What Is a Sacrifice Ratio?
The sacrifice rate is the ratio between the cumulative GDP loss and the reduction in the inflation rate during the period of the implementation of the anti-inflation policy.
Sacrifice rate
- This decline in output and employment is an important cost of economic policies to control inflation and must be considered. In simple understanding, the sacrifice rate reflects the cost of reducing inflation, that is, the reduction in the inflation rate by one percentage point, the amount of output decline. It is expressed by the formula: sacrificing rate = percentage of GDP decline ÷ percentage of inflation decline. For example, assuming that the inflation rate has fallen by 2 percentage points and GDP has fallen by 3 percentage points, the sacrifice rate = 3% ÷ 2% = 1.5.
- In fact, in theory, the decline in output cannot be directly reflected by the decline in GDP. In the middle, it is necessary to use the law of Okun (ut-ut-1 = -0.4 (gyt-3%)) and the Phillips curve (t-t -1 =-(ut-4%)) (where gyt, t, and ut represent the output growth rate, inflation rate, and unemployment rate at time t, respectively), so in general, we need to use the law of Okun s law and Phillips curve.
- According to a study by Laurence Ball of John Hopkins University, in the early 1980s, inflation in the United States fell by 8.83 percentage points (from 12.10% per year to 3.27% per year). Ball estimates that during the declining inflation rate in the 15 quarters, the output loss caused by the inflation control policy is about 16.18% of the potential GDP per year.
- Dividing the loss of 16.18% of the potential GDP by 8.83 percentage points of the decline in the inflation rate yields a sacrifice rate of 1.832 during this period. We can argue that in the early 1980s, every 1% reduction in inflation in the United States required sacrificing 1.832% of potential output.
- Ball used quarterly data from nine countries to calculate the sacrifice data for 28 periods of decline in inflation from the 1960s to the 1980s. The table below is the average sacrifice rate that he calculated for different countries. It shows that the cost of output at the expense of reducing inflation varies widely between countries. France, the United Kingdom, and Japan have an average sacrifice rate of less than 1.0, while Germany is almost close to 3.0. In other words, in terms of output, the cost of reducing inflation in Germany is almost three times that of other industrialized countries. Why is that.
- Average sacrifice rates by country
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- Ball found that one factor influencing sacrifice rates across countries is the elasticity of the labor market. Countries with slower wage adjustments relative to labor supply and demand tend to have higher sacrifice rates. The reason is that for countries with inflexible labor markets, more time is needed to adapt to unexpected changes in aggregate demand growth and achieve long-term equilibrium. Ball also found that rapid declines in inflation are slower than slower ones, often at a lower sacrifice rate. This is evidence that a cold turkey approach is beneficial for gradualism.
- One difficulty in calculating the sacrifice rate is that it is difficult to distinguish how much of the decline in output is due to anti-inflation policies. It is difficult to estimate the output without anti-inflation policy. If the calculation of the output loss is wrong, the calculation of the sacrifice rate is also wrong. Supply factors affect both output and inflation, which also interferes with the calculation of the sacrifice rate. Therefore, in the best case, the sacrifice rate is only a rough estimate of reducing the loss of inflation.
- See Ball's article "what determines the sacrifice ratio?" In N. Gregory Mankiw ed., Monetary Policy