It used to be the case that most elderly people, once widowed, would live with one of their children. Very few do so now, and one can have several conjecture for the reasons thereof: societal changes, government sponsored care for the elderly, better retirement pensions, emancipation of the children or the elderly, etc.
Carlos Bethencourt and José-Víctor Ríos-Rull find that the increases in incomes of the elderly can explain the most in this change. Indeed, their income has increased twice as fast as that of their children in the 1970's and 1980's. They come to this conclusion after estimating a rich model that takes into account household economies of scale, the game that parent and child play when investing in the home (they may have different preferences) and differences in income. Many specifications come to basically to the same conclusion: it is the elderly who want to avoid living with their children, and they started doing so as soon as they had sufficient income. Thus the story is not about ungrateful children who push their parents away.