Miles Kimball has another post on Wallace Neutrality, which is the theoretical argument proving that quantitative easing is not effective. Kimball explains that the math shows that open market operations can have no effect, given Wallace's assumptions. The assumptions, however, are highly unrealistic.
Kimball points out that the Wallace result requires assumptions of perfect knowledge of the fundamental values of whatever the Fed is purchasing as well as an ability to borrow unlimited funds at the zero-risk interest rate and no concerns regarding risk by the arbitrageurs. None of that is even close to reality. Following the convention in financial economics, failure to meet these requirements are "frictions." To me, frictions sound like small things that slightly gum things up. However, might it be that assumptions behind an absence of these "frictions" are so far removed from reality that it tells us approximately nothing about the real world?
What I found more interesting was the "intuitive" explanations that depended on the Fed eventually reversing its open market operations. For example, if there is perfect knowledge of the future equilibrium price of gold, and the Fed creates large amounts of money and buys gold now, this will not impact the price of gold at all. That is because the Fed will sell all of that gold and reabsorb all of the money in the future, and the price will be back where it was supposed to be. What happens in the meantime? "Arbitrage." Kimball didn't explain the process, but I guess someone will borrow gold and sell it short to the central bank. That no one is really in a position to sell gold short in unlimited quantities is just a "friction" in the world of Wallace neutrality.
But one hardly needs "Wallace Neutrality" to understand that temporary changes in the quantity of money have little effect on anything. Krugman's unpublished paper on the issue is probably the best known argument, though we Market Monetarists know that Sumner explained it before Krugman. It has nothing to do with open market operations. If the quantity of money doubles this year, with the new money appearing out of thin air, then we would expect that the price level would roughly double. But suppose all of that money will be sucked away one year later. Then that would cause the price level to fall back to its initial level. This is a temporary increase in the quantity of money. Who would buy a house at twice its current value when it is expected to fall in half in a year or less? What is going to happen then? People will largely hold the excess money balances during the period when they are extra high. The demand for money temporarily rises and velocity temporarily falls enough to offset the temporary increase in the quantity of money.
What is the likely result? At first pass, the price level will rise immediately when the quantity of money increases, but only enough so that as it returns to its initial level, the rate of deflation will equal the real interest rate. If the price level rises more, then the deflation will make holding money more attractive than holding other assets. This motivates the increase in the demand to hold money and the reduction in velocity sufficient to prevent any further temporary increase in the price level.
However, why doesn't Wallace neutrality apply when short and safe interest rates are above the zero nominal bound? Of course, in new Keynesian models, there is no process by which open market operations cause changes in the policy interest rate. The policy interest rate is taken as exogenous. The interest rate is adjusted, and consumption is shifted between now and the future. The future level of consumption is fixed at the full employment level, and so a lower interest rate increases current consumption and a higher interest rate lowers current consumption. The Wallace Neutrality result doesn't come into play because there are no open market operations going on at all. New Keynesian economics is reasoning from a price change. As Sumner constantly points out, that is not sound economics.
Still, whether Wallace neutrality only works when at least one interest rate hits zero, or supposedly keeps the central bank from ever impacting any interest rate (see Kling here,) it still remains true that quantitative easing, in even massive quantities, will have very little impact if the central bank promises to reverse it. Suppose the central bank undertook massive quantitative easing but committed to keeping spending on output on its existing growth path. Would quantitative easing have any effect? And what would be the point of quantitative easing if not to increase spending on output?
Now, suppose that the central bank would be happy for spending on output to rise, but only if there is no inflation. In other words, the central bank wants to reduce the output gap with no increase in inflation. That would have an impact only to the degree this was believed possible. But those who expect that closing the output gap will resulted in higher inflation (rather than reduced disinflation,) then they would expect that increase in the quantity of money would be temporary. And so they would be willing to accumulate more money, implying reduced velocity and so little impact on current expenditures.
It is considerations like these that make Market Monetarists insist that if spending on output should increase, then the central bank needs to target an increase in spending on output. Quantitative easing until labor markets improve unless inflation gets too high is just not very effective.
Now, if spending on output is targeted, then the proper amount of quantitative easing is whatever it takes. But the "whatever it takes" is pointless when a central bank creates expectations that it will prevent any increase in spending on output. Unfortunately, committing to prevent inflation has that effect.