How to Calculate Seigniorage
Real seigniorage equals the increase in the monetary base divided by the price level, the real resources a government collects by putting new money into circulation.
The Seigniorage formula
Calculator
Enter the rise in the monetary base, the price index and money held by the public to get real seigniorage and the inflation tax.
Currency plus bank reserves at the end of the period, minus the same total at the start.
The price level today against a base year set to 100.
The nominal stock of money the public is holding, before deflating.
How fast the price level is rising, which sets the rate of the inflation tax.
Issuing the new money buys $50 billion of real resources, measured in base-year dollars.
- Real money balances
- $800
- Inflation tax
- $40
- Value lost to the price level
- $10
- Seigniorage against the inflation tax
- Seigniorage is larger
The cash the public holds is worth $800 billion in base-year terms, and this is the base the inflation tax is charged on.
Rising prices strip $40 billion of purchasing power from the people holding money, whether or not anyone calls it a tax.
The face value issued is $60 billion, so $10 billion of it is priced away before the government spends a cent of it.
The two line up when new money is what drives prices, and separate when a growing economy absorbs the new money without inflation.
How to calculate Seigniorage, step by step
- 1Measure the rise in the monetary base. Currency in circulation plus bank reserves at the end of the period, minus the same total at the start. That difference is the new money issued.
- 2Deflate it by the price level. Divide by the price index and multiply by 100, which restates the revenue in base-year dollars instead of face value.
- 3Deflate the money the public holds. Run the money stock through the same index so real balances and real seigniorage are quoted in the same units.
- 4Multiply real balances by the inflation rate. That product is the inflation tax, the purchasing power money holders lose while the issuer gains.
- 5Compare the two figures. They line up when new money is what drives prices, and separate when a growing economy absorbs the new money without prices rising.
Worked example: Seigniorage
The monetary base rises by $60 billion while the price index sits at 120, so real seigniorage = (60 ÷ 120) × 100 = $50 billion of base-year purchasing power. The public holds $960 billion of money, worth (960 ÷ 120) × 100 = $800 billion in real terms, so with inflation at 5% the inflation tax = 0.05 × 800 = $40 billion.
Seigniorage questions
Is seigniorage the same as the inflation tax?
No. Seigniorage is the revenue the issuer collects by putting new money into circulation, while the inflation tax is the real loss borne by everyone already holding money as prices rise. The two land close together when fast issuance is what causes the inflation, and come apart when a growing economy absorbs new money quietly.
Why does issuing more money eventually raise less real revenue?
Because the tax base shrinks as the rate rises. Faster issuance means faster inflation, and inflation pushes people to hold less real money, spend it sooner or switch to a foreign currency. Past some point each extra unit of issuance collects less than the last, which is the mechanism behind hyperinflation.
Where does a modern central bank's seigniorage come from?
Mostly from net interest rather than the printing press. The bank issues currency and reserves that pay little or nothing, holds interest-bearing government securities against them, and remits the spread to the treasury. Profit on printing notes is small once most money is electronic.
What if the price level is given as 1.2 instead of 120?
Then divide and stop, with no multiplying by 100. The extra factor of 100 only undoes an index that was scaled with the base year set at 100. Mixing the two conventions moves the answer by a factor of 100, which is the most common slip on this calculation.
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