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Lars Christensen Mail: lacsen@gmail.com Phone: +45 52 50 25 06 Speaker agency: spealistspeakers.com Mail: daniel@specialistspeakers.com

# Dude, here is your model

Here is Scott Sumner:

“Whenever I get taunted about not having a “model,” I assume the commenter is probably younger than me, highly intelligent, but not particularly wise.”

So Scott has a problem – he does not have a fancy new model he can show off to the young guys. Well, Scott let me see if I can help you.

Here is your short-term static model:

An Eaglian (as in David Eagle) equation of exchange:

(1) N=PY

Where N is nominal GDP and P is the price level. Y is real GDP.

An Sumnerian Phillips curve:

(2) Y=Y*+a(N-NT)

Where NT is the target level for nominal GDP and N is nominal GDP . Y* is trend trend RGDP.

(1) is a definition so there can be no debate about that one. (2) is a well-established emprical fact. There is a very high correlation between Y and N in the short-run. If you need a microfoundation that’s easy – it’s called “sticky prices”.

N (and NT) is exogenous in the model and is of course determined by the central bank. And yes, yes N=MV where  M is the money and V is velocity.

In the short run P is “sticky” and N determines Y. Hence, the Sumnerian Phillips curve is upward sloping.

If you want a financial sector in the model we need to re-formulate it all in growth rates and we can introduce rational expectations. That not really overly complicated. Bond yield is a function of expected growth nominal GDP over a given period and so is stock prices.

In the long-run money is neutral so Y=Y* …so if you need a model for Y* you just go for a normal Solow growth model (or whatever you need…). I the long run the Sumnerian Phillips curve becomes vertical.

It don’t have to be more complicated than that…

That said, I think it is very important to demand to see people’s models. In fact I often challenge people to exactly spell out the model people have in their heads. That will show the inconsistencies in their arguments (the Austrian Business Cycle model is for example impossible to put on equations exactly because it is inconsistent). Mostly it turns out that people are doing national accouting economics and there is no money in their models – and if there is money in the model they do not have a explicit modeling of the central bank’s reaction function. So Scott you are certainly wrong when you tell of to get rid of the models. The problem is that far too many economists and especially central bankers are not spelling out their models and their reaction functions. I would love to see the kind of model that make the ECB think that monetary policy is easy in the euro zone…

That damn loss function

Scott further complains:

“Some general equilibrium models are used to find which stabilization policy regime is optimal from a welfare perspective.  Most of these models assume some sort of wage/price stickiness.  And 100% of the models taken seriously in the real world assume wage/price stickiness.  The problem is that there are many types of wage and price stickiness, and many ways of modeling the problem.  You can get pretty much whatever policy implication you want with the right set of assumptions.  Unfortunately, macroeconomists aren’t able to prove which model is best.  I think that’s because lots of models are partly true, and the extent to which specific assumptions are true depends on which country you are looking at, as well as which time period.  And then there’s the Lucas Critique.”

Translated this mean that implicit in most New Keynesian models is a assumption about the the central bank minimizing some sort of “loss function”. The problem with that is that assumes that there is some kind of representative agent. In terms of welfare analysis of monetary policy rules that is a massive problem – any Austrian economist would (rightly) tell you so and so would David Eagle. See my earlier post on the that damn “loss function” here.

Scott has one more complaint:

“To summarize, despite all the advances in modern macro, there is no model that anyone can point to that “proves” any particular policy target is superior to NGDPLT.  There might be a superior target (indeed I suspect a nominal wage target would be superior.)  But it can’t be shown with a model.  All we can do is construct a model that has that superiority built in by design.”

Scott, I am disappointed. Haven’t you read the insights of David Eagle? David has done excellent work on why NGDPLT Pareto dominates Price Level Targeting and inflation targeting. See here and here and here. Evan Koeing of course makes a similar point. And yes, neither David nor Evan use a “loss function”. They use proper welfare theory.

Anyway, no reason to be worried about models – they just need to be the right ones and the biggest complaint against most New Keynesian models is the problematic assumption about the representative agent. And then of course New Keynesian models have a very rudimentary formulation of asset markets, but that is easy to get around.

PS I am sure Scott would not disagree with much what I just wrote and I am frankly as frustrated with “models” that are used exactly because they are fancy rather because they make economic sense.

1. #### Alex Salter

/  May 29, 2012

“Austrian Business Cycle model is for example impossible to put on equations exactly because it is inconsistent”

Et tu, Lars?

2. #### Lars Christensen

/  May 29, 2012

Alex, then I wrote it I knew I would just have to sit around and wait for somebody from GMU get back to me – or maybe Steve “Rush” Horwitz;-)

Anyway, I of course need to answer that question…but my problems with Hayek’s business cycle is pretty much along the lines of the so-called Wilson-Kalder-Hayek debate about the so-called Ricardo effect.

Anyway, mentally I need a bit more time to write about this, but please remind me of this. I would love to write a post on this late.

3. #### Alex Salter

/  May 29, 2012

I don’t mind the “ABCT is inconsistent” so much. Business cycle theory is contentious, and there are many respectable competing theories. What I have a problem with is the “If it can’t be put in mathematics, it’s worthless” mindset. Mathematical and verbal logic are one in the same. There are costs and benefits for expressing one’s ideas in either form. To assert one is superior to the other is to overlook the fact that the rules of logical inference are the same no matter the language in which we’re speaking. It’s a short step away from polylogism/historicism, doctrines which are rightfully consigned to the dustbins of intellectual history.

4. #### Lars Christensen

/  May 29, 2012

Alex, I totally agree. Math and logic is the same and I share your and Scott’s dislike like of mathematical that is just there to be mathematically impressive and not provide us with any economic inside.

So when I talk of “models” I do not necessarily think of it as mathematical model. They might be verbal logical models as well. In fact I prefer those when I read and write about economics. My claim is just that if it can not be formulated mathematically then it is probably because it is logically inconsistent.

Again, Scott does need a formal mathematical model – his verbal logic certainly strong enough to make a very forceful argument.

5. #### Alex Salter

/  May 29, 2012

From your response I think I might’ve misinterpreted your original argument. I apologize, and I’m glad that we agree on this!

One question: You assert that “… if it can not be formulated mathematically then it is probably because it is logically inconsistent.” This leads me to ask, How would you model capital mathematically, if you take an Austrian approach to capital? Austrian capital theory heavily stresses heterogeneity (and rightly so, IMO). However, you can’t just say, “Okay, in my model K will be an n-dimensional vector rather than a scalar. Voilà, heterogeneous capital!” When Austrian and Austrian-influenced economists talk about heterogeneous capital, the ideas they have in mind are far more complex.

I use the capital example to highlight the following point: when we’re theorizing about the economy, we frequently discuss things that are important, but imprecise. You can’t go and point to any one thing and say, “THAT’S what I mean by ‘capital structure!'” but that doesn’t mean the idea of capital structure is unimportant. In this case, verbal logic and its semantic flexibility is probably the best technique. There are other instances where syntactic precision might be relatively more important than semantic flexibility -some areas of game theory come to mind -but there are likely just as many where the opposite is true. That’s why I’m hesitant to even embrace the “probably” in your statement that I quoted.

6. #### Lars Christensen

/  May 29, 2012

Alex, Phew…capital? That is a hard one. Just think what Hayek tried to write about it. Anyway, I think you should consult Nicolai Juul Foss’ new book written with Peter Kiein: http://www.cbs.dk/For-Virksomheder/Alumni/Alumni-News/Menu/Alumni-News-2012/Alumni-News-2012/Maj-2012/Hoejreboks/New-book-Organizing-Entrepreneurial-Judgment

Nicolai if an expert on capital…and I have no clue;-)

7. #### Martin

/  May 30, 2012

Oh that looks nice Lars; quick and dirty estimate:

(2) Y=Y*+a(N-NT)

Y* = 3
a = 0.75
NT = 5.5

RGDP = 3 + 0.75 * (GDP-5.5)

Period is 1980ish to now.

http://research.stlouisfed.org/fredgraph.png?g=7z7

In fact, I’d almost say that the calculated version of Y is better than the official data :P.

• #### Lars Christensen

/  May 30, 2012

Martin,

Yeah I told you it there was a strong empirical correlation, but thanks that is excellent. I hope to have time to do a follow up note to include your “estimate”.

8. #### Mike Sax

/  June 12, 2012

Lars I’ll say one thing for your model here. It’s the first economic model I’ve ever read that I’ve actually been able to folllow. Usually after about 3 steps I’ve lost track about what all the different letters and symbols repressent!

9. #### TomGrey

/  June 12, 2012

Fine model.
Small typo: Where NT is the target level for nominal GDP and NT is the target level for NT. Y* is trend trend RGDP.

What is NT? What is N?
NT is target level for nominal GDP (5.5 from Martin);
N is nominal GDP as measured.

But what happens when this model works during the prior 20-25 years, but the growing house price trend of those years was actually long-term unsustainable?
The huge loss of wealth of so many Americans has probably created a different environment, especially when combined with demographics (the population neutron bomb, in Europe).

10. #### Lars Christensen

/  June 12, 2012

Tom, Oops that for pointing out that typo. N is nominal GDP and NT is the target for nominal GDP. It has been corrected in the text.

Well, the Federal Reserve determines nominal GDP (remember MV=N=PY). It is simply a matter for the the Fed to choose a path for M given the long term trend in V and Y.

Demographics can influences Y, but not N. P will be determined as a residual between Y and N – so if Y grows slower due to for example democraphic then inflation (growth in P) will be higher given a fixed nominal GDP target.

Obviously the Fed never officially had a nominal GDP target, but it nonetheless look as if it did have such a target. Clearly that is no longer the case and one of the key problems going forward is a tremendous uncertainty about what the Fed actually targets.