Using six centuries of data from England, Gregory Clark shows in A Farewell to Alms that from the years 1200-1800AD, the wealthier a person was, the more descendents he tended to have. This long-running, naturally eugenic trend is often presumed to have come to an end in the West with the onsets of the Industrial Revolution, modern education, modern contraception, and other accoutrements of comfortable modernity.
While there is no longer a clearly identifiable positive correlation between wealth and reproductive success, there are good empirical reasons to think assertions that an inverse relationship between fecundity and affluence now exists are, at best, premature.
Here is some contemporary evidence on a metric paralleling the one Clark employed in his book. In 2006, the GSS asked respondents about their total net worth. The mean number of children among those aged 50 and older (to allow for full family formation to have occurred) by total wealth* follows (n = 412):
This isn't necessarily cause for celebration, but it doesn't paint a picture of impending doom, either. Eugenia and Dysgenia are, at present, locked in a stalemate. The middle is currently enjoying a gentle reproductive advantage over both the top and the bottom.
GSS variables used: CHILDS, WEALTH(1-3)(4-5)(6-8)(9)(10-15), AGE(50-89)
* Defined as "the value of your house plus the value of your vehicles, stocks
and mutual funds, cash, checking accounts, retirement accounts
including 401(k) and pension assets, and any other assets minus
what you owe for your mortgage and your debts."