A proof of the need for fiscal policy to escape the liquidity trap

For simplicity, ignore government spending and taxes. "Fiscal policy" means lump-sum transfer payments.

Suppose the economy is in a permanent liquidity trap. If we ignore the central bank's paper and ink operating costs, another name for the permanent liquidity trap is the "Friedman Rule". Both have the nominal interest rate on bonds at 0%, so that currency is not scarce relative to bonds. If it follows the Friedman Rule, the central bank earns zero seigniorage profits. Because seigniorage profits are equal to the interest earned on the bonds that are on the asset side of the central bank's balance sheet.

If the economy escapes the liquidity trap (violates the Friedman Rule), so the nominal interest rate on bonds becomes strictly positive, then the central bank will earn strictly positive seigniorage profits. If the government owns the central bank, the central bank will give those seigniorage profits to the government. The long run government budget constraint tells us that this must increase the present value of government transfer payments. But that means a change in fiscal policy.

Therefore the only way the economy can escape a permanent liquidity trap is if fiscal policy changes.

I think that's the intuition behind Steve Williamson's post, based on his and David Andolfatto's model. (The bit about using bonds as a medium of exchange too is only in there so the government can collect seigniorage on bonds as well as on currency and you can have 0% nominal interest on bonds without having deflation.) Steve says that monetary policy won't work to get the economy out of a permanent liquidity trap, and only fiscal policy will work to increase inflation.

Some of us might want to reverse the direction of causality. If the central bank escapes the liquidity trap (stops following the Friedman Rule), by permanently increasing the money supply growth rate, then it will earn increased seigniorage profits, and the government budget constraint tells us the government must (eventually) spend those increased seigniorage profits by increasing transfer payments. It would be the same if the central bank gave its profits to its favourite charity. "The United Way Theory of the Price Level"?

[An economist (Paul Krugman?) who says that the central bank can't (or can't easily) permanently increase the money supply growth rate, because people won't believe it's permanent, is making a quite different argument about the impotence of monetary policy.]

Comments

[Kevin Donoghue]

When fiscal policy means lump-sum transfer payments (as it would in my ideal world), why would the central bank stop following the Friedman Rule? It's optimal after all. Let the fiscal transfers do the job of stabilizing demand.

[Nick Rowe]

Kevin: if fiscal policy meant lump sum transfer payments, it would also mean lump sum taxes, which you probably aren't so keen on.

Menu costs etc. from deflation. Plus, it would also mean a very large central bank, owning all assets in the economy, with the rest of us holding only central bank money. Milton was a crypto commie when he wrote that paper.

[genauer]

For simplicity, ignore REALITY like government spending and taxes, which were known as "Fiscal policy" in oldspeak.

Redefine monetary terrorism like "lump-sum transfer payments" as "Fiscal policy" in newspeak.

Continue further down the road of an Orwellian Krugtron Nightmare of doubleplusgood speak :

Balanced budgets, price stability are thoughtcrimes ....

[Herbert]

Nick, I like this post very much. The first three paragraphs are perfectly lucid. But I have a question with respect to the following statement:

"If the central bank escapes the liquidity trap (stops following the Friedman Rule), by permanently increasing the money supply growth rate ..."

In a liquidity trap, bonds yield no interest. If the central bank increases the money growth, it starts purchasing more bonds: it accelerates the exchange of zero-interest money for zero-interest bonds.

Why should an exchange of essentially identically assets alter the equilibrium in such a way that the economy escapes the liquidity trap? Don't we see in Japan or Europe that such a policy in in fact ineffective?

[Nick Rowe]

Herbert: Thanks!

A temporary purchase of bonds will be ineffective. But if the central bank were to purchase bonds every year forever, and nothing happened, eventually it would run out of bonds to buy, unless the government printed some more bonds, sold them to the central bank, and spent the proceeds. Or the central banks runs out of government bonds to buy, starts buying private assets, runs out of existing private assets to buy, so the private sector creates new assets to sell to the central bank, and spends the proceeds. There is no endgame where nothing ever happens.

But this requires an increase in the price level or NGDP level path target growth rate, of course, to be a credible equilibrium.

[Majromax]

> [An economist (Paul Krugman?) who says that the central bank can't (or can't easily) permanently increase the money supply growth rate because people won't believe it's permanent is making a quite different argument about the impotence of monetary policy.]

This isn't even a point about monetary policy so much as monetary tools.

Imagine we did have the United Way Central Bank, where the CB changed the money supply strictly through payments to (or from) United Way. Now, there's a monetary shock and the money supply needs to increase to prevent deflation.

But there's a problem: United Way has gone on vacation for the month. The CB can mark up the charity's account, but not one dime of it will be spent until the accountant comes back from vacation and stamps the purchase orders.

In the real world, the CB has a few policy tools to use.

Everyone (I think) agrees that the "interest rate channel" is ineffective in a liquidity trap. Here, I'm using something along the lines of the BoC model that's interest rates in its purest form, by setting deposit/bank rates such that the interbank rate is between those. (Note that this is not the US model, where the interbank rate is strictly less than the deposit rate.)

The "do nothing" counterfactual here is holding interest rates constant while also ensuring the loan market clears. The latter point is very important but often neglected, since this is what gives the possibility of inflationary/deflationary spirals. A CB rate of 2% is fine if the CB is not willing to provide unlimited funds at that level.

Holding interest rates constant in turn sets a horizontal output-vs-interest-rate AD curve, which implies an upward-sloping output-vs-inflation curve.

The other mechanism is asset purchases, traditionally of government debt but also of private debt. At the extreme, this is Nick's "communism" model where the CB buys everything to increase the price level. However, ordinarily the CB buys assets that are term-limited. This means that any individual asset purchase is presumptively temporary.

Here, the asset purchase is the CB "doing something", and the "do nothing" counterfactual is to let existing assets mature. This will have a negative impact on the size of the monetary base, as principal (newly-printed money) used to make the purchase is returned. Seniorage profits may also further reduce the base money, or they may be neutral depending on whether they're used to affect the government's budgetary constraint.

Krugman et al are arguing for fiscal stimulus in an indirect way to force the CB to do something it doesn't want to do.

One way to make this argument is to say that the loan market is not clearing, in that more low-interest money is on offer than is being demanded. This appears to be true in the US, where the effective Fed Funds rate is below the deposit rate. The solution is simple, basic macro in that someone (here the government) should issue an excessive amount of bonds to "crowd out" private lending, forcing market rates back into the desired channel. (This is a classic "zero lower bound" model, where the effective lower bound in privately-issued money must be strictly greater than zero due to default risk.)

Another way to make the argument is to make the assumption that CB holdings of private assets (mortgage securities) are temporary by policy. If those holdings are not replaced with holdings of government debt (which is more traditional and thus more likely to be seen as long-term), then the increase in money supply is more likely to be perceived as temporary.

[Kevin Donoghue]

Nick: "if fiscal policy meant lump sum transfer payments, it would also mean lump sum taxes, which you probably aren't so keen on."

Sure, I'd sooner receive transfers than pay taxes. Who wouldn't? But I can take the rough with the smooth. Anyway, as an administrative matter, I reckon it would be more efficient to incorporate taxes on consumption in the mechanism. So the rule would mean we get a wad of cash and reduced VAT rates in a slump, while in a boom we get no cash and our VAT rates go back up. The whole process could be automated. "God hath wrought things as incredible for his people of old; what hinders now?"

Milton a crypto commie? I never pass up a chance to post my favourite Friedman story:

One incident above all impressed George [Stigler] and me. In the course of a spirited discussion of policies about the distribution of income among a group that included Hayek, Machlup, Knight, Robbins, and Jewkes among others, Ludwig von Mises suddenly rose to his feet, remarked, “You’re all a bunch of socialists,” and stomped out of the room.

Nick, when you're echoing Mises it's time to pause and reflect.

[Steve Williamson]

" If the central bank escapes the liquidity trap (stops following the Friedman Rule), by permanently increasing the money supply growth rate..."

Then, what happens to the nominal interest rate?

[Nick Rowe]

Steve: in the new equilibrium: the money growth rate is higher, the inflation rate is higher, the nominal interest rate is higher, (real) central bank seigniorage profits are higher, and (real) government transfer payments are higher too.

[Nick Rowe]

Kevin: but my tongue was firmly in my cheek. I don't think von Mises' was!

[JKH]

What about the additional fiscal expense of the higher interest rate now payable on the rollover of bonds not held by the central bank?

(Term structure matters for both portfolios, and interest payable accrues one day at a time on each.)

[Nick Rowe]

JKH: to a first order approximation, the real interest rate on government bonds stays the same, so in real terms the government's real interest payments are unchanged. (They might actually fall if some of the bonds are multi-period, so had nominal interest rates fixed before the central bank announces the increased money growth rate, but Steve assumes very short bonds.)

[Steve Williamson]

"Steve: in the new equilibrium: the money growth rate is higher, the inflation rate is higher, the nominal interest rate is higher, (real) central bank seigniorage profits are higher, and (real) government transfer payments are higher too."

What I was thinking about was the narrow question of whether the central bank could create inflation at the zero lower bound, i.e. nominal interest rate is zero before and after they do whatever they do to make inflation go up. But I'm glad to see that you understand that generating inflation requires coming off the zero lower bound.

[Nick Rowe]

Steve: Ah, I misunderstood.

I could probably rig up a story where the central bank could increase inflation a little without causing nominal interest rates to rise above 0%, but I'm not sure it's worth it.

[Steve Williamson]

"Steve: Ah, I misunderstood.

I could probably rig up a story where the central bank could increase inflation a little without causing nominal interest rates to rise above 0%, but I'm not sure it's worth it."

My understanding of the blog discussion is that this is what is being discussed. Can the central bank create more inflation while the nominal interest rate is at zero? I think some central bankers think they can. Krugman seems to be saying no, but he may be contradicting himself. Some people seem to think that helicopter drops will do the trick. But as Krugman correctly points out, that requires that fiscal policy cooperate. Further, under some conditions the helicopter drops produce more inflation only if they take us off the zero lower bound.

[Nick Rowe]

I interpret Paul Krugman as saying that central bankers cannot credibly commit to permanently increasing the money growth rate, because people won't believe them. People expect the increase in the money supply to be reversed in future (temporary). So expected inflation will not rise, so real interest rates will not fall, so demand for goods will not increase, so actual inflation will not rise, so nominal interest rates will not rise.

[Nick Rowe]

My own view is that if the central bank communicates effectively, by announcing a higher (and faster-growing) price level path target, or better yet an NGDP target, people will believe, with some probability, that at least part of the increased money supply will be permanent. And so expected future NGDP will rise, and so current NGDP will rise and expected nominal (and real) interest rates will rise. With sticky inflation, there may be a short delay before actual inflation and actual short term nominal interest rates will rise.

[Min]

Nick Rowe: "if fiscal policy meant lump sum transfer payments, it would also mean lump sum taxes"

How come? And who cares? And what are lump sum taxes, anyway? You can't pay over time?

[Nick Rowe]

Min: a lump sum transfer is when every individual gets the same transfer from the government, regardless of income, wealth, or anything else. A tax is a negative transfer.

My heroine, Mrs Thatcher, tried lump sum taxes once. It was called the "poll tax". It was not a success.

A lump sum tax/transfer, that was sometimes positive and sometimes negative, depending on whether you wanted to decrease or increase aggregate demand, would be negative roughly half the time. So half the time it would be like the hated poll tax, except it would be even less popular than the poll tax, because at least the poll tax was constant, and predictable.

Now, you could frame it so that you pretended it was always positive, but that's purely a framing exercise, and people would see through it. "You mean you are cutting welfare, and letting poor people starve, just because you want to reduce inflation? Why don't you tax the rich to prevent inflation?"

[Philippe]

a permanent increase in the monetary base is like a helicopter drop, right? So isn't a permanent increase in the monetary base essentially money-financed fiscal policy?

[Derivs]

"I interpret Paul Krugman as saying that central bankers cannot credibly commit to permanently increasing the money growth rate, because people won't believe them. People expect the increase in the money supply to be reversed in future (temporary). "

I am fairly certain the general discourse is the exact opposite. Of a CB that gets all too warm and fuzzy running the presses. Having credibility making people think a CB will increase money supply is not something I can perceive as a problem. It is the accepted perception already.

...also not certain, from how it was written, if you are referring to not being believed as capable to maintain a new rate of change (acceptable), or the literal withdrawing the notional increase. (very hard to believe anyone thinks money put in the system will be removed - when was delta m last negative y/o/y?? - upon what foundation would someone assume a reversal)

Most importantly.. happy holidays to all!

[Majromax]

@Philippe:

> a permanent increase in the monetary base is like a helicopter drop, right? So isn't a permanent increase in the monetary base essentially money-financed fiscal policy?

It depends on the mechanism. The more distorting the monetary base increase is, the more it's like a helicopter drop.

Increasing the monetary base by adding an extra "0" onto every piece of currency (including existing stock) is not a helicopter drop, it's a redenomination. On the other hand, increasing the monetary base by writing United Way a gigantic cheque would be a peculiar helicopter drop, which would look more like something the fiscal authority "should" be in charge of.

@Derivs:

> I am fairly certain the general discourse is the exact opposite. Of a CB that gets all too warm and fuzzy running the presses. Having credibility making people think a CB will increase money supply is not something I can perceive as a problem. It is the accepted perception already.

... which explains the ongoing US hyperinflation, clearly.

The US problem is that while the monetary base has greatly expanded since 2007, that base increase appears to be perceived as temporary. It hasn't corresponded to increases in the other money aggregates, so it's sitting there, largely as bank reserves, that can be withdrawn more or less at will by the Fed.

> when was delta m last negative y/o/y??

December 2000, November 2010, and the latter half of 2012. The last two categories in particular are interesting, as these correspond with times that the Fed has been seeking a "loose" monetary policy and we wouldn't expect to see a fall in the monetary base.

[dlr]

Nick, I think you might have this wrong. I think the SW paper is saying something else. I think it simply posits that the liquidity premium on money is permanently zero. In that way, it is impossible to escape the liquidity trap via monetary policy, period. It is not opining on how to frame a situation where the CB increases the price level by increasing the expected future liquidity premium on money. But you could add that into the model, relax the government budget constraint and then the framing issue you are describing in this post disappears entirely. Then it would be as entirely monetary as something could be, but that just isn't part of the paper as far as I can see. You are asking in this post: What do we call monetary policy that changes the future liquidity premium on money but also changes the PV of future surpluses by assumption? The SW paper is, I think, instead simply assuming you cannot change the future liquidity premium on money because it will always be zero.

But this is all besides the point. SW's post is purporting to discuss Krugman's claim about the impossibility of the CB creating inflation at the zero bound. But in my view, he misunderstands Krugman. SW is making an idiosyncratic point that it is theoretically possible to model inflation expectations increasing while real interest simultaneously decline, allowing the economy to stay the zero bound amid inflation. This mistakes the question for whether inflation can be created *while staying* at the zero bound. But that isn't the question, nor is it Krugman's much stronger claim. The point is whether inflation can be created while starting at the zero bound. Both you and SW's model would agree that this is possible (in his model, just reduce the scarcity of bonds).

Krugman: Monetary policy is probably impotent as the zero bound because Japan.
You: Monetary policy is potent at the zero bound because we can change expectations about future liquidity premiums.
SW: Monetary policy is impotent at the zero bound *if* we assume we are permanently stuck in a liquidity trap and future liquidity premiums (for money) will always be zero.

[Philippe]

majromax,

"It depends on the mechanism. The more distorting the monetary base increase is, the more it's like a helicopter drop."

That sounds very arbitrary. Also I don't think that makes sense. If you give $100 to everyone (helicopter drop), why is that distortionary?

"Increasing the monetary base by adding an extra "0" onto every piece of currency (including existing stock) is not a helicopter drop, it's a redenomination."

Well you're basically just giving all currency owners extra nominal dollars in that case, so it is like a helicopter drop, just a different way of doing it.

"which would look more like something the fiscal authority "should" be in charge of".

Something can technically be a form of fiscal policy, but be carried out by the central bank instead of the fiscal authority.

[Min]

Thanks, Nick! And Merry Christmas. :)

Nick Rowe: "Min: a lump sum transfer is when every individual gets the same transfer from the government, regardless of income, wealth, or anything else. A tax is a negative transfer.

My heroine, Mrs Thatcher, tried lump sum taxes once. It was called the "poll tax". It was not a success."

OK. Thanks. :) But there seems to be some ambiguity about whether "helicopter drops" are lump sum transfers.

"A lump sum tax/transfer, that was sometimes positive and sometimes negative, depending on whether you wanted to decrease or increase aggregate demand, would be negative roughly half the time. So half the time it would be like the hated poll tax, except it would be even less popular than the poll tax, because at least the poll tax was constant, and predictable."

Yeah, but when I take a shower, the water does not come out of the same hole that it goes out of. Why should it? If you want to inject money into the economy through one channel, you do not have to take it out by the same channel.

Nick Rowe: "Now, you could frame it so that you pretended it was always positive, but that's purely a framing exercise, and people would see through it. "You mean you are cutting welfare, and letting poor people starve, just because you want to reduce inflation? Why don't you tax the rich to prevent inflation?"

Questions of fairness aside, how do you take money from people who do not have it? Willie Sutton knew better than that. ;)

Also, the Republicans in the US stalled and minimized unemployment benefits in 2010, not only when the economy was reeling from the financial crisis, but also when it was hard to argue that the unemployed deserved their fate, and just weeks before an election. They paid no political price for that.

[Derivs]

"... which explains the ongoing US hyperinflation, clearly."

I wasn't speaking about reality, I was saying that it is hard to believe there is a 'perception' issue, since it appears consistent with the narrative most people are already always spewing. For the record, I have, and will continue to believe, that at 0 interest rates, trying to create inflation is extremely difficult.

I deserve that graph for saying delta y/o/y, when I had intended to mean M2 from dec 31- dec 31. But your graph actually supports my question, and my opinion (one expectation being easily acceptable, and the other being more difficult to accept). Going from a large positive rate of change, to zero, reflects that the growth rate is unstable but the money is not being removed, for that to be true, wouldn't you be showing me a graph where the amplitude would somewhere go equidistantly negative????

[Nick Rowe]

dlr: Ah! I see your point. (When you say "SW's paper" you mean "SW's post", right?)

And now I understand Steve's comments above.

Yes, take an ISLM model, for example. Tighten fiscal policy to lower the real rate, and increase the money growth rate to create higher expected inflation, and the nominal interest rate stays the same, at 0% if you want.

And you could do something that has the same results in Steve's and David's model. Except now you would loosen fiscal policy to increase the inflation tax and liquidity premium on bonds, and increase the liquidity premium on money too by the same amount, so inflation rises while the nominal interest rate on bonds stays at 0%.

But yes, that is very different from what Paul Krugman is saying.

God, but we were all arguing at cross-purposes. You have sorted it out, I think.

[Nick Rowe]

Philippe: If the government owns the central bank, and gets all the profits from the central bank, then eventually the government must spend those profits. So it is almost impossible to separate monetary and fiscal policy. Almost anything the central bank does will have fiscal consequences, eventually. The exception is adding 0's, which is like printing new money to pay interest on existing money.

Min: "Questions of fairness aside, how do you take money from people who do not have it? Willie Sutton knew better than that."

With difficulty. But you can threaten nasty things if they don't come up with the money somehow. Debtor's prison, forced servitude, broken limbs. But then they can jail you if you don't pay income taxes too.

Derivs: "I am fairly certain the general discourse is the exact opposite. Of a CB that gets all too warm and fuzzy running the presses. Having credibility making people think a CB will increase money supply is not something I can perceive as a problem. It is the accepted perception already."

There's some truth in that. People, and economists, still fighting the last war, against inflation. But there's also a third discourse, about central banks setting interest rates, and being unable to create inflation when interest rates are at 0%.

Merry Christmas all!

[Derivs]

"a graph where the amplitude would somewhere go equidistantly negative????"

I just read that.. somewhere i accidentally deleted, ...to the amount relative to the wave being wider than 12 months.. big difference.

[djb]

Keeping printing money until no bonds left to buy then the new money will end up as fiscal stimulus

Even if takes the form goverment issues bonds uses newly created money to buy bonds from self.. uses proceeds of bond sale to fund goverment programs

Making it fiscal policy

Sounds good to me

[Philippe]

NIck,

say the central bank commits to permanently increase the monetary base by purchasing government bonds... well it can't actually do that unless the fiscal authority also commits to permanently run an equivalent deficit over the long term.

[Philippe]

and Merry Christmas to you too!

[Nick Rowe]

djb and Philippe: if the government owns the central bank, it is ultimately impossible to separate monetary from fiscal policy. But as a thought-experiment, imagine the central bank gave all its profits to charity, and only bought commercial bonds, not government bonds. The results would be the same, even though fiscal policy would be separate from monetary policy.

[Philippe]

Nick, if the central bank was wholly private, then it would just be a private bank or clearing house and would act as such, and government monetary policy would be carried out by the Treasury instead.

[Too Much Fed]

Nick said: "If the government owns the central bank, the central bank will give those seigniorage profits to the government."

JKH, let's go over who gets the fed's profits.

Currency holders get a physical asset with 0% interest.

Central bank reserve (demand deposits of the fed) holders get whatever interest rate the fed chooses.

The preferred stock holders get up to 6%.

The federal gov't gets the rest. Is that right?

Also, Nick talked about a gold standard vs a "CPI standard" in another post.

I thought a gold standard meant a fixed conversion rate between currency and gold. Is that right?

[W. Peden]

Philippe,

Care to explain why?

[Too Much Fed]

Merry Christmas all indeed!

[Jacques René Giguère]

Still fighting the last war? No. Fighting this one, reversing the last 60 years and knowing what they do. With the help of the useful idiots in the mediamacro.

[Philippe]

W. Peden, in the absence of a government central bank the treasury would be the only body with the power to create and issue government monetary liabilities.

[Frank Restly]

Nick,

"If the government owns the central bank, it is ultimately impossible to separate monetary from fiscal policy"

Difficult but not impossible. Central bank is limited by government in what it can buy (usually government debt only). Government is not limited by central bank in what it can sell.

Always bothers me when people concern themselves with the "Independence of the Central Bank From Government Influence" without bothering to ask about the "Independence of the Government from Central Bank Influence".

[Nick Rowe]

Philippe: Suppose the Bank of Canada ket doing exactly what it is doing now. But instead of giving its annual profits to the government, it gave those profits to charity.

Frank: you are totally missing the point.

[Frank Restly]

I'll stop now. Something about "government budget constraint tells us the government must (eventually) spend" smells of tail wagging dog while "government owned central bank" implies that the dog owns the tail.

[W. Peden]

Philippe,

Not sure why we switched from talking about "money" to "government monetary liabilities".

[Philippe]

government money, then, if you prefer.

[Philippe]

"The first two liabilities on the balance sheet, Federal Reserve notes (currency) outstanding and reserves, are often referred to as the monetary liabilities of the Fed. When we add to these liabilities the U.S. Treasury’s monetary liabilities (Treasury currency in circulation, primarily coins), we get a construct called the monetary base."

http://wps.pearsoned.co.uk/wps/media/objects/12417/12715130/app/WebApp10.pdf

[W. Peden]

Philippe,

So the assumption is that the government is issuing coins. The further assumption in your comment, I suppose, is that the Federal Reserve notes are part of the unit of account because of its connection to the government.

Correct assumptions, perhaps, but one could imagine the Fed's notes remaining the unit of account due to convention, in which case it wouldn't just be another private bank.

[Philippe]

W. Peden,

Federal Reserve notes and reserve deposits are government liabilities. Private banks can issue their own liabilities (e.g. bank deposits), but they can't issue government liabilities. This is why I said the treasury would carry out government monetary policy in the absence of a government central bank, as the treasury could issue government liabilities, whereas a 'private Fed' couldn't. The treasury could potentially issue cash notes or electronic currency/electronic credit as well as coins and bills.

During the periods in which there was no central bank in the US, the treasury actually carried out a lot of functions that we associate with central banking, such as altering the base money supply and making loans to banks, which served to regulate the broader supply of credit.

"one could imagine the Fed's notes remaining the unit of account due to convention"

A 'private Fed' could issue private bank liabilities like any bank. But private bank liabilities are promises to pay something else - that something else being base money, which is a government liability.

[W. Peden]

Philippe,

Actually we have plenty of cases of notes and coin NOT being government liabilities. I really recommend the research of George Selgin.

[Philippe]

Many banks issued private banknotes in the past. Those notes were basically no different to bank deposits - they were promises to pay base money, usually coin. They were not base money or the unit of account themselves. The privately-issued coins referred to by Selgin were, similarly, private credit tokens or promises to pay, not base money/ the unit of account in themselves.

[Too Much Fed]

W. Peden, Philippe, and others, let's say gold is MOA. Now have a fixed conversion rate to currency. Is currency also the MOA now (dual MOA)?