} \times w_{ijk})} {n \times},$$ $$g_{ikl} \in [0,100],$$

where:
$$z_{ijk}$$ – value of variable $$j$$ in country $$i$$ in year $$k$$,
$$w_{ijk}$$ – value of weight $$j$$ in country $$i$$ in year $$k$$,
$$n$$ – number of sub indicators,
$$g_{ijk}$$ – value of $$l$$ group indicatiors in country $$i$$ in year $$k$$.

In the last work stage, the State Power Index is calculated. The synthetic indicator is the sum of the products of group indicators and their weights.

Formula for the state power index:

$$IMP_{ik} = IKa_{ik} \times 40\% + IM_{jk} \times 20\% + IZ_{ik} \times 10\% + IP_{ik} \times 10\% + IKu_{ik} \times 10\% + IZN_{ik} \times 5\% + ID_{ik} \times 5\%,$$

where:
$$IKa_{ik}$$ – Capital Index,
$$IM_{ik}$$ – Militarisation Index,
$$IZ_{ik}$$ – Land Index,
$$IP_{ik}$$ – Population Index (Human Resources),
$$IKu_{ik}$$ – Culture Index,
$$IZN_{ik}$$ – Natural Resources Index,
$$ID_{ik}$$ – Diplomacy Index,
all for country $$i$$ and year $$k$$.