# «Published Annually Vol. 6, No. 1 ISBN 978-0-979-7593-3-8 CONFERENCE PROCEEDINGS Sawyer School of Business, Suffolk University, Boston, Massachusetts ...»

While Balassa’s RCA index is useful in determining whether or not a country has comparative advantage in a commodity, it had been subjected to intense criticism. Several economists identified problems with the index in empirical estimation. Yeats (1985) pointed out that the traditional method of ranking industries in a country according to the value of the Balassa’s RCA index may fail to indicate that the country could be a leader in a particular industry as compared to other countries. Yeats ranked countries according to the RCA values in a particular industry to check the consistency of this ranking with the ranking of industries in a particular country according to their RCA values. The inconsistency between the two rankings led Yeats to conclude that Balassa’s RCA index does not accurately rank industries according to a country’s real comparative advantage.

Yeats observed, this inconsistency in ranking arises out of the fact that different industries have different distribution of country index values. He also observed Balassa’s RCA index could give misleading results because, the index might signify Refer to Vollrath (1991).

If in an industry, the country index values are highly concentrated around unity, then the country with the greatest Laursen (1998) argued that the asymmetric distribution of the Balassa’s index makes it unsuitable for econometric analysis. The lower bound of the distribution is zero. The upper bound can assume any value greater than unity and would generally tend to infinity. Laursen commented, with such a skewed distribution, the error term in regression analysis would be non-normal and hence, t and F statistics cannot be used reliably.

Hoen and Oosterhaven (2006) recognised the fact that the distribution of the Balassa’s index dependent upon the number of countries and the commodities in the analysis. Considering the original Balassa index, the distribution of the index will vary with the number of reference countries with respect to which the export performance of a particular country is compared. The distribution of the index will also vary with the level of aggregation of the commodity. At more and more detailed sectoral classification, the denominator of the index becomes smaller and smaller, which alters the extreme points of its distribution. An unstable distribution will have unstable mean, making comparison of index values across country or commodity difficult. Hoen and Oosterhaven attributed this problem to the ratio form of the index. Yu et al. (2008) also recognized the problems associated with the variability of mean for the index of Balassa. However, it is to be noted, foregoing arguments about the instability of the mean, holds for arithmetic mean of ratios. In case of ratios with both numerator and denominator varying, geometric mean is the appropriate concept. On averaging Balassa’s index values across countries or commodities by using geometric mean (or ratios of arithmetic mean of numerator to the denominator), it would be evident that the average is not significantly different from unity.

**2.2 Other Indices of RCA**

With due recognition to the problems associated with the RCA index of Balassa for empirical estimation, some of the above mentioned authors came up with a number of alternative RCA indices. Identifying the asymmetrical distribution of the index of Balassa, Laursen (1998) suggested a simple modification of the index in order to make its distribution symmetric. His index

**takes the following form:**

The lower limit of the distribution of this index is -1 with upper limit tending to +1. The comparative advantage neutral point would be close to zero which also defines the mean of the distribution. The mean value can be achieved by considering the geometric mean or ratio of the arithmetic mean of the numerator to the arithmetic mean of the denominator. Country i would reveal comparative advantage in product a, if the value of the index is positive, and reveal comparative disadvantage if the value of the index is negative. Benedictis and Tamberi (2001) however point out that the economic interpretation of the index is not very clear. Moreover, this index, like the index of Balassa, might signify greater comparative advantage for countries or for commodities with smaller market share in the world export market.

Hoen and Oosterhaven (2006) suggested an alternative to the index of Balassa. They replaced the ratio form of the index with

**the deviation form. Their index takes the following form:**

comparative advantage in the industry could have relatively low RCA index value. If on the other hand, in another industry, the country index values are widely distributed around unity, then the country which does not have greatest comparative advantage relative to other countries might have very high index value (Yeats 1985, 62).

If the reference group of countries consists of the world less country i, the lower and the upper limits of the distribution would be 0 (rest of the world completely specialises in product a) and undefined (country i completely specialises in product a) respectively, with 1 being the comparative advantage neutral point. But if the reference group is the entire world, the limits of the distribution would be as mentioned in the text. Use of entire world as the group, ensures comparability of the index values across country.

If the reference group of countries consists of the world less country i, the lower and the upper limits of the distribution would be exactly equal to -1 and +1 respectively, with zero being the comparative advantage neutral point.

The authors term it as the Additive RCA index. They, however, insisted that country i should be deducted from reference group of countries, in which case the lower and the upper limits of the distribution of the index would be exactly equal to -1 and +1 respectively. Zero would be the comparative advantage neutral point. However, in that case, use of the index for inter country comparison is questionable. Hence, with entire world as the reference group, the lower and the upper limits of the distribution would tend to -1 and +1 respectively. If the index takes a value greater (less) than zero then country i would reveal comparative advantage (disadvantage) in product a. An approximate value of zero denotes comparative advantage neutral point.

If geometric mean or the ratio of arithmetic mean of the numerator to the arithmetic mean of the denominator, is considered for computing the mean of a commodity’s (country’s) index values across countries (commodities), the computed value would be close to zero, implying stability of the mean and therefore the distribution.

Yu et al. (2008) by utilizing the probabilistic framework of Kunimoto (1977) came up with a new index for measuring comparative advantage. In this framework, comparative advantage of country i in product a, is measured by deviation of actual i i w w exports of a by i, X a, from its expected exports of the same product in a world of no relative advantages, (X t / X t) X a. The expected exports define the comparative advantage neutral level. The deviation of actual exports from expected exports is further normalized by the world total exports. The Normalised Revealed Comparative Advantage index of country i in product a

**is thus stated in the following form:**

If the index is positive (negative), then country i reveals comparative advantage (disadvantage) in product a.

Yu et al. (2008) argue that their index satisfies most of the desirable properties of the RCA index for empirical analysis. First, the index is symmetric about zero with the lower and the upper limits of the distribution being -1/4 and +1/4 respectively. Second, the sum of a commodity’s (country’s) normalised RCA scores over all countries (commodities) equals zero i.e., the mean value is constant and stable. Given the stability of the mean and thereby, the distribution of the index, it is possible to compare the indices across country, commodity and time (Yu et al. 2008, 274-275).

While Yu et al. (2008) themselves identified several advantages of their index, there are certain other distinctive features of their index that make it particularly attractive compared to other RCA indices, considered in this section. First, most of the other indices are sensitive to the size of the country or the sector or both. In comparison, the index of Yu et al. is not noticeably influenced by the size of the country or of the commodity, due to its deviation form and normalization of the index by total world exports. Second, there are no complications involved in computing the mean of the index values because unlike other indices, the denominator of the index is fixed. Therefore, contrary to other indices, simple arithmetic mean can be used for the purpose.

**2.3 Modified Index of RCA**

Incidentally, an attempt has been made to suggest another index of RCA with reasonably good structural features and which if empirically analysed, might be expected to generate more reliable results than the four existing indices. Hence, in this section a modification of the RCA index fo Balassa on the line of Vollrath (1991) has been suggested.

**To derive the new index we consider the RCA index of Balassa:**

Though Vollrath (1991) suggested an index similar to the one discussed in this section, the reference group of countries and commodities were rest of the world and rest of the commodities exported respectively. However, the modified index suggested in this section considers the entire world to be the reference group of countries and all commodities to the reference group of commodities. This consideration inevitably permits comparison of index values across countries and commodities.

Thus, the new index measures on logarithmic scale, the extent to which exports of commodity a in country i’s total exports differs from exports of the same commodity from world’s total exports. Hence, the new index could be provided an economic interpretation. There are certain additional advantages of this index. Firstly, the index is symmetric about zero with the upper and lower limits of its distribution being +∞ and -∞. Secondly, due to the logarithmic form of the index, the mean of the index values, which is zero, could be computed by considering simple arithmetic mean, either across country or across commodity.

Hence, the stability of mean ensures the comparison of the index across commodity or across country. Thirdly, though this index, like the parent index of Balassa, remains sensitive to the size of a sector or country, this sensitivity is expected to be less compared to the indices of not only Balassa but also Hoen and Oosterhaven and even Laursen, as it is measured on a log scale.

Lastly, an added advantage of the modified index over all the four existing RCA indices considered is, being defined in logarithmic form, the estimated residuals from any regression with the modified index as the dependent variable, could be expected to be normally distributed as economic variables like exports are log-normally distributed. Its only limitation is that the index cannot be defined in case the export of a product by a country is zero. However, this sort of boundary problem is not uncommon in economic theory.

**3 Empirical Analyses of RCA Indices**

Section 2 enumerates the problems with the RCA index of Balassa for empirical estimation, and puts forward various other indices of RCA, suggested in the literature to overcome the deficiencies of Balassa’s index. But the existing literature have not tried to analyse the extent to which the alternative indices of RCA, are consistent with the Heckscher-Ohlin theory on comparative advantage of countries. Hence, in addition to testing the consistency of the existing indices with the HeckscherOhlin theory, the modified index suggested in section 2.3 is also empirically analysed in this section.

**3.1 Data and Methodology**

For empirically analyzing the relevance of the Heckscher-Ohlin theory in the context of the RCA indices, necessary data are collected for each of 47 countries and for the world as a whole, for the year 2005, from United Nations COMTRADE database and International Trade Statistics Yearbook 2009. Three labour intensive and three capital intensive sectors were selected for the analysis. The labour intensive sectors have SITC (revision 3) 3 digit codes of 652 (cotton fabrics, woven), 844 (women and girls clothing, knit) and 851 (footwear). The capital intensive sectors have SITC (revision 3) 3 digit codes of 525 (radioactive and Laursen (1998) has in fact identified this problem with the logarithmic transformation of Balassa’s RCA index.

Several other indices have been suggested in the literature for measuring comparative advantage of countries, such as those by Proudman and Redding (1998) and Vollrath (1991). The RCA index of Proudman and Redding (1998) is not considered for analysis in this paper as the index is very similar to the Balassa’s index, except for the normalization term. It does not address most of the problems associated with the empirical examination of the Balassa’s index, other than the issue of cross commodity comparability. The indices of Vollrath (1991) have also not been included because some of them depend upon import values and as pointed by Balassa, data on country imports could be highly distorted due to the incidence of subsidies, quotas and other import restrictions. Hence, the indices might not reflect the true comparative advantage of countries.

Moreover, since Vollrath insisted on having rest of the world and rest of commodities as the reference group, the indices would not be suitable for cross sectional analysis as attempted in this section.

The group of 47 countries include all the ASEAN countries, SAARC countries excluding Afghanistan; other Asian countries of China and Japan; the European countries of Austria, Belgium, Bulgaria, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Norway, Poland, Portugal, Spain, Sweden, Switzerland, and United Kingdom; Eurasian country of Turkey; Australia and New Zealand from Oceania; African countries of Kenya and Mauritius; Guatemala, Mexico, Peru and United States.