Sacrifice Ratio Formula & Example
By Steve Bain
The sacrifice ratio in economics was first developed in the 1950s in association with the Phillips curve, a curve that depicted a negative relationship between inflation and unemployment. Originally this relationship was thought to be permanent, but that was proven wrong during the 1970s and the events thereafter, and has since been modified to fit a short-term perspective.
Essentially, the sacrifice ratio measures an amount of economic production that must be cut (thereby increasing unemployment) in order to reduce the inflation rate by a given amount (usually one percentage point).
For more background information on the development of these concepts, and subsequent adaptation of the Phillips Curve, have a look at these two articles:
Since the Sacrifice Ratio still has relevance today, both in its relationship to short term output cuts and in its influence on future inflationary expectations, it remains a useful tool for economic policy formulation.
How to work out the sacrifice ratio
While in theory it is a relatively simple concept to understand, it is almost impossible to calculate the sacrifice ratio with absolute precision. The problem is that we are trying to measure moving targets, and we only have estimates of those targets in the first place.
In order to calculate the sacrifice ratio we would need to know precisely what the current level of economic output is, what it would be with a constant rate of inflation, and also what it would be with the inflation rate reduced by 1 percentage point. Of course, we only have estimates of inflation and output to work with, and economic forecasts are notoriously inaccurate.
Nevertheless, despite these difficulties economists do use a branch of statistics called econometrics to try and work these numbers out.
Okun's Law estimates the relationship between output and unemployment, and the short-run Phillips curve estimates the relationship between inflation and unemployment. Using these measures we can derive some idea of the sacrifice ratio formula.
Sacrifice Ratio Formula
Using the short-run Phillips curve with inflation expectations held constant, we can estimate how much the unemployment rate will rise when the inflation rate falls by one percentage point.
Next, Using Okun's law, we can estimate how much output will fall given a one percentage point increase in unemployment.
We then simply multiply those two ratios together:
Sacrifice Ratio = Phillips ratio x Okun's ratio
Naturally, this gives only a very rough idea of what the sacrifice ratio is.