Most people think that in normal times - i.e. when the Federal Funds Rate is well above zero - that the Fed is able to set that interest rate through open market operations. You don't hear a lot of people saying that OMOs have no effect on interest rates.
But that's exactly what's implied by the famous "Wallace Neutrality" paper, also known as Wallace (1979). Neil Wallace was a leading light of the "New Classical" or "freshwater" generation of macroeconomists who revolutionized the discipline in the 70s and 80s. He is one of the main intellectual predecessors of Steve Williamson, Randy Wright, and the rest of the current "New Monetarist" or "money search" movement.
Wallace shows that if the government works in a very specific way, then Open Market Operations can't change interest rates. Specifically, the government has to set fiscal policy to exactly cancel out monetary policy, by making sure that OMOs leave A) government consumption, B) taxes and transfers, and C) income distribution completely unchanged.
In other words, Wallace Neutrality is very much like the so-called "Sumner critique" of fiscal policy. It says that fiscal policy can cancel out monetary policy if it wants to. That makes sense, at least in an idealized world, and it implies that monetary policy is inextricably bound up with fiscal policy, which is interesting.
But I don't think Wallace Neutrality should be our jumping-off point or "base case" for thinking about how monetary policy works!
In a recent post about QE, John Cochrane wrote:
[S]tandard theory makes a pretty clear prediction about [QE's] effects [on interest rates]: zero. OK, then we dream up "frictions," and "segmentation," and "price pressure" or other stories.
The "standard theory" he's talking about is the Modigliani-Miller result. But Modigliani-Miller is about the value of firms, not of government bonds. So what he's really talking about is Wallace Neutrality, which bills itself explicitly as "A Modigliani-Miller Theorem for Open-Market Operations."
But Wallace neutrality is not Modigliani-Miller, for two reasons.
First, a sufficient condition for Modigliani-Miller to hold is the existence of frictionless complete markets. But that is not sufficient for Wallace Neutrality to hold - for that, you need a certain government policy rule. We can think about frictionless complete markets as a sort of "natural base case", and that sort of makes sense. But it doesn't really make sense to use a certain government policy rule as a "base case", especially when that policy rule seems nonsensical in the first place (Why the heck would the fiscal authority try to exactly cancel out the monetary authority's actions??). Modigliani-Miller seems deep and fundamental, while Wallace Neutrality seems more arbitrary and specific.
Second, the government is a policy-maker, not a price-taker. Its decisions create the overall economic environment in which agents act. So even a small departure from Wallace Neutrality-enforcing behavior, or from the other conditions required for Wallace Neutrality, will allow the Fed to target interest rates, simply by doing enough OMOs. See Miles Kimball on this point.
In other words, when someone says that Modigliani-Miller doesn't hold, it makes sense to ask "Why not?" But when someone says Wallace Neutrality does hold, it makes sense to ask "Why?"