Appendix 7.A
Intergenerational Educational Mobility

The General Social Survey (GSS) has been carried out every year since 1972 by the National Opinion Research Center (NORC). It collects information on the nativity of the respondent's parents and grandparents, on the respondent's education, and on the education of the respondent's parents. We categorized all educational attainments as less than high school, high school, or more than high school. For a specific generation of respondent (first, second, or third, based on the nativity questions), we created a set of all linked pairs of parent-child educational attainments, using the information on education of respondent and of each parent of the respondent. We then treated the parents as the reference unit, and for each parental level of education, we calculated the proportional distribution of the children by educational attainment. Even within parental education categories, the children of higher-fertility parents have lower educational attainments. However, we did not weight for this, since the overrepresentation of such children in the sample simply reflects the higher fertility of their parents, which we wish to be reflected in the results for the average parent. We ignore differences in fertility by education of parent, which could bias the results in the optimistic direction.

It is well known that the characteristics of immigrants have been changing over the past several decades. Our controls for educational attainment may be insufficient to capture these changes. As a further control, we estimated separate transition matrices by ethnic origin group for Hispanics, Asians and all others, by immigrant generation and education group. We then formed a weighted average of these matrices for each generation and each education group, with weights equal to the ethnic shares in each generation. For first-generation immigrants we used the educational distribution of recent immigrant flows and base changes in the ethnic shares of subsequent generations on fertility differences between ethnic groups. These weighted average matrices were then used to project educational mobility in the analysis.

To estimate the transition matrices for Hispanics and others, we used educational outcomes for all children age at least 21 years, and born after 1960, in every GSS since 1972. For Asians, sample sizes were quite small, so we had to consider all children age at least 21 years and born after 1950. Even so, numbers were small, so we assumed that their dropout rates at each level of education were proportional to the corresponding dropout rates of others, with a different constant of proportionality estimated for each level of parental education. From these fitted dropout rates, we estimated the distribution of educational outcomes. The resulting matrices by immigrant generation, ethnicity, and educational attainment of parents were used as described in the preceding paragraph.

We also used an alternative procedure to estimate these transition matrices in which we weighted the sample in various ways. (1) Early-born cohorts are

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