Revealed comparative advantage: Origin and Mathematical Formulation
The index most commonly used to measure RCA is the Balassa index (BI), which was developed and popularized by Bela Balassa (1965, 1989), though the concept of a specialization index was first proposed by Liesner (1958). If we wish to examine whether country i has manifest advantage in the export of product line j (at some level of product aggregation) over a set of reference countries represented by the symbol w, we construct the following simple Balassa index:
BIij ¼share of j in country i’ s exports ⁄ share of j in set w’ s exports (1)
If BIij is greater than 1.0, then country i would have RCA in product line j with respect to reference set w, since a proportionately greater share of its exports consist of j. If BIij is less than 1.0, the country is said to have revealed comparative disadvantage in good j. If we wish to be precise, we would have to specify the setwin the index aswell, say as BIijw, since the index depends on the particular set of countries chosen. Exports aremeasured as total export values to the rest of the world expressed in a particular year’s currency units. Clearly this index is very simple to compute from the actual trade data for any level of aggregation of export lines and is intuitively meaningful.
The index can also be extended from a single country i to a set k within a larger reference set w. For example, ifwewish to compute theRCAof advanced industrial countries (AIC) in the export of capital goods, we would need to first aggregate all capital goods exported by all AICs and compute the share of these in total exports. This ratio would then have to be divided by the share of aggregated capital goods in total world exports. The index can be similarlymodified to track the relative strength of any given trading region with respect to any particular characteristic of exports, provided that it canbe quantified, measured, and aggregated across a range of product lines.
In formal terms the Balassa, or revealed comparative advantage, index is often defined as follows for exporting region i, export line j and reference region w, where Xmn stands for export value of good n from region m and t stands for all exports from the particular region.The reference setwis often taken as the whole world:
RCAij ¼(Xij ⁄ Xit) ⁄ (Xwj ⁄ Xwt ) ¼(Xij ⁄ Xwj) ⁄ (Xit ⁄ Xwt ) (2)