# 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.