# Nominal vs real growth of monetary base

Can someone clarify the difference between nominal and real growth of monetary base? I believe it is the policy of some central banks to target for example 0% nominal growth in the monetary base. What would an example of 0% real growth target be - nominal growth of say 2% but inflation also of 2%?

Are there advantages or specific motivations of designing policy according to one vs the other?

For this question, its useful to work off of the equation of exchange. Let's start with the equation:

MV=PY

M = the money supply, V = Velocity of Money, P = Price level, Y = real output

Log both sides

ln(MV)=ln(PY)

Split the terms up according to log properties

ln(M) + ln(V) = ln(P) + ln(Y)

Take the derivative of each term so that we have

dM/M + dV/V = dP/P + dY/Y

to define each of these, dM/M = the rate of change of the money supply(nominal), dV/V = the rate of change of the money velocity, dP/P is the inflation rate, and dY/Y is the real GDP growth rate.

Real Money growth is but a simple algebraic manipulation by doing as such:

dM/M - dP/P = dY/Y - dV/V

Real Money growth = dY/Y - dV/V

Real money growth must be correlated with real GDP growth. The money supply can only be said to have increased in "real" terms if the quantity of goods and services that the money supply can purchase has increased.

So we can see that if we wanted to have 0% real money growth, we would simply need to have the rate of change of the money supply be equal to the inflation rate, or alternatively the real GDP growth rate be equal to the rate of change of the money velocity.

However, we can also see clearly that a nominal money supply increase of 0% is likely undesirable. If dM/M is just 0, then a positive value on the right side, which is to mean that real GDP is expanding faster than money velocity is increasing, the result will be deflation.

As to policy implications, central banks usually no longer target monetary aggregates, as they tend to be unreliable and volatile. Central banks these days target interest rates or alternatively there is some interest in targeting a certain growth of the nominal GDP, which is just the MV of the MV=PY equation (or P*Y if you like). The main disadvantage of interest targeting is that the central bank can be said to have "run out of ammo" in a sense when it pushes interest rates down to the zero lower bound. This is to mean that the target rate can not go below zero, so the stance of the Fed cannot become more expansionary past this point. This is important as the stance of the Fed is derived from the position of the target rate relative to the natural rate of interest. If there is a shortfall in spending in the economy, and the natural rate of interest falls to zero, then The Federal Reserve can be said to have no power in this situation. Even if it were to drop interest rates to zero, the effect would be a neutral stance, which is highly undesirable in a recession. Recommended reading on the subject: https://www.brookings.edu/blog/ben-bernanke/2017/04/12/how-big-a-problem-is-the-zero-lower-bound-on-interest-rates/