Chapter 6 Weights
Weights can have a significant effect on the overall composite indicator and country rankings. Attributing weights to source indicators or pillars of a composite index can be done in several ways. They can be set to equality and such an unweighted index would imply that each pillar has equal importance for measuring inclusive growth. Weights can also be assigned based on expert assessment, policy priorities or theoretical factors. Finally, they can be determined using statistical techniques. Irrespective of which method is used, weights reflect value judgements. Opinions on which approach is the best vary. It should also be noted that even ‘unweighted’ indicators are implicitly weighted.
An equal weight could be assigned to each source indicator i.e. to each of the 27 indicators. The risk is that some source indicators are correlated and may be driven by common factors or trends. Combining correlated variables may potentially introduce an element of ‘double counting’ into the overall index. The equal weights approach also implies that all variables have the same importance to the index, and that a strong statistical, empirical and theoretical basis is missing. Equal weights can be tempting where knowledge regarding the causal relationships between source indicators is insufficient or consensus on the theoretical approach or policy priorities is lacking. Furthermore, as the source indicators are grouped into pillars that are subsequently aggregated, applying equal weights to the indicators implies an unequal weighting of the pillars as each pillar contains a different number of indicators.
For the purposes of this study, pillar weights were determined by quantifying the interconnections of source indicators using PCA. The advantage of this approach is that risk of subjective bias associated with experts’ views or other non-statistical methods is reduced. PCA is one of the most widely recognized statistical techniques used to calculate index component weights. As described above, this methodology transforms correlated source indicators to form new variables referred to as principal components, which account for decreasing shares of the original variance of data. Each principal component was attributed a weight corresponding to the share of variance explained.
6.1 How many principal components to keep?
Based on the OECD Handbook on Constructing Composite Indicators (Nardo et al. 2005), the following rule is applied.
The code is automated to retain number of components based on following criteria:
- SS loadings > 1 &
- Proportion Var > .1The SS loadings (sum of squares loadings) represent the amount of variance explained by each principal component, and the Proportion Var is:
\[\frac{SS\_loadings}{sum(SS\_loadings)}\]
6.2 Final IGI
The year of interest 2021 is chosen to calculate individual weights based on the PCA. At this stage, only IGI for 2021 is produced.
The next goal is to calculate the IGI for all years (2000-2021) by using the 2021 weights. This step has not been implemented yet.
Recoding of countries
There are five countries which were recoded to correspond with the UNCTADstat target economies.
- France: 250 -> 251 (France including French Guiana, Guadeloupe, Martinique, Mayotte, Reunion and including Monaco)
- Norway: 578 -> 579 (Including Svalbard and Jan Mayen)
- Switzerland: 756 -> 757 (Switzerland including Liechtenstein)
- United Kingdom: 826 -> 926 (United Kingdom including Channel Islands and Isle of Man)
- United States of America: 840 -> 842 (United States of America including Puerto Rico and United States Virgin Islands)
Data are collected from various international data sources and country coverage. Detailed metadata should be provided disaggregated by country, indicator and data source.