Contrary to popular opinion, it has always been rare for people to financially support their aged parents.  In earlier times, people died too soon to “collect their pension” from their kids.  Nowadays the elderly live long enough to collect, but they’re still far more likely to give money to their kids and grandkids rather than receive it.  Money flows from old to young, just like Darwin would predict.

You might be tempted to conclude that government spending on seniors has nothing to do with how many kids seniors have.  If kids don’t give money to their parents, why should taxpayers care if seniors have kids?  But you should resist temptation.  Despite the lack of cash gifts from young to old, in-kind transfers are common.  And if you don’t have kids to provide in-kind transfers, the government picks up much of the tab with tax dollars.  As Wolf et al explain:

[I]nformal care provided by family, friends, and neighbors is widely acknowledged to comprise the majority of long-term care and support in the U.S. (Wolff & Kasper 2006). Most disabled elders are not institutionalized, and within that group most receive care either exclusively from informal providers or from a mixture of formal and informal providers. Unmarried individuals without living children are more likely than those with children to be in nursing homes, in cross-section (McNally & Wolf 1996), while childless elders have significantly higher levels of publicly-funded nursing home costs (through Medicare and Medicaid combined) than do parents (Wolf 1999). Other research has shown that having children serves both to delay entry into, and hasten exit from, nursing homes (Garber & MaCurdy 1990; Freedman 1993; Aykan 2003; Gaugler et al. 2007).

Of course, people with kids capture some of these benefits themselves.  Who wants to end up in a nursing home?  The point is that seniors capture only a fraction of the total benefit.  Future taxpayers collect the rest.  And from what I hear, they’re going to need all the help they can get.