Noah Smith discussed the "circularity problem" with using market expectations of inflation to control monetary policy and Scott Sumner replied. There has been some discussion of index futures targeting on the Money Illusion, Sumner's blog.
The circularity problem is related to Goodhart's law. If the Federal Reserve were to begin targeting an index futures contract on nominal GDP, then those trading the futures contract would buy or sell depending on what they expect the Federal Reserve to do. The price of the index futures contract would stay at the Fed's target.
This becomes a problem if the proposed system is a mechanical rule tying open market operations or some other instrument of monetary policy to deviations of the price of the index future from target. The problem is that it may be necessary for the growth rate of base money (or the level of short term interest rates, if you prefer that framing) to change in order for nominal GDP to remain on target. But the "rule" is supposed to be that these instruments can only be changed if first the price of the index futures contract actually deviates from the target. But those actually trading the futures contract will know that the instruments of monetary policy will change until any deviation is reversed. Those who paid more than the target price for the contract will lose when the price falls again. Those selling the contracts for less than the target price will lose when the price rises again. They won't do that, and so if anyone bothers to trade these contracts at all, which is unlikely, the price remains on target always. But if the price remains on target always, then the instrument of monetary policy, whether base money or a policy interest rate, never changes. But that means that nominal GDP will likely deviate from the target.
Sumner's version of index futures targeting and index futures convertibility are a bit different, but can be subject to similar difficulties. The key difference is that the central bank doesn't watch a market price of a nominal GDP futures contract and then change its policy instrument according to changes in the price of the future, it rather buys and sells the future itself at the target price. That means there is no change in the market price of the future at all during the period it is being targeted. And so, there is never a change in the price of the future to communicate what the market thinks nominal GDP will actually be. The market signal that is generated is the central bank's own position on the contract, which only provides information about whether speculators on net believe that nominal GDP will be above or below target.
If there is a mechanical rule that requires that some instrument of monetary policy remain unchanged until speculators actually buy or sell the contract, then the problem of circularity still develops but it is slightly different and weaker. For the instruments of monetary policy to change as needed, speculators must trade the future. Their incentive to trade the future is the expectation that nominal GDP will deviate from target. But when they trade the future, the central bank adjusts base money or its policy interest rate in a way that keeps nominal GDP on target. The speculators would expect no profit after all. But knowing that, the speculators would never trade the index futures contract, and so the instrument of monetary policy would never change. If base money (or short term interest rates) never change, then nominal GDP will deviate from target.
However, it is pretty clear that the actual result would be that if the current setting of the policy instrument (say the growth rate of base money,) is expected to leave nominal GDP on target, then no one will trade the future. Only if the current setting is so far off that the expected deviation is large enough to cover the transactions costs and risk of taking a position on the contract would it be traded. The trades would then lead to changes in the setting of monetary policy so to reduce the expected deviation and the expected profit. However, an expected deviation would remain that compensates those trading the future for transactions costs and risk. The market (and presumably the central bank,) would all know that the policy instruments are being set at a level that will keep nominal GDP away from target.
Due to this logic, Sumner began long ago to speak of subsidies for the market. For example, the central bank should not try to charge trading fees to cover its costs of operating the system. The central bank should not insist that speculators keep funds in margin accounts that only pay low (or no) interest. Sumner has instead proposed that the Fed should pay extra high interest on the accounts!
Interestingly, this entire analysis assumes homogeneous expectations by the market. It is as if "the market" is treated as if it is a single individual. And it is certainly possible that everyone would know and agree that nominal GDP will either be above or below the target. However, it is possible that there would be disagreement. Certainly, this reflects the real world where we have some economists who predict massive inflation and others who insist that recession and disinflation will persist. While it remains true that those who expect nominal GDP to come in very close to target would not trade, the setting of the actual policy instrument would result in a balance between those speculators who believe it will come in sufficiently far above target to provide them with a profit and those speculators who believe it will come in sufficiently below target to provide them with a profit. While the expectations of those who believe that nominal GDP will be close to target aren't counted, because they don't bother to trade, the balancing of those with more divergent expectations does imply that the "market" made up of the actual traders would expect nominal GDP to remain close to target.
Sumner's earlier versions of the proposal were much like this, but some years ago he instead proposed a modified system where the central bank can adjust base money as it sees fit, even without there being any trades of the contract. The central bank creates a tentative target for base money, and then adjusts that tentative target according to the trades of the speculators. This means there is never a problem about the instruments of monetary policy remaining fixed until there are trades of the contract. There is never any situation where everyone, including the central bank, knows that nominal GDP will deviate from target in some particular direction, but no one has an incentive to close the gap. Quite the contrary, if everyone, which would include the central bank, knows what must be done to adjust expected nominal GDP to target, then the central bank will do it. All that would be left is trades by speculators with divergent expectations.
If the central bank always adjusts its policy instrument so that it is hedged, then the reason to take a position on the contract is because of an expectation that some other speculator will disagree and be willing to take the opposing position. I lean towards a similar approach where the central bank is free to adjust its instruments of monetary policy as it sees fit subject to the constraint that it buy and sell the futures contract at the target price. This also avoids the "problem" of the instruments of monetary policy remaining stuck until there are trades of the contract. If no one trades the contract, then the central bank adjusts monetary policy as it sees fit. It is like the contracts don't exist. However, it is likely that those with highly divergent expectations would trade the contract.
While Sumner tends to favor some mechanical rule to require adjustments in some policy instrument when the future is traded, I am skeptical. Instead, I contrast a "conservative" central bank policy of seeking to hedge versus an "activist" policy of taking a position on the contract. The central bank's position on the contract would show its confidence in its own internal forecast relative to that of the market. Again, it is likely that there will nearly always be trades in both directions by people with highly divergent expectations. If market sentiment begins to move in one direction or another, the central bank will find itself with a large and growing position on the contract. Presumably it will also be aware of whatever it is that is moving the market and also take action to offset it . A conservative central bank would take action sufficient to hedge its position--so that those who think it did too much are exactly balanced by those who think it did too little. But keep in mind, that those who think it did almost the right thing, and only slightly too much or too little, wouldn't bother to trade. A more activist central bank would have more confidence that it did the right thing and that "the market" is wrong. It would hold a position on the contract, betting against "the market."
Is there still a "circularity" hiding in here? Yes, there is. Any trade of the future must take into account the possibility that the central bank will adjust its instruments of monetary policy to offset the trade. The reason to trade is an expectation that even after the adjustment by the central bank, nominal GDP will remain significantly away from target. The reason to trade is that the speculator believes that either the central bank or some other speculator will hold the opposite position.
Now, if we assume that the central bank will always fully hedge and that there is only one speculator, then what that means is that the central bank will adjust its instruments of monetary policy so that the single speculator reverses his position on the contract. If that is true, then there is no selfish motivation for the speculator to ever trade the future. If there were only one speculator, then no trades would ever occur. But, of course, since the central bank is free to adjust the instruments of monetary policy, the requirement that it trade the index futures contract would impose no constraint on the central bank. But that isn't the situation in the real world.
Finally, if the central bank were to decide that it "wants" to let nominal GDP deviate from target, and "the market" got wind of this desire, then it would suffer heavy financial losses. And that, of course, is really the point of the proposed reform. It will focus the central bank on the policy target and allow no "tradeoffs" with other things that central bankers may value. Or rather, there will be a large financial bill for any effort to satisfy their personal preferences.