Although Canada is way ahead of the US in many ways, I'm going to venture to say that there are still plenty of patriarchal elements to the culture in all Westen countries, even the Nordic ones. But you are correct, the US is more deeply steeped in it and I am primarily speaking of that. Economic systems are related, but are not the main indicator of what sort of social system is in play, and in the vast majority of countries, and pretty much all of the Western ones, patriarchy is still well in effect.