Andrew K. Rose and Saktiandi Supaat find a connection: Fertility and the Real Exchange Rate (NBER WP# 13263, July 2007).
Here is the slightly reorganized abstract:
Theoretically a country experiencing a decline in its fertility rate can be expected to have higher savings, lower investment, a current account surplus, and accordingly a real depreciation.
We test and confirm this hypothesis, controlling for a host of potential determinants such as PPP deviations and the Balassa-Samuelson effect.... We use a quinquennial data set covering 87 countries between 1975 and 2005 to investigate the relationship between fertility and the real effective exchange rate.
We find a statistically significant and robust link between fertility and the exchange rate. Our point-estimate is that a decline in the fertility rate of one child per woman is associated with a depreciation of approximately .15% in the real effective exchange rate.
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