In George Lakoff’s book Moral Politics, he compares the conservative Strict Father morality and the liberal Nurturant Parent morality. One of the distinctions is that Strict Father morality in terms of parenting is more condoning of physical violence used as punishment to ensure moral behavior.
The following video discusses the research that shows the ineffectiveness (or rather negative effect) of spanking and hitting children. This relates to capital punishment which has also been proven not to prevent criminal behavior. However, spanking and hitting children is even worse than capital punishment because spanking and hitting actually increases the unwanted behavior in that, for example, such children are more likely to be more aggressive themselves towards other children.