In a comment on an earlier post, Robert paraphrases Williamson, who argued that while optimal monetary policy should generate a zero nominal interest rate by creating expected deflation equal to the equilibrium real interest rate, "frictions" exist which will distort relative prices. Avoiding those distortions might require a second best policy.
Assuming Williamson didn't misspeak, I think he is wrong. Patinkin explained this years ago. Assume that all relative prices, including real wages, are at equilibrium. The real quantity of money equals the demand to hold money. Now, the nominal quantity of money falls 10 percent. No money price or wage changes at all. The real quantity of money also falls 10 percent, and to rebuild money balances, less is spent on goods and services. Firms won't produce what they can't sell, and so the surpluses of goods and services result in less production. Firms won't pay people who aren't producing, so employment falls as well.
There has been no change in any money price or wage, so all relative prices, including real wages remain at their equilibrium values. The decrease in the quantity of money has depressed real output and employment below their equilibrium values, but with no distortion of any relative price. In particular, there is a surplus of labor even though real wages are at their equilibrium value.
Now, assume that money wages and prices are not perfectly rigid, but they are all equally sticky. And so, the surpluses of goods and services and labor result in all prices and wages slowly falling. This increases real money balances, and results in a recovery of both production and employment towards equilibrium levels. Once prices and wages have all fallen enough, the real quantity of money has risen back to its initial value, as have real expenditures and real output.
However, at no point during the process were relative prices or real wages distorted. They stayed the absolute same. By assumption, they all adjusted at the same rate. The problem was entirely one of an inadequate real quantity of money to match the real demand to hold money, and never was a problem with distorted relative prices.
Now, it is likely that prices are not equally flexible, and so it is also likely that the process would involve some distortion in relative prices. The more flexible prices fall more and the more rigid prices fall less. The relative prices of the more flexible money prices fall and the relative prices of the more rigid money prices rise. But it is not these relative price distortions that are the fundamental problem.
For example, suppose regulation was used to slow the rate of decrease in the more flexible money prices. Would that help? It would fix the relative price distortion. To take that to an extreme, price floors on all goods and resources would keep relative prices and real wages at equilibrium. Would that solve the problem? Permanent depression?
Now, if there is some means to get the rigid money prices to adjust faster, than would fix the relative price distortion at the same time it hastened the recovery of real money balances. But it is that last part that was the problem.
Of course, reversing the initial 10 percent decrease in the quantity of money, or better yet, avoiding it altogether, would be better approaches.