Saturday, April 28, 2012
Problems with Nominal GDP targeting?
As best I could tell from his questions, he just claims that since it has been over three years since 2008, so why is it that if the problem is "nominal" there just hasn't been an adjustment in prices and wages as well as a renegotiation of contracts. Since that hasn't happened, it must be that the problem is not nominal, and so a return of nominal spending back to something close to the trend of the Great Moderation would result in capacity constraints, bottlenecks, and higher inflation, with little expansion in production or employment.
As an advocate of a regime of nominal GDP targeting, I believe that if there is a large decrease in the growth path of productive capacity, then temporarily higher inflation and a persistent increase in the growth path of the price level is the least bad response. I think it is a good thing that creditors share the burden of an unexpected decrease in productive capacity.
Monday, April 16, 2012
Negative Nominal Interest Rates
Thursday, April 12, 2012
Market Monetarism and the Monetary Constitution
Sunday, April 8, 2012
Do We Need Inflation? Do We Need a Permanent Increase in Base Money?
The Money Multiplier
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.
Convertibility with nominal GDP Indexed Bonds
Suppose the Fed targets the growth path of nominal GDP. The Fed undertakes open market operations in bonds at a rate equal to the target growth rate of nominal GDP. For example, if the target growth path has a three percent growth rate, then the Fed expands its portfolio of government bonds at a 3 percent growth rate. This would result in base money growing at 3%--a simple quantity of money rule. Of course, unless base velocity (nominal GDP/base money) were literally constant, this would not keep nominal GDP on the target growth path.
Now add to this simple proposal a requirement that the Fed also buy and sell special nominal GDP indexed bonds. The bonds are one year bonds. The interest rate on the bonds is equal to the interest rate on Treasury bills plus the gap between actual nominal GDP and the target. If nominal GDP is one percent above target when the bonds mature, the interest rate on the bonds is the T-bill rate over the period plus one percent. If nominal GDP is one percent below target when the bonds mature, then the interest rate on the bonds is the T-bill rate less one percent.
The index bonds are created, sold and purchased by the Federal Reserve. These are not sold by the U.S. Treasury.
The Fed is borrowing when it sells a nominal GDP index bond to a bank, household, or firm. The nominal GDP indexed bonds that the Fed sells are its own liabilities. When the Fed sells the bond, it collects the payment by reducing some bank's reserve balance. If the Fed sold the bond to a bank, then it is that bank's reserve balance that is decreased. Otherwise, the Fed reduces the reserve balance of the bank whose customer bought the bond. Base money, currency held by the nonbanking public plus reserve balances, is reduced when the Fed sells the nominal indexed bond. The Fed's asset portfolio and total liabilities are unchanged. The form of its liabilities have changed. It is issuing fewer monetary liabilities--currency and reserves--and is instead funding its asset portfolio with the nominal GDP indexed bonds.
The Fed is lending when it buys a nominal GDP index bond from a bank, household, or firm. The nominal GDP indexed bonds that the Fed buys are assets to the Fed. When the Fed buys the bonds, it pays for them by adding to some bank's reserve balance. If the Fed bought the nominal GDP index bonds from bank, it adds to that bank's reserve balance. Otherwise, it adds funds to the reserve balance of the bank whose customer sold the bonds. Base money is increased when the Fed buys these bonds. Reserves, and so the total of currency and reserves, expand. The Fed's asset portfolio expands because the nominal GDP index bonds are assets to the Fed. Because the Fed is lending when it buys the nominal GDP index bonds, it should require collateral. The proposal is that those selling index futures bonds to the Fed post treasury bills as collateral.
If base velocity is expected to rise, so that nominal GDP will rise above target, then the interest rate that can be expected to be earned on the nominal GDP indexed bonds will rise above the T-bill rate. This creates an incentive for investors to sell T-bills and buy the indexed bonds from the Fed. The Fed collect payment for the bond when it issues them by reducing the reserve balances of the banks whose customers bought the bonds. This reduces quantity of base money, tending to offset the increase in base velocity. While the sale of T-bills by investors would tend to raise the yield on T-bills, this increases the interest rate the Fed pays on the indexed bonds as well. Since the Fed continues to buy government bonds according to its rule, the sale of the nominal GDP index bonds reduces the growth path of base money.
This process of monetary contraaction would continue until the difference between expected nominal GDP and the target is no greater than the transactions costs of the investors in selling T-bills and purchasing the indexed bonds plus their risk premium for holding these bonds. These indexed bonds are risky because if nominal GDP should end up below target, they will earn an interest rate lower than the T-bill rate.
If base velocity is expected to fall, so that nominal GDP will fall below target, then the interest rate expected to be earned on the nominal GDP indexed bonds will fall below the T-bill rate. This creases an incentive for investors to sell indexed bonds to the Fed. The investors borrow from the Fed, buy T-bills on the market, and pledge them as collateral to the Fed. The Fed pays for the bonds by increasing the reserve balances, which increases base money. Since the Fed is adding to its portfolio of government bonds at the usual rate, this increases the growth path of base money, tending to offset the decrease in base velocity. The purchases of T-bills by investors to secure loans obtained from the Fed would tend to raise the price and lower the yields of the T-bills. But a lower yield on T-bills also reduces the interest rate that the investors must pay on the bonds they have sold to the Fed.
The process of monetary expansion would continue until the difference between expected nominal GDP and the target is no greater than the transactions costs of the investors selling the indexed bonds and buying the T-bills along with the risk premium. These indexed bonds are risky because if nominal GDP should end up greater than the target, then the investors selling the bonds to the Fed will pay more on the loans than they earn on the T-bills pledged as security.
Rather than require the Fed to remain on “automatic pilot,” and always expand its portfolio of government bonds at the target rate, an alternative would be to allow the Fed to make ordinary open market operations as it sees fit, subject to the restriction that its purchases and sales of the indexed bonds match. One possibility is that both purchases and sales are zero, and there is no constraint. However, if more investors expect nominal GDP to be above target than below, then the Fed would find more people buying the indexed bonds than selling them. The Fed could then undertake ordinary open market sales, reducing the monetary base. This should reduce the expected level of nominal GDP, and so reduce the incentive of investors to buy the bonds and increase their incentive to sell the bonds.
If, on the other hand, more investors expect nominal GDP to be below target than expect it to be above target, then the Fed would sell more indexed bonds than it buys. The Fed would then undertake ordinary open market purchases, and expand base money. This would increase the expected value of nominal GDP, and so reduce the incentive of investors to sell the bonds and increase their incentive to buy the bonds.
If the Fed’s purchases and sales of the indexed bonds are exactly matched, then regardless of what happens to nominal GDP, it is fully hedged. If nominal GDP is on target, it collects interest on the bonds it sold and pays it on the bonds it purchased. The interest rate paid by those who sold bonds to the Fed is the T-bill rate as is the interest rate the Fed pays to those who bought the bonds.
If, on the other hand, nominal GDP is above target, then those who bought the indexed bonds earn more than the T-bill rate. But those who sold bonds to the Fed pay more than the T-bill rate. And, if nominal GDP is below target, then those who bought bonds from the Fed earn less than the T-bill rate, but those who sold bonds to the Fed, pay less than the T-bill rate.
Finally, the Fed could be given even more discretion, and make ordinary open market operations as it sees fit, while buying and selling the bonds indexed to nominal GDP. If more investors expect nominal GDP to be above target than below, then the Fed would sell more bonds than it buys. If nominal GDP comes in on target, it would have to pay more interest than it receives, but it will have earned interest on its portfolio of government bonds. If nominal GDP is above target, as investors expected, then the Fed would take a loss, having to pay those to whom it sold bonds more than the T-bill rate. While it would collect more than the T-bill rate from those to whom it whom it bought bonds, it sold more than it bought.
However, if “the market” was wrong, and nominal GDP was below target, then the Fed would pay lower interest rates on the indexed bonds it sold. It would also collect less on the indexed bonds it bought, but having sold more than it bought, it would profit by continuing to earn the yield on its portfolio of government bonds. If it had instead made open market sales, and brought the amount of indexed bonds bought and sold more in balance, it would sacrifice the earnings on the government bonds sold.
If, on the other hand, more investors expect nominal GDP to be below target than above, then they will sell more indexed bonds than they buy, and the Fed will buy more than it sells. Again, if nominal GDP is on target, no one gains or loses money. Those who sold the bonds to the Fed (borrowed from the Fed) pay the T-bill rate to the Fed and earn the T-bill rate on the securities they pledged as collateral. Those who bought indexed bonds from the Fed earn the T-bill rate. The Fed collects that from those who sold bonds to the Fed.
If the market is right, and nominal GDP is below target, then those who sold bonds to the Fed pay less than the T-bill rate. While the Fed pays less than the T-bill rate to those who bought indexed bonds, by assumption, more indexed bonds were bought by the Fed than sold. The Fed earns less than the T-bill rate on the index bonds it sold. If, instead, the Fed had made ordinary open market purchases, rather than lent by buying bonds indexed to nominal GDP, then it would have earned the T-bill rate.
On the other hand, if the market is wrong, then those who had sold nominal GDP indexed bonds to the Fed would pay more than the T-bill rate. The Fed would have to pay more than the T-bill rate to those who had bought indexed bonds, but the Fed sold more than it bought. It profits at the expense of those who borrowed.
In this system, the Fed is not targeting the interest rate. The T-bill rate adjusts with the supply and demand for T-bills. The changes in the quantity of base money could well have liquidity effects on a variety of credit markets. But, of course, the Fed is undertaking this policy by trading bonds whose yield depends on the deviation of nominal GDP from target.
HT to 123 who motivated me to think more about indexed bonds. Also, this approach is very similar to what Dowd has proposed with index futures on the CPI.
Scott Sumner provided helpful comments and pointed out that the proposal is related to a proposal by Robert Hall.