What academic fields contribute most to economic growth?

I imagine that subsidies bias students skew incentives towards fields that don't generate as much economic growth - and despite its issues, an interesting study (Economiclogic via Adamsmith):

Cristiano Antonelli and Claudio Fassio decided to open this Pandora box and concentrate on one impact: economic growth. They perform a cross-country study and take the number of graduates in each field as an indicator of academic output, and see where that leads us in terms of economic achievement. They make the distinction between engineering, hard, social, medical sciences, and humanities in a 11-year panel of 16 OECD countries. The horse race ends with two clear winners, engineering and social sciences, and two big losers, medical sciences and humanities, the latter having a significant negative contribution to growth.

That said, should we believe those results? Beyond the obvious issue with panel cross-country regressions, the problem is that we are still comparing apples to oranges. In some countries, medical studies are at the graduate level only, while it is undergraduate elsewhere. There are also stark difference for Economics as well. In the US, many students graduate in that field and have actually only two years of classes in this major, having to take general education classes first for two years. In Europe, Economics students spend their whole four years on the topic. And the same applies to other fields. Thus counting students, and especially if you want to make the claim they are specialized in a particular field, is rather heroic. I would not yet claim social sciences have won this battle.