Open-Population Inference: An Investigation of the Underrepresentation of the Second Generation in Research on Intergenerational Income Mobility

Studies about intergenerational income mobility are increasingly popular across the social sciences. These studies require individuals’ own incomes and their parents’ incomes to be observed prospectively across decades. Because this longitudinal observation is less difficult among third-and-higher generation persons than among 1.5- and second-generation persons (particularly undocumented 1.5-generation immigrants), studies of intergenerational income mobility risk underrepresenting 1.5- and second-generation persons. This article investigates this underrepresentation of people from immigrant families and provides an analytic framework that adjusts for this underrepresentation in studies of intergenerational income mobility. Using data on the experiences of two US birth cohorts, early baby boomers (born 1948–1953) and late generation Xers/early millennials (born 1978–1983), we illustrate our method of adjusting for the underrepresentation of 1.5- and second-generation persons. We find that within the late generation-X/early-millennial cohort, the underrepresentation of 1.5- and second-generation persons does not substantially bias intergenerational income mobility estimates. However, inferences about change across cohorts are more affected by the underrepresentation of 1.5- and second-generation persons in data used to estimate intergenerational income mobility because the population shares of these groups grew across the two cohorts. We discuss how our approach can be applied to other settings, including other countries, and to cross-country comparisons. We encourage future research on these comparisons because the underrepresentation of 1.5- and second-generation persons might substantially affect understanding of cross-national income mobility differences.