Problems with Nominal GDP targeting?

David Andolfatto asks why market monetarists believe that nominal GDP level targeting will help solve our current problems.     Of course, most market monetarists see nominal GDP level targeting as the best (I always say, "least bad,") monetary regime.   It isn't just a quick fix for current conditions.

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.

Negative Nominal Interest Rates

Matthew Yglesias seems favorably disposed to a cashless payments system and negative nominal interest rates on bank deposits. Ryan Avent is critical and prefers inflation. This allows for a negative real interest rate on currency and bank deposits.

If the Yglesias plan were to have negative nominal interest rates on bank deposits always, then perhaps Avent would have a point. However, the nominal interest rate on bank deposits can (and should) be varied according to supply and demand.

If issuing money is very costly, perhaps because making loans is very risky, then charging a competitive fee to people who want to hold money clears the market. It simultaneously coordinates the quantity of money with the demand to hold it and saving with investment. (Saving is that part of income not spent on consumer goods and services and investment is spending on capital goods.)

If, on the other hand, issuing money is very profitable, because the loans and other financial assets that banks can fund with it are lucrative, then banks can and should pay positive interest on money. This will still coordinate the quantity of money with the demand to hold it as well as saving and investment.

What is Avent's alternative? Is it to raise the inflation rate whenever the market clearing interest rate needs to be negative? Should the inflation rate then fall again when this is no longer an issue? Or do we have high inflation at all times so that real interest rates can go as negative as necessary with nominal interest remaining above zero? If there were many financial instruments that require negative real interest rates frequently, or even always, this might make some sense. Negative real interest rates would be practically normal and so maybe centering the entire macroeconomic order around allowing for them would make sense. As for the fluctuating inflation approach, varying inflation in final goods prices and wages might be worth it if just about all interest rates needed to be negative sometimes.

But in reality, it is a few, very short and safe financial assets, that only rarely need to have negative real interest rates to clear markets. Painting a picture where all nominal interest rates are temporarily negative, much less permanently negative, is unrealistic. I am sure that neither Yglesias nor Avent have this in mind. Unfortunately, care must be taken not to create that impression.

Generally, interest rates on short and safe assets are lower than on longer and riskier assets. If some interest rates are negative, including on checking account balances, people who want a saving vehicle for retirement or making a down payment on a house would need to save using something that has a longer term to maturity. Those who want more yield, would have to take more risk. Maybe they should consider stocks.

And, of course, if people chose to save by accumulating gold or silver, then there is no problem. The price of gold or silver simply rises enough to clear those markets. Those who were already holding the gold or silver earn capital gains, which allows them to purchase consumer goods or else buy capital goods. And, of course, those accumulating gold or silver bear risk, just as they would if they purchased stocks, risky bonds, or capital goods.

In my view, occasional fluctuations in inflation rates to create occasional negative real yields is needlessly disruptive. Of course, if all prices were perfectly flexible and everyone had a perfect understanding of what is happening, it would hardly matter. But that isn't the real world. I think that slow, steady growth of spending on output is the least bad macroeconomic environment for microeconomic coordination. Spending should grow with the productive capacity of the economy, leaving final goods prices stable on average. Nominal incomes should generally grow with real incomes.

I don't favor keeping the price level absolutely fixed. Decreases the the supplies of particular goods and even slowdowns in productivity should result in a higher price level, and so transitory inflation. And increases in the supplies of particular goods or rapid growth in productivity should have the opposite effect. But creating persistent inflation or fluctuating inflation so that a few asset markets can sometimes have negative real yields is a mistake.

Why is it that real interest rates sometimes need to be negative? We live in an uncertain world where production takes time. Real investment projects involve risk and take time. If someone wants to save but bear no risk and be able to spend their money at any time, then they are proposing to shift risk to someone else. Sometimes, they may have to pay for someone else to bear that risk. The least bad way to handle the situation is for nominal interest rates to be negative on those particular financial assets that require negative real interest rates for quantity supplied to match quantity demanded.

Does this make hand-to-hand currency impossible? Not at all. The problem isn't the existence of hand-to-hand currency. The problem is basing the entire monetary order on government guaranteed hand-to-hand currency. It is perfectly short and perfectly safe and has a zero nominal yield. No other nominal yield can be any lower than the cost of storing currency.

If hand-to-hand currency were privately issued, and there was no effort to make it especially safe and secure, then it could continue to be used for small, face-to-face transactions. It could continue to serve as a medium of exchange. But it would not be a particularly secure store of wealth, and so would not prevent the nominal yields on T-bills or FDIC insured bank deposits from being negative for just as long as necessary to adjust the quantity demanded to the quantity supplied.

Are there alternatives to privatizing currency other than persistent or fluctuating inflation? The alternative is for the government, as issuer of money, to purchase long and risky assets and bear the risk for those who want to hold short and safe assets. Fortunately, this should be no more common than the need for negative nominal interest rates. Interestingly, a monetary order that is committed to heroic open market operations when necessary, much like one that would allow for negative nominal interest rates when needed, might be less likely to have the event occur.

Market Monetarism and the Monetary Constitution

A monetary constitution imposes restrictions on political control of the monetary order. It limits both the politicians in the legislative branch and those actually executing any monetary policy-- politicians from the executive branch or else some kind of appointed public officials.

In the context of the U.S., a monetary constitution would restrict the U.S. Congress in legislating regarding the Federal Reserve, as well as put limits on the Board of Governors and the FOMC. Of course, the U.S. already has a constitution, and it even has some monetary restrictions. Unfortunately, either the existing U.S. monetary regime is unconstitutional, or else, the monetary provisions of the U.S. Constitution are ineffective and irrelevant. (I lean to the second view.)

What would be appropriate provisions of a monetary constitution?

In my view, the first provision of the monetary constitution should be that the people will be free to utilize whatever media of exchange they choose. People should be free to issue, hold, earn, spend, and save alternative monies. Mostly, this would provide a last resort defense against a breakdown of the monetary constitution. However, it would also allow people to shift to the use of some money they find more useful, perhaps that issued by the monetary authority of a major trading partner.

However, most of the monetary constitution should be about the definition and regulation of the dollar.

First, the purpose of the monetary powers of the Federal government is to provide for the existence of a medium of exchange for the people to use in their commercial activities. Further, any changes in the quantity of money should accommodate changes in the amount of money people choose to hold.

Such a purpose for monetary powers could be clarified by provisions explaining what it is not. The purpose of the monetary power is not to create money for the government to spend or borrow. Nor is the purpose to help the government collect taxes, make expenditures, or borrow from other sources. Further the purpose is not to help the people obtain funds to borrow. And finally, the purpose is not to help Congress or the executive branch regulate commercial activity.

Again, the purpose of the monetary power is to he serve the welfare of the people by providing them a medium of exchange that will serve their purposes, which might include selling, spending, borrowing and lending. And the quantity of money created should adjust according to the amount people want to hold.

Unfortunately, while the general rule that the quantity of money remain equal to the demand to hold it is sound, this norm is not a complete specification. The demand to hold money depends on its purchasing power. Worse, deviations of the quantity of money away from the demand to hold it leads to market processes that cause changes in its purchasing power such that people choose to hold the existing quantity.

Superficially, this suggests that a requirement that money maintain a constant purchasing power is a necessary addition to the proposal that the quantity of money adjust to the demand to hold it. Further, it suggests it is a sufficient substitute. To keep the purchasing power of money stable requires that the quantity of money adjust to changes in the demand to hold it given its current and expected purchasing power. Further, a stable purchasing power for money prohibits changes in the quantity of money away from the demand to hold it.

However, a requirement that the price level in dollars remain stable would require excessive manipulation of the quantity of money. In place of such a requirement, the constitutional rule should require that dollar spending on output grow with growth in the long run productive capacity of the economy. Putting these two elements together, the purpose of the monetary power of the government is to provide for dollar-denominated media of exchange for the people's commercial activities. The quantity of the medium of exchange should adjust to meet the demand to hold it, so that expenditures on goods and services grows with the long run trend in productive capacity, having the effect of maintaining its purchasing power in the long run.

While this general purpose applies to any officials appointed to direct the monetary authority, it also applies to the elected officials in the legislative and executive branch. In particular, the constitution should specify that legislation determines what specific measure of spending on goods and services should be targeted, the initial level of that target, and the growth rate between the target levels.

Further, the constitution should specify that if Congress should change either what measure of spending is being used or the future levels of that measure, any change can only be implemented in the future, perhaps five years after the new legislation is passed. For example, if nominal GDP was being targeted on a 3 percent growth path, and Congress decided that final sales of domestic product should be used instead and grow at a 4 percent rate, then the target would remain the existing series of levels of nominal GDP for the next five years, and only at that point would there be a shift to a series of levels of Final Sales of Domestic Product growing at the new rate.

What of the monetary authority? The constitution should give Congress the power to appoint a commission to serve as monetary authority of the U.S. Some size should be specified, say from 7 to 15. The members should have some term, perhaps six years. The constitution would explain how they are appointed, presumably by the exectutive with approval by the legislature. For the U.S., that would be appointed by the President with the advice and consent of the Senate.

The key role of the monetary authority should be to see that the quantity of the medium (or media) of exchange is adjusted according to the demand hold it, so that the specific targets specified by Congress for spending on output are reached. While the monetary authority might advise Congress as to what growth rate or measure of spending are best, at any particular point in time, choosing the particular measure of spending and its growth path should not be the responsibility of the monetary authority.

While the monetary authority has discretion, subject to the target rule, the types of monetary instruments issued should be determined by the legislature. The monetary constitution should not be written in a way that assumes that the monetary authority will be issuing any type of monetary instrument, and particularly not zero-nominal interest, hand-to-hand currency. Any such "paper money," or deposit accounts that can be held by banks or the general public, should be specifically authorized by legislation.

The monetary constitution should specify that the monetary power of the government seeks to create a dollar such that the people will have a sound medium of exchange for their commercial activities. Whether or not the monetary authority actually issues any media of exchange itself would require legislative action. In particular, it should be possible for the legislature to allow the monetary authority to regulate privately-issued, dollar-denominated media of exchange.

Any monetary instruments issued by the monetary authority should be considered debt of the government. While the government could borrow in terms of other types of monies, such as foreign exchange preferred by the lenders, it could and probably would borrow largely in terms of money controlled by the monetary authority. The requirement that the monetary authority reduce any monetary instruments along with any decrease in the demand to hold it, even to the point of retiring all of it, makes any such issue of money a type of loan that must be repaid on demand. Rejecting the notion that this is a type of debt implicitly assumes that the quantity of money issued would remain unchanged in the face of a decrease in the demand to hold it, resulting in a loss of purchasing power. It is just such a scenario that the monetary constitution prohibits.

As a practical matter, the monetary authority could adjust the quantity of money it issues through open market operations. Looking at the monetary authority's balance sheet, it would be holding assets in the form of government bonds to match the monetary liabilities it issues. From the point of view of the government's consolidated balance sheet, open market operations would be shifts in the composition of the national debt between monetary and nonmonetary liabilities. An open market purchase would be more borrowing by the issue of monetary liabilities and less borrowing by the issue of nonmonetary liabilities. An open market sale would be less borrowing by the issue of monetary liabilities and more borrowing by the issue of nonmonetary liabilities.

If the monetary authority issues deposit type liabilities, it could adjust the interest rate it pays on them as well. Since any payment of interest on deposit liabilities would be an expenditure of public money, a simple rule placing a limit on the amount paid equal to interest rate on the government bonds securing the deposit would be appropriate. The monetary authority could pay the interest rate it is earning or less.

Finally, the monetary constitution should explain how these rules can be suspended in an emergency. If some emergency does develop, and there is no provision for suspending the ordinary rules, then the resulting constitution would be too brittle. The chains limiting the political system would simply break. It is much better to require that any suspension of these rules be made by the legislature, perhaps with a super majority.

However, some "emergency" provisions are more obvious and could be made subject to whatever rules apply to the constitution generally. For example, if monetary authority thought it was appropriate to pay higher interest on any monetary deposits it issues than is paid on the securing government debt, then it should be required to have authorization from the legislature. Further, if the demand for the monetary liabilities authorized by Congress is outstripping the national debt authorized by the legislature, then the monetary authority would need to ask legislature to authorize additional borrowing and somehow spend the money. This could involve the legislature providing loans to the private sector or else running operating deficits by cutting taxes or raising current expenditures.

An alternative solution to an emergency due to a shortage of money would be to suspend the issue of government hand-to-hand currency and solely issue deposit-type monetary liabilities. The interest rates paid on those could be reduced enough to keep the demand to hold money equal to the existing national debt.

In the unlikely event that the national debt were to be greatly reduced, approaching zero, then the issue of monetary liabilities by the monetary authority would also be greatly reduced, approaching zero. Even in this situation, it would be possible for the monetary authority to use regulation for the settlement of payments, particularly net clearings between banks, to keep the quantity of privately-issued dollar-denominated money adjusted to the demand to hold it so that spending on output grows according to the target determined by the legislature. Should such a scenario arise, then the legislature would develop the rules and the monetary authority implement them.

What role, if any, should nominal GDP futures convertibility play in a monetary constitution? I think that the legislature should be free to require such a system as a way to constrain and impose accountability on the monetary authority. While the monetary authority should be free to look at any private nominal GDP contracts that exist as an indicator of policy, creating such contract and requiring the monetary authority buy and sell them at a fixed price should be authorized by the legislature. At this time, I do not think such a system should be required by the monetary constitution.

Do We Need Inflation? Do We Need a Permanent Increase in Base Money?

Sumner often says that increases in the quantity of base money are inflationary as long as they are expected to be permanent. According to Sumner, it doesn't matter if the money is created by the purchase of Treasury bills that have a zero nominal interest rate. While he doesn't dispute that this is just a swap of two safe, zero interest financial assets today, he argues that eventually the interest rate on Treasury bills is going to rise above zero. Assuming that the Fed doesn't raise the interest rate paid on base money with the T-bill rate, this is going to result in an excess supply of base money. Eventually, this will result in a higher price level.

Sumner usually explains this in the context of some extreme example. Suppose the quantity of base money is doubled, and the Fed has committed to keep it at that new level. It might seem that with short and safe nominal interest rates being very low, a doubling of base money along with a matching decrease in the amount of T-bills in the hands of private investors would have little direct and immediate effect on expenditures.

But consider 5 years from now. Unless interest rates on short and safe assets remain extremely low, then those holding all of that base money, probably banks, will use it to purchase what are now safe assets with higher interest rates. There will be a boom in lending and spending, and much higher prices for goods and services. As a rough rule of thumb, the price level will be approximately twice its current value.

This implies that there will be a 100% inflation rate over the next five years. While we could imagine that it all occurs between year 4 and year 5, this is very unrealistic. Households and firms would be motivated to purchase goods in year four rather than wait until year five when the goods will be twice as expensive. Since loans can be paid back with money worth half as much, borrowing at low interest rates to purchase these goods would be very attractive. Further, lending, including by holding securities with very low interest rates, rather than buying goods now, would be very costly. This is exactly what generates the Fisher effect, which would cause nominal interest rates between year four and five to skyrocket--in theory to something slightly higher than 100%.

But all of those arguments suggest that the inflation would not all be between year four and five. Prices would skyrocket between years three and four too. Perhaps all of the increase would occur between year three and four, with prices remaining more or less stable at the much higher level, between year four and five.

However, this reasoning applies between year two and three. Rather than wait for the high prices in year four, people would buy in year three. But if prices rise between year two and year three, the same arguments apply between year one and two.

And so, if base money is doubled, and it is going to remain doubled, even if it is all created by the purchase of zero interest T-bills, the result will be an immediate rapid inflation. Further, the interest rates on the T-bills will immediately skyrocket. The entire issue of zero interest T-bills and base money being identical financial assets would almost immediately disappear.

Of course, the quantity of base money has increased--more than doubled. And so, why no immediate inflation? Sumner's logic suggests there are only two possibilities. One would be that the near zero interest rate environment is expected to last forever. The other, entirely realistic possibility, is that the increase in the quantity of money is expected to be temporary. When short and safe interest rates begin to rise in five years, four years, or two years, the Fed will contract the quantity of base money as the demand to hold it falls. Or, perhaps the Fed will pay interest on that base money, particularly that part that takes the form of reserve balances, raising the amount it pays so that it is competitive with other short and safe assets.

I always find this argument irritating, because in my view, this is exactly what the Federal Reserve should do. The demand to hold base money rose in 2008 and remains quite high, and the Fed increased the quantity of base money to accommodate that added demand. When the demand to hold base money falls again at some future date, the Fed most certainly should decrease the quantity of base money accordingly.

Sumner claims that any fiat money issuing central bank that wants to inflate can. He argues that a permanent increase in the quantity of base money is always inflationary, regardless of the current level interest rates on short and safe assets.

While I think his arguments are persuasive, I also find them irrelevant. I don't want a central bank to try to inflate. I don't think the Fed should ever "permanently" increase the quantity of base money. Any increase or decrease in the quantity of base money should follow changes in the demand to hold base money, and so should be tentative, reversed if the demand to hold base money later moves the opposite way.

Sumner also has no interest in a permanent increase in base money or generating inflation. He favors a target growth path for nominal GDP, with the targets rising at a 5 percent rate. Suppose the Fed doesn't double base money in an effort to create massive inflation, but rather commits to get nominal GDP to its target growth path as soon as it can. Further, rather than a 5 percent growth path, suppose the growth rate is 3 percent, equal to the trend growth rate of potential output. The trend inflation rate will be zero.

Suppose the initial target for nominal GDP is $10,000 billion and nominal GDP is on target. During the first year, it falls 3% to $9,700 billion. At the same time, there is an increase in the demand for T-bills, and their yield falls to zero. The Fed does expand the quantity of base money to try to offset the decrease in velocity. But its open market purchase of T-bills just swaps one zero interest financial asset for another, and there is no motivation for added expenditure by the private sector. Instead, nominal GDP just remains stuck at $9,700 billion.

The Fed, however, doesn't change its target for nominal GDP. While nominal GDP is $9,700 billion, the target has increased to $10,300 billion after one year. Then it is $10,609 billion, and on and on. The Fed is falling further and further behind its target, but its open market operations in T-bills would seem to have no effect, because T-bill rates remain approximately zero, and swapping one zero interest rate financial asset for another would seem to have no effect on spending.

As above, in year 5, finally the demand for T-bills falls off, and so their yields rise. Now, the Fed's open market purchases of T-bills have some effect. By year five, the Fed's target for nominal GDP is approximately $11,600 billion. Compared to the level after year one, that requires an increase of nearly 20% to return nominal GDP to target, which the Fed can finally accomplish.

Consider three scenarios. In the first scenario, the productive capacity of the economy fell 3 percent in the first year and then has remained stagnant all five years. It so happened that nominal GDP exactly tracked the productive capacity of the economy, and the price level remained constant. Suppose the price index is 100. The approximate 20% increase in nominal GDP that the Fed will finally accomplish in year 5 would cause a 20% increase in the price level.

It is possible, as explained above, that this entire increase occurs between year four and five. And so there will be a 20% inflation rate over that period. However, such a scenario is very unrealistic. In year four, there will be a motivation to purchase goods before their prices rise. Borrowing at very low interest rates to fund those purchases will be very attractive. Further, lending by holding low interest rate securities rather than purchasing goods in year four will be very costly. The demands for goods would rise substantially in between year three and four, and nominal interest rates should rise quite a bit, to something close to 20%. As above, with the permanent change in the quantity of base money, this same argument applies in between year three and four, between year two and three, and between year one and two. In reality, the near 6% inflation rate that would be necessary to bring nominal GDP back to its target of $10,300 billion from its below target $9,700 billion level should immediate result in T-bill rates rising well above zero, making ordinary monetary policy effective.

The second scenario involves the same path for nominal GDP, it falls to $9,700 billion and stays there, but this time, potential output continues to grow 3 percent. Fortunately, all prices and wages are perfectly flexible, so that price level falls from 100 to 94 over the first year. Productive capacity rose from $10,000 billion to $10,300 billion, but spending on output fell from $10,000 billion to $9,700 billion. With a price level of 94, real expenditure rises 3 percent and real output grows with productive capacity.

As before, the Fed is trying to keep nominal GDP on target, but the open market operations supposedly have no impact. Remember, the T-bill rate is near zero and so open market operations swap just one zero interest rate asset for another. So, nominal GDP remains $9,700 billion. And each year, the price level falls roughly 3 percent more. By year 5, the price level is 84. And finally, the T-bill rates rise above enough above zero so that open market operations are effective. (I am not sure that deflation forever is impossible in this scenario. The real T-bill rate is 3 percent and for the nominal rate to rise above zero, the real T-bill rate most rise above 3%.)

Once conventional monetary policy becomes effective, the Fed raises nominal GDP back to target, which will cause the price level to rise back to 100. As before, this involves an inflation rate of approximately 20 percent between year four and five. This is unrealistic, because there would be a strong motivation to buy in year four before the prices rose. And further, nominal interest rates would rise to something like 20 percent. But, if that happens between year 3 and 4, the same argument applies between year 2 and 3 and between one and 2. When the price level approaches 94, the needed 6 percent inflation to get the price level back to 100 in year two would almost certainly cause the T-bill rate to rise well above zero and so make monetary policy effective almost immediately.

Market monetarists are usually most interested in a third scenario. In this scenario, nominal GDP falls to $9700 billion and stays at that level, while the productive capacity of the economy continues to grow. But actual production falls from $10,000 billion in the first year to $9,700 billion, and then remains at $9,700 billion. The price level, being sticky, remains at 100. As before, in year five, the T-bill rate finally rises significantly above zero, and the Fed can generate increased expenditure on output, so production rises approximately 20%, from $9700 billion to approximately $11,600 billion. All of the excess capacity, that has been growing over the years, is finally utilized.

Since the price level remains 100, there is no inflation between year four and five. Avoiding the massive inflation of prices that occurs between year four and five in the previous two scenarios is not an issue. However, the large increase in real income in year five is likely to impact demand for output in year four. For example, consumption smoothing suggests that those who expect a large increase in real income in year five would shift some of the consumption made possible back to year four. This could be done by reduced saving or even increased borrowing.

On the other hand, to the degree that the reduced income was due to unemployed workers earning little or nothing, then those who are already fully employed may expect little or no increase in their income and so do nothing different. The unemployed would have little ability to reduce saving or borrow against their future income. Still, at least some workers and entrepreneurs may be saving out of their currently reduced incomes and reduce that saving due to expectation of higher income.

Also, in a world where people lose jobs frequently, high unemployment implies that anyone who loses a job will have a more difficult time than usual finding a new one. Expectations that unemployment will fall will relieve such worries and so allow for reduced saving, and perhaps some debt financed purchased of consumer durables.

Equally important is the motivation of firms to purchase capital goods to expand productive capacity. Of course, if productive capacity had been maintained all along, with firms producing well below capacity yet still purchasing additional capital goods, this effect would not occur. But that is hardly realistic. One of the reasons why spending on output remains depressed is that firms have little motivation to purchase additional capital goods when their current sales are low. The massive increase in demand in year five is going to give firms an incentive to purchase needed capital goods in year four. (I am not at all sure that this can be managed without an inflation of capital goods' prices, but that just motivates the purchase of the capital goods in year four before their prices rise.)

The increase in demand for capital goods along with purchases of consumer durables results in increased credit demands. Further, firms that currently hold "cash," made up, for example, of the Treasury-bills that had been in such high demand, will sell them to buy capital goods. And some those those who have been saving by purchasing those bonds may sell off some of them to purchase consumer goods now due to the expected increases in income. This decrease in the supply of loans and increase in demand will tend to raise both real and nominal interest rates.

Again, the increase in demand in year 4, will result in increased output and income. And the increase in the demand for credit and reduced supply will raise interest rates, including T-bill rates, making monetary policy effective in year 4. Again the argument steps back to the initial year. Does an expected 6 percent increase in real output, from the initial reduction to $9,700 billion back to $10,300 billion cause the interest rate on T-bills, both nominal and real, to rise enough to make monetary policy effective immediately?

Realistically, some combination of scenario two and three would be likely if the problem were entirely a decrease in spending on output. A reduction in real output and a mild deflation would be the initial effect. The expected recovery of output would tend to generate higher demand in the present as well as a higher real interest rate. And the recovery of the price level, implies an inflation that motivates purchases at current low prices, and an inflation premium on the interest rate on T-bills.

Thinking about the last few years, it is likely that some element of the first scenario would apply as well. The slowdown in productivity growth in the context of nominal GDP targeting would result in a higher price level and inflation. This would tend raise the nominal interest rate on Treasury bills.

On the other hand, all of these processes require that many people have confidence that monetary policy will eventually regain its effectiveness. Of course, if the Fed hasn't even said that it is trying to target the growth path of nominal GDP, and will let spending on output languish at a low level in perpetuity, then making such a commitment now is one obvious solution to the problem.

Still, I believe that rather than limit open market operations to securities with a zero yield, the obvious next step is to expand base money to a point where longer term to maturity securities and even riskier securities are purchased. A target for a growth path for nominal GDP is necessary and might be sufficient. But if it is not sufficient, then large open market operations, including purchases of securities with yields above zero, would certainly be sufficient to break through any perverse expectations and bring nominal GDP to target.

The Money Multiplier

The money multiplier is the ratio between base money and some broader measure of the quantity of money. Base money is the sum of currency held by the nonbanking public and reserves. Reserves are made up of vault cash, which is currency held by banks, and reserve balances. Reserve balances are funds that banks hold on deposit at the central bank, the Federal Reserve in the U.S. The nonbanking public is households and firms other than banks.

There are a variety of measures of the quantity of money. The M1 measure of the money supply is made up of checkable deposits, currency held by the public and travelers checks. The M1 money multiplier is the M1 measure of the quantity of money divided by base money.

Simple algebra shows that the M1 money multiplier is equal to (1+c)/(c+r), where c is the currency deposit ratio and r is the reserve deposit ratio. "Deposits" are understood as checkable deposits. Since those ratios can change, there is no reason to assume that the M1 money multiplier, or any of the other ones, such as the M2 money multiplier or the MZM money multiplier, are fixed.

Still, the algebra is interesting. For example, if households and firms choose to hold more currency or the banks choose to hold more reserves, the resulting increase in the demand for base money, will result in a decrease in the broader measures of the quantity of money unless offset by an increase in base money.

Old fashioned monetarists favored targeting some measure of the quantity of money. The rule of thumb was that any change in the relevant money multiplier should be offset by an inversely proportional change in base money. Since money statistics are generated weekly, monetarists generally saw little problem with making these adjustments in real time.

Monetarists were quite aware that this approach was inconsistent with having the central bank target interest rates. For example, if there was a increase in the demand for bank loans, then banks would have to raise interest rates charged on those loans. To some degree, this would reduce the quantity of the loans demanded, but it could also allow banks to obtain funds from some source not included in the target. For example, if M1 were being targeted, and banks increased the interest rates paid on time deposits and attracted additional funds they could expand the amount of bank loans without increasing M1.

Monetarists recognized that banks might choose to reduce their reserve balances to fund the additional loans. If higher interest rates could be earned on loans, this would provide an incentive to economize on reserve holdings. That would raise the money multiplier, and as explained above, the rule would require a contraction of base money to offset that, keeping the quantity of money on target.

It is even possible that those holding currency would choose reduce those holdings and instead hold interest bearing deposits. This could be checkable or not. Regardless, this would reduce the ratio of currency to checkable deposits, and so raise the money multiplier. Again, a target for the quantity of money would require that base money be reduced.

Monetarists have long been aware of interbank lending. And so, along with a higher demand for loans causing banks to seek to attract additional deposits to fund the loans, any one bank can fund its loans by borrowing from other banks. Not all banks can do this at once, and what happens is that the interbank loan rate rises along with interest rates on deposits.

Suppose that the demand for bank loans were to fall. If the quantity of money is targeted, then the interest rate on loans must fall too. This will increase the quantity of loans demanded, and so limit the decrease in the quantity of bank loans. However, with banks earning less on loans, they would pay less on deposits as well. If M1 is targeted, and the decrease in the interest rate paid on time deposits resulted in less funds being deposited in them, then both bank loans and time deposits would contract. Banks could also purchase securities like government bonds with funds that would have used for bank loans, lowering those interest rates as well.

Finally, banks would be more interested in lending to other banks overnight, and less interested in borrowing. This would result in a lower interest rate on the interbank loan market.

It is quite possible that because of low interest rates on deposits, people would choose to hold more currency. It is also possible that banks would choose to hold more reserves. These two effects would tend to lower the money multiplier. With a target for the quantity of money, the central bank would need to expand base money enough to offset that decrease.

For many years now, the Federal Reserve has targeted the Federal Funds rate. Monetarists have been quite aware that when an increase in the demand for bank loans results results in a shortage of funds on the interbank loan market, then if the Fed is targeting that rate, it expands base money. The quantity of money then rises above target.

Similarly, if there were a decrease in the demand for bank loans, and this results in a surplus on the interbank loan market, if the Fed is targeting that rate, it will decrease reserves, and prevent the interest rate from falling. The quantity of money would fall below target.

Monetarists never argued that the quantity of base money should be fixed. But they did say that it should not be changed to keep any interest rate, including the interbank loan rate, from changing. It was never the case that monetarists were unaware that the Federal Reserve adjusted the quantity of reserves to keep the interest rate on interbank loans at a targeted level. It is rather that they opposed that policy. They favored changing the quantity of base money according to a different principle--keeping some measure of the quantity of money on a targeted growth path.

Now, most economists do favor having central banks target interest rates. Traditionally, they argued that if there is a change in the demand to hold money, the liquidity effect would tend to change interest rates. For example, if there is an increase in the demand to hold money, then at least some of those short of money will sell securities, raising their yields. By targeting interest rates, the central bank would expand the quantity of money, by purchasing securities, dampening and reversing the increase in interest rates. The Fed would have increased the quantity of money enough to match the increase in the demand to hold money.

Because the interbank loan rate is tied to other interest rates, stabilizing the interbank rate tends to simultaneously adjust the quantity of money to the demand to hold money. Also, if there is some change in the desire to hold currency or reserve balances at any given interest rate, those changes will tend to cause changes in the interbank loan rate. For example, an increase in the demand for currency would draw down bank reserves and create a shortage on the interbank loan market. By expanding the quantity of reserves, the central bank automatically offsets the change in the money multiplier, leaving the quantity of money unchanged.

These arguments in favor of targeting interest rates are completely consistent with the monetarist account of the money multiplier. They just are inconsistent with the monetarist policy goal of keeping some measure of the quantity of money on target by adjusting base money according to changes in the money multiplier. By the way, the monetarist response to these arguments in favor of targeting interest rates is that changes in the demand for bank loans should result in changes in interest rates and not changes in the quantity of money. As I repeat over and over, an increase in the demand to borrow money from banks is not at all the same thing as an increase in the demand to hold money.

How is it that the quantity of money changes when there is an increase in base money? There is a terribly unrealistic story often told in introductory textbooks. The story starts with a bank having excess reserves. The bank lends those reserves out. The borrower spends the money and the sellers deposit the checks. The checks clear, and the bank that made the loan no longer has the excess reserves, but the bank used by the seller now has the excess reserves. It makes a loan, and so on. Assuming banks' demand for reserves increases with their supply of deposits, then the amount lent each time is smaller. The initial quantity of excess reserves is "multiplied" into many deposits and many bank loans.

Now, there is an element of truth to this account. If there is an excess supply of base money, there will be a tendency for banks to create credit. They don't necessarily have to make loans and instead can purchase existing securities--often government bonds, but possibly corporate bonds as well. With a bank loan, the story is that those borrowing the money spend it, and those selling to the borrowers deposit the check. This does result in shift of reserves between banks, but the total amount of reserves that banks have are unchanged. For the excess supply of base money to clear up, the demand for base money must rise. This could occur because with a higher quantity of deposits, banks demand higher reserve balances. It could be that people like to keep their total money holdings in fixed proportions between deposits and currency, and so more deposits increases the demand for currency.

In my view, by far the most important process is that the increase in deposits results in additional expenditures on output. The growing nominal income results in an added demand for currency and reserve balances.

Also, I often point out to my students that the simple story of banks making loans based upon their existing level of excess reserves is very unrealistic. Do banks put out a sign saying, "excess reserves available today, come get your loans?" In reality, banks set interest rates on both loans and deposits intending to use their deposits to fund their loans. In a growing economy, this generally involves setting interest rates on loans and deposits so that demand for loans from banks is matched by the supply of deposits to banks. The banks then use money market instruments to adjust for any temporary imbalances between the demand for loans and the supply of deposits. Higher loan demand would immediately result in banks selling off government bonds, reducing overnight lending to other banks, or borrowing more overnight from other banks. An increase in the supply of deposits would result in banks buying government bonds, reducing overnight borrowing from other banks, or lending more overnight to other banks.

This suggests that the immediate effect of any excess supply or demand for base money will directly impact money market interest rates. Only if those new rates are expected to persist would the result be changes in the interest rates that banks charge on loans and pay on deposits. And so, only if the change in money market rates are expected to persist would bank loans expand or contract.

With interest rate targeting, both the current level of money market rates and those expected in the future are going to be driven by current and expected future central bank policy. (Of course, I don't favor targeting interest rates or any measure of the quantity of money.)

Anyway, if a central bank wants to expand the quantity of money, it undertakes open market purchases. This creates an excess supply of reserves. Banks use the reserves to purchase money market instruments. The impact on overnight interbank loans just reduces the interest rates on those loans. Further, purchases of government bonds by banks from other banks has no impact on the quantity of money, and only results in lower interest rates on the bonds. However, purchases of government bonds from firms other than banks and households increases the funds in their checkable deposits, as well as lowering the interest rates. The increase in the checkable deposits of those households and firms other than banks is an increase in quantity of money.

Is this effort to increase the quantity of money consistent with keeping short term interest rates on some "target?" No, it is not. Does this effort to increase the quantity of money result in more bank loans? Perhaps not.

Suppose that the banks respond to lower interest rates on government bonds by selling them and instead just hold reserve balances. This is a decrease in the money multiplier, and tends to reduce the quantity of money. How then can a central bank expand the quantity of money? It buys all of the government bonds the banks want to sell, and also buys bonds from households and firms. And the result is an increase in the quantity of money. Base money expands enough to offset the decrease in the money multiplier and increase the quantity of money. Nothing in the process requires that banks make any loans.

What would be necessary for the simple textbook story of the money multiplier to be realistic? First, suppose that bank deposits take the form of hand-to-hand currency rather than interest bearing deposits. If that is true, there is little question of banks adjusting the interest rates they pay to obtain funding for loans. So, the "realistic" story where banks set the interest rates they charge and pay to match deposits and loans doesn't apply. Interest rates only apply to lending. Further, all of the banks' liabilities are monetary.

Second, suppose that usury laws create binding price ceilings on bank loans. At the legal maximum there is a shortage of loanable funds, and banks ration out the funds however they think best. A responsible approach would be to provide them to the best credit risks.

Third, suppose there are no good markets for money market instruments. Communications and transport are primitive. Bank asset portfolios are made up of reserves and loans. Bank liabilities are made up of deposits. And, of course, the bank owners have equity in the bank.

If a bank obtains added reserves, then the only options are to either hold them or else lend them. Because of the usury laws, there is a shortage of funds at the legal interest rate, and so no problem with lending out all the funds. Those borrowing the funds spend them, and the funds are mostly deposited in other banks, which then have excess reserves to lend. And so, there is a multiple expansion in the quantity of money, the banknotes, and in bank loans.

If banknotes are replaced with checking accounts that bear no interest by law, then the account changes little. It is only when we have a system where banks can use money market instruments to manage their reserves, and banks are funding their loans and securities portfolios with a variety of interest bearing deposits, does a quite different approach to understanding the banking business become reasonable. In particular, changes in the interest rates on money market instruments and the interest rates that banks pay and charge become very important for any reasonable account of the banking business.

Still, if there is an excess supply of base money, the result will be increased spending on something--goods, services, or perhaps just financial assets--until the demand to hold base money rises to meet the quantity. Unless, of course, the issuer of base money, the central bank, chooses, to to reduce the quantity of base money to prevent the effects of that expenditure. Interest rate targeting is an example of such a policy.

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.