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.