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

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 associated materials), 541 (medicinal and pharmaceutical products, other than medicaments of group 542) and 751 (office machines).

In accordance with the Heckscher-Ohlin theorem, with two factors of production, labour and capital, labour abundant countries would produce and export relatively more of labour intensive products and could be considered to have comparative advantage in such products. Similarly, capital abundant countries could be considered to have comparative advantage in capital intensive products. Using the physical definition of factor abundance, if the ratio of labour force of a country relative to the world, to the gross capital formation of the same country relative to the world, exceeds unity, the country could be considered to be labour abundant. On the other hand, if the ratio falls short of unity, the country could be considered to be capital abundant.

Therefore, for each labour intensive and capital intensive manufactures on which data are collected, Spearman’s rank correlation coefficients and Pearson’s product moment correlation coefficients are computed between the alternative RCA indices of countries and the ratio of labour force of the corresponding countries relative to the world, to the gross capital formation of those countries relative to the world.

The parametric correlation results are further reaffirmed by reporting bivariate regression results with White’s heteroskedasticity corrected robust estimate of standard error in each case. Bivariate regressions of the following form are

**fitted to the data:**

Variable Y signifies the index values for the group of countries considered for each sector. Variable X refers to the ratio of labour force of each country relative to the world, to the gross capital formation of the same country relative to the world.

The results obtained by above methods in the context of the five indices are further reaffirmed by computing the product moment correlation and bivariate regression coefficients with logarithmic transformation of the variables. As the observations for the indices of Laursen, Hoen and Oosterhaven and Yu et al. are a mixture of positive and negative values, a shift of origin is necessitated for these three indices in order to make all the observations positive, thereby facilitating a logarithmic transformation of the variables. Hence, keeping in mind the limits of the distribution of these three indices, a value of 1 has been added to each of the observations for the indices of Laursen and Hoen and Oosterhaven, and a value of 0.25 has been added to each of the observations for the index of Yu et al. But as the observations for the index of Balassa are positive, computation of correlation and regression coefficients with logarithmic transformation of variables would be possible without any shift of origin. Although the coefficients for these four indices are reported in double log form, the same is not true for the modified index, as it is already in log form. Instead an attempt has been made to fit a semi log form for the modified index. The coefficients for the semi log form of the modified index would however be equivalent to the double log form for the index of Balassa.

SITC stands for Standard International Trade Classification. The classification of commodities into labour intensive or capital intensive sectors is based on UNCTAD Trade and Development Report 2002. The report classifies the sectors 652, 844 and 851 as ‘labour intensive and resource-based manufactures.’ The sectors 525, 541 and 751 are classified as ‘manufactures with high skill and technology intensity’ in the report and have been considered to be capital intensive sectors in this paper. This classification by UNCTAD has been made on the basis of mix of different skills, technology and capital intensities and scale characteristics.

The parametric correlation and regression analyses would especially be relevant for sectors, where the sample size is large. In the case of two out of three labour intensive sectors, the sample sizes get reasonably reduced (about 14 observations) when countries with only comparative advantage are considered. In all other cases, since the sample sizes vary from 21 to 42, the parametric correlation and regression results can be relied upon.

Rank correlation coefficients are not reported as they would remain unchanged even after the shift of origin and log transformation of variables.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 It is to be noted, the coefficient of determination or the square of the product moment correlation, r values between X (ratio of relative labour force to relative gross capital formation for the Heckscher-Ohlin theory) and Y (RCA indices) variables for the linear form are not strictly comparable with the r values between lnX and lnY for the corresponding non-linear form. However, this limitation is not so important when we are comparing the indices on the basis of the number of significant coefficients. But it’s a little more relevant when we are comparing the strength of association between the variables. Being fully aware of the limitations involved in the process, a rough and ready comparison between r XY = r XY* and r lnXlnY* where, Y*=Y+A, A being the value by which the origin is shifted for each of the indices wherever applicable, has been attempted.

With reference to the Heckscher-Ohlin theory, more the labour force of each country relative to the world exceeds (falls short of) its gross capital formation relative to the world, more (less) will it produce and export labour intensive products, and can have higher revealed comparative advantage (disadvantage) in such products. Thus, higher the value of the ratio of relative labour force to the relative gross capital formation, greater would be the value of RCA indices of countries in labour intensive products. Following similar arguments, higher the ratio, smaller would be the value of RCA indices of countries in capital intensive products.

To test the consistency with the Heckscher-Ohlin theory, following hypothesis is considered: RCA indices in labour intensive commodities would rise with a rise in ratio of relative labour force to relative gross capital formation. RCA indices in capital intensive commodities would fall with a rise in ratio of relative labour force to relative gross capital formation.

The hypothesis is tested against the null hypothesis of no association between the variables.

3.2 Discussion of Results The correlation and regression results, without any logarithmic transformation of the variables, for each of the four existing indices and the suggested modified index are presented in table 1 below. Considering first the results for the indices of Balassa, Laursen, Hoen and Oosterhaven and Yu et al., an attempt is made to determine which, among the existing indices are more consistent with the hypotheses. In the next stage, the results for the modified index are compared with the findings.

Table 1: Correlation and Regression Analyses for the Heckscher-Ohlin Theory: Year 2005

A takes a value of zero in case of the index of Balassa as the origin is not shifted.

Notes: ** denotes significant at 5% level (1 tail); * denotes significant at 1% level (1 tail). ρXY, rXY and bYX denote rank correlation, product moment correlation and bivariate regression coefficients respectively; X being the ratio of relative labour force to relative gross capital formation and Y being the RCA index values. A coefficient of 0.00 implies that the value is less than 0.01.

The correlation and regression results are based on 42 observations as certain countries had to be dropped due to nonavailability of relevant data. For the modified index, the numbers of observations are 42 each for the sectors 652, 764 and 851, 41 each for the sectors 844, 541 and 751. The figures in parentheses denote corresponding t values. Products are indicated by SITC codes as defined in the text.

Considering the first four indices in table 1, rank correlation coefficients have the expected signs and are significant for all cases except for the products with SITC codes 764 and 751 in the case of the index of Yu et al. The product moment correlation coefficients are however significant with expected signs only in the case of sectors 844, 851, 764, 541 and 751 for the index of Laursen. Since, parametric tests based on actual values of the variables, are more powerful than non-parametric tests, and also that the number of observations is reasonably large, the results generated by the product moment correlations could be attached more importance. This in effect implies the index of Laursen could be considered to be reasonably consistent with the hypothesis stated in sub-section 2.1.1. Among the four indices, the bivariate regression coefficients are significant in largest number of cases for the index of Laursen.

In addition to the number of coefficients with expected signs, conclusion about any particular index should also be based upon the proportion of variation in the RCA index explained by the ratio of relative labour force to relative gross capital formation, which is the square of the product moment correlation coefficient. A careful analysis in this regard would reveal that the index of Laursen scores higher than any of the other three indices. Hence, examining the correlation and regression results, the RCA index of Laursen seem to be largely consistent with the stated hypotheses.

Comparing the correlation and regression results for the modified index with that of Laursen, it would be evident from table 1 that the former performs at par with the index of Laursen, in terms of the number of significant coefficients with expected signs.

However, compared to the index of Laursen, the product moment correlation coefficients in case of the modified index are significant in greater number of cases for capital intensive products. Converse is observed in case of labour intensive products.

In cases where the product moment correlation coefficients are significant with expected signs, the square of the coefficient for the modified index is less than that for the index of Laursen for labour intensive products and greater for capital intensive products.

The product moment correlation and bivariate regression coefficients in double log form for the indices of Balassa, Laursen, Hoen and Oosterhaven and Yu et al. are reported in table 2. The coefficients for the semi log form for the modified index are not reported in any separate column as the values are equivalent to the double log form for the index of Balassa.

As the number of observations is large, the magnitude of the rank correlation coefficient is not considered.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 Table 2: Non-Linear Correlation and Regression Analyses for the Heckscher-Ohlin Theory: Year 2005

It would be evident from table 2, in terms of the number of significant coefficients with expected signs, the modified index is at par with the index of Laursen. In terms of the strength of association between variables, the modified index performs better than the index of Laursen in most cases. Hence, considering the strength of association between the variables and the number of significant coefficients with expected signs, the modified index could be judged to be performing empirically at par with the index of Laursen.

Incidentally, to test the reliability of t statistics based on which testing of hypothesis has been performed, normal probability plots of the residuals estimated from bivariate regressions, particularly in cases where the coefficients were significant, were attempted. A graphical representation of the standardized normal probability plots (without log transformation of variables) for the first four indices showed that index of Laursen generated normally distributed residuals in most cases. The other three indices seemed to generate largely non-normally distributed residuals. The modified index however, generated normally distributed residuals in all cases thus establishing its structural superiority over other indices. Even with the log transformation of variables, the modified index (whose semi-log form is equivalent to the double log form of Balassa) generated normally distributed residuals in cases greater than that of Laursen. The latter although performs better than the other two indices in terms of normally distributed residuals.

**4 Conclusion**

Empirical analyses, based on cross sectional data, of the existing and modified indices of RCA, were attempted in order to test their consistency with the Heckscher-Ohlin theory on comparative advantage of countries. It revealed that the index of Laursen (1998) performed empirically well. However, its structural features are not entirely satisfactory. The index of Yu et al. (2008) although is structurally superior to the index of Laursen, it does not generate results consistent with the hypotheses in most cases. The modified RCA index has reasonably good structural features and at the same time generated results consistent with the Heckscher-Ohlin theory. Thus, taking into consideration the structural advantages and empirical findings in different situations the suggested modified RCA index seems to be a reasonable choice for examining the revealed comparative advantage of countries.

Conference papers © Knowledge Globalization Institute, Pune, India, 2012 Acknowledgement KD acknowledges the Department of Economics in Darla Moore School of Business, University of South Carolina, for their kind hospitality, during which part of the work was completed. Especially, the authors would like to thank Dr. William R. Hauk for various useful discussions on the subject matter and for providing critical comments for improving the manuscript.

References Balassa, B. (1965), “Trade Liberalisation and 'Revealed' Comparative Advantage”, Manchester School of Economics and Social Studies, Vol. 33, pp. 99-123.

Benedictis, L.D., and M. Tamberi (2001), “A Note on Balassa Index of Revealed Comparative Advantage”, Universitẚ di Macerata and Universitẚ di Ancona, Italy, Working Paper 158.

Davis, D.R. (1995), “Intra-Industry Trade: A Heckscher-Ohlin-Ricardo Approach”, Journal of International Economics, Vol. 39, pp.

201-226.