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Rating Method Sovereign Wikirating Index (SWI)

Criteria and Base-Data

The Sovereign Wikirating Index (SWI) is a framework which evaluates the credit rating of sovereign countries/territories based on economic indicators. The following five mid-term and three long-term criteria are used:

The resulting value is calibrated by multiplying it with a ‘scaling factor’, which is composed by three long-term indicators, the Human Development Index (HDI), the Corruption Perceptions Index (CPI) and the Economic Freedom Index (EFI). Originally, the third index Political Instability Index was used for the first version of the SWI[1]Unfortunately this index has not been updated since 2010 from “The Economist”, therefore it has been removed as criteria from the SWI, and the ratings for 2011 are retroactively … Continue reading. Each criterium is calibrated with respect to the relative minimum and maximum value of all countries. For some criterion a threshold value is defined in order to avoid distorted values.

Short TitleLong TitleValueWeightReal MinReal MaxSWI MinSWI Max
HDIHuman Development IndexWeighted index of development indicators50%01[2]Raw Data of social scaling factors is divided by the Real Max value to normalize the input.01
CPICorruption Perceptions IndexIndex of perceived corruption30%010[3]Raw Data of social scaling factors is divided by the Real Max value to normalize the input.01
EFIEconomic Freedom IndexIndex of economic freedom20%010[4]Raw Data of social scaling factors is divided by the Real Max value to normalize the input.01
PIIPolitical Instability IndexIndex of political instability (not used any more)[5]Unfortunately this index has not been updated since 2010 from “The Economist”, therefore it has been removed as criteria from the SWI, and the ratings for 2011 are retroactively … Continue reading010[6]Raw Data of social scaling factors is divided by the Real Max value to normalize the input.01
PDPublic DebtDebt/GDP as %, reflects the economies ability to honour loans.40%00.22.0
ABCurrent Account BalanceCurrent account balance as % of GDP, reflects foreign inflows and outflows.15%-∞-0.20.2
PGGDP GrowthDomestic growth an an annual %15%-1-0.030.06
IRConsumer Price IndexConsumer Price index as %15%-10.020.2
URUnemployment RateRate of unemployment as %15%010.020.3
RRatingResult of SWI calculation as %0101

Formula

DefinitionExplanation

Let c be an element in the set of countries C:

c \in \left\{ \mathbf{C} \right\}
That means that every c is a country.

Let R be the vector of ratings, so that

\forall c:\ R_c \in \left[0,1\right] \subset \R
That means that Rc is the rating for the country c and every rating is ranging from 0 to 100%.
Let \operatorname{dim}\left(v\right) be the dimension of vThe function \operatorname{dim} basically counts the number of elements in the vector. In example, \operatorname{dim}\left( R \right) is the total number of ratings and thus the number of rated countries.
Let \operatorname{min}\left(v\right) the minimal, and \operatorname{max}\left(v\right)the maximal value of vThese functions find the smallest and the biggest number in a set of numbers, such as a vector. This is needed for normalization.
\operatorname{norm}(v) = \frac{v-\min(v)}{\max(v)-\min(v)}We are defining a scale-normalizating function on an vector v.
Let \operatorname{B}(x) = {\mathbf C} \times \left\{ \mathrm{HDI, CPI, EFI, PD, AB, PG, IR, UR} \right\}x is a matrix. We define the base B of this matrix, so that it contains vectors with factors for individual countries in the direction x_c, while the economic and social factors are in direction x^i.
Let s\in\left\{\mathrm{HDI,CPI,EFI}\right\} and e\in\left\{\mathrm{PD,AB,PG,IR,UR}\right\}s is an indexer for the social factors and e is the indexer for economic factors.
w^\mathrm{HDI} = 50%, w^\mathrm{CPI} = 30%, w^\mathrm{EFI} = 20%, w^\mathrm{PD} = 40%, w^\mathrm{AB} = 15%, w^\mathrm{PG} = 15%, w^\mathrm{IR} = 10%, w^\mathrm{UR} = 15%Applying the weights. The vector w^i contains the (scalar) weights for the individual economic and social factors.
r = \left( x^s\,w^s \right) \cdot \left( x^e\,w^e \right)By using the Einstein notation, we weight and sum the social factors to get the scaling factor. We also weight and sum the economic factors. Then we multiply the two results.
R = \operatorname{norm}\left(r\right) + \left(1-n \right)\cdot \left( 1-\operatorname{norm}\left(r\right) \right)We finally do some normalisation on the rating r, so that the resulting values are ranging from 0 to 100% and the values represent the performance relative to the other rated countries. The result of this formula is the SWI rating R. n is a vector that contains the number of given ratings for a specific country and thus the trust in the values.

Calculation

General Variable Modifiers
For example, the variable AB.

• AB = Number used in calculations for SWI.
• rAB = Raw or real value, actual data from source in whichever format it is acquired.
• wAB = Weighting value for the data.
• minAB = Floor value of variable, will cause ABC to equal 0 or 100 if ABC is below this value.
• maxAB = Ceiling value of variable, will cause ABC to equal 0 or 100 if ABC is above this variable.
• nAB = Number of ratings (for rating)

So for instance, if the real value (rAB) was 4 on a 10 point scale, this would be divided by 10 to create the value for calculations (AB) which, in calculations, is multiplied by the weighting (e.g. 0.5 for 50% weight.)