## Sunday, September 11, 2016

### If The Mathematics Of New Keynesian Economics Were Solid...

Alexander Douglas has an interesting article on Modern Monetary Theory (MMT) and (mainstream) New Keynesian models. The question is what happens if the economy is at "full employment," and whether the MMT description is better than the New Keynesian analysis. My response is: why are we having this verbal debate in the first place? If the mathematics of the New Keynesian Dynamic Stochastic General Equilibrium were even halfway as rigourous as their proponents claim, they could actually demonstrate their results mathematically, and not wave their hands about vaguely defined concepts like "full employment."

Alex Douglas in "More on Keynesianism, MMT and interest rates":
Central banks, outside the ZLB, have the power to keep the economy at the full employment level with inflation at a target level. Given this, the New Keynesian conclusions follow, regardless of how the state finances its spending.
It works like this: if we’re outside the ZLB and the central bank is doing its job, we’re at full employment with inflation on target. If the state engages in new deficit spending, the extra spending threatens to drive inflation over target. To avoid this, the central bank must raise the interest rate to suppress enough private spending to make room for the new public spending.
It follows that public deficit spending crowds out private investment, just as the textbooks say.

## If We Assume Output Is Maximised...

Defining "full employment" is an interesting question. But let us keep things simple, and assume that the current output is fixed at 100 "units," (which are a basket of goods and services, and is a real quantity, not nominal)  of which 20 units are government spending.

What happens if the government increases its spending to be 22 "units"?

Since we assume that maximum output is 100 units, and there is no reason for total output to fall, the implication is that private consumption drops to 78 units (from 80). The multiplier on government spending to total GDP is 0. All that has happened is that the government share of the economy has increased, at the expense of the private sector (by definition).

Such an outcome is perfectly well understood by Functional Finance (primer), and MMT largely follows Functional Finance. In other words, this is not a point that is disputed by MMT (properly understood).

## What If We Want To Model What Happens To Output?

The analysis I have in the previous section was obviously dodgy. Assuming that output is fixed at 100 units hardly makes sense, and does not even seem to be supported by the mathematical framework used by New Keynesian models.

What we need to do is to actually run the full mathematical model, and see how variables are affected by the change in government spending.

This is the point where the hand-waving starts. Even if we grant all of the obviously incorrect assumptions embedded in New Keynesian models, I still have not seen a worked out solution. The usual dodge is to linearise (model the effects of small disturbances to the baseline scenario) -- which obviously is invalid, since we are making a macroscopic change to the baseline economic scenario. The usual hand waving about changes to fiscal policy is to assume that monetary policy cancels it out (or Ricardian Equivalence does the job), so we can ignore modelling its effects. (The scientific method in action!)

I realise that a fully worked out solution might exist somewhere. However, it is remarkably well hidden, given that it would be quite interesting to study. The reality that mainstream economists revert to hand waving about full employment, instead of actually demonstrating the results within a simulation, reinforces my skepticism.

(c) Brian Romanchuk 2016

1. Is this hand waving thing something I can learn and practice at home? Or does it require an advanced degree...

If Ricardian Equivalence is involved, I guess it requires an advanced degree. It must take many years of education to believe people behave that way.

1. It's some pretty impressive hand waving; I doubt that I could do it myself. Definitely need a doctorate to do it properly.

2. "Central banks, outside the ZLB, have the power to keep the economy at the full employment level with inflation at a target level."

Is this an assumption of NK macro or a proven statement? In the latter case, I would love to see the NK proof. If anyone can point me towards NK papers or books where the case is convincingly argued, I would be really grateful.

1. It's what they are supposed to be proving; however, all of the assumptions are made so to arrive at that pre-determined conclusion. Whether it is actually "proven" depends upon how charitable one is towards their mathematics; every paper I have tried plowing through involved leaps of logic that looked questionable.

The discussion in the NK literature might not describe the results like that; instead they will discuss the effect of how a policy rule (e.g. Taylor rule) stabilises the economic trajectory. The definition of terms like "full employment" tend to be vague.

My best references are in (expensive) textbooks; there are working papers from central banks. (I linked to one published by the Federal Reserve a couple of years ago; they also explained it in blog articles. I believe it was the New York Fed which published it.) I am in the process of getting ready to hop on a plane, so I would have to get back to this later. Let me know if you cannot find references.

3. The kind of references I am looking for are the ones that NK economists would consider to be authoritative, be they textbooks - expensive or not - or papers. I have tried searching online, but I am not sure if I am using the right search terms, or if the references I come up with would be considered to be authoritative by NK economists.
So yes, if you could point me towards what you consider to be good sources, then I would be very grateful.

1. Despite the best efforts of the railway, I made it to the airport. Will give a short response.

I think I have full references in my books (ðŸ˜º), but two I look at are Jordi Gali (forget the title, but it was first year grad students) or Woodford's book (Interest and prices?). The Woodford text has a lot of imposing mathematics, but a lot of stuff relies on the hundreds of references, and I never has the stomach to chase down the reference chain. (When I disparage DSGE mathematics, I always forget to note that book as an exception.) The Woodford book does have a lot of explanation about the philosophy of inflation targeting; it is pre-Crisis, but it covers the non-ZLB case well.

In the public domain, I linked to the New York Fed model. If you run a search on "new york fed DSGE" on this site, it is top result; my title includes the text "the circularity of productivity shocks." The referenced staff paper would also have some leads.

4. Thanks for the reply.

By Gali' s textbook I suppose you mean 'Monetary Policy, Inflation and the Business Cycle'. I had planned to read that book at some point but I decided against it after reading the following sentence in the introduction : ' In the baseline model used in the first part of Chapter 2, as in the rest of the book, money' s role is limited to being the unit of account.[ ...] Its potential role as a store of value[ ...] is ignored.' I may give it another go, although I must say that I cannot immediately see how one can meaningfully discuss inflation if one ignores money as a store of value. Maybe after reading Gali' s book I will understand. I will have a look at Woodford also.