For an excellent article on the relationship between wealth, belief in God and fertility, see "Population, Economy, and God," by Tom Bethell, published by The American Spectator and available at http://spectator.org/archives/2009/05/12/population-economy-and-god
A brief excerpt will give you a hint of the author's premise:
A rise in prosperity also encourages people to think that they can dispense with God. Religion diminishes when wealth increases—that’s my theory. But with a twist that I shall come to. Wealth generates independence, including independence from God, or (if you will) Providence. God is gradually forgotten, then assumed not to exist. This will tend to drive childbearing down even further. Hedonism will become predominant. Remember, Jesus warned that it’s the rich, not the poor, who are at spiritual hazard.
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I could summarize the argument with this overstatement: The intelligentsia stopped believing in God in the 19th century. In the 20th it tried to build a new society, man without God. It failed. Then came a new twist. Man stopped believing in himself. He saw himself as a mere polluter—a blot on the landscape. Theologians tell us that creatures cannot exist without the support of God. A corollary may be that societies cannot long endure without being sustained by a belief in God.