It is also a question of habit and social norms. A lot of what we claim is internal moral values, is really just social conformism. We don't throw garbage around and shop lift in large part because we don't want to be worse people than everybody else we know.
We see this in countries with a lot of cheating on taxes. It is hard to break out of, because nobody wants to pay taxes while knowing that none of their friends pay. Nobody wants to be the lone sucker doing the good deed. On the flip side you don't want to cheat on taxes if you know everybody else is really particular about paying it.
So I think the establishment of social norms is very important. And to do that one might need to create incentives and rules to kickstart people. As the norms develop you could cut back on the incentives and rules.
I've seen this in my native Norway. Fathers and mothers could split the maternity leave. Although almost no father took advantage of this. It simply wasn't an established social pattern. Your boss would look funny at you if you did it. Then the government mandated that some weeks should be taken by the father otherwise those weeks were lost and could not be used by the mother.
Within few years the social norms around father staying home looking after kids, changed radically in Norway. Hence government policies DO matter for how personal values and behavior develops.