In answer to David’s challenge to name “one controversial issue that had been resolved with econometrics,” I nominate the self-interested voter hypothesis – the idea that voters maximize their narrow self-interest.  While many people – scholars included – take this view for granted, the vast majority of people familiar with the data now agree that it’s wrong.  In reality, objective self-interest and political views have almost nothing to do with each other.  Any apparent connection usually just reflects the observers’ confirmation bias.

Of course, the “people familiar with the data” tend to be political scientists, not economists.  But it was econometrics that convinced them.  (And yes, political scientists do use the word “econometrics” when they apply statistics to political questions.  “Politimetrics” never caught on).