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.

Kaminskia on Free Banking

Izabella Kaminska wrote a defense of the Bank of England on her blog at the Financial Times . It was apparently motivated by the new "positive money" proposal to fully separate money from debt and banking along with those who would like to see bitcoins replace fiat currency.   (I am pretty dismissive of both of those groups as well, and might defend central banking against them, despite my free banking sympathies.)

 However, she made a passing criticism of free banking:

As an aside, it’s worth pointing out that the Scottish period of free banking that preceded the great inflation — often touted by free-banking enthusiasts as an excellent example of how the free-banking model is inherently stable — revealed how cartels and monopolies could be used to stabilise the currency. In fact, it was only because the Scottish banks were so good at forging oligopolistic cartels that happily restricted competition that the Scottish free-banking period proved so stable in the first place (defeating the pro free-banking argument altogether).

The link is to a blog called   "SOCIAL DEMOCRACY FOR THE 21ST CENTURY: A POST KEYNESIAN PERSPECTIVE," which is not a title that generates much credibility with me.   Worse, when you try to find out the author of the blog, there is nothing.

However, the linked post at least cites Goodhart (1987,) which seriously critiqued free banking on a theoretical level.   Most of the rest of the post was pretty weak   The various episodes described as "free banking" were shown to have included at least some some government regulation of banking.   

George Selgin responded to Kaminska in the comments, and I thought he was much too harsh.    I admit that this is the frying pan calling the kettle black and that I am suggesting that Seglin do as  I say and not as I do, but at first pass, playing the role of the patient professor might have been a better place to start.

Still, I agree with Selgin that Kaminska's version of 19th century British monetary history was more than a bit skewed.    She certainly seemed to suggest that Peel's Act was a necessary corrective to inflation caused by the uncontrolled issue of paper currency by "country" banks in England.   Of course, it also spelled the end of the Scottish system of private note issue as well.   But really?  Does anyone think that Peel's Act was necessary or even sensible?   100% marginal reserve requirements for hand-to-hand currency?  Why?

Kaminska appeared to have replied to Selgin on her blog--Dizzynomics.    She didn't refer to him by name, and if Selgin's comment on her original article was too harsh, her reply was absurd   Free banking advocates (Selgin?) seem to be "reason and logic deniers."    Apparently, the key element of reason and logic they deny is:

But the main issue I have with them is that they appear to have no understanding or appreciation of the cyclicality of systems or the fact that whenever we’ve had free-banking systems they’ve resulted in chaos or alternatively co-beneficial collusion to the point the system is not free by the standard definition of free.

I don't think the "cyclicality of systems," is a principle of reason or logic.   The claim about "chaos" is hyperbole at best.

Kaminska writes on in a way that suggests that "free banking" means the monetary institutions of anarcho-capitalism.   Since many of the leading lights of "free banking" lean in that direction, and even more so those they have influenced, I can imagine that one can find people who will argue that all potential bank misbehavior can be handled by private arbitration.   While that may or may not be true, what I count as "free banking" hardly  requires that the banking industry be singled out for fully-privatized law enforcement.

Perhaps more interesting is her claim that more-or-less successful free banking systems are not truly "free" but rather instances of collusive oligopoly.

Unlike many, if not most, free bankers, I see free banking as a series of reforms rather than conceiving of a banking system without any government intervention.

One key reform, and one that superficially seems radical, is the private issue of redeemable hand-to-hand currency.   In my view, redeemability is pretty much all that is necessary to keep a competitive banking system in line.   By that I mean,each bank's market share in the issue of currency will reflect the preferences of those using the currency and the total amount of currency issued will reflect the preferences of the public to use currency relative to deposits.

Now, this constraint works though a clearing system.   And while there have been private clearinghouses that have handled the task quite well, this particular reform is consistent with having a central bank handle the clearing system--like the Federal Reserve.   The way I see it, whether or not it is desirable to privatize the clearing system or leave it in the hands of a government-run "bank" is a separate question from whether or not redeemable privately-issued hand-to-hand currency creates special problems.

A second reform, which I had thought was no longer controversial, is branch versus unit banking.   In the U.S., there were many regulations aimed at protecting unit banks.   These would be single office banks.   To bring it back to Kaminska's history, some of the regulations of the "country banks" in 19th century England were aimed at keeping them small.   One strength of some of the "free banking" systems, including both Scotland and Canada, was widespread branching.

The key reason why branch banking is superior to unit banking is geographical diversification.   To the degree that a unit bank receives deposits locally and makes local loans, when the local economy is troubled, the bank will have trouble collecting on loans exactly when its depositors are in need of their funds.   In the U.S., a key rationale for deposit insurance was to overcome this weakness.

However, the branch banking system does make private currency more feasible.   While thousands of unit banks might each issue private currency, and the currencies might each do just fine in their local community, the experience of the U.S. "free banking" era suggests that that they were less than suitable for a national currency.

But really, unit banking was not all that suitable for promoting a payments system by check either.   And so a system of banks,each with extensive branching, not only provides geographical diversification, it also allows both privately-issued hand-to-hand currency and checkable deposits to form a national payments system.

Now, is a nationally branched system an "oligopoly?"    In fact, the unit banking system was more about protecting local monopoly than creating competition by having a large number of banks.   In practice,a system made up of a smaller number of banks, able to open and close branches in various localities, has proven more competitive than a system of many small banks each tied to a particular locality.

Would a U.S. banking structure of 20 large banks all with branches nearly everywhere be "oligopolistic?"   Well, I suppose it doesn't meet the neo-classical definition of perfect competition.   But that is hardly a reasonable standard for real world competition.

There are more reforms that are associated with free banking.   Some are no-brainers like ending reserve requirements or allowing free entry.   Others are much more challenging, like ending deposit insurance and capital requirements.  But rather than treat them separately, I will focus on what I consider the point where the "oligopoly" and "collusion" charge is most likely to stick, and that is the clearinghouse.

This points to Goodhart's criticism of free banking.   Consider a clearinghouse organized as a private club. (Say each bank owning stock in the clearinghouse in proportion to capital?)    For the payments system to work well for the nonbanking public, each bank needs to accept banknotes and checks drawn on other banks at par, depositing them at the clearinghouse, cancelling offsetting claims, and settling up net clearing balances.

To start with, by accepting each other's items for deposit at par, the members of the clearinghouse serve as creditors to each other.   Goodhart, following Timberlake's study of U.S. practice in the 19th century, argues that the clearinghouse serves as lender of last resort.  This expands the club's role as creditor. It is important that the clearinghouse have information about its members in order to determine if they are good credit risks, but since the member banks are all competing with one another, they will not want to share that information.   QED, the Bank of England should exist.

Since Goodhart's argument was closely tied to arguments about banks being subject to runs, I didn't find it convincing    The solution to runs is an option clause.   They were banned long ago, because governments understood that it served as an alternative to holding reserves.   Encouraging banks to hold (gold) reserves was a key policy goal at the time.

Still, limiting membership to the clearinghouse would be an obvious mechanism to provide for a barrier to entry.   That each member is a creditor to the others provides a plausible rationale.   Perhaps membership could be limited to "sound" banks as proved by their unwillingness to pay more than a "fair"  interest rate on deposits or charge less than a "fair" interest rate on loans?

All this shows is that in a world without anti-trust, a clearinghouse association could be an avenue for collusion.  But we live in a world with anti-trust, so abuse of clearinghouse rules to organize and enforce a bank cartel would be illegal.   Unless, of course, free banking is taken to mean that the banking industry must be singled out for an exemption to anti-trust law.

However, I do think there is something very special about the clearinghouse.   It is what turns a variety of financial instruments into a medium of exchange.   Of course, it isn't exactly homogeneous, but retailers typically accept payments by check or electronic equivalent and deposit the funds in their own banks.   Banknotes, privately-issued hand-to-hand currency, can smoothly fit into the system.

The clearing system is very effective in limiting each bank to a market share determined by the preferences of depositors.   The same should be true of banknotes, even though it has been many years since redeemable banknotes have had much circulation.   The problem is that the aggregate quantity of money of all types is limited to the demand to hold money by some kind of response to macroeconomic disequilibrium.   This response is closely tied to the determination of the nominal anchor for the system.

Historical free banking systems were small open economies with monetary liabilities tied to gold--an international money.   As repeated by the anonymous Post-Keynesian cited by Kaminska, Goodhart's point that much of the redeemability by these free banking systems were with credit instruments drawn on a major money center should be no surprise.   What other routine calls for redemption would exist other than a demand for foreign exchange?  And while the quantity of those securities/reserves would not be fixed, neither would the quantity of bars or even gold coins from the point of view of the banking system of a small open economy in a  gold standard world.

What we think of as monetary theory these days would best apply to the entire portion of the world using the gold standard.   The price level depends on the supply and demand for gold.   While gold strikes might be inflationary, the major source of macroeconomic disruption would be shifts in the demand for gold.   It really doesn't matter if it is due to finance or fashion.   A shortage of gold requires a higher relative price for gold and so a lower price level.   Until prices and wages adjust, real output will be depressed.  Further, it is hard to see how liquidating debts based upon higher expectations of nominal income can be anything but disruptive and painful.   The notion that by having a "free banking system," some portion of the gold standard world could be insulated from these problems is implausible.

According to the wiki for free banking, cited by the anonymous post-Keynesian, an alternative to a free banking system tied to gold is one tied to a fixed quantity of fiat currency.   Selgin, in his Theory of Free Banking, describes such a scenario.    While I think the market process he describes, where nominal income tends to be stabilized, is instructive, there is something very problematic about a system where the nominal anchor depends entirely upon the demand for an asset solely held by members of  a private club--the clearinghouse.   Changes in the settlement rules at the clearinghouse could have a major impact on macroeconomic conditions.

Greenfield and Yeager's Black-Fama-Hall payments system was a type of free banking.   The constraint on the banking system was indirect convertibility.   I always argued that indirect convertibility would have its primary impact at the clearinghouse--as a practical matter, no one else would have any reason to do anything other than spend money.  In fact, I have always thought that a rule requiring indirect convertibility at the clearinghouse would be sufficient to constrain the banking system.

Practical considerations eventually convinced most of us thinking about this sort of system that indirect convertibility would need to involve some kind of index futures contract.   While Greenfield and Yeager aimed at stabilizing the price level, and Kevin Dowd has continued to promote free banking tied to that nominal anchor, I think slow steady growth of nominal income (NGDP) is a better approach.    Index futures convertibility provides tremendous flexibility regarding the nominal anchor.

I certainly don't think that having the nominal anchor determined by a private club of banks is a sensible monetary regime, no more than giving clearinghouses the right to vary the price of gold would have been sensible in a historical free banking system.   And that is where I think free banking theory is today.   What rules should be imposed on the clearing system to keep the total quantity of money created by the banking system consistent with the nominal anchor?

And to bring this back to Kaminska, the anonymous Post-Keynesian, and Goodhart, at some fundamental level, I grant that a desirable free banking order will require a clearinghouse with appropriate rules.   Collusion?   Well, I don't think that such rules should be anti-competitive, but they certainly involve constraining the banking system--what might broadly be described as regulation.

As for the historical record--I don't think that the free banking portions of the world were especially chaotic or the source of instability under the gold standard.   And the actual behavior of both the proto and actual central banks of the gold standard era most certainly caused massive macroeconomic disruption.    

Hummel on Quantitative Easing

Jeff Hummel wrote a nice article for Reason.   Most of it isn't new and is similar to his chapter from Boom and Bust Banking.

His basic argument is that Bernanke used quantitative easing to bail out the banking system to maintain the flow of credit.   This policy involved directing credit to where the Fed felt it was most needed.

This is in contrast with a more traditional monetarist approach, which Market Monetarists have emphasized.   The reason to expand the quantity of money is to prevent (or reverse) decreases in spending on output.

Hummel's emphasizes some policies (much criticized by Market Monetarists) that appear counter-productive if the goal of quantitative easing was to prevent (or reverse) decreases in spending on output.   First, the Fed undertook open market sales of Treasury bills to at least partly offset the expansion of loans to banks.   And then the Fed introduced interest on reserves--a clearly contractionary policy.

What Hummel doesn't mention and a concern that many Market Monetarists have emphasized over the last five years, is the temporary nature of the quantitative easing.   A temporary increase in the monetary base should have little effect on spending on output.   However, it should be able to support particular credit markets.

For example, suppose a central bank is committed to an inflation target.   Investors refuse to buy new issues of mortgage backed securities and sell off existing holdings.   The central bank buys the mortgage backed securities, but insists that this is only temporary.   If inflation starts to rise, it will sell off some sort of assets  or perhaps raise interest on reserves.   Any expansion in base money or broader measures of the quantity of money is temporary.   For the most part, the demand to hold this additional money expands to meet the supply.   There is little or no inflationary effect.

Perhaps more troubling, this logic appears to apply even more strongly to a central bank with a nominal GDP level target.   Suppose that nominal GDP is on target.   Further suppose that the central bank decides to support the President's plan for poor people to have homes, and so begins to buy mortgage backed securities.   The quantity of money expands, but people hold the additional money balances--they believe that the expansion is temporary.   There is little or no impact on total spending on output.   This certainly appears to create an opportunity for malinvestment.

Reserve Currency Status

What are the benefits of providing a reserve currency?

I was recently reading a post by David Glasner, where he explained that the benefit is seignorage.   Glasner was mostly responding to a proposal for replacing "the dollar" with gold.  

If we think of replacing gold with the dollar, and see the dollar as being paper hand-to-hand currency, then we can imagine foreign central banks holding stacks for $100 bills in their vaults, just as they once kept bars of gold.  

The U.S. government, then, can print up these dollar bills, and so creates a flow of revenue much as the gold mining industry received a flow of revenue from its output of money.  

But how realistic is this?

Doesn't the use of the dollar as a reserve currency really mean that various foreigners, including foreign central banks, purchase dollar-denominated bonds?   At first pass, then, I would see this as creating a ready market for low interest rate U.S. government debt.   Assuming the U.S. has a national debt, then it can be financed at lower interest rates than otherwise.

Presumably, this benefit spills over to private borrowers as well.   U.S. borrowers of all sorts can borrow in terms of our own unit of account at lower interest rates.  

To the degree that this results in a larger banking system, the demand for reserves is somewhat higher.   And further, there may even be some increase in the demand for U.S. hand-to-hand currency.   Certainly, the conventional wisdom is that there are substantial holdings of U.S. dollar notes in foreign countries.

But most of the "high finance" related to the role of reserve currency is not based upon sacks full of currency.  

Of course, I have become a "seignorage" skeptic anyway.   If there is a strong commitment to some nominal anchor other than the quantity of base money, then seeing base money as a type "paper gold" is a fallacy.   Monetary liabilities are rather a type of short term debt.    Those parts of it that are issued at a zero nominal interest rate, like tangible hand-to-hand currency represent at zero interest loan.   From this perspective, to the degree serving as reserve currency increases the demand for base money rather than other sorts of dollar-denominated debt, simply means more borrowing at lower interest rates.

Monetary Policy and Fiscal Policy

I have always been skeptical regarding "necessary" relationships between monetary policy and fiscal policy.   Most recently, these relationships supposedly play a key role distinguishing the neo-Fisherite and neo-Wicksellian approach to interest rate targeting.

The neo-Wicksellian approach to lowering the inflation rate is to raise the target for the interest rate.   Of course, this is only a tentative adjustment that might soon require a reduction in the interest rate to keep the inflation rate from falling too low.

The neo-Fisherite view is that the way to lower the inflation rate is to lower the target for the interest rate.

Which is correct supposedly depends on assumptions about fiscal policy in the long run.

In my view, if the "target" for the nominal interest rate is something close to a target for the growth rate for the quantity of money, then a lower target for the nominal interest rate will result in in a lower growth rate for the quantity of money   This will result in lower inflation.   If this is expected, then the lower inflation will lower the equilibrium nominal interest rate.  This approach doesn't necessarily involve the central bank hitting the target for the nominal interest rate consistently.

There is an alternative neo-Fisherite process that I find problematic.  If the expected future price level is tied down, then a fixed target for the nominal interest rate can be self-stabilizing.   In that situation, if the real interest rate is too high to clear markets, the price level falls.   If the expected future price level is given, then the expected inflation rate rises.   This lowers the real interest rate.  The price level level falls enough so that the expected inflation rate rises enough for the real interest rate to fall enough to clear markets.

If the price level falls too far, given the expected future price level, expected inflation will rise too much and the real interest rates will fall too low, which causes prices to rise.    The price level should gradually rise to the expected level.   The actual inflation rate should equal the expected inflation rate.

The neo-Fisherite result follows because if the nominal interest rate is increased, then it immediately would raise the real interest rate.   The price level would fall.   And then when it is low enough that higher expected inflation lowers the real interest rate back to the level needed to clear markets again, we now  have higher inflation for the price level to return to the expected level.

Unfortunately, it is not at all obvious what ties down the future price level under this system.   And that is where we get these fiscal theories.   As for using it to explain actual performance?    Really?   People supposedly have an expectation of the future price level?

Anyway, I reject the assumption that excessively high budget deficits must lead to inflationary default.   I realize that it is a possibility, but I consider it inferior to explicit default on the national debt.   The monetary constitution should not allow for inflationary default.   It is default either way, and inflationary default of government debt just creates a massive externality, causing the simultaneous inflationary default of private debt.

As for the notion that deficits must be sufficiently large to generate sufficient government debt for the central bank to purchase, this is simply based upon the assumption that the central bank must purchase government debt.    Perhaps the most extreme version of this framing is the "bills only" doctrine.   That is the view that the central bank should solely purchase short term government debt.

That might be a nice policy if there is sufficient short term government debt, but when the demand for base money outstrips the amount of short term government debt, then the obvious answer is for the central bank to expand its horizon and purchase something else.   After five years of the Fed purchasing mortgage backed securities, it is hard to understand why anyone would consider the amount of short term government debt outstanding to be a constraint on monetary policy.

If government were sufficiently frugal that the national debt falls, perhaps even to zero, does that require that the nominal anchor be changed?  Must there now be a deflationary policy, down to zero?

How about having the central bank purchase private debt?   Isn't there a long history of insisting that central banks should solely purchase private debt?    Real bills?

Don't like the central bank picking and choosing between borrowers?   Privatize the issue of hand-to-hand currency and end reserve requirements.

Demand for reserves still too high?    Make the sole asset of the central bank overdrafts to banks with adverse clearings.   Charge high interest rates on those overdrafts and pay low, maybe negative, interest on reserve deposits.   In other words, use the corridor system.      (Woodford's neo-Wicksellian world.)

Suppose we lived in a world with no government debt and an evolved gold standard.   Banks issue hand-to-hand currency and deposits.   The banks deposit gold at the clearinghouse to settle net clearing balances.    Want to stabilize the price level, inflation, or better yet, a growth path of nominal GDP?   Vary the price of gold--somewhat like Fisher's compensated dollar.

Or better yet, let the price of gold be determined by the market and make the monetary liabilities redeemable with index futures contracts on the nominal anchor.

Of course, the current monetary order does include a key role for government-issued hand-to-hand currency.  Reserve balances are huge and are at least quasi-government debt.

However, models that determine the current price level based upon rational expectations about what must happen to the quantity of base money in the distant (infinite?) future, is making an assumption about what systems will exist in the future.   I am not sure that it is really rational to assume that monetary institutions will remain the same in the distant future.

Of course, as a long-time money reformer, perhaps that is wishful thinking.

Neo-Fisherites

The neo-Fisherite view is that a higher target for the interest rate will result in higher inflation, and a lower target for the interest rate will result in lower inflation.

The Fed has kept its target interest rate at close to .02% for some years now, and it has been saying that they will stay there for some time.   The inflation rate has remained a bit low during this period.

So, evidence tells us that a low target for the interest rate results in low inflation.

This follows from a very simple theory--the Fisher relationship.   The nominal interest rate is equal to the real interest rate plus the inflation rate.

             .
R = r + P

                                   .          
And so, obviously, P = R - r.

If we have the Fed follow a rule of targeting the nominal interest rate, which is realistic, and the real interest rate depends on some kind of real economic factors independent of monetary policy, then a higher target for the interest rate will generate a higher inflation rate, and a lower target for the interest rate will generate lower inflation.

While it is only a model, we can test it.   And the low target for the nominal interest rate set by the Fed recently has generated low inflation.   The model predicts the data.

Rowe especially, but also Sumner have responded to this nonsense.

From a monetarist perspective, the Fisher relationship holds in the long run.   If the quantity of money grows more quickly, then the inflation rate rises.   For any given nominal interest rate, this reduces the real rate.   This benefits debtors and injures creditors.   The demand for credit rises and the supply falls, raising the nominal interest rate, and shifting the real interest rate back towards its initial value.  With all sorts of somewhat implausible assumptions, the real interest rate returns exactly to its initial value, and so the nominal interest rate is now equal to the initial real interest rate plus the new, higher inflation rate.   All of these implausible assumptions are necessary for "super neutrality" to hold, which means that the real economy is independent of the growth rate of the the quantity of money.

Suppose the central bank had the following rule for the growth rate of the money supply:

 .                           .       .
M     =  R* - rn + yp - V
                                                                                                                      .
 Where R* is   target for the nominal interest rate, rn is the natural interest rate,
 .                                                            .
M is the growth rate of the money supply, yp is the growth rate of potential output, and
 .
V is the growth rate of velocity.
                                                                   .         .       .     .
The inflation rate in the long run is P  = M + V - yp

So, by substitution:
 .
P   =    R*  - rn

This rule requires that when the target for the nominal interest rate rises, the central bank raises the growth rate of the quantity of money and so the inflation rate rises.

If one assumes that the natural interest rate is equal to the growth rate of potential output and the growth rate of velocity is zero, then the rule for the money supply is:
 .        
M   = R*

If the target for the nominal interest rate is just taken as fixed, then the economy is stable.   It is just a fixed quantity of money rule.   Sure, inflation will change with productivity shocks and inflation and real output will change with shifts in velocity,, but as long as prices and wages adjust to surpluses and shortages as they ought, then real output should adjust to potential in the long run.

If velocity growth, potential output growth, or the natural interest rate change, then the appropriate growth rate in the money supply will change--if the goal is really to keep nominal interest rates fixed?

And why would that be?   Right.. optimal quantity of money.

The nominal interest rate needs to be zero, more or less, so that there is no opportunity cost from holding hand-to-hand currency.

And if R* is zero, and the natural interest rate is equal to the growth rate of potential output and velocity is constant, then the quantity of money should be held constant!

Of course, actual central banks are not targeting the nominal interest rate in this way..   They adjust the nominal interest rate to target inflation and unemployment.   And they raise their target rate to slow inflation and raise unemployment and lower their target rate to raise inflation and lower unemployment.   And the way their trading desk raises interest rates is to slow money supply growth and the way they lower interest rates is accelerating money growth.

And so, it is difficult to see what the neo-Fisherite theory can tell us about what happened from 2008 to 2014.   It is rather a proposal for how monetary policy ought to operate.   With the only plausible goal being a zero nominal interest rate and so a deflation rate equal to the real natural interest rate.   And the only rationale for the goal is to allow for the optimal use of zero nominal interest rate currency.

Pascal Salin's Confusion: Inflation or Money Supply Targeting

Pascal Salin critiques Market Monetarism on the grounds that nominal GDP is not a good target.   However, his argument is confused.    His argument appears to be that a quantity of money rule would lead to stable inflation.   And then he correctly recognizes that stable nominal GDP growth is inconsistent with stable inflation when supply-side factors causes changes in real GDP growth.

And then, he becomes confused.   Is he criticizing Market Monetarism as being inferior to inflation targeting?   Or is he criticizing Market Monetarism as being inferior to targeting some measure of the quantity of money?

Or does he just have no idea what Market Monetarists propose?  Why would he suggest that Market Monetarists favor raising money growth to raise inflation on the grounds that this will dampen or reverse a slowdown in real GDP growth due to supply side factors?

In  truth, a quantity of money rule does not lead to stable inflation when supply-side factors influence real GDP growth.   A quantity of money rule has the exact same consequence as a nominal GDP target in that circumstance.   Given velocity, a constant growth rate of the quantity of money leaves nominal GDP on a stable growth path.   With both rules, a slow down in real GDP growth due to supply-side factors results in higher inflation.

For inflation to remain stable in the face of a slow down in productivity growth due to supply side factors, the quantity of money must grow more slowly as well.   This is exactly the policy required to target inflation.

Market Monetarists argue that slowing money growth when productivity slows due to supply-side factors is unwise in most circumstances.   In general, it is better that nominal incomes continue to grow at a stable rate, even if final goods prices rise at a faster rate.     Factor prices, like wages, are more stable under quantity of money and nominal GDP level targeting than under a rule targeting inflation in final goods prices.

Since Market Monetarists advocate  a rule rather than a discretionary monetary policy, we would argue that a stable growth path for nominal GDP, which is the same thing in this circumstance as a stable growth path for the quantity of money, is the least bad rule.   Yes, there could be some supply-side shocks where allowing nominal GDP to vary would have better consequences, and an omniscient and benevolent central banker could do better than targeting the quantity of money or nominal GDP.  But we don't have such a central banker.

But somehow Salin has Market Monetarists proposing to accelerate money growth to cause extra inflation to try to offset the adverse productivity shock.    Who knows where that comes from?

So what is the difference between a quantity of money rule and a nominal GDP target?   It is the response to shifts in velocity.   Market Monetarists believe that the quantity of money should shift in inverse proportion to any shift in velocity.   For the most part, this is equivalent to saying that the quantity of money should adjust to accommodate changes in the demand to hold money.

Of course, a quantity of money rule does not allow a change in the quantity of money due to a change in velocity.   The quantity of money does not shift in response to changes in the demand to hold money.   Rather inflation of final goods prices and factor price like wages change until the real quantity of money adjusts to the demand to hold it.   Inflation slows or shifts to a lower growth path, and so real output can be maintained (or recover) despite the lower velocity.

Market Monetarists are fully symmetrical on this matter.   We favor restricted money growth when velocity rises, so that inflation does not increase.

Interestingly, the Market Monetarist view of the proper response of policy to shifts in velocity is similar to that of inflation targeting.   The only real difference is that Market Monetarists favor a level target--that is a growth path for nominal GDP.   Inflation targets a growth rate.

Salin describes the following scenario.   The money supply is growing 3%.   Real GDP is shrinking 2%, so the inflation rate is 5%.    Market Monetarists supposedly would respond to this scenario by having nominal GDP grow 5%.   According to Salin, we would anticipate that this would cause real GDP to grow more rapidly (or shrink less,) but he insists that the actual impact would be inflation of 7%.

Well, where did this 3% money growth rate come from?

The 5% nominal GDP target comes from a scenario where the quantity of money is growing 5% and has been for some time.   Real GDP usually grows at 3%, resulting in 2% inflation.   (This is the high end of Milton Friedman's proposal for a money supply rule.)    Unfortunately, disastrous supply-side policies result in real GDP shrinking 2% a year.   The result would be 7% inflation.   This would be true whether the money supply target was 5% or the nominal GDP target was 5%.    (We can certainly hope that these policies solely lower the growth path of real GDP, so that after a run up in the price level, the inflation rate returns to something like 2%.  )

Now, if the growth rate of the money supply had been 3% for some time, then the natural target for nominal GDP growth would also be 3%.    Real GDP is usually growing at 3%, and the price level is stable.   And then, we have this disastrous productivity shock, and real GDP begins shrinking 2%.   The inflation rate is 5%.   This is the same result if the quantity of money continued to be targeted at 3% or nominal GDP is targeted at 3%.

Again, we can hope that the adverse policies shift real output to a lower growth path, and then it resumes growing.    If real GDP growth permanently slowed down, perhaps to 2%, then after the run up in the price level, inflation would stabilize at 1%.

By the way, Market Monetarists would propose fixing this problem by improved supply-side policies.

An inflation target is somewhat different.   To keep inflation stable in the face of real output shrinking 2%, the quantity of money would need to shrink roughly 2%.     Market Monetarists think that this would almost always be a horrible policy.

Salin argues that if the money supply remains on a constant growth path, velocity will settle down.  From the point of view of Market Monetarists, at first approximation, this would imply that keeping nominal GDP on a stable growth path would require a stable growth path for the quantity of money.   We certainly have no problem with that.

One reason Salin claims that velocity fluctuates is due to changes in inflation expectations.  However, a nominal GDP target and a quantity of money target generates the same inflation expectations--leaving aside possible changes in velocity.   To the degree that changes in the quantity of money can offset changes in velocity and accommodate changes in the demand to hold money, it will reduce fluctuations in inflation and so tend to stabilize inflation expectations and velocity compared to a quantity of money rule.

How do we pick a target for nominal GDP growth?   How do you pick a target for the growth rate in the quantity of money?   What you do is anticipate the growth rate in real potential output and add to it the inflation rate desired.   I go with zero.   And so, that results in 3% growth rate for nominal GDP.   And that, of course, is the low end for Friedman's proposal for the growth rate of the quantity of money.

Many Market Monetarists go with the high end of Friedman's proposal, which is consistent with adding the 3% trend growth rate in real output to the more or less arbitrary 2% inflation target that has been adopted by many central banks.   The resulting 5% nominal GDP growth rate happens to be very close to the actual trend growth path of nominal GDP during the Great Moderation.   A 5% nominal GDP growth rate seems pretty consistent with the 2% inflation target in the long run.

Salin accuses Market Monetarists of being a sort of new Keynesian.   This is because Market Monetarists supposedly believe that raising the inflation rate will reduce unemployment.   Salin explains to us that this can at best work in the short run.

I think it is fair to say that most Market Monetarists are especially interested in avoiding an increase in unemployment due to a slowdown in spending on output.  While this will also tend to cause some disinflation, what happens to final goods prices isn't our prime concern.   Our view is that by returning spending on output to its trend growth path, there will be a more prompt recovery in output as well as a more prompt reduction in unemployment.   That the disinflation might be simultaneously reversed is of little concern.   Yes, there might be some reflation along with the recovery in output.   And yes, it is all a short run phenomenon.

Suppose the quantity of money was on a 3% growth path, but banking troubles caused the quantity of money to fall 10%.   An advocate of a money growth rule would be compelled to support a rapid reversal, with the quantity of money rising roughly 13% to return to its previous growth path.

Now, would that temporary decrease in the quantity of money be associated with a sharp increase in unemployment?   Would real output fall?   Would there be some disinflation if not outright deflation?

And when the quantity of money recovers, wouldn't the result be a more prompt recovery of real output and reduction in unemployment?   And wouldn't any disinflation or deflation be reversed?

So, in some sense, there would be temporarily higher inflation associated with a reduction in unemployment.   That is all Market Monetarists really have in mind.

The only difference between Market Monetarists and Traditional Monetarists along these lines is that Market Monetarists favor institutions that cause the quantity of money to accommodate shifts in the demand to hold money, or more exactly, that offset shifts in velocity.