So, yes, I’d say Mankiw’s opinion is within the range of normal economist variation. Obviously there are many professional economists who think there are sound market failure arguments in favor of a central bank or that the history of free banking shows a failure rather than success; Mankiw can only be saying that he finds their judgments inadequate, not that they don’t exist. Otherwise, he’s ignorant. And obviously one can’t say that almost the entire economics profession has completely ignored the question. It’s still an ongoing debate even among employees of the Fed.
Scott Sumner is aware of free banking and seems somewhat supportive of it. Same for Lars Christensen. Alex Tabarrok is critical of the Fed and Cowen in response is critical of the anti-Fed case. (But note that the anti-Fed case is not the same as the case FOR free banking—I don’t know Tabarrok’s actual policy preference.) I can’t find any Krugman mentions of free banking but he has offered arguments for a central bank. David Andolfatto, VP of the St. Louis Fed, has said that he sees some merit in free banking arguments but finds some of its modern proponents focusing on weak criticisms of the Fed. He even claims that he invited George Selgin to give a lecture on free banking to that Fed branch. Vera Smith, a Hayek student, claimed that central banking won out due to political motives and historical accident rather than sound economic theory. Keynes, in a passage that isn’t quite about free banking, offered a criticism of bank incentives that suggests banks suffer a problem of liquidity preferences that central banks do not, and this can be read as an argument for central banking. (His argument is similar to yours about bank runs.) Brad DeLong included on a course syllabus a 1974 paper on free banking which argued that there was enormous variation in success in free banking in the U.S., with massive hyperinflation in some areas and stable currency in others. I don’t know DeLong’s actual position on the topic, but “the data suggests that free banking is unreliable” wouldn’t surprise me. Of course the footnotes in that paper refer to other papers on central banking, and searching citation will find other research on free banking v. central banking, some of it negative. One of these papers, Whaples’, surveyed economic historians and found they near universally agree that the free banking period in the U.S. didn’t hurt the economy.
So, yes, I’d say Mankiw’s opinion is within the range of normal economist variation. Obviously there are many professional economists who think there are sound market failure arguments in favor of a central bank or that the history of free banking shows a failure rather than success; Mankiw can only be saying that he finds their judgments inadequate, not that they don’t exist. Otherwise, he’s ignorant. And obviously one can’t say that almost the entire economics profession has completely ignored the question. It’s still an ongoing debate even among employees of the Fed.