Back propagation induction does not work under inflation targeting

Suppose you lived in a world where, whenever the price level fell/rose by 1%, the central bank responded by decreasing/increasing the base money stock by the same 1%. A world like that would not have a long-run Omega point, from which some present equilibrium can be pinned down by back propagation induction.

That's the sort of world we live in, under the inflation targeting regime. A drunk doing a random walk does not have a destination, from which we can infer his route by working backwards. His long run variance is infinite.

Stop arguing about whether a market macroeconomy is or is not inherently ultimately self-equilibrating. It's a stupid question. It depends. It depends on the monetary regime.

Instead, let's solve the stupid question by adopting a nominal level path target.

Comments

[Brad DeLong]

Touché...

You do realize that only me, David Glasner, and a very few other people will understand this? That it needs to be unpacked at considerably greater length if you want it to have reach?

Yours,

Brad DeLong

[Nick Rowe]

Thanks Brad!

Unfortunately, unpacking it properly and clearly will be a hard job for me.

[marcus nunes]

Nick
Krugman rebukes Brad. To Krugman it´s "postmodern"!
https://thefaintofheart.wordpress.com/2015/06/03/krugmans-answer-to-delong-were-in-a-postmodern-economy/

[Phil Koop]

"unpacking it properly and clearly will be a hard job for me"

Well, you could start by stating what it is that does not have a long-run Omega point. What is it that has no equilibrium, in your view? What is it that is doing a random walk? I take it to be trajectory of future NGDP. Is it something else?

[Nick Rowe]

marcus: well, I think Paul Krugman is correct that "postmodern" recessions are different, but I think they are different in not having an Omega point. The gold standard was a really crappy standard, but it did at least have an Omega point. So all sorts of cr*p could and did happen in the short run, but there was a long run nominal anchor, of sorts.

Phil: thinking of it as the trajectory of future NGDP would be one good way of looking at it, but maybe not the only way. There's a nominal thing, and a real thing, and the two interact, and it's hard for one to have an Omega point unless the other does. So multiplying the two together into NGDP would be a useful simplification.

[Tom Brown]

Nick, how would you know if you're wrong? Can you describe what one or two sets of future empirical data would look like that would convince you that you're wrong? Just curious.

[Alex Godofsky]

FWIW, I am pretty sure I understand most of what Nick means. But I've been reading him a long time and he's made this point a bunch of different ways before.

[Jeff]

To counter the "must unpack" critique, I am a complete layman but I think I get the gist. Correct me if I'm wrong, but isn't this analagous to what is called "chasing the needle" in flight training? If a pilot's "corrective" control inputs are always targetted exactly to how far the needle (or any indicator) is from the desired reading, the plane will never stabilize at the desired reading but will always overshoot due to both inertia and indicator-time-lag effects, resulting in what's called "pilot induced oscillations". If the stated effects are large or the pilot's "correction" attempts are/get aggressive, the oscillation can amplify until there is complete loss of control of the aircraft.

[Nick Rowe]

Tom: No. Not yet. The 1933 US case, where FDR announced a higher price level target, and the economy recovered a lot, is one bit of evidence in favour. Tests for unit roots are difficult.

Alex: yep, this is a theme I keep approaching from different angles.

Jeff: that's more like "instrument instability".

A pilot starts out on the equator. He tries to fly west. Random sidewinds push him temporarily north or south, but he corrects his course to due west after a short delay. The longer he flies, the further away from the equator he gets. That's inflation targeting. Under price level (or NGDP) targeting, he keeps heading back towards the equator after he gets pushed north or south. But the metaphor fails after that point.

[Nick Rowe]

Whenever the plane drifts off course by 1 mile North/South, the pilot changes the destination programmed into the automatic pilot by 1 mile North/South.

[louis]

Seems pretty simple to me (not to say it isn't powerful). For the Omega point to have any effect, there needs to be some point in the future where people had one expectation for the price level before the central bank moved, and a new higher expectation after the bank moved. If the bank tells you "my 1 year ahead price level target is 2% higher than today's price level, no matter how far off today's level is from the target I set a year ago" then this is impossible, because the expectation is always a random walk with a 2% drift. Unless monetary policy has a memory, it can't be trusted to converge on a target.

[Jussi]

I do not get Krugman's position. Does he imply that economic agents are really short-sighted at the lower bound but rational expectations will rule after the lift-off. Or is he saying that CB will control inflation mainly by its real action not by the expectation channel?

Nick: I get your pole balancing metaphor and liked it. But here I'm not probably within those "few other people" because I do not get this one. Why do you say inflation targeting is the same as one to one relationship between base money and price level? Given your pole balance: shouldn't the CB overshoot the base money movement to be able to push the price level to the other direction? And you often embrace Band of Canada's track record - so what kind of world we are living in?

I can easily think about economy without a Central Bank. Why not? It is a quite recent innovation anyway. I think economy without a CB will be almost necessarily self-correcting (and was) - but maybe more volatile.

[Nick Edmonds]

This is where I think we need to be careful about how we interpret models. For modelling purposes it is convenient to assume that we can set, at this point in time, a policy or policy rule to apply for eternity. Reality is not so obliging. Policy will certainly respond to political considerations. Will the authorities in fifty years time feel obliged to abide by a NGDP target path set now? Maybe reality has no omega point.

[Tom Brown]

Nick Rowe, thanks for your response. In light of that, what confidence (say from 0% to 100%) would you say you had your beliefs here? Thanks.

[louis]

Nick Edmonds - but for as long as the level path targeting policy stands, the expectation is that the further you fall behind target one year, the harder the monetary authority will try to hit the target the next year. If you were a market participant and the central bankers told you this was their policy, it would be rational to believe them and act accordingly unless you saw some indication that they were not credible (missing several years in a row, getting outside pressure not to act, etc).

[Gibbon1]

Nick: In control theory terms, that sounds like trying to control for the derivative (inflation in this case). Hint, engineers never control just for the derivative and when they do they filter the snot out of it.

Tom: I think chasing the needle is essentially too much correction based on small deviations of the needle. Gain is too high which results in oscillation.

I'm not sure I'm following the argument properly, but it seems to me that markets won't anticipate potential shocks when there is no actual feedback that tells people the shock is coming. Meaning there is no probability information that tells a player if we exit the zero bound next quarter, or ten years from now. A good assumption then is the exit exists in the long tail somewhere. IE, the short term probability is nil. In a classic fed induced recession it's a good bet the fed isn't going to keep rates high for very long, thus the probability distribution of the exit is short.

I also think that the most agile market players assume that is the exit comes they will have enough time to adjust portfolio's before the sheep notice. Which means they will use current conditions only when making decisions about investment.

[Nick Edmonds]

louis - If NGDP(today) is a function of target NGDP(today) and expected NGDP(tomorrow) then NGDP(today) depends on expected target NGDP to eternity. Now maybe NGDP doesn't in fact depend on future expectations, but then I'm not sure the omega point issue is relevant.

[louis]

Nick - if I know what NGDP will be in 5 years, I don't need to know what it will be in 10. I have the answer I need to trade today. And if you use level path targeting vs inflation rate targeting, the expectation of what NGDP will be in 5 yrs will have a tighter band.

[Jussi]

On Omega: is it for the difference or for the level? It seems to me that Nick is talking about the level of the base money which difference, growth rate, is assumed to dictate the price level, which loosely connects to interest rate level. DeLong on the other hand is talking about Omega in terms of equilibrium interest rate. Does it matter, I do not know, but if the level of the base money is random walk (with a drift), its difference is stationary (with a mean of 2 %).

[Majromax]

I think we can construct this as a financial model without too much difficulty.

Imagine the central bank sets an inflation target, and there are two financial instruments: overnight-period bonds and perpetuities. By policy, the central bank implements monetary policy through the purchase and sale of only overnight bonds, using some sort of Taylor-type rule for interest rates.

Everyone shares the same fixed prior about what the long term real interest rate is, so the equilibrium yield for the perpetuity is that plus the inflation target.

However, this central bank has a ZLB problem as defined: with a sufficiently large, negative shock to the short-term real rate, it loses efficacy. Combining a Taylor rule and a basic Philips curve, the negative short-term real rate is expected to persist (because 0% money is too tight). In turn, this means that there is no strong expectation about when the interest rate environment will return to normal, since doing so is contingent on another (unknowable) positive shock to the real interest rate (or less well-understood mechanisms of reversion to a mean).

The perpetuities, which in equilibrium trade at inflation+real yields, will trade at a discount to that long-term rate depending on the effective discounting period and how long the ZLB is expected to be binding. The CB cannot credibly promise to make the ZLB not binding without unconventional policy, so we're stuck.

A price-level target alleviates this, because the CB can promise to be as reckless as it wishes to be whenever the ZLB stops binding. This means that perpetuities will not trade at a discount to their long-term value, since a future nominal return will 'make up' for the near-term shortfall.

[Jussi]

I read Majromax like there is a time structure where near future is more important than far future, kind of discounting. Then it is feasible that the central bank loses it, the relative short term ZLB problem will out-weight the long run equilibrium level. Even if on average, without discounting, the long run would always rule and backward induction would work.

That makes sense. I think I like that, maybe that is Krugman's approach too even though it is not very clearly put.

[louis]

Majro - when you say the perpetuities would trade at a discount when the overnights are stuck at the ZLB, surely you mean they would trade at a premium (and their yields would be lower than the LT equilibrium). And as long as the perpetuities are overvalued that way, the economy remains depressed. If the CB could credibly promise a higher future price level, that would induce a fall in the price of the perpetuities.
Or am I misunderstanding?

[Nick Edmonds]

louis - "if I know what NGDP will be in 5 years, I don't need to know what it will be in 10." How do you know what NGDP will be in 5 years? Do you mean that NGDP in 5 years does not depend on the then expectation of what will happen after 5 years? Or are you saying that the NGDP becomes more certain (adjusting for discounting) the further you look into the future?

[marcus nunes]

Nick
An early "destination is key" post:
https://thefaintofheart.wordpress.com/2011/07/01/playing-with-words/

[JKH]

" Suppose you lived in a world where, whenever the price level fell/rose by 1%, the central bank responded by decreasing/increasing the base money stock by the same 1%. A world like that ..."

So the premise there is that the central bank is constantly readjusting the base to allow for prior inflation target misses.

Why should such an error premise be fundamentally different for price level path target misses?

And when such level target misses appear, the result shows up as adjustments in the IMPLIED next period inflation target - the one that gets backed out as that which
is required to make up for the realized discrepancy from the target price level path point.

So under a similar rule for base response, why doesn't the same essential problem remain?

[JKH]

... or for NGDP level target misses ?

[Alex Godofsky]

JKH: because that's the opposite of what 'level' means?

[JKH]

A price level target (which changes for each time period - unless you are also targeting 0 inflation) is no more fixed under price level targeting than is the case under inflation targeting (which also has an implied price level target for each time period).

Similarly, the target for NGDP level targeting is no more fixed than is the case for NGDP targeting.

So there's no basis there for differentiating these various alternatives according to this back propagation stuff.

[Majromax]

@louis:

>Majro - when you say the perpetuities would trade at a discount when the overnights are stuck at the ZLB, surely you mean they would trade at a premium (and their yields would be lower than the LT equilibrium).

You're right. I was thinking in terms of yields throughout, which are obviously inverse price.

[Nathanael]

There's a group which makes a lot of money from instability, and doesn't care about the long run. (Call 'em "Wall Street" or "The City").

They will oppose any stable policy on political grounds and they will make up economic gibberish as rationale for their opposition.

Gibbon1 is right to look at this as a control theory problem, but one of the things you're trying to control is political dynamics... very tricky to model.