In this article we identify sample underenumeration, changing cohort quality, and selective emigration as problems that threaten the validity of findings on immigrant socioeconomic assimilation derived from cross-sectional data. Using information on Mexican immigrants from the 1990 U.S. census and a unique binational source of data, we address the effects of these problems on cross-sectional regressions of English proficiency and wage attainment. Our results suggest that the underenumeration of temporary and undocumented migrants biases the estimated effects of human capital variables downward, but that selective emigration does not significantly affect cross-sectional models. We do find, however, that period of entry is a poor proxy for total migrant experience, and when we disentangle duration and cohort effects, we find some evidence for shifts in cohort quality over time, but not the systematic decline seen by others. © 1994 Academic Press.

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