Cancelling Currency According to Cochrane

Rogoff has a paper discussing the costs of and benefits of a cashless payments system.   Cochrane responded with the following:

So, quiz question for your economic classes: Suppose we have substantially negative interest rates -- -5% or -10%, say, and lasting a while. But there is no currency. How else can you ensure yourself a zero riskless nominal return?  

• Prepay taxes. The IRS allows you to pay as much as you want now, against future taxes. 

• Gift cards. At a negative 10% rate, I can invest in about $10,000 of Peets' coffee cards alone. There is now apparently a hot secondary market in gift cards, so large values and resale could take off. 

• Likewise, stored value cards, subway cards, stamps. Subway cards are anonymous so you could resell them. 

• Prepay bills. Send $10,000 to the gas company, electric company, phone company. 

• Prepay rent or mortgage payments. 

• Businesses: prepay suppliers and leases. Prepay wages, or at least pre-fund benefits that workers must stay employed to earn. 

Here are the ones I can think of:  
Comments section: how many more can you think of? 

He goes on:

So, bottom line, we cannot have strongly negative nominal rates without a legal revolution essentially negative-indexing the entire economy and payment system, and upending centuries of law giving you the right to pay bills at face value.

I suppose a finance academic would focus on a zero riskless nominal rate of return.   As a monetary economist, I focus on the supply and demand for money.   

If there is a shortage of money, it is very disruptive and fixing it is a good idea.   The solutions are to increase the quantity of money or reduce the demand to hold money.   Most money usually pays relatively low nominal interest , and so reducing that yield is one obvious method of reducing the demand to hold money.   Shifting from paying people to hold money, to a zero nominal yield, to charging them to hold money seems pretty straightforward.  Money provides services, and people would be willing to pay for them.  In some situations, they should pay for those services.

Of course, the other method of fixing a shortage of money is to expand the quantity of it.   And the lower the yield paid on money, the more profitable that approach would be.   However, if the interest rates banks can earn by lending money, including holding various sorts of bonds, are exceptionally low, then it is possible that monetary equilibrium would require a negative nominal interest rate paid on money balances.   The interest rates on other sorts of assets, especially those assets banks buy, would be somewhat higher.    

With extremely low credit demand and a very high demand for money, it might be possible that equilibrium would involve banks earning negative yields on at least some of their assets.  That implies that someone is able to borrow at negative rates, while the banks pay still lower yields to their depositors.

While I don't see much value in a monetary regime that generates a 10% trend deflation rate, I think it is likely that equilibrium would require that nearly all nominal interest rates be negative.   And further, zero nominal interest rate currency would be very disruptive.

If hand-to-hand currency was privately issued, since it is hardly practical to charge people for holding it directly, then in a very low credit demand environment, banks would stop issuing currency.   The result would be a cashless payments system.   

Now, I don't have any problem with banks issuing currency at a loss if that is what they want to do.   But I don't think they should be forced to do so.   And if no one wants to issue a zero nominal interest rate asset, then there won't be one for people to hold.   

Of course, that isn't the world we live in.   The government issues a zero-nominal interest rate asset--hand-to-hand currency.   And it declares that it is legal tender for all debts.   This is especially relevant because all of the bank issued money must be paid off on demand with government currency.   The entire monetary order is based upon the government currency.  

Since holding government currency--effectively lending to the government at  a zero nominal interest rate--is always possible, this government intervention creates a floor on the nominal interest rate-the cost of storing paper currency.   

On the other hand, the evolved commodity money systems of the past also had a similar zero nominal bound--the cost of storing the monetary commodity.  

Anyway, the point of my digression is twofold   First, the purpose of negative nominal interest rates on money isn't to prevent people from having a riskless nominal rate of return.   It is to reduce the demand to hold money so that it will be in balance with the quantity of money supplied.   

And second, there is no problem with people being able to hold assets that other people want to issue.  The problem is limiting the demand to hold assets when there is a shortage of them.

So, I am going to start with Cochrane's second example.    People could supposedly get a riskless zero nominal rate of return by purchasing gift cards.    Cochrane even notes that there is already a secondary market in gift cards.    My wife tells me that you can sometimes buy a $100 card on sale for $90.   That is a pretty good rate of return, I guess.   

First, if retailers want to issue gift cards at face value, and so provide investors a zero nominal return, that is fine.   Of course, there is a risk--suppose the retailer fails?    Did Cochrane forget that?    

Under usual circumstances, when a retailer sells a card it is getting a loan.   Leaving aside discounting the cards, it is a zero interest loan.    And so, now the retailer has the money.  What do they do with it?   If the interest rate on money is sufficiently negative, then the retailer will find borrowing money at a zero interest rate and then paying to hold it  unattractive   Of course, perhaps the retailer can invest by purchasing assets that have a positive yield.   Or maybe they will accumulate inventory to be prepared for the greater sales when the cards are spent.   It doesn't matter.    As long as the retailer doesn't hold the money, the lower (below zero) nominal interest rate has done its job.   

Now, if this becomes too burdensome for the retailers, then they might stop issuing the cards.  Or, they might issue them but charge a premium and require that they be used by a certain date.   

In my view, in a privatized system, if banks quit issuing private hand-to-hand currency because it was not profitable, then I would expect that retailers would expand their sales of gift cards.     They might even issue paper currency.   For example, Walmart might issue something like Walmart currency that can only be "redeemed" for products at Walmart.    But in the end, Walmart would only issue gift cards or currency if it wanted to--found it profitable.    

And what does Walmart do with the money it receives?   If it holds it, that is a problem.   But that is what the below zero interest rate on money aims to deter.   If Walmart purchases other assets or purchases inventories of goods, constructs new buildings, or whatever, the problem is solved.

Consider Cochrane's fourth example--pre-paying utilities.   Now, my utility companies vary the amount billed according to use.   If you prepay, then you get a credit balance on your account.   And then, at the normal billing time, they debit the balance.   You get a bill that says that you don't owe anything this month and it tells you your new, lower credit balance.    If you have a debit balance, they add to it as each bill comes  due.   They charge penalties, of course, if you are too late.

Now, few people intentionally hold credit balances with utilities.   I am not sure if it is illegal for utilities to pay interest on such balances.   I suspect if some utility started to do so and began to finance its operations with the credit balances of customers, they would run into legal problems. (Industrial firms operating banks is frowned upon.)  Regardless, if the utility had to pay to keep money in its checking account, I think they could figure out a way to charge people for holding credit balances.   

Just because many firms will allow for credit balances in an account hardly means that they have some kind of legal obligation to allow people to do so.  I have had a credit balance sometimes with my dentist.  Does that mean that anyone can come in off the street and open an account with the dentist?   Can they later come in and say that they are switching dentists and they want their money back?   

Regardless, even if the utility companies allowed people to have credit balances on their accounts and didn't charge any fee, the question remains, what does the utility do with the money?    All the negative yield on money is supposed to do is reduce the amount people want to hold.   If the utility spends the money on other financial assets or spends it to construct a new plant, the negative yield on money has done its job.

Cochrane also says that people could prepay their mortgages or their rent.   Now, I hardly count regulations allowing the refinance of mortgages without penalty to be some tradition from the centuries.   Regardless, if someone pays down their mortgage, what they have is not a riskless asset but more equity in their home.   They are bearing more risk.   

But what are the monetary consequences?   Paying down bank mortgages tends to contract the quantity of money.  However, any single bank receiving such repayments will accumulate reserves.   And the interest rate on that form of money is negative as well.  

For most institutional setups, that is what is driving the negative yields on deposits.   Banks are motivated to purchase other assets due to these negative yields on reserves.   (My own preference is for the interest rate on reserves to float at a  few basis points below the interest rate on  short Treasury securities.)

Further,  I don't see why a landlord would need to say, "you are paid up for 6 months," rather than credit a account with a prepayment and then debit it as the rent comes due.  In other words, like my electric company does.  

Of course, if landlords want to allow people to do this at a zero interest rate, that is fine.   What does the landlord do with the money?   If they find borrowing at a zero interest rate desirable and then spend the money on financial assets or buying more houses, then the problem is solved.  The point of the negative yields on money is to reduce the demand to hold money.

Businesses are going to prepay suppliers?    Well, I guess.   But if this is a spot transaction, then the likely result of prepaying in an environment of negative yields on money, is that the price you pay will be higher.   I will give you $100,000 now and how much copper will you give me in six months?   Less than if I took delivery now?   Maybe I should buy now.  

But again, if the suppliers will accept deposits on their account, then that is fine  What do the suppliers do with the money?   Prepay wages?    What do the workers do with the money?    Prefund benefits?   What does that mean?   A firm pays an insurance company early?   What does the insurance company do with the money?

And finally, there is Cochrane's first example.   Nominal interest rates cannot fall below zero because the IRS allows people to pre-pay their taxes.   What does the U.S. Treasury do with the money?   If it uses it to pay off government bonds, then there is no problem.   Holding onto money at a negative yield would hardly be attractive to the Treasury.   And those receiving it in exchange for the government bonds would have the money.  What do they do with it?   The point of a negative yield on money is to reduce the demand to hold money.

If the Treasury were to receive money to prepay taxes, then it is borrowing money at a zero interest rate.   It should be no surprise that the Treasury is usually happy to do this, since it is usually funding most of the national debt with interest bearing bonds.   If the interest rate on money is negative, and there are no more government bonds to pay off, and the Treasury simply holds onto the money, then the Treasury takes a loss.   It is borrowing money at a zero interest rate and then lending it at a negative interest rate by holding money.   

And this would be a problem.   The demand for money would not fall.  Those prepaying taxes would reduce their demand to hold money, but it would be just matched by an increase in the balances the government holds.   Traditional conventions for measuring the quantity of money would count this as a decrease in the quantity of money.   

Again, if there is no national debt to be repaid, then unless Congress can be convinced to lower taxes or raise outlays, the Treasury would take a loss.   And the demand to hold money would not be reduced.  (Again, this would actually show up as a decrease in the quantity of money.)  

And, of course, maybe, just maybe, the Treasury would provide taxpayers with a credit account for pre-paid taxes and charge them interest on it--maybe something like what the taxpayers would have to pay if they kept their funds in their own checking account.

In a world where the interest rate on money is negative, or really, a world where those receiving payments have no good investment opportunities, then making some open ended commitment to allow unlimited prepayment would be costly to those parties choosing to provide that opportunity.   They will likely stop.

And, other than the government, it is obvious that none of these transactions create a riskless asset.   These are all loans to private institutions that could fail. 

In my view, there is really little value in assets with no nominal risk.   The value is in assets with no real risk.   Reducing the real risk of nominal assets requires a decent monetary regime.   One that just holds the nominal quantity of money stable and allows the price level to adjust so that the real quantity of money accommodates the real demand to hold money implies real risk   A monetary regime that adjusts the nominal quantity of money to the demand to hold money at a stable price level or growth path of nominal GDP is not free.   There should be no expectation that the monetary regime must create a monetary asset that has little real risk and a zero, much less positive, real yield.    It depends on the cost of operating the regime and the demand for credit.  

Government bonds do have a low credit risk under most circumstances, and with a good monetary regime, the real risk due to aggregate supply shocks and aggregate demand shocks is dealt with reasonably well.   If the demand for government bonds becomes so high that a negative nominal yield is necessary to clear the market for government bonds, then a negative nominal yield on government bonds is the least bad option.    Creating a monetary disturbance so that there is a sufficient liquidity effect to keep the nominal interest rate on government bonds above zero would be foolhardy.

Now, if the real interest rate on government bonds is negative, then it certainly seems that running  budget deficit would be sensible. Not because it would raise the yield on government bonds to benefit the government's creditors--charging them less for this low risk asset.   But rather because government spending programs would cost future taxpayers less than current taxpayers.   That this would provide investors with a low risk asset at a lower charge should not be the goal of fiscal policy.   

While government bonds may have little credit risk for the lenders, this can be nothing other than a shift of risk to the taxpayers.   Suppose destructive government regulations cause real output to fall ten percent.    How are government bond holders protected from this disaster?   The taxpayers must pay more taxes for fewer services. 

And so, budget deficits and a national debt are adding risk to future taxpayers.   If the interest rate on the national debt was negative forever, then that would be a good reason to expand the national debt.  However, what if the interest rate on short government bonds is negative right now, but likely will turn positive in the near future.   Should the government refinance the national debt immediately, borrowing short rather than long?   This should make the interest rate on short term government bonds less negative and so provide investors a better return.   Or should the government try to lock in relatively low long term rates?    

Should the government cut taxes or increase government spending, running a deficit now?  To me, I am much more confident that if the government is purchasing long lived assets, and the long interest rate at which it can borrow is lower, then it is reasonable to buy assets that would be purchased in the future anyway right now.   Start the project now, when financing costs are low.

I don't have the answers exactly as to how the government's fiscal policy should respond to low or even negative nominal and real interest rates.   I am sure that the monetary regime should not be held hostage to the answer to these questions.   I favor a monetary regime that will allow the yields on government bonds to turn negative when there is a sudden increase in the demand for government bonds.   I favor a monetary regime that will allow the interest rate paid on money to turn negative if necessary to keep the quantity of money demanded equal to the quantity of money supplied, as what might happen with a large drop in credit demand.   

Having the monetary system based upon a zero nominal interest tangible government currency seems inconsistent with those principles.

By the way, I don't favor outlawing government currency.   People should be free to do what they want with old Federal Reserve notes, just like they are free to do what they like with old Confederate currency.   I just favor demonetizing it.    

Fed's Dirty Little Secret II

David Beckworth has expanded on his argument that the Fed's policy of quantitative easing was relatively ineffective because it did not permanently increase base money.   He points out that there is plenty of evidence that quantitative easing increased aggregate demand some.   I suppose the obvious point is that the reason why a huge amount of quantitative easing had a small impact on aggregate demand is that it is expected to be temporary.   In both the posts Beckworth said that he favored a nominal GDP level target, explaining that whatever portion of the increase in base money needed to get nominal GDP to the target would be permanent and so effective.

Beckworth also criticized Krugman's defense of advocating fiscal policy.  In Krugman's view, due to obstinate Republicans, there was little chance that the Fed would undertake the sort of regime change necessary for monetary policy to be effective.   That leaves fiscal policy.

My view is that if the problem is that Republican's are obstinate, then fiscal policy is a nonstarter.   Fiscal policy is rife with political controversy due to allocation and distribution issues.    Sure, a permanent decrease in marginal tax rates combined with a credible plan to slow the growth of government spending and gradually balance the budget might expand aggregate demand immediately.  But that is hardly what Krugman had in mind.   And yes, a temporary increase in government spending with the future interest cost funded by taxes on the rich might work as well.   Why would anyone think that it makes no difference?    Of course, if you are a committed partisan, then "fix the recession" is really just one more arrow in the quiver to support your team.

Whose taxes should be cut?   Whose preferred government programs should be expanded?

Beckworth, however, argues that Krugman (and I) are mistaken to believe that fiscal policy could work.    He argues that for the same reason that the increase in base money is temporary and so largely ineffective, any fiscal policy action will necessarily have a limited impact on aggregate demand.

Let's first review Krugman's standard new Keynesian argument for fiscal policy.   First, the way that monetary policy increases aggregate demand is by reducing the real interest rate.    In the models, this causes each individual to seek to substitute current consumption for future consumption.   In the models, with representative agents and consumption only, this is impossible.   What really happens is efforts to increase current consumption increase real income.

The way the central bank reduces the real interest rate is by lowing its target for the nominal interest rate.    Given that inflation expectations are well behaved and more or less on target, this reduces the real interest rate.

However, at the zero nominal bound,the nominal interest rate cannot be lowered.   And so, the only way to reduce the real interest rate is to raise the expected inflation rate.    This is how Krugman insists on characterizing any regime change.   Somehow or other expected inflation must increase so that the real interest rate decreases and aggregate demand increases.

Increased government spending raises aggregate demand without there being any need for a lower real interest rate.   Even if Ricardian equivalence hold, the increase in government spending is only partly (and presumably slightly,) offset by reduced current consumption.   Taxpayers reduce their consumption a bit over all future periods.

Under "normal" circumstances, an increase in government spending requires the central bank to increase its target for the nominal interest rate.   This crowds out current consumption enough so that consumption plus government spending remains equal to productive capacity.   Failure to do this would result in an unsustainable boom and inflation rising above target.

However, if consumption plus government spending is below potential output, then this is not an issue.  In fact, the simple models imply that inflation will be below target unless the nominal interest rate falls or government spending rises.

I am sure Beckworth understands all of this.   And, like other Market Monetarists, doesn't see this as how monetary policy works.   Monetary policy is about changes in the quantity of base money, with the "baseline" thought experiment is that they are permanent.   While these changes in the quantity of base money have a liquidity effect, a transitional impact on nominal interest rates, it isn't the change in interest rates that causes aggregate demand to change.  

With Beckworth's framing, if the Fed is committed to return base money to its previous growth path, then future aggregate demand will not have changed much.   And so current aggregate demand won't change much.   And so, other things, such as fiscal policy, cannot impact aggregate demand much.

It seems to hang together.

One obvious problem is a question of causation.   Only a permanent increase in base money will cause aggregate demand to rise much.   But that doesn't mean that given the growth path of base money, something else, such as a temporary increase in government spending might cause aggregate demand to rise.

I think Beckworth's intuition is that the Fed is implicitly committed to keeping base money high enough so that inflation doesn't fall much below two percent.   To the degree that a temporary increase in government spending would otherwise push inflation above 2%, then the Fed is going to make just that much less of the extra base money permanent.   Put this way, the argument is a bit puzzling.   It appears to be about how fast the Fed will shrink base money at some future time when the economy is growing strongly.

Suppose the Fed followed Christensen's proposal that it keep on the current 4.5% growth path for nominal GDP.   How could it do so?   By making permanent changes in base money.   The change in base money will be permanent as long as that is what is needed to keep nominal GDP on the target growth path.

If nominal GDP could be kept on that growth path with permanent changes in base money, then changes in government spending would be irrelevant.   They would be offset by permanent changes in base money.

But that isn't the world we live in.

Monetary Policy Effectiveness

Paul Krugman responded to David Beckworth's post regarding monetary policy effectiveness.   Beckworth had pointed out that temporary changes in the quantity of money have approximately no effect on aggregate demand.

Beckworth's point was that the Benanke and Yellen have both emphasized that the huge increases in base money that have occurred since 2008 are temporary.    Beckworth repeated his frequent theme that the Fed should have announced a regime change so that there would have been an expectation that the increase in base money was permanent and aggregate demand would expand.  Beckworth pointed out how Roosevelt's break with the gold standard in 1933 resulted in a large increase in aggregate demand.   This worked because it increased the expected value of base money.

Krugman claimed "dibs" on the argument that temporary changes in the quantity of money have little effect citing his 1998 paper.   He went on to argue that it was not practical for the Fed to engineer a regime change in 2008 or since.   He blames Republican politicians.   That was his defense of emphasizing fiscal policy.   The conservative Republicans wouldn't allow the Fed to change its target. He also argues that leaving the gold standard (or devaluing, really) isn't something that can be done more than once.

Sumner again has pointed out that his version of the argument was published before Krugman wrote his note.   Sumner's argument appeared in the  Journal of Economic Histrory in 1993 in a paper titled, "Colonial Currency and the Quantity Theory of Money:   A Critique of Smith's Interpretation."    I appreciate that he copied a long excerpt.    The price level now can only rise to a point where the expected future deflation rate equals the real interest rate.

Rowe has a post germane to this issue.   He  wrote a very simple model that attempts to translate Sumner and Krugman's argument to nominal GDP.   In my view, that is the right direction for market monetarists.  However, I do not think his argument was entirely successful.  The most interesting implication he drew was that the less interest elastic is the demand for money, the larger the impact of a temporary increase in the quantity of money on nominal GDP.

I am not sure that it is possible to dispense with prices.   It is the real return on money itself that is being impacted rather than solely the nominal interest rate on other assets.  At some fundamental level, the ineffectiveness of a temporary increase in the quantity of money is due to the fact that people don't want to purchase durable goods at temporarily high prices.   That there is some zero-interest outside money to hold as an alternative is implicit in the argument.    When we shift to nominal GDP, the permanent income hypothesis is being thrown in as well--temporary increases in real income are likely to be saved.   But Rowe has at least started on a version of the argument that applies to nominal GDP targeting.

Most interesting is Glasner's post on the debate.   He points to an argument in Hirshleifer's 1970 textbook Investment, Interest and Capital.     Oh yes, I remember that passage.  (Just kidding)

Anyway, Glasner argues that it is better to focus on the current and expected future price level rather than the level of base money consistent with either of those price levels.   Glasner likes this approach because it ties directly to the Fisher effect.    Glasner, of course, has often emphasized the troubling implications of the Fisher effect when the deflation rate is greater than what would otherwise be the equilibrium real interest rate.

But Glasner also emphasizes what I consider the key issue.   What is the monetary regime?    The reason why the changes in base money since 2008 are temporary is because of the monetary regime--inflation targeting.   Further, making the large increases in base money that have occurred permanent would certainly be a regime change--some kind of quantity rule-- and a true hyperinflationary disaster.

Glasner gives his characteristic slam on traditional monetarism, but surely he is correct.  The U.S. does not have a quantity of money rule.   The problem isn't whether a change in base money is permanent or not.   The problem is the nominal anchor--"flexible" (read discretionary) inflation targeting.

Beckworth on the Fiscal Theory of the Price Level

David Beckworth wrote a post where he gave too much credence to the Fiscal Theory of the Price Level.   His question was what do Sumner, Krugman, and Cochrane have in common.

I don't give the Fiscal Theory of the price level much credence.

Beckworth gives an equation where the real value of the monetary base plus the other portions of the national debt depend on the expected present value of government surpluses forever.

That requires that people must expect that an existing monetary regime last forever.   Well, people might expect that, but it is not exactly rational.  

No doubt I am biased because I favor a shift in monetary regime that would make it independent of expected future government budget surpluses.   Cochrane's approach is that the price level today depends on the assumption that there is no chance that my preferred monetary reform is implemented ever.  I am sad.

Anyway, I still don't believe it.   Consider Beckworth's quote from Cochrane here:

The fiscal equation affects prices in an intuitive way. If people start to think surpluses will not be sufficient to pay off the debt, they try to unload government debt now, buying other assets or goods and services. This is just “aggregate demand.”

The problem with this analysis is that when people unload government debt now, the price of government debt falls and its yield increases.   This tends to clear the market for government debt without any change in the price level.

But what about the monetary base?   If people start to "unload" that, spending it on other assets, goods, or services, then the result is inflationary.   But if the monetary regime adjust the quantity of base money with the demand to hold it, then any decrease in the demand for the monetary base simply results in a lower quantity at a constant "price."   The price level remains the same.

If, as is conventional, the central bank sells government bonds, then this reinforces the tendency of government bond prices to fall and their yields to rise.

If we consolidate the balance sheet of the central bank and the government, what is happening is that less of the national debt is being financed by monetary liabilities and more by interest bearing debt.   The price level remains stable and the interest rate on government bonds increases.     Aggregate demand and the price level remain the same.   Paying interest on base money would also help maintain the demand for it.

This process breaks down when the price of government bonds falls to zero or else demand to hold the monetary base falls to zero at the current price level.

A zero demand for base money doesn't mean that an inflation or nominal GDP target cannot be maintained, but it does mean that adjusting the quantity of base money according to the demand for it conditional on the target for the price level, inflation, or nominal GDP won't work.   You are in a cashless payments system world.

Implicit in the Fiscal Theory of the Price Level is that money is held as an investment vehicle--it is just like government bonds. Since there is really no role for a medium of exchange in a general equilibrium model, then economists can't say anything about it, right?    Further, if we calculate the price level in terms of interest bearing bonds, then a lower price of bonds is a higher price level.   In a general equilibrium framework, why not?   One numeraire serves as well as any other.

Anyway, suppose at some future date, a central bank owns lots of government bonds and fiscal difficulties by the government imposes losses on the central bank.   At that time, suppose the central bank goes into bankruptcy.   Does that imply inflation?   Not really.   It can pay off its existing liabilities with new ones--maybe pennies on the dollar.   This is deflationary, but the reorganized central bank can then expand the quantity of base money again, presumably purchasing assets other than government bonds.

But what about the government's fiscal problems?   Well, the central bank could inflate away the government's debts, but that is not necessary.   Instead, the government could go bankrupt and pay off its creditors partially.

The reason to do this would be that inflationary default is still default on the government debt, but it also disrupts all of the other private contracts too.   It is a massive externality.

Now the chance that central bank will explicitly default will reduce the demand for its monetary liabilities now.   But that only means inflation now if the quantity of those liabilities is fixed.  Otherwise, this possibility of explicit default in the future just means the demand for central bank monetary liabilities today is lower than otherwise.   And it really isn't too much different from the possibility of inflationary default.

By the way, if the quantity of base money is taken as fixed, or on a constant growth path, then I will grant that worries about the ability of the government to keep up with its interest payments on government bonds would be inflationary.   But notice that there is an implicit assumption of a money supply rule here.

As for the analysis of Krugman, he is equally wrong regarding the deflationary effect of budget surpluses.    Of course, there, the problematic corner sultion is that if the demand for the monetary base rises more than the national debt, then open market purchases of government bonds won't be sufficient to maintain monetary equilibrium.    However, as Beckworth notes at the end of his post, central banks can purchase other sorts of assets, such as foreign exchange.   And, of course, there is always negative interest on reserves too.

Interest on Reserves Again

I did some math about interest on reserves and the money multiplier.

If=

c  = A - B*id

id = ir - K

r  = Z + G* ir

and:

mm = 1+ c/c+r

then:

dmm/dir  < 0   if:

G  >  (1-r)/(1+c) B

where c = currency deposit ratio,  r = reserve deposit ratio, id = interest rate on deposits, ir = interest rate on reserves.

If the responsiveness of the  reserve ratio to interest on reserves is sufficiently high that it is no less than 1 minus the reserve ratio divided by 1 plus the currency deposit ratio times the responsiveness of the demand for deposits to the interest rate on deposits, then an increase in the interest rate on reserves is contractionary.

In other words, if the responsiveness of the reserve ratio to the interest rate on reserves is greater than the responsiveness of the currency deposit ratio to the interest rate on deposits, an increase in the interest rate on reserves is contractionary.   And it can be somewhat less.

I am a bit worried about the result in that if the currency deposit ratio falls too zero, this result must be wrong.    The mm = 1/r or 1/(Z+G*ir) .    The money multiplier is obviously negatively related to the interest rate on reserves.    (I guess I should check again and make sure the 1 is in the denominator.)

However, I still stand by my verbal argument that for the expansionary scenario to hold, the banks were not maximizing profit and should have increased the interest rate on deposits and expanded loans.   I don't think that the money multiplier result above is inconsistent with that being true.

In a world with no interest on deposits, or else, a world where banking is with banknotes, and even more so when usury laws create a shortage of bank loans, then something like the money multiplier is a  fine framing.    Of course, there is no interest rate on deposits to impact the the currency deposit ratio.   In the result above, B = 0 and interest on reserves is contractionary..

When banks can charge competitive interest rates on  loans and deposits, then there remains an element of truth in the money multiplier approach.   I don't doubt that a change in preferences leading to a reduced currency deposit ratio would be expansionary.   But if banks pay higher interest on deposits in order to attract currency to deposit at  the central bank, it is hard to see why they would lend that money out.  On the contrary, they would be contracting lending as well to increase reserve holdings.   And, of course, the increase in the interest rate on deposits is contractionary in and of itself, along with the decrease in the quantity of money.

One final note:  If holding reserves is considered a cost of operating a bank, which is certainly true, to a degree, and especially with required reserves, then paying interest on reserves could result in lower interest on loans and higher interest on deposits both.   This tendency would be for bank balance sheets to be larger, but it is unlikely to be expansionary--that is, create an excess supply of money.  

Can Interest on Reserves be Expansionary?

Josh Hendrickson has written some posts critical of New Keynesian macroeconomics over the last few months.   In one post, he questioned whether increased interest on reserves is really contractionary.   Now, his  broader point is that New Keynesian models are problematic because they try to do monetary economics without money.   I certainly agree that this is a problem.  However, I find it difficult to believe that increasing the interest rate paid on one portion of base money does not increase  the demand for base money.

Hendrickson's analysis is that a higher interest rate on reserves raises the opportunity cost of holding currency while reducing the opportunity cost of holding reserves.    The currency/deposit ratio would fall while the excess reserve ratio would rise.    A lower currency deposit ratio increases the money multiple while a higher excess reserve ratio decreases the money multiplier.  The net effect is ambiguous and so is the effect on broader monetary aggregates.   The impact on spending on output and inflation is therefore also ambiguous.   It is possible that higher interest on reserves could be inflationary, deflationary, or have no effect.

I don't believe it.

First, suppose the increase in the interest rate on reserves is expansionary.    The higher interest rate on reserves will motivate banks to increase the interest rate on loans and the interest rate on deposits.   The higher interest rate on loans results in a lower quantity of loans demanded and so a smaller quantity of bank deposits while the increase in the interest rate on deposits results in an increase in the demand for deposits.   This is contractionary.

However, the higher interest rate on deposits creates an incentive to reduce currency holdings by depositing currency into banks.  

The deposit of currency into banks increases the quantity of bank reserves.   This causes the banks to expand lending, which they do by lowering the interest rate on loans.   The additional lending increases the quantity  of deposits.   The lower earnings on the bank's asset portfolios lead banks to lower the interest rate on deposits.   This is expansionary.

Which effect is larger?

Well, it seems to me that the expansionary scenario is going to require that the interest rate on deposits and loans both be lower than their initial values.   But if the interest rate on deposits is lower than its initial value, then there would be no incentive to deposit currency into the banks.   Looks like a contradiction.

Now, let's consider a corner solution.   Once the interest rate on reserves is so high that all of the currency has been deposited, then clearly any further increase in the interest rate on reserves cannot possibly result in a deposit of currency and an expansion in the quantity of money through that avenue.   All that is left is a decrease in bank lending and so a decrease in the quantity of deposits which is the same thing as money after all the currency is deposited.   While a higher interest rate on reserves would still lead to a higher interest rate on deposits, that would increase the demand for money, reinforcing the contractionary impact.

Of course,  the section of Woodford cited by Hendrickson describes a "cashless" payments system, and so would be just such a corner solution.  I would note that if all hand-to-hand currency is private, redeemable banknotes, then all base money is reserves and so an increase in the interest rate on reserves is unambiguously contractionary.

Since we don't live in a world with privatized currency or where all currency has been deposited into banks, that corner solution is of little practical significance except to show that even if there is some range over which an increase in the interest rate on reserves is expansionary or at least not contractionary, a sufficiently large increase in the interest rate on reserves must be contractionary.

Now, consider a scenario where banks hold 100% reserves.   An increase in the interest rate on reserves has no impact on bank loans, because there are none.   But it still results in  higher interest rate on deposits.   While this would attract more deposits of currency, the result would leave the total quantity of money unchanged.   However, the higher interest rate on deposits implies an increase in the demand for money.   This is contractionary.

Suppose there were a monopoly bank.   The interest rate on reserves increases.   The interest rate on reserves is greater than the interest rate on deposits.   The bank raises the interest rate paid on deposits to attract more deposits of currency so that the currency can be in turn deposited at the central bank to earn interest.    Is it sensible to say that the bank would then take this extra currency and lend it out?   There was no increase in the interest rate that it can earn on loans.  It intended to raise the interest rate on deposits to obtain currency to deposit at the central bank to earn interest on reserves.  

Now, with  competitive banking system, we can image that each bank increases the interest rate it pays on deposits to attract deposits from other banks.   Each bank attempts to increase its reserve holdings and so the amount it can earn on reserves.    This is different from the monopoly bank that can only be raising interest rates on deposits to attract deposits of currency.   Still, even with a competitive system, one reason why they would be raising interest rates on deposits would be to attract more currency deposits.   So why would the banks, to some degree seeking to obtain currency to be deposited at the central bank and earn interest on reserves, end up expanding loans instead?

What must be going on for there to be an expansionary scenario?   The banks receive all of these deposits of currency, which they deposit at the central bank and are now earning interest on their reserves.  They then notice that they could make even more interest by lending the funds out.   And then as they lend the money out, the money multiplier process expands the total quantity of deposits.   If the increase in the quantity of deposits is greater than the increase in the demand to hold them due to the higher interest rate on deposits, then the result is expansionary.

But then, why didn't the banks already increase the interest rate on deposits to obtain market share and attract currency deposits in order to make these added loans?   If they were already maximizing profit before, then there is no reason to expect them to expand loans at all.  Quite the contrary, they will contract lending to hold more reserves.  

Suppose there are two types of banks, one set is 100% reserve and the other is no reserve.   Both issue checkable deposts, and the zero reserve banks lend out the funds.   The interest rate on reserves increases, and the 100% reserve banks pay higher interest on deposits.  Currency is deposited in the 100% reserve banks.   The quantity of money is unchanged, but because the interest rate on deposits has increased, the demand for money is higher and so this is contractionary.

Now, suppose the no reserve banks must increase their deposit interest rates to match those paid by the 100% reserve banks.   With higher costs, they raise the interest rate charged for loans, the quantity of loans demanded falls, and as old loans are repaid and borrowers checking accounts are debited, the quantity of deposits falls.   This is contractionary.   Higher interest rates paid on deposits and a smaller quantity of deposits.

But these higher interest rates on deposits attracts currency deposits for the no reserve banks too.  Doesn't this result in more lending and an expansion in the quantity of money?   Of course, that is inconsistent with the raising interest rates on loans due to the higher costs.   If it would be profitable for the zero reserve banks to expand lending in response to an influx of currency deposits due to a higher interest rate on deposits, then they would have already increased the interest rate on deposits and lowered the interest rate on loans, and expanded their balance sheets.

It just doesn't add up.