Given that gradient, one would expect it to be reflected in students expectations: low SES students should expect to do worse than high SES one's. Its simply the rational thing to do.
Good comparative data on such expectations is hard to come by [I think] but the PISA 2000 data [and possibly other waves] has a measure of how students expect to end up and one can compare it with where their parents actually are. The index is due to Ganzeboom et al (1992) and though it may be not how an economist would do things it seems to make sense.
So below I graph students expected SES against their father's for Ireland and Sweden. As predicted, it slopes up. Its interesting that there are flat bits at the bottom. Rightly or wrongly, students there don't think SES matters. Perhaps its a case of how, in Bob Dylan's memorable words, "When you got nothing, you got nothing to lose".
Sweden, of course, is a much more egalitarian country than Ireland. Other evidence shows that the dependence of one's education on one's parents is particularly high in Ireland compared to other OECD countries [shameless plug for my own work below]. So I would have expected the gradient to be steeper in Ireland than Sweden. I bet you would too.
Wrong! Sweden's is noticebly steeper: in numerical terms the correlation is 0.25 in Sweden and only 0.19 in Ireland. Why I don't know.
Chevalier, A., K.Denny, and D.McMahon (2009) “Intergenerational Mobility and Education Equality”. In Education and Inequality across