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A weighted average is the summation of variables, each of which are each multiplied by their relative weight.
In order to calculate aggregate inflation a weighted average is used. The ECB multiplies each county’s inflation rate by the relative size (the weight) of each particular country, and then adds all the rates together.
Let’s say the EMU consisted of only Germany, France, and Ireland. Assume these countries had the following level of GDP (used to gauge the size of the country) and inflation rate:
- To calculate the aggregate inflation rate
- You first calculate the total size of the economy:
- Total GDP = 1000 + 900 + 100 = 2000 €
- Then you find the relative size of each country:
- Germany - 1000/2000 = 0.5
- France – 900/2000 = 0.45
- Ireland – 100/2000 = 0.05
- Then you find the weighted average by adding up each county’s inflation value multiplied by its respective weight:
- European inflation: 0.5*1.3% + 0.45*2.0% + 0.05*6.2% = 1.82%
- EMU aggregate inflation rate would be 1.82%.
Notice that the ECB will not notice the high inflation in Ireland because of its small size relative to France and Germany. See challenges to monetary policy in the EMUThe following graph illustrates this point. The last bar is the aggregate inflation rate for the EMU members (called the Euro Area). It is a weighted average of each of the other countries listed. Notice that the aggregate masks the high inflation rate in Spain and low inflation rate in the Netherlands.