Calculating the composite indices

The following technique is used to develop smooth index number series to facilitate aggregation and comparison of data from different sources: the original data is transformed into indices ranging from 0 to 100, based on minimum and maximum values in a set of reference countries.

The scaling between minimum and maximum values, however, raises the question of possible distortions arising in cases where distributions are skewed or have long tails. In these cases, the ranking of countries could be unduly bunched and would obscure the extent of the differences among the majority of countries. Therefore, to minimize these problems, bounds are imposed on the extreme outliers to allow for better comparison of values in the distribution. The bounds are numbers used to define the low and high end of the distribution of the index number series before application of the "max-min" procedure. Accordingly, the bounds replace the actual country data in the calculation of the index concerned. For instance, in the case of population, a minimum bound of 150,000 persons and a maximum bound of 100,000.000 persons were imposed on countries with populations below or above those levels, respectively, in the 2006 review (see table below). Thus, countries with populations smaller than the lower bound had the value of that variable replaced by 150,000, while 100,000,000 was used for those countries with populations above the upper bound.

The index numbers are derived by subtracting the minimum value in the distribution from each observed value in the series and expressing the result as a percentage of the difference between the maximum (max) and minimum (min) values in the distribution as indicated by the following formula:


I = [(V-min)/(max-min)] x 100

where,

• V is the observed value in the series, and
• I is the new, rescaled, index-number representation with a value ranging from 0 to 100.

The indices are defined in such a way that the higher the value of the component variables of the HAI, the better the human assets score (and vice versa). In contrast, higher values of the EVI components indicate the presence of increased vulnerability (and vice versa).

Some adjustment in the formula is needed in the case of certain components. For instance, if the max-min procedure described above were applied to such variables as under-five mortality and population, the procedure would generate indices whose values would be the opposite of what they were supposed to reflect in the HAI and EVI indicators. A higher index value for under-five mortality (one of the component variables in the HAI) should contribute to a lower HAI score since this would indicate, ceteris paribus, the existence of lower human assets in that country. Thus, if unadjusted, countries with high child mortality rates would yield relatively high index number values and high HAI scores (indicating a high level of human assets). Similarly, countries with large populations (a proxy for economic size) would yield high index number values and high EVI scores (indicating high vulnerability), which is not the case, as countries with larger populations usually have relatively greater resilience to shocks. In such cases, the following variant of the max-min procedure is used:


II = [(max-VV)/(max-min)] x 100,
II = 100-I

where,

• V is the observed value in the series, and
• II is the rescaled index number representation with values ranging from 0 to 100.

Redefining the relevant components in this manner now gives the desired result of countries with the highest child mortality rates having relatively lower index numbers and lower HAI scores. Similarly, countries with larger populations would have lower index values and lower EVI scores.

The reference group

As HAI and EVI are relative measures, eligibility of countries for inclusion into or graduation from the list depends on the distribution of scores within a larger reference group.

Starting with the 2012 review, the reference group will consist of all LDCs (independent of their income status) and all other countries whose per capita income in any of the three years used to determine average incomes (e.g., 2008-2010 in case of the 2012 review) has been less than 20 per cent above the low income thresholds determined by the World Bank. As in the past, countries with economies in transition are not included in the reference group.

Previously, the reference group contained all LDCs and other countries whose per capita income in any of the three years preceding the review has been below the World Bank's low income thresholds. However, as the number of low income non-LDCs has shrunk considerable, that rule has been adjusted to ensure that eligibility of countries continues to depend on the development progress of LDC relative to non-LDCs.

Refinements of the EVI introduced for the 2012 review

The indicator "victims of natural disasters" replaces "homelessness caused by natural disasters". It is defined as the share of populations that are killed or affected (i.e., people requiring immediate food, water, shelter, sanitation or medical assistance) by natural disasters. It improves coverage of natural disasters by additionally representing climate-related disasters such as drought and extreme temperatures, other weather and climate-related disasters such as floods and storms as well as geo-physical disasters such as earthquakes or volcanoes.

The new indicator on the percentage of population living in low elevated coastal zones—currently the only component of the new environment sub-index—captures vulnerability to coastal impacts associated with climate change. The population-based indicator reflects the exposure of population and economic assets better than alternative indicators based on land area only.

Additionally, the Committee decided to assign equal weights to the components of the exposure index (previously population carry a heavier weight) to increase transparency as well as to avoid bias in view of the introduction of the indicator on low elevated coastal zones. Finally, some other minor refinements were introduced in EVI as follows.

• The "smallness" component is renamed "size sub-index" a more generic term.
• The structural index is now termed "economic structure sub-index" in order to improve clarity.