38
Gourdon
The Gini Index The Gini index is not sensitive to the number of observations: regardless of the number of sectors in the sample, a change in the number of sectors does not affect the value of the indicator. Brown’s formula is used: for each country and year, the sample is sorted by export lines, indexed by k, by increasing order of trade value x, so that xk < xk + 1. Cumulative export n
k
shares are X k =
∑ ∑ x . Cumulative shares in the number of export xl /
l =1
l
l =1
lines are simply k/n. Brown’s formula for the Gini coefficient is then n
G = 1−
∑ (( X
k
k =1
)
− X k −1 ) (2k − 1) /n .
(2.A.3)
The weight granted to each product line in the Gini coefficient depends on its rank and not its absolute value. Consequently, the Gini coefficient translates a function sensitive to variation in rank more than to the variations of export share. If the share of an export sector increases but does not lead to a progression in the ranking of the export sectors, it will not be fully translated in the index. Gini coefficients are very high, corresponding to Lorenz curves that are almost right angles. The reason has to do with the level of disaggregation rather than any conceptual difference between trade, production, and employment shares. At that level of disaggregation, there are a large number of product lines with small trade values, a relatively limited number of which account for the bulk of all countries’ trade (especially in developing countries but also for industrial ones). Thus, the data include a large number of economically irrelevant observations, and economically important categories in machinery, vehicles, computer equipment, and other industries are lumped together in “mammoth” lines. High Gini indexes are thus to be expected for all countries. (The interest here is in the evolution of the Gini index, not its level.)
Decomposition of the Theil Index Following Cadot, Carrère, and Strauss-Kahn (forthcoming), let us now look at concentration measures within and between three groups of products indexed by j (each group being country specific): traditional products (products exported by the country for at least two years), new products (products that were not active in the country’s export trade in