# Two residuals multiplied become an illusion

You are a Monetarist.

You think Y=C+I+G+NX is just an identity, it doesn’t tell you much.

You believe fiscal policy is ineffective.

You believe the Keynesian multiplier is Zero.

You believe in the Sumner Critique.

Hence, the multiplier is nothing more than an ILLUSION, the shadow of Central Bank incompetence.

You are a Keynesian.

You believe fiscal policy is effective.

You believe monetary policy is effective (except in the Zero Lower Bound).

Monetary Policy is conducted through variations in the Monetary Base (which may affect interest rates).

You think M=mB is just an identity, it doesn’t tell you much.

Hence, the Money Multiplier is just a RESIDUAL.

You think MV=PY is just an identity, it doesn’t tell you much.

Therefore, the Money Velocity is just a RESIDUAL.

Let’s all be friends again?

Imagine two things:

You have a lot of unemployed resources in the economy, so an expansionary policy will only move Y (P is fixed).

You shall use a Helicopter Money. A Money Financed Deficit. Monetization. Whatever you want to call it.

Basically the Government spends newly-printed (or newly electronically  created) Monetary Base.

What will happen???

Hyperinflation!!! Zimbabwe! Weimar!

Nope.

Let’s build an example.

So, we have have dG= 1000 and dMB =1000.

The increase in Government Spending somehow (magic?) increases Output (Y) in 3000.

So… the Keynesian multiplier (dY/dG) of the increased spending would be 3.

Shall we continue? Of course.

We  know mBV=PY. We know P is constant (assumption), we know the Monetary Base increased 1000, and Real Output increased 3000 (multiplier effect).

So..By definition, we must have that the effect of the Money multiplier and Money velocity should lead to an increase in Output of 3000, given the increase of 1000 in the Monetary Base.

Basically the expansionary effect will be the result of the Money multiplier and the Money velocity, which must “multiply” the increase in Monetary Base by….3.

Some caveats:

1. We can’t (in this model) disentangle which (V or m) “multiplies” the Monetary Base into Real Output, we must assume it’s a combination of both the indicators
2. The Keynesian multiplier is about a flow, (an increase in GDP), the Money multiplier and velocity are about a Stock (the Money stock), so in this example both the multiplier and velocity represent variations of the Base (flow)

But in the end of the day, we can say this:

(Using flows, using deficit monetization and assuming fixed prices)

The Keynesian Multiplier is equal to the Money Velocity times the Money Multiplier

Or as I said in the tittle

Two residuals multiplied become an illusion

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