One of the most important ideas to emerge from market monetarist writing in the blogosphere, in my opinion, is the “Sumner critique.” This critique named after Scott Sumner has been worded many different ways, but I would state it like this:

If the Fed is successfully stabilizing a nominal anchor – e.g. if the Fed is successfully maintaining 2% inflation or 5% NGDP growth – then the fiscal multiplier will be zero, since the Fed will offset any fiscal impact on aggregate demand.

Two important caveats. First, fiscal stimulus or austerity can still have real effects through supply side effects. Even if the Fed tightens policy after a tax cut, that tax cut will still be beneficial by reducing incentive distortions.

Second, if the Fed is not doing its job, the fiscal multiplier might not be zero. The word “successfully” is an important one in the definition.

The intuition is very straightforward. If Congress passes fiscal stimulus to boost demand, higher demand will boost inflation (and NGDP growth, if that is the Fed’s target), and the Fed will offset it by tightening monetary policy. If Congress cuts spending or raises taxes to reduce the deficit, that will reduce inflation (and NGDP growth), and the Fed will offset it by loosening monetary policy.

The important implication is that Congress should have no role in responding to recessions, since stimulus will only increase the national debt and replace action that the Fed would have taken anyway, which would not have increased the national debt. Additionally, if Congress implements austerity, one should not be extraordinarily concerned about the economic effects except for the supply-side consequences.

This is the tenet of market monetarism which has been the hardest for progressive supporters of the movement to accept.

In this post, I want to walk through a simple model to demonstrate that the Sumner critique is accurate, and what assumptions are necessary to the model to produce the result. The model is from a 1998 paper by Nick Rowe and Simon Power. By walking through the assumptions in the model, we can see what needs to be true for the Sumner critique to be accurate.

The model

The model is a game theoretic one. There are two players, Congress (which controls fiscal policy) and the Fed (which controls monetary policy). Aggregate demand (AD) is determined by the sum of fiscal policy (F) and monetary policy (M).

AD = F + M

Neither Congress nor the Fed intrinsically cares about the level of monetary policy. M only matters for its effect on aggregate demand.

On the other hand, Congress and the Fed both care about the total amount of fiscal policy, F. Both have the same optimal target for fiscal policy F*. If F is too low then perhaps the roads start to crumble, too high then the tax burden will be too high, or the debt will grow too much.

Congress and the Fed also both care about the total level of aggregate demand. Neither wants it to be too high for fear of inflation or too low for fear of recession. However, they disagree about the optimal level of AD.

Assume that Congress wants AD to be higher than the Fed does. Perhaps Congress wants higher inflation to reduce the debt, or hopes that higher than expected inflation in the short run will boost employment and thus popular support.

A*F > A*M

We can represent Congress’ and the Fed’s dissatisfaction as actual fiscal policy F diverges from desired fiscal policy F* and as actual aggregate demand AD diverges from desired aggregate demands AD*F and AD*M respectively. We assign each a loss function that is quadratic, though the form of the loss function isn’t important.

LF = (F – F*)2 + (AD – AD*F)2

LM = (F – F*)2 + (AD – AD*M)2

It is clear that Congress and the Fed each has to take into account the other’s action when setting its own policy to best achieve its objective. But what type of game is this?

The game type that makes most sense to me is known as Stackelberg competition. In Stackelberg games, one player moves before the other. In this case, it makes sense for Congress to move first and set F. After viewing this action, the Fed moves and sets M.

My argument would be that Congress is slow-moving and typically only sets the level of spending and taxation once a year (…if it’s doing its job). The Fed, meanwhile, meets every six weeks to decide policy and can meet more frequently if conditions warrant.

Congress thus optimizes first. It seeks to minimize its loss function, LF. It knows that no matter the F that it chooses, the Fed will be able to set M such that aggregate demand equals the Fed’s goal. That is, the Fed’s reaction function is M = AD*M – F.

Proof:

min [choose M] LM = (F – F*)2 + (AD – AD*M)2

Substitute for the definition of AD

min [choose M] LM = (F – F*)2 + (M + F – AD*M)2

Take the first order condition (second order conditions check out)

dLM/dM = 2M + 2F – 2AD*M = 0

Solve

M = AD*M – F

Bingo! This is the essence of what we’re trying to show. The Fed will always set M to offset any attempted manipulation of AD by Congress. Realizing that the level of F chosen will have no impact on aggregate demand, Congress sets F = F* so it can at least perfect that objective.

Mathematically:

min [choose F] LF = (F – F*)2 + (AD – AD*F)2

s.t. M = AD*M – F

Plug in the constraint to the objective function (AD*M = M + F = AD)

min [choose F] LF = (F – F*)2 + (AD*M – AD*F)2

Take the first order condition (second order conditions check out)

dLF/dF = 2F – 2F* = 0

Solve

F = F*

Then the Fed chooses M such that AD is precisely what it wants. M = AD*M – F* and AD = AD*M.

The Sumner critique mechanism is evident here, where Congress refuses to engage in any sort of Keynesian aggregate demand management because it rationally anticipates the monetary offset cited by Sumner.

What assumptions were necessary?

As with any model, this one requires assumptions about how the economy works. As a particularly simple model, this one has quite a few. Below I pick out a few key assumptions and discuss whether they are necessary to achieve the result that the Sumner critique is accurate.

Assumption 1: The Fed can affect aggregate demand precisely as much as desired.

This assumption might seem very important to the conclusion (and the real life accuracy of it, even as a very good approximation, is certainly debatable), but it’s not.

Say we instead said that the Fed sets M, but that AD = M-bar + F, where M-bar = M + ϵ and ϵ is a random error term normally distributed around zero.

(If the error was distributed around anything else, that would mean that the Fed is incompetent, and would be a serious issue. Plausibly, one could argue that the Fed is incompetent when the fed funds rate is near zero since it seems to believe itself to be impotent.)

This error term means that sometimes fiscal stimulus would have a positive ‘net’ multiplier – but that also sometimes it would have a negative one! The expected value of any kind of stimulus, however, would still be zero, and Congress would thus still not attempt to influence AD.

Assumption 2: The Fed is the Stackelberg follower and moves second.

In some respects this is the key assumption, at least for the intuition behind the Sumner critique. However, Rowe and Power show in the paper that even if the game is simultaneous Nash – i.e., Congress and the Fed set their policies at the same time without seeing what the other player is going to do – AD ends up being equal to AD*M. In other words, the Sumner critique still holds.

It is true that if Congress is modeled as the Stackelberg follower, than AD ends up higher than desired by the central bank (but still not as high as Congress wants it). But this assumption seems implausible.

The one argument that could be made here is that monetary policy impacts the economy with long lags. This actually what many argue, saying for example that the Fed is unable to offset spending cuts like the sequester since any actions it takes won’t have any effect until it is too late.

Such an argument is worthy of another post, but suffice it to say that the supposed problem of monetary policy lags is vastly overblown. As most economists accept today and all dominant DSGE models assume, the most important aspect of monetary policy is its effects on expectations. If the Fed is expected to offset spending cuts, even if it cannot do so right away, the fact that it is expected to do so in the near future is highly stabilizing.

Assumption 3:The Fed’s reaction function is invariant to fiscal policy.”

This assumption was pointed about by Noah Smith. I quote his example: “Consider a world in which the Fed targets a 3% growth rate for NGDP if there is no stimulus, but raises the growth rate target in the event of a stimulus. In this case, it would make perfect sense to say "fiscal stimulus increased NGDP growth," in the sense that we normally think of causality.”

This is an important point, but there doesn’t seem to be any reason to believe that the Fed’s goals change if Congress changes the level of fiscal policy.

In conclusion, the important assumptions underlying the simple model outlined above that demonstrates the Sumner critique seem reasonable.

 

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