How to Calculate the Sacrifice Ratio
The sacrifice ratio equals the cumulative percent of one year's output given up divided by the percentage-point fall in inflation that the squeeze bought.
The Sacrifice Ratio formula
Calculator
Enter the yearly output gap, how long it lasted and the inflation rates to get the output cost of the disinflation.
How far real output ran under potential in a typical year of the squeeze.
Length of the period output stayed below potential.
The rate the central bank set out to bring down.
The rate once the disinflation was finished.
Used to price the lost output in dollars rather than percentage points.
Removing one percentage point of inflation cost 1.2 percentage points of a year's output.
- Cumulative output lost
- 6%
- Fall in inflation
- 5%
- Output lost, billions of dollars
- $1,200
- Reading
- More than 1 point of output per point
Adding the yearly gaps gives 6% of one year's output forgone across the whole episode.
Inflation came down 5%, measured in percentage points rather than as a percent change.
Applying the cumulative loss to potential GDP puts the cost at $1,200 billion of output never produced.
A larger ratio means the disinflation bought each point of lower inflation with more lost output, which is what credibility reduces.
How to calculate Sacrifice Ratio, step by step
- 1Measure the output gap each year. For every year of the squeeze, take actual real output as a percent below potential output.
- 2Add the yearly gaps. Summing them gives the cumulative loss, stated in percentage points of a single year's output.
- 3Measure the disinflation. Subtract the inflation rate at the end from the rate at the start, in percentage points.
- 4Divide. Cumulative output lost divided by the fall in inflation gives the output cost of removing one point of inflation.
- 5Price it if you want dollars. Multiply the cumulative percent lost by potential GDP to turn the ratio into output the economy never produced.
Worked example: Sacrifice Ratio
A central bank drives inflation from 9% down to 4% while real output runs 2% below potential for three years. Cumulative output lost = 2 × 3 = 6 percentage points of a year's output, and inflation fell 9 − 4 = 5 points, so the sacrifice ratio = 6 ÷ 5 = 1.2. With potential GDP of $20,000 billion, the disinflation cost 6% of 20,000 = $1,200 billion of output.
Sacrifice Ratio questions
What makes the sacrifice ratio smaller?
Credibility. When workers and firms believe the central bank will hold the line, they cut expected inflation right away, so less of the adjustment has to come out of output and jobs.
Why is a disinflation costly at all?
Wages and prices set in advance do not move the moment policy tightens, so tighter money hits output first and inflation only later. That lag is the cost the ratio measures.
How does the ratio relate to the Phillips curve?
It is the short-run trade-off written as a single number. A flatter short-run Phillips curve means more output has to be given up for each point of disinflation, so the ratio is larger.
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