Targeting, Tautologies, and Double Divine Coincidence

For Tyler Cowen. I think I see his point, and I've been trying to get my own head around this question.

1. Suppose I live in a world where the central bank targets the price level, as measured by the GDP deflator. And suppose I believe the central bank should target Nominal GDP instead. Given my preferred target, if NGDP fell below target I would say that money is "too tight"; and if NGDP rose above target I would say that money is "too loose". And suppose in 2016 the central bank hits its price level target, but RGDP falls. By definition, NGDP must fall too, since the GDP deflator is defined as: P=NGDP/RGDP.

If I blamed the fall in RGDP on tight money causing NGDP to fall, or on tight money allowing NGDP to fall, would I be making a tautologous statement?

No. I would be making a counterfactual conditional statement. I would be saying: "If the central bank had instead been targeting NGDP, and had prevented NGDP falling below target, the fall in RGDP would not have happened".

2. Now let us imagine a parallel universe where the central bank targets NGDP, and suppose I want the central bank to target the price level, as measured by the GDP deflator. Given my preferred target, if P fell below target I would say that money is "too tight"; and if P rose above target I would say that money is "too loose". And suppose in 2016 in that parallel universe, the central bank hits its NGDP target, but RGDP falls. By definition the price level must rise.

If I blamed the fall in RGDP on loose money causing P to rise, or on loose money allowing P to rise, would I be making a tautologous statement?

No. I would be making a counterfactual conditional statement. I would be saying: "If the central bank had instead been targeting P, and had prevented P rising above target, the fall in RGDP would not have happened".

3. In both cases we have the same accounting identity: RGDP=NGDP/P. Someone who knew nothing whatsoever about economics, except for that accounting identity, would find both claims equally plausible, or equally implausible. To keep the ratio constant, where we can target either the numerator or the denominator but not both, should we try to keep the numerator constant, or try to keep the denominator constant? Actually, if the only thing you knew is that one variable is the ratio of two other variables, and that we can target numerator or denominator but not both, both claims would look utterly implausible.

For someone who knew no economics, and who knew only that RGDP=NGDP/P, it would be a divine coincidence if stabilising P were consistent with stabilising RGDP. And it would be an equally divine coincidence if stabilising NGDP were consistent with stabilising RGDP. And it would be a double divine coincidence that both those divine coincidences were true: so that stabilising either P or NGDP would be consistent with stabilising RGDP.

4. Now what is really weird is that the real world did in fact seem to be a place where double divine coincidence were true. Until it wasn't. An outside observer, who did not know that central banks were targeting inflation (OK, it was CPI not GDP deflator inflation), and who mistakenly thought they were targeting NGDP instead, would infer from the data that stabilising NGDP did indeed seem to be consistent with stabilising RGDP, and that the NGDP version of divine coincidence were true. Furthermore, that outside observer would see no reason to change his mind since the recent recession. It is the P version of divine coincidence that has failed empirically, when we look around the world. The NGDP version of divine coincidence is hanging in there.

[P.S. If it weren't for the accursed Lucas Critique, and the fact that central banks cannot be assumed to be able to hit their targets perfectly, I think it would be easy to test which version of divine coincidence is better. Find which of NPGD and P has the higher variance, and target it.]

Comments

[Julius Probst]

Great post !!!
This is very crude, but just looking at NGDP and the GDP deflator for the US, the shortfall of NGDP during the crisis was indeed much larger than the shortfall had Central Banks targeted the price level.
[Link here NR]
This is probably because Western economies also experienced a temporary negative supply shock (high oil prices) when the crisis hit.
Of course, over the last 1-2 years we have exactly the opposite scenario where the shortfall in the price level is larger than the shortfall in NGDP because of a positive supply shock, which is precisely why a NGDP level target is preferable to a price level target.
Even though the latter is presumably still better than a pure inflation target, not to mention asymmetric inflation targets where the 2% is regarded as a ceiling.

[John Handley]

Nick,

Suppose there is a central bank that has a price level target. Normally, any time the price level is below target, the central bank simply expands the money supply until the price level is on target in the given period. There are two primary challenges to this in this hypothetical world though: 1) the central bank doesn't know what level of the money supply is consistent with the price level being on target and 2) the central bank needs to set the money supply in advance.

In order to fix the first problem, the central bank decides to adopt a mechanical rule which has it adjust the money supply proportionally to how far the price level is off target. The central bank may instead choose to adopt a rule for the nominal interest rate, which will probably help to ensure against money demand shocks.

The second problem is a little more difficult. Now, the central bank can't do anything in the current period to fix the current price level being off target (Practically, I'm thinking along the lines of the fact that central bankers don't meet every day and that data are updated really slowly, which makes real-time monetary policy impossible). In this case, the central bank adjusts the money supply/nominal interest rate based on how off target last period's price level was. Alternatively, assuming information about the current period is not know until the next period, the central bank may choose to target what it expects the current price level to be.

If the current price level is below target, do we blame the central bank for making money too 'tight' in the period before? It seems to me that, if the price level falls below target in this model, it's because of some shock that the central bank didn't know about in the previous period and/or a shock that it won't know about until the next period (depending on whether the central bank simply sets policy in advance or has delayed information). Can a central bank really be blamed for not anticipating a shock that it couldn't have anticipated?

At this point, is the proper assessment of a below target price level not "shock [x] happened, had the central bank loosened monetary policy, the price level would have remained on target" instead of "money was tight, now the price level is below target"? The market monetarist analysis always seems to be the second one, which (personally) really doesn't seem to capture the essence of any situation.

[dlr]

That someone like Tyler could write a post like that is helpful, as it really exposes an underlying communication failure. He spends the post thinking he is searching for other metrics. But the search is very odd. For example, he cites a November 13, 2015 survey of professional forecasters which had 2016 headline PCE at 1.8%. The unmentioned February version came out last week and dropped to 1.3%. He doesn't specify the plunge in every market based inflation measure in 2016 but instead brushes aside weakness as due to real shocks, and makes a common but unhelpful distinction between passive and active fed tightening. The fact that smart economist Tyler Cowen can think that these arguments are "alternatives" to NGDP-centrism, when in fact they would apply 100% equally to someone who thought the Fed was too tight because they believed in targeting, say, market-implied one-year forward inflation breakevens, shows how bad the communication failure is.

Although I agree with your post, I don't think it solves the communication problem. The double divine coincidence and how it played out in 08-09 (this is not quite as straightforward as you imply thought the period, because market-implied forward inflation breakevens did eventually also decline precipitously despite some liquidity-based noise and some people think that expectations are what matters, so a forward looking inflationist could argue that a forward-looking breakeven target would only have been a little worse than an NGDP target) is merely an argument for the NGDP counterfactual conditional. But it doesn't persuade everyone. And the tricky thing about the NGDP-RGDP counterfactual conditional is that there are definitely universes in which the correlation holds very often but the counterfactual doesn't. This makes the unpersuaded think they are being flimflammed when they hear about it, and it can be lead to a lot of strange responses.

[jonathan]

Two points:

(1) The NK divine coincidence doesn't say that stabilizing P implies stable RGDP. It says that stabilizing P eliminates inefficient fluctuations in RGDP. Efficient fluctuations (e.g. due to technology shocks) remain.

(2) You also can't observe the counterfactual, so you can't observe which theory is supported by the covariance of P, NGDP, and RGDP. If the central bank succeeds in stabilizing P, but RGDP (and thus NGDP) fall, how do you know that stabilizing NGDP would have resulted in higher RGDP, rather than just higher P?

Mechanically, if you stabilize P you will observe correlation 1 between RGDP and NGDP. Likewise, if you stabilize NGDP, you will observe correlation -1 between P and RGDP. Given that we're under former regime, you would expect to observe the NGDP "divine coincidence" by construction.

[Nick Rowe]

Julius: thanks! Yes, in any reasonable model, it is supply shocks that make the difference between targeting NGDP and targeting inflation.

John: True, trying to target X, and actually keeping X on target, are not the same thing. If anything, I would think it is easier for a central bank to hit its NGDP target than hit its inflation target, but this post is really just trying to address Tyler's point, so I left that out.

dlr: my hunch is you are right about the communication problem. My parallel world was trying to get at that, but I'm not sure it works 100%. And I agree on the active/passive thing.

"this is not quite as straightforward as you imply thought the period, because market-implied forward inflation breakevens did eventually also decline precipitously despite some liquidity-based noise and some people think that expectations are what matters, so a forward looking inflationist could argue that a forward-looking breakeven target would only have been a little worse than an NGDP target)"

I think the breakdown of P divine coincidence is clearer outside the US. Like the UK, where inflation went above target during much of the recession. And Canada, where inflation was sometimes above and sometimes below (depends as well on core vs headline) target during the recession.

"And the tricky thing about the NGDP-RGDP counterfactual conditional is that there are definitely universes in which the correlation holds very often but the counterfactual doesn't."

That sounds possible. Trying to think of what such a universe would look like.

jonathan:

1. True. I avoided that one for simplicity. But in the recent recession, the fall in RGDP looked much bigger than efficient, so I don't think it matters much.

2. We don't *know* it. And we don't have an NGDP targeting vs inflation targeting experiment. But we use what theory we have to try to make sense of the data.

"Mechanically, if you stabilize P you will observe correlation 1 between RGDP and NGDP. Likewise, if you stabilize NGDP, you will observe correlation -1 between P and RGDP. Given that we're under former regime, you would expect to observe the NGDP "divine coincidence" by construction."

If we see P, NGDP, and RGDP, all positively correlated, (because even under inflation targeting central banks sometimes miss their targets) we can't tell whether IT or NGDPT would be better. That's the world of double divine coincidence. But the UK case especially, where NGDP and RGDP fell while P did not fall and actually rose (all relative to trend) violated P-divine coincidence by confirmed NGDP-divine coincidence.

[Roger Sparks]

Maybe I am too mechanical, meaning, maybe I am too literal. Too exacting.

It seems to me that we begin with three terms (P, RGDP AND NGDP), two of them unknown (P and RGDP). We measure NGDP so it becomes the only known term.

We then reduce the two unknowns to one unknown by defining P = NGDP/RGDP. Now we only have one unknown (RGDP). From now on, P is always a ratio of NGDP and RGDP.

Again, we only measure NGDP. RGDP is a calculated term based on other criteria. What other criteria? Things like the cost of labor, taxes, interest rates, and other factors influencing the cost of production of goods and services. "Other factors" could include competition drivers such as the ease of obtaining credit.

Now we turn our attention to what central banks around the world are presently doing. They are targeting "inflation", trying to obtain a change in the criteria used to calculate RGDP. We are faced with the challenge of measuring the results of their efforts.

I would venture to say that the central banks DO target NGDP, reasoning that increased NGDP will increase inflation due to increased competition for goods and services. I would further venture to say that the central banks have ignored the supply side of the economic circle, forgetting that increased production forces prices lower due to increased competition for market share.

[Nick Rowe]

Roger: take a very simple example. An economy that produces only..........apples. We could measure the price of apples, we could measure the quantity of apples, we could measure the dollars spent on apples, or any two, or all three. And we should get the same answers either way. That is quite separate from the question of what the central bank should target.

[Eliezer Yudkowsky]

Oh, well said.

[Nick Rowe]

Eliezer: Not even a quarter as well said as your recent piece. Which was not only accurate and very thorough, but hilarious. But I only managed to read it because Morgan Ricks emailed me a copy (thanks Morgan). It's on Facebook, or something?

If anyone who is on Facebook can post a link, for others who are on Facebook, that would be great. (It's a Socratic dialogue between a market monetarist and a central banker.)

[John Handley]

Nick,

"True, trying to target X, and actually keeping X on target, are not the same thing. If anything, I would think it is easier for a central bank to hit its NGDP target than hit its inflation target, but this post is really just trying to address Tyler's point, so I left that out."

It's interesting to actually read this from someone who claims to be a market monetarist. Usually whenever I talk to Sumner about implementation he calls me crazy for suggesting that there's a difference between "trying to target X and actually keeping X on target." Naturally, I'm intrigued -- perhaps you can be the first market monetarist that bothers to talk about implementation that I've ever seen.

I'd like to hear your reasoning for why an NGDLT would be easier to hit than an inflation target, because right now I can't think of a single reason why this would be the case.

[Nick Rowe]

John: can I target the speed of my car (within limits, assuming it's working right)? Yes. I can make it go faster, or slower. That would be my fist answer. But if you pressed me I might then hedge a little and say "Yes, but not with 100% accuracy". Because of lags between headwinds and my noticing those headwinds, and between pressing the gas and speed increasing, and speedometer inaccuracies, etc. (This is why some gearheads hate turbos, because of turbo lag.)

In brief (because this is not what this post is about) NGDP responds with a shorter lag to changes in central bank policy (understood as *communication*, because the communicated *actions* may come later) than P, simply because many prices are sticky. The shorter lag makes control easier (OK there will be exceptions).

But here I am talking about *actual* NGDP. Scott is talking about targeting *market forecasts* of NGDP. The lag there is so short you might as well say it's real-time data. Which is why it makes sense for Scott to give an unqualified "Yes".

[Market Fiscalist]

If we knew what the optimal level of RGDP was and that we could hit that level by adjusting the money supply then we could just target RGDP and the price level and NGDP would also be optimized. Monetary policy would be easy.

It is the fact that we do not know the optimal level of RGDP that means we have to find a something to target that will led RGDP find it "natural" level. But as we don't know the optimal level of RGDP we have no true way of knowing for sure if the thing we are targeting is optimizing RGDP or not.

Hitting an NGDP target while RGDP falls might actually make RGDP fall more than it needs to if the extra inflation has a detrimental effect on the economy.

Hitting an inflation target while RGDP falls might make RGDP fall more than it needs to if the IT leads to unnecessary monetary tightening after the supply shock that caused RGDP to fall.

The fact that we don't know optimal RGDP and we don't if our chosen target helps us hit this (unknown) optimal RGDP makes monetary policy very hard.

[Typo fixed NR]

[Market Fiscalist]

Typo Correction: *find a something to target that will led NGDP find it "natural" level* = *find something to target that will lead RGDP to find its "natural" level*

[Fixed it NR]

[Nick Rowe]

MF: Yep. Targeting RGDP has been tried and it failed. Not just because we don't know the "natural" level of RGDP, but because it left P and NGDP indeterminate.

I like to think of NGDP targeting as a halfway house between targeting RGDP and targeting P. You target the product of the two, which is like targeting an unweighted average of the two (in logs). Thesis (RGDP), antithesis (P), synthesis (NGDP).

[Tom Brown]

"I like to think of NGDP targeting as a halfway house between targeting RGDP and targeting P."

Does that have any implications for the relative challenge in targeting P, NGDP and RGDP? In other words, does that put an NGDP target somewhere between a P and an RGDP target in terms of ease of successfully hitting the mark.

[Nick Rowe]

Tom: I don't think so. At the limit, where the weight on RGDP becomes 100% and the weight on P 0%, it becomes impossible (or maybe close to impossible) to hit the target in the long run. That's because of the neutrality of money. The system eventually explodes or implodes.

[Tel]

This has also been my complaint about Sumner. He uses retrospective definitions about "tight" and "loose" money. This is a good way to be right all the time, but not very useful with either prediction or policy suggestions.

Suppose I want to teach someone to drive, and I explain to them that "steering left" is anything that causes the vehicle to move to the left, and "steering right" is anything that causes the vehicle to move to the right.

What about if you are in a fishtail and the rear wheels are sliding? Summer the driving instructor says "Why are you steering left so hard? You should steer it back right again to compensate." Of course the learner driver has the wheel turned full lock to the right already and Summer just keeps saying "The problem is you steering left all the time."

The correct thing to do is steer into the fishtail (i.e. turn the wheels to the left) then pick up the back again so it stops sliding and you have control, now you can turn it back to the right. Summer's explanation cannot even encompass such a maneuver. I'm not saying there's an exact equivalent between an economy and driving a car, but it must surely give pause for thought.

[Nick Rowe]

Tel: you ought to love my post on the Scandinavian flick!

That's the weird thing about nominal interest rates as a monetary instrument. With base money as an instrument, we know which way to turn the wheel.

[raylopez99]

Rowe: "P.S. If it weren't for the accursed Lucas Critique, and the fact that central banks cannot be assumed to be able to hit their targets perfectly, I think it would be easy to test which version of divine coincidence is better."
- the absurdity of this is amusing. Rowe proposes an accounting identity "NGDP = P*RGDP", assumes the economy will follow this if prices are raised (pace the recent experience with deflation; in the comments section: "If anything, I would think it is easier for a central bank to hit its NGDP target than hit its inflation target"), then imposes the Lucas Critique on top of this, which assumes people will conspire to defeat this action (why is not clear, as the Lucas Critique itself is more or less of a 'stuff happens' fudge factor, but I digress).

Like balancing spinning plates on top of spinning plates, the entire edifice of Rowe's post is unstable. It's much simpler to say, like Nobelian Shiller suggests, that the economy is nonlinear and "animal spirits" is the only parameter that matters. It might be career death insofar as crystal ball gazing goes, but more honest and transparent.

[Henry]

"In brief (because this is not what this post is about) NGDP responds with a shorter lag to changes in central bank policy (understood as *communication*, because the communicated *actions* may come later) than P, simply because many prices are sticky."

Nick,

If NGDP has increased and prices haven't moved are you then implying that RGDP has fallen?

[Henry]

"Julius: thanks! Yes, in any reasonable model, it is supply shocks that make the difference between targeting NGDP and targeting inflation."

Nick,

But won't supply shocks impact inflation indices also (think of the oil shock)?

[Henry]

"If NGDP has increased and prices haven't moved are you then implying that RGDP has fallen?"

Nick,

Forget the question. Got my knickers in a twist.

[Nick Rowe]

ray: " Rowe proposes an accounting identity "NGDP = P*RGDP", assumes the economy will follow this if prices are raised (pace the recent experience with deflation;..."

The difference between you and Henry is that Henry realises (quickly) when he's said something daft. It's an accounting identity. I don't *assume* it's true. It's just a definition.