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 Coincidence, other forces were much more impoortant 
 What were the other forces? 
 The extreme expansion of the monetary supply 1914-1971 caused a massive growth of the state, it imposed a too big burden in taxes and regulation. Humans, society and the economy is very plastic, but there are limits. Cutting the ties to gold probably became a release valve, and in fact the expansion of the monetary supply gradually (but bumpy) came down a little bit.  
 Exactly. You both are talking about the same. 

Money supply increased. Families got debased. Families became poorer. Which impacted fertility rates. And Gold became the release value.