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As discussed in our article on data aggregation, the metrics for the Blavatnik Index of Public Administration normalised versions of the source data to re-scale them into the range 0 to 1, where 0 represents the lowest performance and 1 represents the highest performance of the group of countries the data relates to.
For the majority of metrics this re-scaling is a simple min-max normalisation, however there are 24 metrics which undergo some other form of transformation.
All the re-scaling operations take place after the source data has been limited to countries identified for inclusion in the Index. Thus, the re-scaled data represents performance relative to countries included in the Index, it does not necessarily represent performance relative to all countries that are included in the original source for that specific metric, nor does it represent the performance relative to any absolute/theoretical scale limits.
Min-max normalisation
65 of the 89 metrics are re-scaled using min-max normalisation. This normalisation converts the minimum value in the observed data to 0 and the maximum value in the observed data to 1, all other values are re-scaled accordingly.
The metric value for a given country (\(m_c\)) is calculated as the difference between the country’s score in the source data (\(x_c\)) and the minimum score (\(x_{min}\)), this difference is then divided by the range of scores in the source data (difference between the maximum score in the source data, \(x_{max}\), and the minimum score in the source data, \(x_{min}\)), see equation 1.
\[ m_c = \frac{(x_c - x_{min})}{(x_{max} - x_{min})} \tag{1} \]Inverted min-max normalisation
For 8 metrics their base scaling is such that the highest score represents worse performance than the lowest score, for these metrics the normalisation is inverted. This is equivalent to conducting a min-max normalisation above but subtracting this score from 1, see equation 2.
\[ m_c = 1 - \frac{(x_c - x_{min})}{(x_{max} - x_{min})} \tag{2} \]Distance re-scaling
For 4 metrics their re-scaling is based on their distance from a reference point. For these metrics both the highest and lowest scoring countries represent the worst performance and countries closest to the reference point represent the best performance.
- For the two metrics relating to gender equality the reference point is 50%, i.e. the country with the proportion of women in public employment closest to 50% is the country with the highest performance, and vice versa.
- For the metric relating to the gender pay ratio (the ratio of female to male pay in the public sector) the reference point is 1, i.e. the country where female pay is closest to male pay is the country with the highest performance, and vice versa.
- For the metric on staff turnover in tax administrations the reference point is the median value, i.e. both countries with no/very low turnover and countries with very high turnover are low performers. For the gender measures the reference points can be set conceptually – gender equality implies a 50:50 split in the composition of staff and equality of pay between men and women. However, while high and low turnover are both problematic there is no consensus on what an ideal level of turnover should be, therefore the median of the observed data is used.
First, for each country its distance (\(d_c\)) is calculated as the absolute difference between the country’s score in the source data (\(x_c\)) from the reference value (\(r\)), see equation 3. The distances are then used as the inputs to the min-max normalisation to calculate the metric value for the country (\(m_c\)), see equation 4.
\[ d_c = | x_c - r | \tag{3} \]\[ m_c = \frac{d_c - d_{min}}{d_{max} - d_{min}} \tag{4} \]BTI and SGI re-scaling
The Blavatnik Index of Public Administration makes use of two sources from the Bertelsmann Stiftung: the Bertelsmann Transformation Index (BTI) and the Sustainable Governance Indicators (SGI). While these two sources have similar aims, to assess the quality of governance and achievement of public policy goals, and use similar methodologies they have different scopes for country inclusion – the BTI covers countries that were not members of the OECD prior to 1989, while the SGI covers all current OECD and EU members. The SGI was a key data source in the InCiSE 2019 report, in seeking to expand coverage globally, for the Blavatnik Index of Public Administration we have paired 5 of the SGI variables with 5 from the BTI.
153 countries are measured across the two sources: 26 countries are only included in the SGI, 122 countries are only included in the BTI, while 15 countries are included in both the BTI and the SGI. Both the BTI and SGI both ask expert assessors to rate countries on a scale of 1 to 10, and while they have similar aims the questions and intent of the studies is calibrated to the differing development levels of the different sets of countries included in each study. Table T1 shows the average scores across the 10 variables from the BTI and SGI sources split by country coverage, it shows that the 15 countries included in both datasets score higher in the BTI than the other countries the BTI (6.8 vs 4.8) but in the SGI they score lower than the other countries in the SGI (5.5 vs 6.8).
| Data source | Countries only included in BTI | Countries included in both BTI and SGI | Countries only included in the SGI |
|---|---|---|---|
| Bertelsmann Transformation Index | 4.5 | 6.8 | |
| Sustainable Governance Indicators | 5.5 | 6.8 |
| Data source | Mean minimum score | Mean maximum score |
|---|---|---|
| Bertelsmann Transformation Index | 3.7 | 9.1 |
| Sustainable Governance Indicators | 2.9 | 8.4 |
As implied by the differences in Table T1, and as shown in Table T2, across the 15 countries included in both sources their average minimum and maximum scores in the BTI are higher than their average minimum and maximum scores in the SGI. These results suggest that in combining these two different sources there should be some form of calibration of their re-scaling such that data from the SGI is effectively weighted higher than data from the BTI.
Based on the minimum and maximum scores shown in Table T2, a pragmatic calibration has been adopted such that re-scaled scores from the BTI using min-max normalisation have a range of 0.0 to 0.8 (see equation 5) and re-scaled scores from the SGI using min-max normalisation have a range of 0.3 to 1.0 (equation 6).
BTI normalisation:
\[ m_c = \frac{x_c - x_{min}}{(x_{max} - x_{min}} * 0.8 \tag{5} \]SGI normalisation:
\[ m_c = \left( \frac{ x_c - x_{min}}{x_{max} - x_{min}} * 0.7 \right) + 0.3 \tag{6} \]