# Calculating annual inflation rates confusion

Im surprised as to why im finding this question so complicated , I'm assuming its due to the miscommunication and misuse of the term in inflation without explaining the context they are using it in .

I have been trying to see how we calculate annual inflation rates, and I have seen a multitude of explanations online , I'm trying to see which one is right , or which ones are equivalent to each other , I'm not really trying to delve into why they are wrong because they don't consider the fluctuations in energy oil etc , I'm trying to see if they are outright wrong and don't make sense and why they dont .

• The first method I saw for calculating annual inflation rates were calculating the percentage change between a cpi value this year and the cpi value of the same month last year .

• 2nd method was finding the percentage change in the CPI from december to January

• 3rd method finding the percentage change in the CPI of each month in a year so you essentially find the inflation rates of each month , you average these values ie sum them up divide them by 12 and then times them by 12 to get a rough annual inflation rate.......Im very sure the person who wrote this got it wrong , as this method disregards the compound effect of inflation every month and the fact that dividing by 12 to get an average for each month and then timsing by 12 just cancels out the initial division.....

• 4th method is an extension of the first method where you find the CPI change of the same month last year and this year ie june 2021 and june 2022 , but you do this for every month of the year , then you add these values up and divide by 12 .

• the final method was essentially I think more mathematically sound , we find the the monthly inflation rates using the CPI data , and we convert each figure into a percentage multiplier essentially and then we find the product of that , minus one from it(if that product end upe bing 1.something , if its 0.something you don't have to ) and times it by 100 to get the actuall percentage figure which should be the same figure that we would get if we found the percentage change in prices from jan to December

Furthermore now that we used the monthly data to find the annual inflation rate , we can also say that the average annual inflation rate over a certain number years can be found using the geometric mean (I was surprised by how many people used the arithmetic mean instead , I'm starting to think I'm wrong about using the geometric mean )

Could someone clear this up for me ,ie which method is right , or maybe which method is right for certain scenarios , or maybe why someone suggested an alternative method but the context perhaps might have been different(i find these methods online so very often people don't exactly point out the context they were using it in) .

• The first method is the best method. The last method should give the same result if done correctly, from Jan to Jan not Jan to Dec
– dm63
Feb 29 at 3:28

Most of the above mentioned methods are a right way to calculate some rate of inflation depending on context. They do not all calculate yearly rate of inflation.

The first method I saw for calculating annual inflation rates were calculating the percentage change between a cpi value this year and the cpi value of the same month last year.

This is correct method if you want to have yearly inflation number for a year defined by some 12 month period. Based on the description it does not need to be calendar year (i.e. January-December).

2nd method was finding the percentage change in the CPI from december to January

Presumably you mean to say from January to December. This would be calendar year, if it’s just actually December to January then it’s just 1 month inflation rate, which would be the correct rate if you wan to know inflation rate between December and January.

3rd method finding the percentage in the CPI of each month in a year so you essentially find the inflation rates of each month , you average these values ie sum them up divide them by 12 and then times them by 12 to get a rough annual inflation rate

This method tells you what the average of monthly inflation was over the course of a year. This does not correspond to the total rate of inflation, as you said there isn’t any compounding (like when you annualized monthly rate), but it tells you what the average of monthly inflation was over the year. However, this can still have interesting applications such as for example Romer uses this to see whether most recessionary periods are inflationary or deflationary.

4th method is an extension of the first method where you find the CPI change of the same month last year and this year ie june 2021 and june 2022 , but you do this for every month of the year , then you add these values up and divide by 12.

This method calculates the monthly inflation rates on year-on-year basis, which is one way of adjusting the monthly inflation rates for seasonality. Afterwards average of monthly inflation rate is calculated. This again does not correspond to yearly inflation but it would be correct if you want to calculate average of monthly seasonally adjust rate.

the final method was essentially I think more mathematically sound , we find the the monthly inflation rates using the CPI data , and we convert each figure into a percentage multiplier essentially and then we find the product of that , minus one from it and times it by 100 to get the actuall percentage figure which should be the same figure that we would get if we found the percentage change in prices from jan to December

This is correct way to calculate inflation rate of annual inflation from monthly inflation data as opposed to calculate it from CPI as method 1 does.

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– 1muflon1
Mar 2 at 1:08