I think monetary regime options are basically a two-axis question: they go from maximally politically likely and least desirable to maximally desirable and least politically likely. The most politically likely monetary regime is the one we actually have: flexibly targeting CPI inflation at 2% per year. It's not the worst target in the world—it will prevent a great depression—but it allows deep recessions and slow recoveries like those we've been experiencing recently.
The most desirable monetary regime is free banking and private supply of money. But it's the least politically likely despite the evidence it lends itself to both monetary and financial stability. The monetary side of things—typically you see nominal income (total spending) grow stably or stay flat predictably under free banking, and a concomitant lack of harsh demand-side recessions and mass unemployment—suggests that we can find mid-points.
Thus, I spend my time advocating that we target nominal GDP—the total amount of spending/income/output in the economy measured without correcting for inflation—which I view as a spot in the middle. Less desirable than free banking but orders of magnitude more politically feasible and achievable.
There's one very Hayekian reason for this. The basic Taylor Rule framework that New Keynesian-dominated central banks use performs well only if those central banks can make good guesses of the output gap—the difference between actual output and potential. If they have imperfect information, then targeting nominal income works better.
Standard monetary policy analysis built upon the New Keynesian model suggests that an optimal monetary policy rule is one which minimizes a weighted sum of the variance of inflation and the variance of the output gap. As one might expect, the Taylor rule evaluates well under this criteria. Recent calls for nominal GDP targeting therefore must contend with Taylor rule as an alternative approach to monetary policy.
In this paper, we argue that the information requirements placed on a central bank by requiring policymakers to have real-time knowledge of the output gap need to be taken into account when evaluating alternative monetary policy rules. To evaluate the relevance of these informational restrictions, we estimate the parameters of an otherwise standard New Keynesian model with the exception that we assume the central bank has to forecast the output gap using lagged information. We then use the model to simulate data under different monetary policy rules. The monetary policy rule that performs best is the nominal GDP targeting rule.
Previously I've argued that we might call nominal GDP targeting 'Hayek's Rule' because it would achieve his preferred view of macroeconomic stability—a stable flow of payments. But I think we have another reason to call it Hayekian—it emphasises the importance of information-constrained central planners, in this case of money.