Increased Price Flexibility is Destabilising in New Keynesian Models. (And a Price-Level Path Target is Stabilising)

Start with a very simple New Keynesian "IS" (or "Aggregate Demand") equation:

y(t) = E[y(t+1)] - a[r(t)-r*(t)]

The "real" (inflation-adjusted) interest rate r(t) is defined as the "one period" nominal interest rate, minus expected inflation for the following "one period". In order to stabilise output y(t), relative to expected future output E[y(t+1)], the central bank needs to ensure that the real interest rate r(t) always equals some "natural rate" r*(t), which varies over time as shocks hit the economy.

But the central bank can only do this if it responds to shocks instantly. And that is implausible, because it usually can't see the shocks until after they hit, and after it sees the effect of those shocks on output and inflation.

Let's assume instead that there's a "one period" lag between a shock hitting the economy and the central bank observing that shock and responding to it.

If the central banks sets a real interest rate, it's simple to see what happens when a shock hits. A 1% negative shock to r* causes an a% negative shock to y(t), which lasts for one period, after which the central banks adjusts r(t), and output can return to normal (unless another unexpected shock hits). There's a recession that lasts "one period".

But central banks in New Keynesian models set a nominal interest rate, not a real interest rate. So it's the nominal rate, not the real rate, that stays constant for "one period" after the shock hits. Which complicates things, and makes the recession worse than it would be if the central bank sets a real interest rate.

When the negative shock hits, and the economy goes into a recession, actual inflation falls, and so expected inflation will presumably fall too, so the real interest rate will rise. And that rise in the real interest rate is the exact opposite of what the doctor ordered. And the more inflation falls, and the more expected inflation falls, the more the real interest rate rises, and the bigger the recession will be, and the more inflation falls. There's a nasty positive feedback loop at work.

The best case scenario is if there's a "one period" lag before inflation responds at all. So the central bank, with the same "one period" lag, can cut the nominal rate in response to the shock, before falling inflation and expected inflation worsens the effect of the shock.

In other words, increased price flexibility is destabilising in New Keynesian models.

OK. So what, if anything, can the central bank do about this problem? It can try to improve its crystal ball so it learns about the shocks more quickly, and can better distinguish permanent from temporary shocks, and demand shocks from supply shocks. But unless it finds a perfect crystal ball, some lag between shock and central bank response is inevitable.

It can target the price level (or price level path) rather than target inflation. It can make an advance commitment that if there is a recession, and if inflation falls, it will eventually (when it does respond) bring the price level back up to where it would have been without that recession. It will "repair" its past "mistakes". Which means that expected inflation, between now and "one period" ahead, won't change at all. Which eliminates that nasty positive feedback loop between lower inflation and higher real interest rates that would worsen the effect of the negative shock.

In other words, a price-level path target, relative to an inflation target, acts like an automatic stabiliser in New Keynesian models.

It's more complicated than this, of course. Because I have over-simplified the model by assuming that the central bank has a lag of "one period", and that the only real interest rate that matters is that same "one period" real interest rate.

But you get the gist.

Comments

[Trevor Adcock]

This is another one of those things that show that the Monetarist and New Keynesian models have to be equivalent. Once you have a model that explains the relationships between all variables then the two viewpoints are by definition equivalent. It is only when the relationships are left ambiguous and people are left to fill in the blanks with their own intuitive ideas of the relationships that the models differ.

Each model differs not in what it says, but in how it shapes the implicit intuitions of the people who use it, who fill in the blanks with unstated assumptions.

It's like your previous idea of upward sloping IS curves. It is an implicit and unjustified assumption that the IS curve should be downward sloping. An assumption that the IS and LM curves are independent when the are not, even in the short run

[Nick Rowe]

Trevor: I would put it this way: a lot of the difference between different macro perspectives are just in framing. Do we think of the central bank as choosing a nominal interest rate or choosing a monetary aggregate? What does "doing nothing" mean?

[Hariharan Jayashankar]

I am a bit unclear and probably have the case of partial knowledge.

Even with a 1 period lag in the fed interest rate rule, if the fed has a strong enough beta (the weight it places on achieving its inflation target), wouldn't the fed be able to correct the whole downward spiral.

Negative shock hits -> inflation falls -> one period recession -> but people know that the fed is super tough on inflation -> expected inflation doesn't fall cause people expect the fed to increase rates super high.

Also an increase in price flexibility takes us closer to an RBC model correct? Where monetary policy has no effect anyway. Intuitively it seems like no matter what targetting rule the fed targets, the effectiveness of monetary policy just reduces here in an NKM.

Thanks Nick.

[Trevor Adcock]

Nick Rowe: I asked my intermediate macroeconomics teacher why a movement along the downward sloping monetary reaction function was considered "doing nothing" when a shift of the curve was "doing something", while both were just the central bank arbitrarily determining an interest rate.

She responded that it was just truly an arbitrary choice and how things were done in this model. Maybe there is hope still!

[Nick Rowe]

Hariharan: provided "one period" isn't *too* long, relative to how quickly inflation falls, the downward spiral in inflation isn't explosive (implosive?). So the central bank (not "the Fed" here; this is a Canadian blog!) wakes up and brings inflation back to target before the price level falls to zero. Indeed, with a 2% inflation target, the price level might not fall at all, but the inflation rate drops to (say) 1% for one period, so the price level is lower than it would otherwise have been. But with a price level path target, the central bank does what is needed to bring the price level back to where it would have been without the shock.

Now in a discrete time model (like this one), the shortest period of time is "one period" (I have carefully stayed silent on whether that means 1 month, 1 quarter, 1 year, or one decade, or what). So we can't say what happens *during* that period.

Trevor: sounds like you've got a good intermediate macro teacher!

[Charles Steindel]

I'm teaching Money and Banking, and that distinction between the shifting the money reaction function and shifting the target rate is indeed an odd one, unless one supposes the Central Bank announces every day the Taylor rule it's following!

But on the point about flexibility. RBC types, or whatever one wants to call them nowadays, like to assert that Keynesian economics is all about price and wage rigidity and then get some yuks when cycles continue to exist even after structural reforms. And there are the others who dive into the data and say, yes, workers do sometimes take nominal pay cuts--at least when they are disguised as reduced bonuses--so why don't we just role out more and more variable pay systems and get the economy humming with some automatic stabilizers (pro cyclical real wages) working better on the private side. My thought is that, perhaps, Keynes's insight--the "General" of his theory--is the the two sides are not completely rigid wages (and prices) vs. flexible ones, but infinitely variable wages (and prices) vs. the general case that everything isn't always changing. That seems to be to be similar to the usual distinction one draws between financial asset markets and markets for real goods and services. We seem to know that just a smidge of rigidity (sounds like Keynes's
"widow's cruse" though he brought that up in another context) gives us grounds for thinking Keynesian thoughts like fiscal policy and expected monetary policy affect real variables. A smidge of rigidty--not absolute, total flexibility--looks like a General case, not something cooked up to explain peculiar British conditions of the 1920s and 30s.

[Nick Rowe]

Charles: I tend to agree.

[Paine]

The price level path should be assigned
To a mark up cap and trade market
Designed by experts
and superImposed
on the oligop corporate sector

Neo galbraith

The central bank should regulate the
Sovereign paper market
To maintain a zero real ceiling
On short notes and consoles alike a

Just a little futurism for fellow
Socialists

[Egmont Kakarot-Handtke]

What’s the trouble with some Canadian economists?
Comment on Nick Rowe on ‘Increased Price Flexibility is Destabilising in New Keynesian Models’

The general trouble with economists is that they are either stupid or corrupt or both. The major approaches — Walrasianism, Keynesianism, Marxianism, Austrianism, MMT — are mutually contradictory, axiomatically false, materially/formally inconsistent and all got the foundational economic concept profit wrong. Economics is a failed science from Adam Smith/Karl Marx onward to New Keynesianism, DSGE, and MMT but economists cling desperately to their provably false proto-scientific garbage.

This is not only stupid but amounts to a violation of scientific standards: “In economics we should strive to proceed, wherever we can, exactly according to the standards of the other, more advanced, sciences, where it is not possible, once an issue has been decided, to continue to write about it as if nothing had happened.” (Morgenstern 1941) #1-#14

What is needed in economics is NOT repetitive critique and futile cosmetic repair but a Paradigm Shift. This is long known: “There is another alternative: to formulate a completely new research program and conceptual approach. As we have seen, this is often spoken of, but there is still no indication of what it might mean.” (Ingrao et al. 1990).

The specific trouble with some Canadian economists is (i) that they cling to false approaches and a failed methodology, (ii) that they have NO idea how to perform a Paradigm Shift, but (iii) that they prevent it by (a) stubbornly recycling provably false approaches, and (b), by actively suppressing critique and refutation in the econoblogosphere.#15-#17

In this, though, the agenda-pushing Canadians are by no means alone but follow a widespread pattern.#18, #19

Egmont Kakarot-Handtke

References
https://axecorg.blogspot.com/2019/12/whats-trouble-with-some-canadian.html