Two links. The first one is a summary of an economics paper: Tiger moms and helicopter parents: The economics of parenting style by Matthias Doepke and Fabrizio Zilibotti, who use cross-country data to support their conclusion that in times of rising inequality, a more authoritarian parenting style will likely be chosen by parents:
This column argues that the choice of parenting style is driven by incentives. Parents weigh the expected costs and benefits of implementing a certain parenting style. The popularity of the authoritarian style is declining because the economic returns to the independence of children have risen. The rising inequality implies higher returns to education. This calls for pushier parenting styles, such as the authoritative one. A decline in inequality is likely to prompt a more relaxed parenting.
The second is a column by Pamela Druckerman: A Cure for Hyper-Parenting.