In the first stage of the analysis, OP is regressed on several human capital indicators for each migrant in the relevant sample. These are (i) work experience (proxied by age and age squared), (ii) general assimilation effect (represented by a dummy variable indicating whether migration took place in the first or the second half of the decade),<sup>10</sup> and (iii) level of education. This is captured by six dummy variables that group the years of education into the following categories: less than five, five to nine, ten to twelve, high-school level, some college, Bachelor’s Degree or higher. Finally, we add country dummies for each migrant.

The estimation samples include only migrants who earned their final degrees before migration to the United States. Since a variable indicating the place where education was obtained is not directly available in the census, we construct it using the number of years of education and the age at migration.<sup>11</sup> Age restrictions ensure cohort comparability across censuses.<sup>12</sup> Regressions for each of the three OP indices are weighted and run _separately_ for each census year _t_ (where _t_ =1980, 1990 or 2000) and decade of arrival _d_ (where _d_ = 1970-1979 or 1980-1989). The first cohort (1970-9 arrival) is observed three times (in each census) whereas the second cohort (1980-9 arrival) is observed only twice (1990 and 2000 censuses). These _five_ estimations are performed separately for each OP measure, resulting in a total of _fifteen_ estimations. The estimated equation is given by: 10 Usage of intervals is justified by the fact that Census 1980 and Census 1990 do not provide the exact individual years of migration, but only the year interval.

11 A person is considered “US educated” if he arrived in the US before he would have normally acquired the declared education level. For example, if a university graduate arrives at the age of 23 or older, then he is considered “foreign educated”. Likewise, a high-school graduate arriving at 18 is assumed to have completed his studies abroad. Time since migration is reported as intervals of 5 years in Census 1980 and as smaller intervals for Census 1990. As such, to construct the age at migration variable for those Censuses, we make the imperfect assumption that migrants reported by Censuses 1990 and 1980 arrived in the middle year of the reported interval. We use different ages at which individuals complete their education. For example, we use 23 years Bachelor’s and higher Degree holders. On the other hand, it takes into account inadvertently those individuals who have completed their Master’s degree, Professional degree or PhD in the US after the age of 23. This is because Censuses 1980 does not allow identification of individuals with Bachelor’s degree, Master’s degree, Professional degree and PhD, so we use the more restrictive education 1980 classification for cross-Census comparability purposes.

12 Censuses report occupation only for people aged 16 or more. When following the members of the 1980s arrival cohort through 1990 and 2000 censuses, we set the minimum age to 16 for Census 1990 and 26 for Census 2000, whereas when analyzing individuals arriving in the 1970s, whose performances can be captured by all three censuses, the minimum ages are defined as 16, 26 and 36 for Censuses 1980, 1990 and 2000, respectively. To reduce the effect of cohorts shrinking across censuses because of older individuals, we also place upper limits on the age intervals used in the samples: 40 for Census 1980, 50 for Census 1990 and 60 for Census 2000.

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