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and the taxes they pay depend strongly on their earnings. Migrants to the United States do not all have the same human resources, which heavily influence earnings. Our analysis captures some of this heterogeneity by distinguishing three categories of educational attainment of immigrants and others: less than high school, exactly high school, and more than high school. For our longitudinal analysis, we need to project educational attainment for the children and grandchildren of immigrants, according to the immigrant's education at arrival. For this purpose we analyzed data from the General Social Survey in a merged sample, calculating intergenerational transition matrices for these three educational categories.
Our analysis distinguishes three lengths of an immigrant's time since arrival: less than 5 years, 5 to 9 years, and 10 years and more. For every age, for every program, and for taxes, we estimate three age schedules from the CPS data, one for each duration. That is, we fully incorporate all the ways in which age and duration of residence here interact for these three duration categories and five-year age groups. The durations were chosen to correspond to potential qualification for entitlement programs, such as Aid to Families with Dependent Children (AFDC) and Old-age, Survivors, Disability, and Health Insurance (OASDHI).7
We also analyze the taxes paid by immigrants according to their education, age, and time since arrival. Because immigrants arriving in different periods have had different characteristics, the time of arrival variable may overstate the degree of earnings progress that can be expected of current immigrants. Those who have been in the United States for more than 10 years in 1994-95 may be different from more recent arrivals in ways not fully captured by their education and age.
For this reason we have done the analysis in two ways: first, assuming that the taxes paid by immigrants do follow the progress indicated by the trajectory estimated according to "time since arrival" and, second, assuming that the earnings follow this trajectory only for the first 10 years, and that thereafter the ratio of earnings between immigrants and native-born workers is fixed.8 There are
For immigrants who arrive after age 55, we constrain benefits after 9 years' duration to conform to those for 5 to 9 years' duration. This procedure avoids confusing qualifiers and nonqualifiers for OASDHI for people at age 70 and above at durations of 10+ years. However, many elderly immigrants whom the data describe as having been in the United States for only a short time, and who therefore would not be expected to qualify for many benefits such as OASDHI, must actually be earlier immigrants who worked in the United States long enough to qualify for OASDHI and other programs, and who have recently returned after a stay abroad. The duration variable will be misleading for such people, and this creates problems for estimates of the costs of elderly first-time immigrants, and for calculating the effects of the 1996 welfare reform legislation on the costs of elderly immigrants. In addition, some elderly first-time immigrants are refugees, who qualify for certain benefits despite their short durations of residence in the United States and lack of U.S. work histories. For these elderly immigrants, the duration variable should have different effects.
Duleep and Regets (1976) compare the 1994 and 1995 CPS data and conclude that the longitudinal changes accurately reflect the cross-sectional duration profiles.