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Published: января 15, 2013

Revealed comparative advantage: Origin and Mathematical Formulation

One problem with the basic Balassa index is that it is not symmetrically distributed around the neutral value 1.0, ranging from0 to 1 for comparative disadvantage and indefinitely upward from 1.0 for comparative advantage products. This problem is easily corrected by taking natural logarithms of the ratios with the index defined as follows:

RCAij ¼ln (Xij ⁄ Xit )ln (Xwj ⁄ Xwt ) (3)

The revised index is now symmetric around 0. This form is particularly useful for econometric studies. An alternative transformation, which yields RCA values between 1 andþ1 around 0, is given in Laursen (1998), but it is probably less useful than the log form for econometric work.

Vollrath (1991) proposed the following alternative index of trade specialization, which brings imports into the calculation:

RCAv1 ¼RXARMA (4) Where RXA¼(Xij ⁄ Xit) ⁄ (Xwj ⁄ Xwt ), the original export specialization index, andRMA¼(Mij ⁄Mit) ⁄ (Mwj ⁄Mwt ), which is a similar import specialization index.

An alternative formulation of the Vollrath index takes the following form:

RCAv2 ¼ln RXAln RMA (5)

The Michaely index MI (see Laursen 1998) for country i and product j is defined as the difference between the share of sector j in total exports minus the share of sector j in total imports. There is no reference set of countries, so the index ranges from 1 toþ1 and is 0 if import shares areperfectlybalanced with export shares:

MIij ¼Xij ⁄ Xit Mij ⁄Mit (6)

A particularly useful measure of normalized revealed comparative advantage (NRCA), proposed by Yu et al. (2008), is defined in equation 7, where w refers to the entire world and t to total exports. This index can be interpreted as the deviation of the normalized value of country i exports of product line j with respect to total world exports (the first term) from its expected comparative advantage neutral value (the second term).

NRCAij ¼Xij ⁄ Xwt Xwj Xit ⁄ X 2 wt (7)

The equivalent form of equation 8 shows an alternative deviation kernel (term one) normalized by the relative weight of country i exports in world exports (term two).

NRCAij ¼[Xij ⁄ Xit Xwj ⁄ Xwt ]fXit ⁄ Xwtg (8)

This index has some useful properties: it is symmetrical about zero and displays additive consistency across product lines and country groupings. It just needs to be scaled up by an arbitrary factor to facilitate numerical comparisons, since both terms in equation 7 yield very small values; but this is no problem since RCA is a relative measure in any case. Furthermore the sum of NRCA across all commodities for any one country is zero as is the sum of NRCA across all countries for any one commodity.

Overall the RCA concept has proved to be an enduring and easily computablemeasure that can be used to track patterns of trade and production specialization. It has been used to study the performance of individual countries or groups of countries with respect to a larger set or even to comprehensively compare countries with one another, as in Batra and Khan (2005), which compares the evolution of India and China. RCA is therefore a very useful and powerful tool of trade analysis, used by academics and economic consultants to study evolving patterns in the world economy.