Construction of the Index
Overall transformation index
We construct an overall African transformation index, the ATI, by combining subindexes constructed for the five indicators discussed above. Our measure of economic transformation therefore goes beyond GDP growth. Yes, we want high GDP growth to raise the level of GDP per capita. But we want more than that: we want growth with DEPTH— Diversification of production and exports, Export competitiveness, Productivity increases, Technology upgrading, and improvements in Human economic well-being.
Each of the DEPTH indicators is constructed as a subindex, in most cases by aggregating indexes of subindicators. The five resulting subindexes are combined to form the ATI.
Indicators and associated subindicators
- D: Diversification of production and exports
- Production diversification: share of manufacturing value added in GDP. (D1)
- Export commodity diversification: 100 minus the share of top five exports. (D2)
- Export sector diversification: share of manufacturing and service exports in total exports. Manufacturing exports include processed agricultural products. (D3)
- E: Export competitiveness
- Country’s share of world nonextractive exports of goods and services divided by country’s share of world nonextractive GDP (equivalent to the exports-to-GDP ratio of the country divided by the world’s exports-to-GDP ratio, with extractives taken out of exports and GDP for both the country and the world).
- P: Productivity
- Manufacturing: manufacturing value added per manufacturing worker (2005 US$). (P1)
- Agriculture: cereal yield (kilograms per hectare). (P2)
- T: Technology
- Production: share of mediumand high-technology products in manufacturing value added. (The Lall approach is used for the technology decomposition of manufacturing value added.) (T1)11
- Exports: Share of mediumand high-technology products in merchandise exports. (The Lall approach to technology decomposition of commodity exports is used; resource-based and agricultural exports are separate; low-, medium-, and high-technology refer only to manufactured exports.) (T2)
- H: Human economic well-being
- The level of GDP per capita (2005 US$ PPP). (H1)
- The ratio of formal sector employment to the labor force. (H2)
Normalization of subindicators
Each subindicator for each country is normalized to produce an index ranging from 0 to 100 according to the procedure below:
NCS = [RCS – Min (RCS)]/
[Max (RCS) – Min (RCS)] * 100 (1)
where NCS is the normalized country score (on subindicator), RCS is the raw country score (that is, the raw data on the subindicator for the country), Min (RCS) is the minimum raw country score among the group of countries (on subindicator), Max (RCS) is the maximum raw country score among the group of countries (on subindicator) and where
NCS = 0 when RCS = Min (RCS)
NCS = 100 when RCS = Max (RCS)
Specification of DEPTH subindexes
Subindexes for the five DEPTH indicators are constructed from the subindicator indexes as follows:
- Diversification of production and exports, D = 0.5D1 + (0.25D2 + 0.25D3)
- Export competitiveness, E = 1.0E
- Productivity, P = 0.5P1 + 0.5P2
- Technology, T = 0.5T1 + 0.5T2
- Human economic well‑being, H = 0.5H1 + 0.5H2
Since each subindicator index ranges from 0 to 100, the five DEPTH subindexes constructed using the above weighting scheme also lie in the same range. The DEPTH subindexes score each country on each of the five main economic transformation indicators, with a higher score indicating better performance. Countries can be thus compared on each transformation indicator.
Specification of the aggregate African Transformation Index
The ATI is constructed from the five DEPTH subindexes using equal weights.
ATI = 0.2D + 0.2E + 0.2P + 0.2T + 0.2H (2)
Since the ATI is a weighted sum of indices, it also is an index ranging from 0 to 100. Each country has an ATI score, and countries can be compared according to their ATI scores. The higher the score, the better the performance.
The five DEPTH subindexes are given equal weights in the aggregate index for the simple reason that we have no strong reasons to think one is more important than the other in a country’s transformation. For constructing each DEPTH subindex, we have again followed this principle of equal weights. For the first subindex, we have weighted production diversification (D1) and export diversification (D2 + D3) equally. The second subindex, export competitiveness, involves no subindicators. Equal weights are also given to productivity in manufacturing and in agriculture in the third subindex. For the fourth subindex, technology in production and technology in exports have been weighed equally. The fifth subindex, which comprises GDP per capita and the share of formal employment in the labor force, are again weighted equally. We use GDP per capita instead of GNP per capita because we want to focus on production.
We show country rankings on the ATI and on the DEPTH subindexes for the two three-year periods centered on 2000 and 2010 (the average for 1999–2001 and the average for 2009–11). We take averages because, given the volatility of the commodity-dependent economies of Africa, the values of the relevant variables for any given year could give misleading results. Averaging helps diminish this possibility.
Scores and rankings
For any given period, the scores on the ATI (and on the associated DEPTH subindexes) provide a ranking of the countries. In addition, for that particular period the difference in the scores of any two countries indicates how far apart the countries are on an index. When we compare performance across two periods, we focus only on the changes in country rankings over the periods. We use a country’s change in rank over two periods on the ATI (and the associated subindexes) to measure whether it is improving (lowering its rank) relative to other countries or deteriorating (lifting its rank).