# Putting NGDP into macro models

David Beckworth directed me to a new paper by Roger Farmer and  Giovanni Nicolò, recently published in The Manchester School.

They develop a different type of Keynesian model, which replaces the Phillips curve with an equation describing NGDP growth expectations:

In contrast to the NK-Phillips curve, the third equation of the FM-model is a belief function. Following Farmer (1993, 2012), the functional form for the belief function that we use in this study is described by Equation (3.b),

(3.b) Et [xt+1] = γxt + (1 − γ)Et−1 [xt ] ,

where xt ≡ πt+(yt − yt−1) is the growth rate of nominal GDP. The belief function is a mapping from current and past observable variables to probability distributions over future economic variables and the functional form that we chose for the belief function, captured by Equation (3.b), asserts that agents’ expectations about future nominal GDP growth are adaptive. When we estimated the model, we found that the data strongly favour the parameter restriction, γ = 1 and in Section V we report the estimates of the FM-model under this restriction. When we incorporate this restriction into the belief function, our model implies that beliefs about future nominal income growth are equal to current nominal income growth. By modeling beliefs about future nominal income growth as a new fundamental we resolve both dynamic and static indeterminacy.

Their model does still use the other two standard NK equations:

The FM- and the NK-models that we estimate in our empirical work have two equations in common. One of these is a generalization of the NK IS curve that arises from the Euler equation of a representative agent. The other is a policy rule that describes how the Fed sets the fed funds rate.

This is great, but my dream model would go even further, eliminating interest rates, inflation and real GDP.  I would replace interest rates with market NGDP growth expectations from an NGDP futures market.  If that market did not exist, then I’d have the central bank estimate NGDP expectations using other market prices.  For simplicity, I’ll assume an NGDP futures market does exist.

NGDP growth expectations would be determined by the monetary policy regime.  An expansionary monetary policy would raise expected future NGDP.  This is what Keynes presumably meant by an increase in “animal spirits”.  The increase in NGDP expectations, aka animal spirits, would cause an increase in current NGDP.  Another equation would link unexpected moves in current NGDP with employment, because nominal wages are sticky in the short run.

The central bank’s dual mandate would be stable growth in NGDP and employment close to the natural rate.  Both goals would be achieved via stable growth in NGDP (i.e. a “divine coincidence”).  And that stable growth in NGDP would be achieved by pegging a NGDP futures contract price at a level where market participants expected stable growth in actual NGDP.

There would be no circularity problem, as the market would be predicting the instrument (monetary base) setting that led to on target NGDP growth.  The central bank would not be responding to changes in NGDP futures prices.

PS.  Josh Hendrickson has a great discussion of the problems with using the Phillips curve in this twitter thread.

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10 Responses to “Putting NGDP into macro models”

1. Paul
26. July 2019 at 13:10

Okay Scott, I have a faint idea what your model might look like in real life, but it would still, much to your chagrin, include nominal interest rates. Here it is:

CB sets 5% NGDP level target, then, some time later, NGDP grows 7%. The market therefore lowers its NGDP growth expectations for the near future. Nominal interest rates fall as a result, which raises the demand for money and leads the CB to lower the monetary base to preserve its policy rate target, and therefore lowers NGDP back to the target.

I was helped tremendously by this paper by Robert Hetzel (who you have praised before): https://www.richmondfed.org/~/media/richmondfedorg/publications/research/economic_quarterly/1993/summer/pdf/hetzel.pdf

Interest rates matter.

2. ssumner
26. July 2019 at 13:42

Paul, Yes, both interest rates and zinc prices matter. And monetary policy affects both interest rates and zinc prices. But you do not need to put interest rates or zinc prices into the model. They don’t help us to understand the macroeconomy. The Fed should target NGDP futures prices, not interest rates or zinc prices.

3. ssumner
26. July 2019 at 13:44

Paul, BTW, I am working on a paper comparing NK and NeoFisherian models, where interest rates will play an important role. I use them as needed.

4. Paul
26. July 2019 at 18:58

A NK could likewise say:

“Yes, money growth and NGDP matter, and monetary policy affects money growth and NGDP. But you do not need to put them in the model. The Fed should target short-term interest rates and inflation, not monetary aggregates or NGDP.”

In Hetzel’s explanation of the QTM, the Fed targets interest rates, and the effect of expected inflation on the nominal rate drives the shifts in money demand that fulfill expectations.

5. Matthias Görgens
26. July 2019 at 19:37

Paul, you are right that there’s a symmetry at that superficial level. So you need to see the rest of Scott’s arguments for why a model with nGDP is better than one with inflation.

One aspect that I haven’t seen many people stress is that inflation / price level is actually really hard to measure. Not even so much in practice, but conceptually. There’s substitution effects and hedonic quality adjustments. And especially the latter is very ambiguous.

Scott, do you think we could avoid most of those difficulties by restricting our basket to labour only? That’s the one sticky price we care about, and we can approximately ignore quality improvements.

There’s a nice symmetry between tageting the price of one hour of labour (inflation targeting) vs adjusting for unemployment, underemployment and labour participation rate (ie targeting total nominal labour compensation per capita).

6. Paul
26. July 2019 at 20:38

Matthias, how can there be a significant substitution effect in a measure of the aggregate price level? What are we substituting away from that could have any more than a tiny impact?

7. rayward
27. July 2019 at 06:48

I suppose it would be described as speculative. What? That the Fed would respond to the possibility that it might have to purchase bonds, because the futures market indicates that Fed policy was below target, by taking the actions necessary to avoid said purchase (i.e., by hitting the target). It makes sense to me. Then why does Farmer raise the stakes by proposing that the Fed commit not only to purchase bonds but equities if the futures market is below target? Farmer calls this the path to Prosperity for All. What if asset prices are already high as the result of “animal spirits” and all, does the Fed maintain the animal spirits by committing to keep asset prices high (with the commitment to purchase assets if prices fall)? If investors believe the Fed will always come to the rescue, won’t that provide an incentive to bid up asset prices in a speculative fever (those animal spirits again)? Isn’t that moral hazard?

8. Lorenzo from Oz
27. July 2019 at 18:40

Liked the Farmer & Nicolo paper. But anything that helps gives culture a bit of a look in in a usefully rigorous way gets my tick.

9. Lorenzo from Oz
27. July 2019 at 18:42

Also, I published a paper for the Parliamentary Library years ago that documented that the Philips curve in Australia kept coming and going, so was not remotely a reliable policy tool.

10. John Hall
29. July 2019 at 11:29

I think there’s a lot of interesting stuff in this post.

One area where you start to lose me is on stuff like natural rates. I find natural rates of interest or unemployment can be useful for explaining things, but tricky when starting to get into statistical modelling. Particularly if we are dealing with a central bank, you’ve got to make sure that how they are being evaluated is transparent.

The stuff about natural rates also reminds me of your post in late June where you discuss Mankiw’s chart on the Phillips curve. That was a great post too.

I’m also not sure if you should be conflating NGDP futures with animal spirits, particularly when you consider the original quote. [1].