Saturday, April 7, 2012

Does index futures targeting imply a target for the interest rate?

The Taylor rule suggests that the Fed undertake open market operations in bonds, creating or destroying money, until the Federal Funds rate, the interest rate on overnight loans between banks, is equal to something like 1.5 times the inflation rate plus .5 times the output gap, the difference between real GDP and potential GDP. With interest rate smoothing, small periodic changes in the Federal Funds rate are made, gradually shifting the current rate to the one implied by this rule.

The logic of the Taylor rule, and any version of interest rate targeting, depends on the liquidity effect of changes in the quantity of money. With the Federal Funds rate being directly targeted, if the actual rate rises above the target rate, the Fed’s open market trading desk buys bonds, with money created out of thin air. This money is directly credited to the reserve balances of the banks whose customers sold the bonds. This increases the supply of funds that banks have available to lend overnight, while at the same time reducing the need for banks to borrow reserves, having received additional reserves as they or their customers sold the bonds. This pushes the actual rate back down to target.

If, on the other hand, the actual Federal Funds rate falls below target, then the open market trading desk sells bonds, and collects payment by taking the funds out of the reserve balances of the banks whose customers bought the bonds. Money, in the form of reserve balances held by banks, has been destroyed. This reduces the funds available to banks for lending overnight while leaving other banks short of funds and needing to borrow. The resulting shortage of fund on the overnight interbank lending market pushes up the actual Federal Funds rate back to target. By creating and destroying money, in the form of reserve balances, the Federal Reserve manipulates supply and demand conditions on the overnight loan market so that the market rate equals the target.

The point of changes in the target interest rate is to minimize the output gap and keep inflation growing at a target rate. If inflation should rise above target or output rise above potential, the target for the Federal Fund rate would increase according to the formula. The Fed would be causing the Federal Fund rate to rise in a series of small steps. These higher interest rates are supposed to slow spending on output, slow inflation, and slow growth of real output. Once the inflation rate is no higher than the target, and output is no higher than potential, then interest rates are no longer increased.

If, on the other hand, prices rise less than the targeted amount, or output falls below potential, then the Fed begins a series of interest rate cuts. The lower interest rates are supposed to cause spending on output to rise more quickly. This will cause inflation to pick up and output to grow more quickly. Once the inflation rate is back to target and there is no output gap, then the decreases in the interest rate stop.

Market monetarists instead favor a target for the growth path of nominal GDP. This implies a series of target levels of nominal GDP, the difference between each target level being at a constant growth rate. Growth rates such as 5%, 4.5%, or 3% are often suggested.

It would be possible to design a Taylor-like rule that would relate a target for the Federal Funds rate to the gap (either recent of forecasted) between nominal GDP and the target. For example, it could be one plus .5 times the nominal GDP gap. The means by which the Fed would cause the changes in the Federal Fund rate would be the same, it is just that the Federal Fund rate would be adjusted based upon a different criteria. If nominal GDP were above target, then a series of increases in the Federal Fund rate would be engineered. This would slow spending on output, and once the rate of growth is less than the growth rate of the targeted growth path, the gap between the nominal GDP and target would close. Once closed, there would be no increases in the Federal Fund rate. Similarly, if nominal GDP should fall below the targeted growth path, then a series of decreases in the Federal Funds rate would be generated. This should raise spending on output, and when it grows more quickly that the growth rate of the targeted growth path, the gap will close. Once the gap is closed, there is no need to adjust interest rates.

However, most market monetarists have been skeptical about interest rate targeting. There has been little interest in developing any mechanical feedback rule between nominal GDP gaps, the difference between actual or forecasted nominal GDP and target, and open market operations. The focus has been on a commitment by the Fed to undertake open market operations of whatever magnitude is necessary to reverse any deviation of nominal GDP from target.

This is not a very concrete instruction for those actually undertaking open market operations. Perhaps it is no surprise that central bankers want something more specific.

Many market monetarists favor index futures targeting. The Fed would buy and sell index futures contracts on nominal GDP at the target value, and undertake open market operations according to its position on the contract. If the Fed is long on the contract, it would buy a quantity of bonds equal to its long position. If it is short on the contract, it would sell an amount bonds equal to its short position. This is a specific instruction to those actually responsible for open market operations.

The purchase or sales of bonds would impact the monetary base in the usual way. Most directly, the purchase of bonds would result in newly created money being credited to the reserve balances of the banks whose customers sold the bonds. The sale of bonds would result in money being destroyed, directly being taken from the reserve balances of those banks whose customers bought the bonds.

The changes in the banks’ reserve balances would impact supply and demand conditions on the interbank loan market, but the interest rate on that market would adjust to equate the quantity supplied and demanded for those loans. There is no target for the Federal Funds rate. The changes in base money impact spending on output, expectations of nominal GDP, the trades by speculators of the index futures contract, and so the Fed’s position on the contract.

In a recent comment on Scott Sumner’s blog, a Mr. 123 claimed:

“Person A holds a bond whose interest is calculated with reference to NGDP gap. Person B holds the margin deposit at the Fed plus NGDP future with a payoff calculated with reference to NGDP gap. A and B hold portfolios with identical payoffs. The payoff of NGDP future is economically equivalent to interest”

Does Mr. 123’s argument imply that index futures targeting implies a target for the interest rate after all? Certainly, existing futures contracts require margin accounts. Further, there are good reasons to require such margin accounts for index futures targeting.

However, the system could operate without any margin accounts at all. The margin accounts play no essential role in index futures targeting. The reason for margin requirements is to avoid having the Fed trying to collect from speculators who lose money on the contract. In other words, the purpose of the margin requirements is similar to the requirement for collateral for a loan. It is a type of performance bond.

Considering the amount that must be placed in a margin account, and comparing that to the actual amount that will be paid, the realized difference between nominal GDP and target, there appears to be a yield on principal.

Certainly, a bond could be created that pays that same yield as the index futures contract payoff on the margin account “investment.” Does this mean that index futures targeting involves targeting the Federal Funds rate, or any other interest rate? The key question is whether there is some market process that would cause the Federal Funds rate, the overnight interbank loan rate, to adjust to the return that can be earned on the index futures contract.

Suppose that the Fed sold a one year bond that promised to pay a fixed rate of interest. (The index futures contacts provide a payoff in 15 to 18 months.) Assuming the Fed would sell unlimited quantities of the bonds, it would seem that other market interest rates could be no lower. Who would lend for less, when they can lend to the Fed at its “target rate?” With index futures targeting, the Fed is effectively providing such a bond. And so, it would seem that other interest rates could be no lower than the expected payoff on the “bond” effectively created by index futures targeting.

The argument is plausible. It certainly would seem that a central bank could sell one year bonds that pay a fixed interest rate, and use that to raise market rates to that level. With one year rates at the target level, overnight rates would be driven up too, because a bank lending overnight would buy the bonds rather than lend to a bank needing to borrow overnight.

However, this entire argument is mistaken. When the Fed sells bonds that itself issues, it collects on them by reducing the reserve balances of the banks whose customers buy the bonds. Both the quantity of money and the quantity of credit contract until market rates rise to the rate targeted by the Fed. The process is similar to what happens when the Fed pays interest on reserve balances, except that these bonds have a one year term to maturity.

Suppose that instead the Fed were to sell its own bonds and simultaneously buy government bonds. There would be no contraction of money and credit and no tendency of all market rates to rise to the targeted level. While the interest rate that people could earn might rise, the interest rate people, or at least the government, must pay, would fall.

And this leads back to the margin accounts. It would be possible for the Fed to require that those trading the futures contracts have margin accounts. And they could require that people pay “cash.” The Fed could collect on the funds by reducing the reserve balances of the banks whose customers bought or sold the futures, and so had to meet the margin requirement. However, the Fed can and should make open market purchases of government bonds to “sterilize” this monetary impact of margin accounts.

If nominal GDP is expected to be above target, then speculators buy index futures contracts. The margin accounts would effectively tie up their money for a year, and would create a monetary contraction. Offsetting this by open market purchases would tend to offset the needed monetary contraction. However, if nominal GDP is expected to be below target, then speculators sell futures contracts. The margin accounts they would be required to hold would also tie up funds for a year, creating a perverse monetary contraction. As explained above, these monetary impacts of the margin accounts are irrelevant to the operation of the system and they should always be offset—sterilized by ordinary open market purchases.

If margin requirements were assumed to be 100%, then the effective “yield” on the margin “investment” would seem like an interest rate. However, the purpose of margin accounts is to provide a performance bond, and so their size is determined by the likely size of the loss on the contracts. For example, suppose the contract is for $100, and nominal GDP is expected to be 1% above target. The expected payoff is $1. If the margin requirement were 100%, and margin account pays no interest, then the expected return is 1%. However, with a more reasonable 5% margin requirement, the $100 contract requires a $5 “investment” and the $1 payoff on the contract provides a 20% yield on the margin account.

Now, if it is assumed that when funds are placed in these margin accounts, reserves at the banks whose customers who bought the future are destroyed, then perhaps other market interest rates would be driven up to 20%. This has a passing resemblance to interest rate targeting. Spending is expected to be too high, and so interest rates are increased (a huge amount.)

But this is mistaken. Suppose that instead nominal GDP is expected to be 1% below target. If the contract is for $100, the expected payoff is $1. The margin requirement is $5, and that provides a 20% “interest rate.” If the expectation that spending is going to be too low resulted in a massive credit contraction so that market rates would rise to 20%, the result would be a disaster.

Of course, this is just another way to see that when funds are placed in margin accounts, the Fed should sterilize any monetary impact of the accounts. While the implied contraction in the quantity of money is appropriate if nominal GDP is expected to be too high, it is perverse if nominal GDP is expected to be too low.

Interestingly, the interest on margin accounts does seem to provide an equilibrium condition if nominal GDP is expected to be “too high.” When speculators respond by purchasing the future, the Fed sells the future. While any monetary effects of the margin accounts can and should be sterilized, the “rule” is for the Fed to make open market sales equal to its short position on the contract. These sales reduce base money, directly by reducing the reserve balances of the banks whose customers purchased the government bonds. The sales of government bonds, the decrease in reserves, plausibly raise interest rates. Again, assuming that margin accounts pay no interest, then if nominal GDP were expected to be 1% above target, and margin accounts were 5%, then if market interest rates rose above 20%, it would no longer be advantageous to buy futures. Even ignoring the risk, the yield on other securities would be equal to the expected yield on the “principal” of the margin account and the payoff on the future.

If, on the other hand, nominal GDP were expected to be below target, and speculators sold index futures contracts, the Fed would buy. The rule would require that the Fed make open market purchases of securities to match its long position on the contract. The Fed pays for the bonds by creating money, directly crediting the reserve balances of the banks whose customers sold the bonds. This creation of money and credit would plausibly lower market rates. The interest rate on the “margin account/futures payoff” opportunity is 20%, and so lower market interest rates provide no equilibrating force.

The analysis above has assumed that the interest rate on margin accounts is zero. Sumner, however, proposes that interest be paid on these accounts. While his proposals suggest that the interest be at higher than market rates (providing a subsidy to offset the effects of risk aversion,) suppose that instead that the rate is that paid on one year T-bills.

Suppose that the T-bill yield and so the yield paid on margin accounts is initially 2%. Nominal GDP is expected to rise 1%, so that the payoff on a $100 contract is $1. The margin requirement is $5. It will pay 2% interest, which is 2 cents. The payoff on the margin account investment is now $1.02, which is still approximately 20%. Now, suppose that the credit contraction generated by sales of securities goes so far as to drive up the one year T-bill rate to 20%. The interest rate on the margin accounts is also 20%. And so, the $5 investment now pays $2, which is 40%.

In the opposite scenario, where nominal GDP is expected to be 1% below target, the return is initially the same. The pay off is $1 plus 2 cents interest on the $5 margin account, approximately 20%. If the expansion of credit and money should drive the interest rate down, say to 1%, then the payoff on the contract will be $1 plus 1 cent interest on a $5 investment, and so still approximately 20%.

What then, would keep the quantity of money from zooming off to zero or infinity? Probably the most immediate limit on the size of the positions the market takes on the contract is the risk premia required by the speculators. However, the point of index futures targeting is rather that the changes in the quantity of money (and any associated changes in interest rates) would impact the expected value of nominal GDP, closing the gap with the target, and so the expected payoff. What it does not do is fix the value of any interest rate, much less the interest rate on overnight loans.


  1. Very interesting commentary.

    A practical question: Is it possible to test different monetary policies, in the real world? Learning do doing can be expensive, but sometimes the only way.

    Your wife can't learn to drive no matter how many videos she watches or simulators she sits in. So you risk the family car--but first on little side streets etc.

  2. Some initial thoughts.

    1. I did not argue that futures convertibility is equivalent to fed funds rate targeting according to a Taylor-like rule. Futures convertibility is equivalent to IOR targeting according to a Taylor-like rule instead, overnight interbank rates are not targeted.

    2. My perspective is very simple. If we desire futures convertibility, we should use futures as money.
    Suppose that there is no federal debt outstanding after the Clinton gridlock era. Suppose Friedman's 1959 argument that IOR should be paid at the market rate is universally accepted. Suppose we target 5% NGDP growth path. Suppose we take the futures index convertibility requirement literally and decide that the monetary base is the NGDP future and margin account all-in-one. IOR is 4.5% plus x times the current NGDP gap. IOR is paid on a daily basis. The only assets central bank holds are NGDP futures too. The central bank collects IOR plus 1% on the futures it holds on the asset side of the balance sheet, and requires that enough private sector collateral is continuously posted so the credit losses on the futures portfolio are expected to be below 0.2% annually. As this business is profitable, the central bank stands ready to purchase the unlimited amount of conforming private sector futures on a daily basis and pay for them with base money aka futures. Base money is accepted by the central bank as a payment when the private sector wants to withdraw collateral and close the expensive IOR+1% futures position.

    3. My conjecture is that such a scheme would do a reasonable job in stabilizing AD. The convertibility requirement would be satisfied by definition. Overnight interbank rate is free to fluctuate in the free market. If you say that your or Scott's futures targeting arrangement is superior, then what is the source of that superiority? The existence of zero IOR base money? Holding of government securities on the asset side? Laxer margin requirements? Anything else?

    More comments are forthcoming... (related to free banking etc...)

  3. Thank you 123.

    I am not quite sure about the central bank holding index futures as its only asset.

    Is it buying futures, selling them, or both?

  4. In my bare bones central bank model all the central bank assets and all the liabilities are NGDP futures. Central bank goes long futures on the asset side, and goes short on the liability side.

    NGDP futures on the liability side are base money, NGDP futures on the asset side represent refinancing operations.

    When NGDP is above target path, central bank income is higher on the asset side, payouts are higher on the liability side. Net profit stays the same and is equal to the 100 bps spread between the base money NGDP future interest rate and asset side NGDP future interest rate (minus any credit losses).

    Base money represents short NGDP position for the central bank, and long NGDP position for the users of money.

    Refinancing NGDP futures on the asset side of central bank balance sheet represent long NGDP position for the central bank, and short NGDP position for the refinancing counterparties of the central bank. Counterparties have to post collateral on a daily basis so credit risk is managed, the value of collateral is marked to market on a daily basis.

    Central bank operates in a passive manner, there are no OMOs. Every day base money is accepted as a means of payment when the refinancing counterparties want to close their short NGDP positions and withdraw collateral.

    Every day the central bank pays newly issued base money in a passive manner whenever refinancing counterparties post additional collateral in order to expand their short NGDP positions.

    This model is as simple as possible. What is missing?

  5. 123:

    I don't know what is missing exactly, but they don't seem like futures to me.

    When people sell futures they don't receive money. They rather pay money to place in a margin account.

    Then someone goes long on a futures contract for a commodity, they are promised the commodity, but they still have to pay for it in the future. If they actually received the commodity, the money they paid might be greater or less than the value of the commodity. How is that an asset?

    If they sell a future, they are promising to deliver a commodity, but they are also going to collect money. Whether the money is more or less than the commodity depends on the price of the commodity at the future time. If the price of the commodity is less than the amount of money received, how is that a liability?

    It seems to me that you are proposing some variable interest rate bond rather than a futures contract.

  6. Bill,

    There is a continuum between NGDP linked bonds and NGDP futures. It is just that for convenience NGDP indexed bonds with high sensitivity to changes to NGDP are called NGDP futures, and NGDP futures with high margin requirements are called NGDP linked bonds. And it is trivially easy for the users of such instruments to transform one into other by adding or subtracting the regular bonds to their portfolios.

    If someone goes long on a futures contract for a commodity, they get an exposure to the underlying commodity, that exposure is an asset. At the same time, this asset is combined with a liability to pay for that commodity it the future.

    If they sell a future, they are promising to deliver a commodity, but they are also going to collect money. So basically an asset (exposure to a commodity) is sold, and another asset (financial asset, a right to collect money) is acquired.

    So no matter if you acquire a NGDP future, or if you acquire a NGDP linked bond, in both cases you have acquired an NGDP-linked asset. In both cases there is a loan involved, explicit in case of a bond, implicit in the case of the future. Only the terms and conditions of that loan are different.

    Your post on NGDP linked bonds has shown that it doesn't really matter if you have futures or linked bond convertibility. What is important that the financing terms of future or linked bond change the money supply or demand in the right way. Thus you have added a couple of paragraphs about the sterilization of monetary impact of NGDP bond trades.

    In my proposal NGDP futures (or NGDP linked bonds if you like) are constructed in a way that automatically creates sterilization effects that are needed.

    In the case of the liabilities of the central bank, these NGDP-linked instruments directly serve as base money without the involvement of margin accounts.

    In the case of the assets of the central bank, their creation does not tie up money, as they are collateralized by the private sector collateral.

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