From my colleague Russ Roberts:

I continue to ask the question: name an empirical study that uses
sophisticated statistical techniques that was so well done, it ended a
controversy and created a consensus–a consensus where former opponents
of one viewpoint had to concede they were wrong because of the quality
of the empirical work.

If you put it that way, I can’t meet Russ’s challenge.  But his challenge is excessive for two reasons:

1. Ending a controversy and creating a consensus almost always takes dozens, if not hundreds, of empirical studies.  As well it should – virtually every specific study is open to reasonable doubt.

2. What exactly counts as “ending a controversy and creating a consensus”?  Does every active researcher in the world have veto power?  Or is convincing two-thirds of them enough?  What if the “former opponents” just quietly give up rather than admitting error?

In light of these points, suppose we modify Russ’s challenge thusly:

Name a body of empirical work that is so well done, it won over two-thirds of active researchers and induced half of the unconvinced to quietly give up or recant?

By this standard, the obvious response for economists is behavioral economics.  I don’t know any economist under the age of 40 who denies that there are major exceptions to the standard rational actor model.  Many older economists are unconvinced, but they don’t publish much about it.

For political science, I’d point to the literature demonstrating the falsity of the self-interested voter hypothesis.  I’ll defer to people in the field, but my strong impression is that a solid consensus of active researchers now admits that objective self-interest tells you very little about voter behavior.  The people who aren’t convinced do very little contrary empirical work; they just retreat into mathematical modeling.

For psychology: How about the three laws of behavioral genetics?

I’ve noticed that people skeptical of the value of empirical work often ask to see the one “bulletproof” study that “proves X.”  But their request is confused.  Solutions to homework problems can be bulletproof because they’re self-contained.  Since theory papers in econ are usually just solutions to really hard homework problems, theorists, unlike empiricists, have a warehouse full of of bulletproof research.  The problem, unfortunately, is that this bulletproof research answers questions of of little or no practical interest.  It’s far better to focus on the real world and marginally advance our knowledge about something that matters.