The net grandparents-grandchildren association can be summarized by a single uniform association parameter. Net of parents’ social class, the odds of grandchildren entering the professional-managerial class rather than the unskilled manual class are at least two and a half times better if the grandparents were themselves in professional-managerial rather than unskilled manual-class positions. This grandparents effect in social mobility persists even when parents’ education, income, and wealth are taken into account.
They do add the caveat that these study results might not hold for other societies, and of course there are a lot of things besides grandparental status that influences life chances. But you can't count grandparents out. And, as a parent, keep in mind that you are influencing not only the lives of your children, but of their children as well.