Steve Horwitz has a great comment on this post, and I would restrict my response to that thread, except there are two really important points I want to make - which I think merits a new post. First, he agrees the burden of proof is on free bankers. On the institutional robustness point, I think this is definitely right, simply because they've proven less robust. I take more issue with his second and third point. He writes:
"...the increased role played by government in money production, whether in the form of NBS type regulation or true central banks, were the result not of failures of free banking but of rent-seeking by private interests and/or the desire of government actors to have access to revenue through money creation. I'm quite confident that the cases where pretty free systems became central banks fit this pattern."
This is an odd point to raise, I think. if you're vulnerable to rent-seeking in this way it means you're not a very robust institution! Communists often complain that totalitarian-minded rent-seekers spoiled the worker's paradise. We usually don't take this to be a good argument supporting the institutional robustness of Communism! If you need angels to get a system of free-banking to work, then you're out of luck - because men aren't angels.
Next Steve writes that free bankers should:
"Do what White, Selgin, and Lastrapes have done and demonstrate that generally accepted macro outcomes have been worse under central banking than more free systems. Again, I think a real preponderance of the evidence is on the side of free banking here."
White, Selgin, and Lastrapes do have an interesting paper, but coming from the world of labor market program evaluation it's always been hard for me to know what to make of it. It's essentially a pre-post test, which would never get any creedance elsewhere. What you really want is some way to identify the counter-factual, because there are lots of reasons to believe that the twentieth century was very different from the nineteenth century, and had different requirements of its monetary and financial system.
One solution I've noodled over before is reproducing the White, Selgin, and Lastrapes analysis but with Great Britain as a paired economy in a difference-in-differences analysis, a common approach in labor economics and virtually the only viable counterfactual I can think of for the sort of policy analysis they're attempting. Details on difference-in-differences estimators can be found here. The idea is that Britain had a central bank through this whole period, so if you difference out the difference between the British economy post-1913 and the British economy pre-1913, you can identify the impact of the Fed. Maybe. It's still a dicey proposition.