Sumner and DeLong on Index Futures Convertibility

Scott Sumner provided a good explanation of the benefits of money expenditure targeting on National Review Online. He even gave a brief plug for index futures convertibility

In an ideal world, we’d remove all discretion from central bankers. The Fed would simply define the dollar as a given fraction of 12- or 24-month forward nominal GDP, and make dollars convertible into futures contracts at the target price. If the public expected NGDP to veer off target, purchases and sales of these contracts would automatically adjust the money supply and interest rates in such a way as to move expected NGDP back on target. It would be something like the classical gold standard, but with the dollar defined in terms of a specific NGDP futures contract, instead of a given weight of gold. The public, not policymakers in Washington, would determine the level of the money supply and interest rates most consistent with a stable economy.

I am very comfortable with describing the gold standard in terms of defining the dollar as a weight of gold. This is equivalent to fixing the dollar price of gold. Similarly, the BFH payments system defines the dollar in terms of a broad bundle of goods and services. This is equivalent to fixing the dollar price of the bundle, which is the sum of the dollar prices of the items in the bundle. Such a system is, in effect, a rule for stabilizing some measure of the price level.

Yet, somehow, defining the dollar as a fraction of 12 or 24 month forward nominal GDP leaves me puzzled. I do favor a rule keeping money expenditures (which can be measured by nominal GDP) on a stable growth path. I am persuaded that stabilizing its expected future value is both desirable and the best that can be done in an imperfect world. Sumner is trying to make the system appealing to those sympathetic to a gold standard. But to me, Sumner is proposing to define the dollar as a unit of fiat currency combined with a rule for stabilizing expected nominal GDP. Translating that back into a definition of the dollar in terms of a fraction of forward nominal GDP doesn't help me understand. (The privatized versions of the system I favor amount to the dollar being a debt claim that is settled according to a rule that keeps expected money expenditures on a target growth path. So, maybe I need to think harder about definitions of the dollar as a fraction of future money expenditures.)

More troubling is Sumner's claim that with dollars convertible into futures contracts, purchases and sales of the contracts automatically cause changes in the quantity of money and interest rates that move the expected value of NGDP to target. The problem with his brief explanation is that it creates the impression that money is created or destroyed when the Fed buys or sells futures contracts. While it might be possible to create a new type of security with a nominal interest rate that varies with deviations of NGDP from target, it would not be a futures contract. Index futures convertibility requires that the central bank use more conventional tools of monetary policy depending on its trades of the index futures contract. (Sumner understands all of this. We have been going back and forth on these issues for nearly twenty years.)

Brad DeLong commented on Sumner's article and explained how he thinks the system would operate.

As I understand Scott's proposal, it is this: Nominal GDP in the fourth quarter of 2007 was $14.291 trillion. A 5% growth rate from that base would give us a value of $17.455 trillion for the fourth quarter of 2011.

So far, DeLong's interpretation isn't bad. I think Sumner would be satisfied with using the quarter before the recession began as a base, and creating targets based upon a 5 percent growth rate from there. My approach has been to find the trend for the Great Moderation and then extend it into the future. The target I propose for fourth quarter 2011 is $17.896 trillion for Final Sales of Domestic Product. Not too different from DeLong. (I think the reason for the difference is that NGDP growth had been slow for the year before the recession began.)

DeLong continues:

Add on another 3% for the average short-term nominal interest rate we would like to see, and we have $18.153 trillion. Therefore the Federal Reserve would, today, announce that it stands ready to buy and sell dollar deposits to qualified customers at a price of $1 = 1/18,155,000,000,000 of 2011Q4 GDP.

Here DeLong begins to go wrong. He adds in 3 percent because he believes that is a proper target for the long run average nominal interest rate. His figure assumes a 3 percent average nominal interest rate between 2007 and 2011. Whether or not that would be desirable, it plays no role in determining what the Fed should be doing during either the 4th quarter of 2011 or the 4th quarter of 2010. He has effectively put NGDP on an 8 percent growth path. Neither $18.155 trillion nor its reciprocal should play any role in the system.

Why does DeLong make this error? It is because he understands the proposal as automatically changing the quantity of money when futures are purchased and sold. In DeLong's view, when the Fed buys these contracts, it is providing money now, in the fourth quarter of 2010 and will receives the money back in the fourth quarter of 2011. The Fed is making a type of loan when it buys contracts. It makes sense that the Fed would charge interest on these loans. If the Fed charges 3 percent interest on the loans per year, then it provides dollar deposits (makes a loan of a dollar now) in return for (1+.03) times 1/$17.455 trillion of 4th quarter NGDP to be paid in one year. That is 1/(17.455 trillion/ 1.03) or 1/16.947 trillion of 4th quarter 2011 NGDP. When the Fed sells the contracts, it is borrowing (accepting a deposit) of a dollar in exchange for paying 1/16.947 trillion of 4th quarter 2011 NGDP in one year. It pays 3 percent interest on these deposits, again, adjusted for any deviation of NGDP from target.

DeLong's error was to calculate the interest payment for 4 years compounded, and then multiplying when he should have divided. If the contract was defined based on the borrowers paying the Fed a dollar when the loan comes due, like a T-bill, then multiplication would have been appropriate. The appropriate adjustment, however, is 1.03 times $17.455 trillion, which is $17.979 trillion, not $18,155 trillion. More importantly, because the adjustment for the deviation of NGDP from target would not be known up front, this would be inappropriate. Division is really the only sensible approach.

DeLong continues, explaining how the system operates:

If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be lower than $18.15 trillion, they would take the Fed up on its offer: demand the cash
now, pay off the contract in a year by then paying 1/18,155,000,000,000 of
2011Q4 GDP, and (hopefully, if they were right) make money--thus the money stock
would increase.

While the proper number is 1/16.947 trillion, everything is correct except that what is really happening is that the Fed is lending money at an interest rate of 3 percent adjusted by the deviation of NGDP from target. If NGDP was expected to be 1 percent below target, the amount repaid would be 99 percent of 1.03, which is a nominal interest rate of about 2 percent.

While I agree that more will be borrowed from the Fed at a lower interest rate than at a higher interest rate, unless that natural interest rate was 1 percent, (the 3 percent target for the nominal interest rate DeLong built into his system less the 2 percent trend inflation implied by a 5 percent growth path) this is not necessarily expansionary.

If investors thought that nominal GDP in the fourth quarter of 2011 was likely to be greater than $18.155 trillion, they would take the Fed up on its offer: give cash to the
Fed now, collect the contract in a year by receiving 1/18,155,000,000,000 of
2011Q4 GDP, and (hopefully, if they were right) make money--thus the money stock
would fall.

Here people are making a sort of term deposit at the Fed. The Fed pays 3 percent on these deposits Again, leaving aside that the numbers are just a bit off, if NGDP comes in above target, then it pays more than 3 percent. Higher interest rates will attract more of these deposits, and so the amount of reserves and currency available now will be lower than otherwise. Of course, if the natural interest rate is above one percent, this approach will not keep NGDP on target.

The actual characteristics of such a system would be for the expected deviation of NGDP from target to generate an effective interest rate charged on loans or paid on deposits that cause an expected interest rate to equal to the natural interest rate. The scheme automatically limits the size of any deviations of NGDP from target. If the natural interest rate is 1 percent, then it should keep NGDP on target.

DeLong continues:

If nominal GDP were expected to fall, the Federal Reserve would be shoveling money out the door at negative expected nominal interest rates. If his scheme were applied today it would be quantitative easing on a pan-galactic scale, as everybody would run to the Fed with bonds to use as collateral for their promises to pay the expected futures contract in a year in exchange for the cash now.

The Federal Reserve would then become truly the lender of not just last but first resort. Why would anybody borrow on the private market even at 0% per year when they could borrow from the Fed at -3%/year? Savers would simply hold cash rather than try to match the terms that the Fed was offering borrowers. Borrowing firms
would borrow from the Fed exclusively. The Fed would thus create a wedge between
the minimum nominal interest rate that savers would accept (zero, determined by
the alternative of stuffing cash in your mattress) and the nominal interest rate
open to borrowers.

If NGDP was expected to be below target by more than 3 percent, then the Fed would lend at negative nominal interest rates. DeLong's error here was embedding the 3 percent interest rate target into the NGDP target and then to forget what he had done. If negative nominal interest rates at the Fed are necessary to stop a downward deviation of NGDP from target, then the scenario of all lenders holding currency, and all borrowers borrowing from the Fed seems plausible--at least for credit transactions with a duration of one year or less. I think the most problematic part of the negative nominal interest rate scenario is that people could borrow from the Fed and just hold currency and make a profit.

DeLong continues:

I see how this would solve a monetarist downturn--a shortage of liquid cash money projected to lead to nominal GDP below its target. Once arbitrage had kicked in there would be no shortage of cash money.

I see how this would solve a Keynesian downturn--a shortage of savings vehicles that means that balancing savings and investment at full employment requires a nominal interest rate of -3%, which the zero-bound keeps you from getting to. The Fed would lend to all comers at a nominal interest rate of -3%.

I cannot quite see how this would solve a Minskyite downturn--a flight to quality because of a collapse in the market's risk tolerance and a shortage of safe assets.

The only problem created by a Minskyite downturn (with the DeLong rule,) involves the collateral that the Fed requires for loans from the Fed. Generally, the borrowers that the now risk adverse lenders reject can go to the Fed. DeLong's scenario where the Fed crowds out all private sector credit would imply this. The only thing different from the Keynesian scenario is that if the Fed is liberal regarding the collateral it accepts, nominal interest rates don't need to be negative.

Anyway, index futures convertibility does not involve the Fed making loans or accepting deposits at a 3 percent interest rate adjusted for deviations of NGDP from target.

In the fourth quarter of 2010, The Fed buys and sells a one dollar index future on fourth quarter 2011 NGDP (or Final Sales of Domestic Product) for one dollar. When the figures for fourth quarter 2011 NGDP come in, the contracts are settled. For every percentage point that NGDP exceeds its target, sellers pay buyers a penny per contract. For every percentage point that NGDP falls short of its target, buyers pay sellers a penny per contract. (Make the contracts $100, then the payoff is a dollar per percentage point, and cents for fractions of a percent. Index futures contracts of $10,000 or $100,000 are more common.)

These payoffs create incentives to buy or sell the contacts during the fourth quarter of 2010. Those expecting NGDP to be above target in the fourth quarter of 2011 have an incentive to buy the contracts. Those expecting NGDP to be below target in the fourth quarter of 2011, have an incentive to sell the contracts. Because the Fed buys and sells them for $1, then the price remains at $1, at least during the fourth quarter of 2010.

Suppose Tayor, thinking that Fed policy is too inflationary, believes that NGDP will be above target in the fourth quarter of 2011. Taylor is a "bull." He goes long on the contract. He buys the contract.

Krugman, on the other hand, thinks that monetary policy is ineffective or, maybe just too tight, and expects that NGDP will be below target in the fourth quarter of 2011. He sells the contracts. Krugman is a "bear," and goes short.

If Taylor and Krugman trade the exact same amount, then the Fed is fully hedged. The Fed's net position on the contract is zero, Taylor is long, and Krugman is short. If Taylor is correct, and the Fed's policy created massive inflation, with NGDP for the fourth quarter 2011 coming in at 5 percent above target, then he will earn 5 cents on each contract he bought. Where does that money come from? From Krugman, who must pay 5 cents on every contract he sold.

But suppose Krugman was right. If the liquidity trap keeps NGDP below target no matter what the Fed's does, and it comes in 10 percent too low, then Krugman will make 10 cents on each contract he sold. Where does the money come from? The money comes from Taylor, who must pay 10 cents on each contract he bought.

Finally, if NGDP comes in exactly on target, then the contracts expire without any payments being made. Tayor and Krugman neither collect nor pay anything.

Now, suppose that the bulls, like Taylor, purchase more contracts than the bears, like Krugman, sell. At the current price, the desired long position by the market exceeds the desired short position. The market expectation is that NGDP will be above target. In an ordinary index futures market, the price of the contract would rise until the bears balance the bulls. The price rises until the desired long and short positions match.

However, with the Fed buying or selling at a price of $1, no such price change would occur, even for a second. Instead, the Fed would sell to the bulls, taking a short position to balance the long position of the market. If Taylor, and the other bulls are correct, and NGDP comes in above target, then the Fed, like Krugman and the other bears, must pay. On the other hand, if NGDP comes in below target, then the Fed collects from Taylor and the other bulls, along with Krugman and the other bears.

The opposite scenario is possible too. Suppose the market expects NGDP to be below target. This means that bears, like Krugman, sell more than bulls, like Taylor, buy. Rather than the price of the contract falling to reflect the market expectation of below target NGDP in the fourth quarter of 2011, balancing the desired short and long positions, the Fed buys contracts from the bears at a price of one dollar, taking a long position to match their short position. If Krugman and the other bears are correct, then they will make money on the contracts. The Fed, like Taylor and the other bulls, must pay. On the other hand, if Taylor and the other bulls are correct, then they and the Fed make money at the expense of Krugman and the other bears.

Again, if the NGDP is on target, then the contracts expire without any payments being made. Regardless of whether the Fed had to take a short position or a long position to keep the price of the contracts at $1, it pays or receives nothing.

Superficially, the Fed creates or destroys money when the contracts are settled to the degree it makes or loses money. When does this happen? When the contracts are settled.

If NGDP is on target, no one makes or loses money, including the Fed. If the Fed is hedged, and the market expectation is that NGDP will be on target, then money may be transferred between longs and shorts if NGDP actually deviates from target, but the Fed neither makes nor loses money.

Only if the Fed is compelled to take a position on the contract and that position loses money, does the Fed pay out and so, create money. And, similarly, if the Fed must take a position on the contract and it makes money, the Fed collects the funds and destroys money. However, any such changes in the quantity of money are undesirable, and the Fed should sterilize such changes. If the Fed makes money, it should buy ordinary securities--maybe T-bills--with its profits. Similarly, if it loses money, it should sell off ordinary securities, such as T-bills to fund its payoffs.

What about during the fourth quarter of 2010, when the contracts are being traded? Isn't money being created and destroyed? No. When Krugman and other bears sell the contracts, they receive no money now. What they have done is received a promise to receive money in a year if NGDP comes in below target in exchange for a promise to pay money in a year if NGDP comes in above target. Similarly, when Taylor and the other bulls buy contracts, they don't pay anything for the contracts now. They are being promised money in one year if NGDP comes in above target in exchange for a promise to pay money in one year if NGDP comes in below target.

What about margin requirements? Don't index futures contracts require margin accounts?

Yes, they do. Margin requirements are performance bonds. The purpose is to make sure that those losing money on the futures contracts make the promised payments. While it is true that those buying futures must put up a margin payment, and so, superficially are making a kind of down payment, they are really posting a performance bond. They are promising to pay the difference between the future price they contracted and the spot price when the contract expires.

Of course, those selling futures also must meet margin requirements. Clearly, the sellers are not receiving money now for some kind of future delivery. And they aren't selling at a negative price. Just like they buyers, they are posting a bond to cover any loss from the difference between the agreed price and spot price when the contract expires.

With index futures convertibility, both bulls, like Taylor, and bears, like Krugman, must keep "funds" in a margin account. The amount per contract depends on the size of the likely deviations of NGDP from target. Perhaps 10 cents per contract would be appropriate.

It would be possible to require "cash" margin requirements. Those trading the contracts would write checks (or wire funds) to the Fed, and then the Fed would decrease the reserve balances of the traders' banks. While the traditional monetary base would shrink by the volume of futures trading, there would be a new type of Fed liability, which would be a margin deposit at the Fed. Other things being equal, any trading of the security would be contractionary. (Sumner sometimes assumes this institutional framework and insists that the Fed pay interest on these margin accounts at a bonus rate. This would be even more contractionary.)

Ignoring what kind of margin requirements might apply to the Fed itself, consider a situtation where NGDP is expected to be below target and bears sell contracts. The bears must all post margin requirements equal to, say, 10 percent of their short positions, and so base money contracts by that amount. The Fed, and whatever bulls are in the market, take the matching long positions. The bulls also post margin equal to 10% of their positions, further adding to contractionary pressure. The effect of the margin requirements is perverse.

If, instead, the market expects NGDP to be above target, then the bulls buy contracts. They must post margin requirements equal to some fraction of their positions, which reduces base money. The contractionary consequence is desirable. The Fed must take the offseting short position, but if there are any bears who also take a short position on the contract, their margin payments reinforce the contractionary impact of those of the bulls!

Existing commodity exchanges use continuous settlement. As the price of a future contract changes, funds are transfered between the margin accounts of the shorts and the longs. For example, if the price of a contract rises by a $1, a dollar is moved from the margin account for each short contract to the margin account of each long contract. If the price of a contract falls by a dollar, the change is reversed. Funds are moved from the longs to the shorts. When the contract expires, there is no need to make significant shifts in funds for settlement because the funds were already shifted as the market price of the futures contract changed.

With index futures convertibility, during the fourth quarter of 2010, when the Fed is buying and selling futures contracts for fourth quarter of 2011 at a price of a dollar, the price of the contract does not change, and no funds are shifted between the margin accounts of longs and shorts.

Once the Fed stops trading that particular futures contract, then it would certainly be possible for those with short or long position to continue to trade at whatever market price they find agreeable. Following the conventions of existing commodity exchanges, funds could be transfered between margin accounts based upon changes in the market price of the futures contract.

To the degree that the Fed was hedged, having no short or long position on the contract, these changes would shift funds between longs and shorts in the private sector and have no contractionary or expansionary impact. However, if the Fed was left with a position on the contract, then continuous settlement would involve the creation or destruction of money depending on if the Fed suffered losses or made profits.

For example, if the market expected NGDP to be below target, and the Fed took a long position on the contract, when the Fed ceased targeting the price, and the price began to fall, then the Fed, like any other long, would begin to lose money. While the transfers between the shorts and any private sector longs would simply transfer funds, any payment by the Fed to cover its own losses would be an increase in the quantity of this special type of base money. If, as is customary, those making money can remove excess funds from margin accounts, then this would be expansionary. The Fed would, presumably, wire funds to their banks, and credit their banks' reserve balances.

Further, if the bears were wrong, and further information shows that NGDP will turn out to be above target, then the price of the contract would rise. As the Fed made money, it would decrease the margin accounts of those bears. If they had to make margin calls (replenish their margin accounts,) then there would be a further contractionary impact. On the other hand, if they refuse to make the margin calls, their positions could be closed out by selling to any private sector bulls, which simply transfers funds. If the Fed were permitted to close out its position by selling at a price greater than one, it would be taking profits. While the margin accounts of shorts would be somewhat depleted, when there accounts are closed and any remainer is returned to the shorts, the effect would be expansionary.

Worse, consider the situation where the market expects NGDP to be above target and buys, with the Fed being forced to take the matching short position. Once the Fed stops trading the contract at a price of $1, continued trading on the market could cause the price to rise. Using continuous settlement, the margin accounts of the bulls are increased. The bulls begin to make money at the expense of the Fed. If they are permitted to take profts from those margin accounts, then the Fed would wire funds to their banks, crediting the banks' reserve balances. The Fed would be creating a perverse expansion in the quantity of money. Similarly, if the market turned out to be wrong and the market price of the contract fell below $1, then continuous settlement would have the Fed decreasing the margin accounts of the longs, creating an additional contractionary effect.

The most sensible approach is for the Fed to sterilize the impact of the creation of any special margin accounts by offsetting open market purchases. Similarly, any changes in such margin accounts due to continuous settlement should be offset by additional open market operations as needed.

In my view, a better approach is to require those trading the futures to meet margin requirements with securities, such as T-bills. While changes in the demand for securities to meet margin requirements might have some kind of contractionary or expansionary effect on the economy, it is likely to be minimal and does not play any significant role in the process that tends to keep expected money expenditures on target.

As explained above, index futures convertibility requires that the Fed use some conventional tool of monetary policy to impact future money expenditures and bring the expected value of money expenditures back to target. The Fed could change reserve requirements, change the level of the interest rate it pays on reserves balances, change the primary credit rate it charges banks for loans at the discount window, undertake open market operations with T-bills, with longer term to maturity government bonds, or even with some other kind of security.

In my view, the Fed's goal should be to remain fully hedged. The market expection should be that NGDP remain on target. The long positions of the bulls should be exactly offset by the short positions of the bears.

If the market expectation is that NGDP will be above target, then the purchases of the bulls will be greater than the sales of the bears. The Fed will be left with a short position on the contract. To avoid the risk of loss, the Fed needs to undertake a contractionary policy--raise reserve requirements, raise interest rates paid on reserve balances, raise the primary credit rate to charge more for loans at the discount window, or make open market sales of T-bills, longer term government bonds, or whatever other assets it owns. Those bulls who expected only a slight increase in NGDP will start to find the risk of loss too great, and sell. Those who already thought that Fed policy was too contractionary sell more. Some who held no position on the contract perhaps will notice the Fed's contractionary policy and sell. When the Fed is hedged, and its position is zero, then the policy is right.

If the market expectation is that NGDP will be below target, then the sales of the bears will be greater than the purchases of the bulls. The Fed will be left with a long position on the contract. To avoid the risk of loss, the Fed needs to undertake an expansionary policy--lower reserve requirements, lower interest rates paid on reserve balances (perhaps to something less than zero,) lower the primary credit rate and charge less for loans at the discount window, or make open market purchases of T-bills, longer term government bonds, or some other type of security. This expansionary policy will result in those bears who were expecting that NGDP will be only slightly below target to close out their short positions by purchasing futures contracts. Those bulls who already expected NGDP to be above target will perhaps purchase more. And others, who weren't in the market, may buy as well. Once the market expectation of NGDP in the fourth quarter on 2011 is on target, then the Fed is fully hedged. The Fed's policy is right.

The Fed policy is right, or rather, the market expectation is that NGDP will be on target in the fourth quarter of 2011. Some of Sumner's versions of the system leave the Fed much less discretion and could be implemented by computer. For example, the Fed could be required to make parallel open market operations with the trades in the futures contract. If Taylor expects NGDP to be above target and buys a future contract at a price of $1, then the Fed not only sells the future, it also sells T-bills worth a dollar. Base money contracts by dollar for every futures contract purchased by bulls. If Krugman expects NGDP to be below target and sells a futures contract, then the Fed buys the futures contract and at the same time buys a dollar's worth of T-bills. Base money increases by a dollar.

If the market expectation is that NGDP will be on target, then the purchases of bulls like Taylor and sales by bears like Krugman offset, and while the Fed might purchase and sell equal amounts of T-bills, leaving the monetary base unchanged, the simplest approach is for the Fed to net out the required T-bill transactions, trade no T-bills, and leave base money unchanged.

The Fed then would change base money through conventional open market operations according to the size of its net position on the futures contract. Sumner argues that the equilibrium quantity of base money will keep the market expectation of NGDP on target.

It is a type of arbitrage argument. Suppose the current value of base money is expected to result in NGDP being above target in the fourth quarter of 2011. Base money is "too high." The market expects to profit by purchasing futures contracts from the Fed. The Fed sells the contracts at a price of $1, and it also sells a dollar's worth of T-bills, shrinking base money. If this new, lower level of base money is still too high so that NGDP is expected to be above target, then there must be expectations of profits from buying index futures from the Fed. The Fed sells still more futures contracts and more sells T-bills, with base money again decreasing by the value of the T-bills sold. In equilibrium, there can be no more expected profits from buying the futures, and so NGDP must be on target, and so, base money must have decreased enough for NGDP to be on target.

Notice that the Fed is left exposed with a short position. To the degree transactions cost, risk aversion, or anthing else leaves NGDP above target, the Fed will take a loss on this short position. Those trading with the Fed will earn enough profit to cover any costs. Unfortunately, if some unancipated shock causes NGDP to rise above target, then the Fed could be subject to heavy losses. In fact, it is the chance of just such an event that motivates those buying the futures to maintain the long position.

Of course, this scenario requires that base money was initially too high. How did it get so high? Consider the opposite scenario, where base money is too low. NGDP is expected to be below target. With a 5 percent target growth path for NGDP, all hand-to-hand currency being base money, and banks being required to keep base money reserves, the quantity of base money should generally be increasing.

Suppose base money is "too low," so NGDP is expected to be below target. There are profits to be made by selling the index futures contract, and the Fed must buy at at price of $1. The Fed makes open market purchases of T-bills in parallel with its purchases of the futures contract. This causes base money to rise. But if base money is still "too low" so that NGDP is still expected to remain below target, there are still profits from selling futures contracts--shorting NGDP, or at least the index futures contract on NGDP. In equilibrium, there can be no profits from selling the index futures contract, so NGDP must be expected to be on target. That means that the level of base money must be at the correct level.

Notice that this leaves the Fed exposed to a long position on the futures contract. If transactions costs or risk aversion leaves the expected NGDP below target, then the Fed will take a loss. This will compensate those short positions resulting in the increase in base money for any costs. Of course, if some unexpected shock causes NGDP to fall substantially below target, the Fed would be subject to heavy losses.

If the institution of parallel open market operations were taken literally, then the entire quantity of base money would need to be matched by purchases of futures by the Fed. The private sector would have to take a short position on the futures contract of hundreds of billions of dollars each and every quarter, growing by the year. To avoid that consequence, the obvious solution is for the rule to apply solely to changes in base money, and so, the Fed's security portfolio and the quantity of base money would initially be the level from the previous quarter (or whatever period,) and then change according to the Fed's net position on the futures contract for the current quarter. A rather simple modification would allow the Fed to use conventional open market operations to increase base money according to trend (say, 5 percent) at the beginng of each period, and then make changes from that level based upon changes in its net position on the futures contract.

Sumner has gone so far as to suggest that the Fed set base money however it thinks best at the beginning of each period, and then make adjustments to its target according the net position on the futures contract. In effect, the Fed sets base money and then allows the market to fine tune. As explained above, those who believe that the quantity of base money determined by the Fed is too high (Taylor) would buy contracts and those thinking the quantity of base money is too low (Krugman) would sell contracts. If "the market" agrees with the Fed, purchases and sales match, and the Fed leaves base money unchanged at what it thought was the appropriate level.

If instead, the bulls purchase more than the bears sell, "the market" expects NGDP to be above target, and the Fed sells futures contracts and T-bills, decreasing base money relative to its tentative target. While a requirement that the Fed always trade T-bills in parallel to its trades of the futures contract would suggest that if the decrease in base money results in bulls selling futures to close out their long positions, or bears selling even more, the matching purchases of futures contracts by the Fed, which hedges and closes out its short position, should be matched by purchases of T-bills which would again raise base money. A more sensible approach would be for the Fed to do nothing as its short position shrinks. Only if the selling goes so far that the Fed has a net long position should the Fed begin buying T-bills and raise base money.

Suppose "the market" finds the Fed's tentative level of base money too low. The bears sell more than the bulls buy, and the Fed purchases futures contracts and T-bills, increases base money relative to its tentative target. As the Fed purchases T-bills and expands base money, some bears may purchase futures to close their short positions, and bulls may expand their long positions. As the Fed sells futures, it hedges and closes its long position. The Fed should not sell T-bills and contract base money as sales shrink its long position. Only if the purchases by "the market" go so far as to cause the Fed's long position to disappear and turn into a short position, should be the Fed begin to sell securities and shrink base money.

Such a rule may be workable--the Fed must buy T-bills in parallel with its purchases of futures contracts if it is hedged or already has a long position, while selling T-bills in parallel with its sales of futures contracts if it is hedged or already has a short position. However, I still think the better approach is to allow the Fed discretion to adjust monetary policy as it chooses subject to the constraint--always stay hedged. While the Fed would have some discretion, this rule would require that "the market" expects money expenditures to remain on target.

P.S. And the proper target is an adjusted 3 percent growth path for Final Sales of Domestic Product starting at the end of the Great Moderation.