Read it at CNBC NetNet
The Problem With Social Security
by John Carney/ Senior Editor
Looks to me like the causation of lower fertility rate is complex and welfare programs like Social Security cannot account for it, although it seems to be a contributory factor. See, NEBR working paper, Fertility and Social Security by Michele Boldrin, Univ. of Minnesota, Fed. Res. Bank of Mpls, and CEPR, Mariacristina De Nardi, Univ. of Minnesota and Fed. Res. Bank of Mpls, amd Larry E. Jones Univ. of Minnesota, Fed. Res. Bank of Mpls, and April 29, 2004, Preliminary and Incomplete. See also, Baby Boom and Baby Bust: Fertility Rates and Why They Vary, by Robert L. Brown, Contingencies, Jan/Feb 2004.
This seems to argue the other way with the world facing exponential population growth and finite resources. It appears to me that anything that contributes to controlling population growth is a plus for economic sustainability.
Moreover, productivity is not correlate with population but in increase in output per work unit, which comes not chiefly from the side of labor, but rather from scaling up technological innovation and increasing efficiency of production. For example, firm productivity goes up after a visit from the efficiency experts and expendable workers are laid off. Over the previous several decades, many US firms have been shedding workers, resulting in productivity gains.