The life cycle of family size, at least in the U.S., has a very humped shape rather similar to that of income, though with a somewhat earlier peak. As a result, one might expect, and generally finds a fairly constant rate of saving in the central age group, but lower saving or even dissaving in the very young or old.
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Franco Modigliani, "Life Cycle, Individual Thrift and the Wealth of Nations" Lecture to the memory of Alfred Nobel, December 9, 1985, in: Nobel Lectures, Economics 1981-1990, Editor Karl-Göran Mäler, World Scientific Publishing Co., Singapore, 1992.