Hanke’s Golden Growth Rate

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If money grows too fast, inflation rises; if it grows too slowly, the economy stalls. Evidently, Monetarism explains why inflation happens, but it also raises a practical question: if a country wants stable prices by setting an explicit target, how fast should its money supply grow? Luckily, The Quantity Theory of Money guides us to an exact number. The magic number for money supply growth that achieves a specific inflation target is called the Hanke’s Golden Growth Rate. It gives a simple rule of thumb for keeping inflation on target.

Deriving the Magic Number—Hanke’s Golden Growth Rate

This page shows how Hanke’s Golden Growth Rate (GGR) follows directly from the Quantity Theory of Money. The goal is simple: connect a country’s inflation target to the correct growth rate of money.

The formal math is straightforward—and the intuition matters just as much.

1. The Starting Point: Quantity Theory of Money

The Quantity Theory of Money is summarized by a single identity:

M×V=P×Y

where:

M = money supply
V = velocity of money
P = price level
Y = real GDP

Both sides of the equation equal nominal GDP.

This identity holds at all times. What changes is how each component evolves.

2. From Levels to Growth Rates

Start from:

M \times V = P \times Y

Take the time derivative of both sides:

M'V + MV' = P'Y + PY'

Divide both sides by MV = PY:

\frac{M'}{M} + \frac{V'}{V} = \frac{P'}{P} + \frac{Y'}{Y}

In percentage changes:

\%\Delta M + \%\Delta V = \%\Delta P + \%\Delta Y

3. The Golden Growth Rate

Rearranging the growth-rate identity gives money growth as a function of inflation, real output growth, and velocity growth:

GGR \coloneqq \%\Delta M = \%\Delta P + \%\Delta Y - \%\Delta V

This is Hanke’s Golden Growth Rate (GGR).

In words: to hit an inflation target ( $\%\Delta P$ ), set money growth ( $\%\Delta M$ ) equal to the inflation target plus real GDP growth ( $\%\Delta Y$ ), minus the change in velocity ( $\%\Delta V$ ).

4. Notes on Implementation

In GGR calculations, the long-run average percentage change in money velocity for the upcoming period is estimated using data from a representative historical period.
The same approach applies to estimating long-run real GDP growth, or alternatively, published economic forecasts may be used.
For many developing economies, the long-run average percentage change in money velocity typically lies between −2% and −3%.
The Golden Growth Rate is therefore forward-looking, serving as a monetary policy guideline.