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I am looking for a data about the attainment of college degree (response variable) based on the parent's education and other demographics.
This kind of data is e.g. referenced in Categorical Data Analysis for the Behavioral and Social Sciences, and I remember [vague] references to it when I was in school. But I can't find any dataset.
I believe the General Social Survey (GSS) has this. And there are the longitudinal education surveys that have been launched every few years for decades: Baccalaureate & Beyond, Beginning PostSecondary, National Educational Longitudinal Survey, etc.
[edit: added links]
I've gotten used to blogs and websites that reject comments that contain too many links so I no longer worry about providing links. But I've been requested to supply links so here's a decent one for the educational longitudinal surveys, at the National Center for Education Statistics. There are a number of additional surveys that all have acronyms such as NLS, NELS, or ELS that for some reason are not listed but this is a very good starting point. It also does not link to the GSS.
And here's another NCES webpage that gives an overall introduction to some of the longitudinal surveys -- but only four of them.
Check out Opportunity Insights, now at Harvard and led by Chetty, Friedman and Hendren. Not only is their work fascinating, but they are great about transparency in methodology and releasing data tables.
For instance last year's Mobility Report Cards: The Role of Colleges in Intergenerational Mobility https://opportunityinsights.org/paper/mobilityreportcards/
Raj Chetty, John Friedman, Emmanuel Saez, Nicholas Turner, Danny Yagan
NBER WORKING PAPER NO. 23618, REVISED VERSION JULY 2017
We characterize intergenerational income mobility at each college in the United States using data for over 30 million college students from 1999-2013.
