split into three sub-components (versions 4a-4c). The decision to produce the final matrix utilizing the foreign-born definition was based on the fact that a greater number of countries report data by place of birth, that this definition is less vulnerable to differences in naturalization policies across countries and that it more readily accords to the actual movement of migrants, which is the economist’s principal interest. These three iterations of version 4 are described in greater detail below.

# **_Version 4a_**

The 2003 United Nations data set (United Nations 2004), covering migrant stocks for the year 2000, is generally considered the most comparable source on international migrant stocks, despite the fact that some of the data were extrapolated from older sources. Indeed, it is still held in high esteem even though, where no foreign-born data are available, numbers are interpolated from data based on nationality and ethnicity concepts. Where no other data were available it was deemed sensible to use the United Nations data for country totals and our data are essentially calibrated to the United Nations totals.

A high degree of correlation has previously been understood to exist between the foreign-born and foreign-nationality populations (Harrison, Britton and Swanson 2003). If this is indeed the case, then it would be feasible to use information from the nationality matrix to supplement that of the foreign-born. First, it was important to check that this association existed in relation to the data collected. For those 35 countries where data were available for both the foreign-born and the foreign population for comparable years, a technique based on the entropy measure devised by Walmsley and McDougal (2004) was used (Annex 2).

This methodology calculates the differences in the shares between the foreign-born matrix and the nationality matrix as the equally weighted average of the simple share from a particular coefficient in the foreign-born matrix multiplied by the natural log of the ratio of that share, to the equivalent share in the nationality matrix. The two major advantages of this technique are first that it is possible to compare shares between two tables whilst ignoring any zero entries; and second, that the differences between two large shares are given less weight than the same absolute difference in two relatively smaller shares.

On average, the entropy difference between shares for the 35 countries for which data were available for both the foreign-born and the foreign nationality was negligible. Having found that the series were indeed highly correlated, the shares from the nationality matrix were multiplied by the United Nations totals in the foreign-born matrix for those countries where no bilateral information was available. South-East and East Asian countries<sup>18</sup> with detailed bilateral data were not subjected to this treatment as naturalizations are so rare that it is fair to assume that these data may be directly equated to the foreign-born population. We calculated the magnitude of the margin of error of treating foreign nationals as equivalent to the foreign-born to be approximately 1.22 percent for Japan, and 0.15 for South Korea.<sup>19</sup> The foreign-born coefficients for those 75 countries until now lacking any bilateral foreign-born information were therefore filled.

> 18 Namely Japan, Korea, Macau, the Philippines, Thailand and Myanmar.

> 19 These are calculated as the number of naturalizations divided by the total number of foreign nationals.

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