Purely private money doesn't really work so well, because you can't really believe it'll be worth anything tomorrow.
Now, what the Austrians have right is that overly out of whack money supply is pretty bad, and no central body can really do that good a job at guessing right. But instead of throwing the baby with the bathwater, what can be done is to give the fed a mandate that directly lines up with something we want.
For instance, we could have a fed that alters the money supply looking straight at NGDP. A stable NGDP growth is extremely valuable, as it's the best approximation we have of economic health. So if the Fed targetted NGDP growth, and used markets due to their forward looking nature, we'd get a better policy overall, without really risking the instability that comes from having money that can't really be trusted.
Now, what the Austrians have right is that overly out of whack money supply is pretty bad, and no central body can really do that good a job at guessing right. But instead of throwing the baby with the bathwater, what can be done is to give the fed a mandate that directly lines up with something we want.
For instance, we could have a fed that alters the money supply looking straight at NGDP. A stable NGDP growth is extremely valuable, as it's the best approximation we have of economic health. So if the Fed targetted NGDP growth, and used markets due to their forward looking nature, we'd get a better policy overall, without really risking the instability that comes from having money that can't really be trusted.