# Simon Wren-Lewis, MMT, maths

Simon Wren-Lewis has written a series of posts on MMT — ‘Modern Monetary Theory’. He wrote these, from what I can tell, because every time he writes a post on macroeconomic policy he receives many replies, varying in politeness, from online followers of MMT. Here is the latest. I was asked, so I’ll write a brief reply (please forgive me for rushing, as it’s start of term and I’m meant to be doing other things).

#### On Policy

For brevity’s sake, I’m going to skip over the stuff on macroeconomic policy, except to say this: The big difference between MMT and mainstream macro on *policy*, Wren-Lewis says, concerns whether or not monetary policy is a useful tool for fighting inflationary and recessionary forces in the economy. Wren-Lewis claims that there is a lot of empirical evidence to suggest that it is, most of the time, but so far as I know he never links to any. It’s a lot to take *ex cathedra*, especially since there are substantial econometric studies claiming to show otherwise (here’s one example).

#### On Method

Since I work on the philosophy of macroeconomics, I’m more interested in Wren-Lewis’s methodological criticisms of MMT:

the things that annoy me about MMT are trivial, like a failure to use equations and their wordplay. You will hear from MMTers that taxes do not finance government spending, or that spending comes first, but you will hardly ever see the government’s budget constraint which makes all such semantics seem silly.

This doesn’t seem fair to me. If you look just at introductory sources — Randall Wray’s primer on MMT, Wray and Bill Mitchell’s macro textbook, Warren Mosler’s *Soft Currency Economics** — *you’ll find many equations, including various forms of the government ‘budget constraint’ (though they don’t call it that). This is to say nothing of the academic papers by MMTists, which are, as you’d expect, far more heavy on equations (e.g.).

MMT blogs might not often use equations (although Bill Mitchell’s does, as does Brian Romanchuk’s — both of them were trained as applied mathematicians). But it’s only fair to note that equations rarely appear on the mainlymacro blog. It would be silly to conclude from this that Wren-Lewis’s school of macro is averse to equations; his academic papers are, of course, full of them.

The *specific* equation Wren-Lewis thinks that MMTists should write down is the government budget constraint(GBC). I’m not sure if he means the basic GBC or the intertemporal version. The basic constraint is an accounting identity which is almost too obvious to write down. One extremely streamlined version appears in a critique of MMT by Thomas Palley (now apparently taken offline):

the government budget constraint [is] given by

(1) G-T = θ + β

G = government spending, T = net tax revenues after transfers and interest payments, θ = amount of budget deficit financed by issuing high-powered (sovereign) money, and β = amount of budget deficit financed by selling government bonds.

If that’s the equation Wren-Lewis means (he himself doesn’t write it down!), I don’t see how it “makes all such semantics seem silly” with regard to MMT’s operational analysis of the order of fiscal operations. Eric Tymoigne and Randall Wray have an extensive reply to Palley and other critics, discussing this GBC equation in some detail. They do at least try to explain why simply writing it down doesn’t make everything they have to say about fiscal operations ‘seem silly’.

Here is why I don’t think it’s silly. One way you might interpret the equation is as follows. First the government chooses the size deficit it wants: some value for G-T, which I’ll call D. Next, it chooses how much of D it will finance by selling bonds and how much by ‘issuing high-powered money’. **The range of possible solutions for (1) will then include all values of (D, θ, β) such that θ+β=D, i.e. the set {(D, θ, β) | θ+β=D}.** I think many macroeconomists do interpret it this way; Palley seems to, and at times I have thought Wren-Lewis did too, though I’m not sure.

But now suppose the following. First, the government *tries* to target some deficit level D. It then tries to fund this by selling a certain number of bonds — thus it tries to target β. But then the central bank, in order to maintain its interest rate target, either buys or sells bonds, changing the values of β and θ from those which the government was targeting. Next, people’s spending decisions change in response to these central bank operations. This changes the value of T, thus of D. So now **the range of possible solutions for (1) will be restricted to a proper subset of {(D, θ, β) | θ+β=D}. **The restriction will be expressible as some function f(G,T,β,θ)**,** which will reflect a wide range of structural features of the economy — not only operational facts of the sort cited by MMT but also features such as the public’s propensity to respond to policies (and each other’s decisions) in various ways.

Wren-Lewis would presumably agree with some of this. He is himself a proponent of microfoundations, so he would presumably agree that the viable solutions to the government budget constraint will be restricted by the effects of policy on the behaviour and expectations of households and firms. But then by the same token it will depend on the effects of government policy on central bank policy and vice-versa.

Building a correct *causal* model of these effects would surely require us to know the order of fiscal operations. If I want to understand how an engine works, I need to know which parts move first so I can know which parts move others and which are moved by others. Why, then, might mainstream macroeconomists like Wren-Lewis think that the actual order of spending and financing operations is irrelevant in this case?

I suspect it’s because mainstream macroeconomics doesn’t care about causation; in fact, insofar as mainstream macro works via general equilibrium solutions, it *can’t* reasonably care about causation. There simply is no realistic causal explanation of how a general equilibrium comes about, since every unit must be assumed to be a price-taker (maybe with some stochastic Calvo stuff mixed in). In the background, there’s always some implicit appeal to a Walrasian auctioneer, or some other purely hypothetical mechanism for bringing historical processes into the citadel of eternity to become a problem with an instantaneous solution.

But MMTists, like many heterodox economists, don’t work with general equilibrium models. So for them the order of operations does matter. The complex function f(G,T,β,θ), which specifies the range of possible solutions to the GBC, will depend on operational and behavioural factors; it won’t be the outcome of an abstract Walrasian problem. What happens and *when* it happens will matter a great deal.

That’s my best current attempt at explaining where Wren-Lewis might be coming from, if he’s thinking of the GBC in this basic sense.

The other possibility is that he’s thinking of the transversality condition on the intertemporal GBC, i.e. the condition that looks something like this:

Here the current stock of government debt, Bt, must equal the entire discounted stream of future primary surpluses. More complicated versions add terms for expectations, etc.

All this is, in my opinion, both logically and mathematically monstrous. Put aside the very misleading notation that makes what is actually a statement of a *limit*, which is in turn a proposition of analysis, look like an ‘infinite sum’. Worse problems lie deeper. If you construe the IGBC on a finite time-horizon, there’s no reason to assume transversality: when the asteroid hits or the government collapses there might be many people left holding debt in excess of the sum of discounted future surpluses equal to the value of current debt. And if you construe it on an infinite time horizon there’s still no reason to assume transversality, since you can’t run the backward induction that grounds the assumption that people will value debt by its real return rather than what they can sell it on for (see this post). To repeat my slogan: *had we but world enough and time, a Ponzi scheme would be just fine*.

So I hope Wren-Lewis doesn’t mean to excoriate MMTists for not writing down *that* equation. I don’t think anyone should write it down, except for the purpose of warning others.