Interest Rates, new Keynesians, and Market Monetarists

When Market Monetarists read new Keynesians, we are often puzzled by their focus on the policy interest rate.      They argue as if (and sometimes say,) that the only interest rate that really counts is the expected future path of the policy interest rate.

This approach is institution specific.   What would happen if there were no policy interest rate?   Sure, central banks like targeting monetary market interest rates, but they don't have to do that.   Plenty of economists favor letting all interest rates depend on supply and demand.   

Suppose that a central bank targets the monetary base.   All interest rates depend on supply and demand in credit markets.   There is no policy interest rate.   There is no expected future path of the policy interest rate.   It is impossible for a policy formula to spit out a policy interest rate that is below zero.   Comparing spending on output over time with a hypothetical scenario where the policy rate falls below zero according to the rule to one where it fails to fall enough but rather just stays at zero for a protracted period of time is impossible.

With a base money rule, if spending on output is too low, the target for base money is increased.   If spending is too high, the target for base money is decreased.   

Further, consider the scenario where spending is too low, and so  base money is being increased.   What do we make of the zero nominal bound in this scenario?     The only obvious zero nominal bound is that base money cannot be negative, and with spending being too low and base money increasing, that is hardly a problem.     The other bound is slightly more relevant.   The central bank might purchase all the assets that it can, and so it cannot raise base money any more.   Let's ignore that "upper bound" for now.

No, the problem must be that some financial asset other than the central bank's own liabilities has a zero nominal yield.   I think the most plausible candidate would be that the central bank is purchasing some kind of asset with newly created base money, and the central bank is bidding up its price by doing this, and so driving down its yield.    At some point, the yield is driven down to zero.   The yield on the asset the central bank is buying to create base money has a zero nominal yield.

However, it is certainly possible that private investors might demand more of the asset the central bank usually purchases and push up its price and drive down its yield.   For example, suppose the central bank generally buys T-bills, and private investors worried about losses on other financial assets like stocks sell them and buy T-bills.    This effect would be independent of purchases of T-bills in anticipation of central bank purchases to raise base money in response to inadequate spending on output.    Conceivably, private investors might force the T-bill yield to zero, and so now if the central bank purchased T-bills to expand base money, it would be buying an asset with a zero nominal yield.

So here we have a possible zero-nominal bound problem.   The central bank is purchasing assets that have a zero yield.   Now, Market Monetarists and new Keynesians agree that spending on output today will be influenced by spending on output in the future and the level of base money in the future will impact spending on output in the future.   For the new Keynesians this occurs because at some point in the future, keeping the policy interest rate at zero will result in growing expenditure--presumably at ever increasing rates.   Keeping spending from growing in the future would require increases in the policy rate.   By increasing the policy rate less than that, spending can increase to whatever amount is desired.   (Only if nominal interest rates are expected to be zero forever would this be impossible.  Let's leave that possibility aside.)

From a Market Monetarist perspective, a level of base money consistent with some higher level of nominal expenditure on output would start to cause spending to rise to that higher level once the demand for base money at that future date falls below the quantity at the future date.   So the question then has nothing to do with the impact of different targets.    Nominal GDP level targeting will tend to keep spending on output from falling as compared to a pure inflation target or even a Taylor-type rule.   

However, it is also true that Market Monetarists agree with new Keynesians that spending on output can fall below target, even with a nominal GDP rule.   The issue, then, is whether "extra" increases in base money will increase spending on output beyond the increases in spending that would occur anyway due to the expectation that eventually spending on output will return to the target path.      To  clarify, assuming there is a nominal GDP level target, assuming that spending will not be permitted to rise above target at any point, will increases in base money while spending on output is below target cause spending on output to be closer to the target or reach the target more rapidly?

Suppose we knew what level of base money will be necessary in 2015 to get nominal GDP back to the target path.   Base money has reached that point.    The interest rate on assets the central bank buys is already zero.   The new Keynesian argument is that purchasing more of that asset now, knowing that the additional purchases will be reversed and base money will return to the proper 2015 target, when spending will also reach its proper target, will do nothing for spending today.      Extra purchases of this asset, and the extra increases in base money, will do nothing to raise spending closer to target than it otherwise would be or hasten the return of spending on output to target.   As long as people believe that base money will be adequate in 2015 for spending to return to target in 2015, then spending today will be as high as the central bank can make it.   Any additional increase in base money is pointless.

Why is it that open market purchases of an asset with a zero interest rate create no extra increase in spending now.   Market Monetarists and new Keynesians would agree that ephemeral changes in base money or reductions in policy interest rates would have little effect.   So, the question is whether extra purchases of zero rate assets with newly created base money that will persist for some extended period of time will help.   Again, will they either cause spending on output to be closer to target while remaining below target or will they hasten the return of spending on output to target?

Woodford gives a very traditional Keynesian argument for the ineffectiveness of open market operations when the interest rate is zero.   The demand for base money becomes perfectly elastic.   Now, when the supply of a good increases and demand is perfectly elastic, then the price remains the same--it doesn't fall as would occur if demand has the usual downward slope.   And so, Woodford appears to be saying that when the nominal interest rate is zero, an increase in the quantity of money cannot result in a lower nominal interest rate.   But perhaps the real significance of the argument is that the quantity of money demanded shifts dollar-for-dollar with the increase in the supply of money.

The Barro argument is that when interest rates on the assets the central bank purchases are equal to zero, then they become perfect substitutes for base money.   If the central bank purchases such an asset with newly created base money, it increases the quantity of money in the form of base money and reduces the quantity of money in the form of these zero interest bonds.   The total quantity of money, inclusive of both base money and the zero-interest bonds remains the same.   It would be like replacing a $20 bill (unit of currency) with two $10 bills.   The quantity of money is not effected.

The Yeager argument is that when there is a shortage of some bond at a yield of zero, the excess demand for the bonds might be shifted to an increased demand for money.   If a central bank seeks to accommodate the added demand for money by increasing the quantity of money, and does so by purchasing more of the very same bond that is already facing an excess demand, then while it is creating more money, it worsens the shortage of the bonds by purchasing more of them.   When that is shifted over to an added demand for money, the central bank is left where it began.   It has failed to correct the underlying shortage of money.

From a Market Monetarist perspective, the only reason why spending on output falls below target is an excess demand for money.   That doesn't mean that the problem must be caused by a reduction in the quantity of base money or that an increase in the demand to hold money beyond an increase in the quantity of money occurs as a "bolt from the blue."   It could occur for any number of reasons.   Still, increasing the quantity of base money should relieve the problem unless there is some special situation where the very process by which base money increases results in a matching increase in the demand to hold base money, leaving the underlying shortage unchanged--or conceivably worsened.

The Woodford, Barro, and Yeager arguments all suggest that a central bank purchasing assets with a yield of zero would not relieve the underlying excess demand for money.   Yes, Market Monetarists and New Keynesians agree that at some future time, this won't be an issue, an appropriate path for base money or policy interest rates will return spending on output to target, and that expectation of this recovery will limit current deviations of spending from target.   But, increases in base money created by purchases of an asset with an interest rate of zero are likely to do nothing now directly.

In other words, if base money is at the level  now that will bring nominal GDP back to the target growth path at some future date, increasing base money beyond that point now will not cause spending to rise closer to the current target during that period it remains below target nor will it help reach the target sooner.   There is no point to raising base money.   (Of course, no one really knows what the level base money needs to be to reach the target in the future, so raising base money during the period when spending is too low might still be sensible.)

Of course, from a Market Monetarist approach, the question is by how much base money needs to increase in order to get nominal GDP back to target.    If increasing base money by purchasing assets with a zero nominal interest rate has little effect, and those assets are going to be purchased anyway, then this simply implies that a larger increase in base money is necessary.   All of the zero yield securities must be purchased and then other securities must be purchased as well.

Once the central bank is purchasing securities that don't have a zero yield, then the Barro and Yeager arguments no longer apply.   The securities being purchased would not be perfect substitutes for base money, and so, the quantity of money would be increasing.    There is not a shortage of those securities at their current positive yield, and as long as the purchases don't go so far as to create a shortage, there is no shortage to be shifted to an increase in the demand for money.    The quantity of money rises, without any self-inflicted increase in the demand to hold money, and so the underlying excess demand for money is relieved.

This suggests that a sufficient expansion of base money now, which would require that on the margin assets be purchased that have yields greater than zero, would result in an increase in spending on output.   The shortfall in spending on output could be reduced, and spending on output could return to target more quickly.   Since expectations that spending on output will be higher sooner should result in more spending due to the effect expectations of future spending, this would be a second avenue by which the extra increases in base money would help raise spending.

What about the Woodford account?   The demand for money is supposedly perfectly elastic at an interest rate of zero.   But the interest rate for the securities the central bank is purchasing is not zero.   Of course, Woodford's assumption is that the interest rate on those securities would be reduced by the central bank's purchases,  lowering the opportunity cost of holding money, so that in the end, the quantity of money demanded rises to match the added quantity.     From Woodford's interest-centric view, what is happening is that once the interest rate on one particular asset is driven to zero, then the interest rate on some other asset is lowered.   If that one is also driven to zero, then another is lowered.

This process of driving one interest rate and then another to zero occur until the central bank has lowered the interest rate on all assets it can buy to zero.   This is very much parallel to the "upper bound" for base money targeting.  Once the central bank has purchased every asset it is permitted to purchase, then no further increase in base money is possible.

This points to another institutionally specific element of new Keynesian thinking.   Central banks like to target interest rates, and new Keynesian economists narrowly focuses on interest rate targeting.   Central banks like to purchase safe money market instruments.    New Keynesian economics focuses on just such instruments.

Market Monetarists insist that the problem of a shortfall of spending from target is that the quantity of money is less than the demand to hold money.   If small modest increases in base money used to purchase safe money market instruments are inadequate to expand the quantity of money enough to meet the demand under some circumstances, then heroic purchases of longer term and riskier securities should be used.

Woodford argues that heroic open market purchases of assets with interest rates above zero will not be effective.   They will not raise spending  closer to target or allow it to reach the target sooner.   The effect is the same as if base money simply expands (or contracts) whatever amount is needed to keep the policy rate equal to zero until spending returns to target.     But what does this mean with base money targeting?   Spending will not rise closer to target or reach the target sooner due to any increase in base money beyond the level needed to keep spending on output at target when the interest rate on the asset the central bank usually buys rises above zero.

But surely this depends on what particular bond the central bank typically buys.    Suppose the central bank usually buys government bonds with maturities between 2 and 5 years.   Now suppose further that the interest rate on 3 month bill T-bills falls to zero.   The central bank never buys any of those anyway.   It continues to purchase the longer term bonds as usual.   Is it impossible to relieve an excess demand for base money because the 3 month T-bills has a zero yield?    Suppose instead that the central bank targets a yield for  bonds with 4 years to go.   Can it not continue to make adjustments in that interest rate even if the 3 month T-bills is zero?

Now, suppose that the Treasury never sold T-bills at all.   Whatever market conditions would have caused that yield to fall to zero still occur, but there are no T-bills.   Of course, the central bank doesn't buy nonexistent T-bills.   It buys government bonds with 3 to 5 year maturities.    Do market conditions that would create a zero yield on nonexistent T-bills make increases in base money ineffective?

Suppose now that there is no national debt at all and the central bank only purchases private securities that bear default risk.   (Perhaps the liabilities of the central bank should  count as government debt.)   Suppose market conditions that would have caused the interest rate on T-bills to fall to zero occurs, but there are no government bonds at all.   Does the central bank's expansion of base money by purchasing risky private securities become ineffective?

Suppose one business finds that it is able to borrow at a zero nominal rate.   Does this make increases in base money by the central bank when it purchases bonds issued by other firms ineffective?

Now consider a cashless (or currency-less) monetary regime.   All payments are made by transfer of bank balances.   The interest rate on balances at the central bank are slightly less than the interest rate on short term government debt.   If the yield on that debt falls, then the interest rate the banks receive on their balances at the central bank fall in proportion.

There is no zero nominal bound on interest rates.   Interest can be as negative as necessary to keep spending on output on target.   What is it about these negative interest rates on short term government bonds that solves the problem?    If we have an economy that only has consumer goods and everyone is the same, then the only way for spending to rise is for everyone to consume more now.    The lower interest rate on government debt, central bank balances, money balances held in banks, and everything else, have to deter desired saving in the current period and so raise desired consumption.   There is nothing else.

But in reality, when there are different people, then a sufficiently negative interest rate on government bonds would motivate households that save to lend more to households that dissave.   This involves bearing more risk, on the assumption that households that dissave are more likely to default than the government.    Further, in an economy with investment, then some of those holding government bonds might sell their bonds due to the low yields and spend the money on capital goods now in order to get consumer goods in the future.   Others might lend to firms that will purchase capital goods rather than lend to the government.   Of course, this involves more risk, assuming that investments in capital goods are more likely to fail than the probability the government will default on its debt.

Something happens that makes market-clearing interest rates on short and safe securities negative.   If the central bank's own liabilities are short and safe and it keeps the interest rate on them at zero, then no interest rates are going to fall to the market clearing rates because people will hold the liabilities of the central bank instead.     But if the central bank expands the quantity of base money enough, it will bear the risk and so all of the impact of hypothetically negative nominal interest rates on short and safe assets in terms of motivating purchases of capital goods or debt financed consumer goods are still obtained.   Only by assuming those are nonexistent, that is, in a consumer good only, representative agent economy, will it look like the expansions in base money have no effect.

Finally, suppose that all hand-to-hand currency is issued by risky private firms.   The central bank only offers deposit accounts to banks, and the banks using the central bank only issue deposit accounts.   The interest rate on short-and-safe government bonds can turn negative.   The interest rates on bank deposits can turn negative.   The zero-nominal interest rate on privately-issued currency is irrelevant, because it is quite risky.   It is only held for its "liquidity" yield.   Presumably criminals still use it as do people making small face-to-face transactions.     This currency is not base money.   It is like travelers checks issued by fly-by-night firms.

If the central bank makes open market purchases of T-bills, and drives their prices above par and their yields below zero, then the interest rates paid on reserves and the interest rates banks pay on deposits are also driven below zero.   Saving is less attractive and consumption more attractive, but also there is a motivation to bear more risk by lending money to dissavers and financing capital goods either through lending to firms or selling of short and safe securities to buy capital goods.

Now, suppose the risk of these investments in capital goods or loans to dissaving households approaches that of the risky hand-to-hand currency.    Then, there will be an increase in the demand for that currency and the firms issuing it presumably will have less rather than more incentive to issue it.   Currency becomes more difficult to obtain for small face-to-face transactions and criminal activities.     To keep spending on target, other sorts of spending must expand.  (Presumably the criminal activities weren't measured anyway.)  This would be spending undertaken by check or electronic payment.

Of course, if all deposits were made redeemable in this hand-to-hand currency, even though it is risky and issued by private firms, then it would be impossible to expand spending by check or electronic payment to offset the reduction in spending of hand-to-hand currency.   On the contrary, the shortage of hand-to-hand currency would generate a shortage of deposits and reduced spending on output too.

So, central banks are governmental institutions issuing hand-to-hand currency that is safe, short, and has a zero nominal yield.   All other money is redeemable in that currency.   The central banks like to make periodic changes in money market interest rates implemented by modest changes in purchase of short and safe assets--generally short term to maturity government bonds.   If there is a large increase in the demand for those short and safe  government bonds, then central banks must do something different to keep spending growing at a slow and steady growth path.   Bearing more risk itself to motivate more investment in capital goods and more consumer loans is possible.   This raises spending on output now, and when the market clearing rates on short and safe assets rise to zero, then it can go back to holding those and bear less risk.   While it may appear undesirable for central banks to bear such risk, it is the least bad alternative if they insist on issuing zero-risk, zero-nominal-yield, hand-to-hand currency, or rather, in making all other money redeemable in their currency.