Calculating CPI Over Time: Multiplication or Other Methods?

[nomadreid]

Suppose you have a set of monthly Consumer Price Indices, and you want to find the factor for a period of two years: it seems dodgy to just multiply all the indices together. But is that the correct way to do it?

 

[Svein]

Yes, but you will also multiply the errors (including roundoff).

What I would do:

1. Create a column with the numbers 1 -24 in Excel
   
2. Insert all the monthly CPIs in a column to the right of the 1-24 numbers
   
3. Create a new column to the right of the CPIs containing the logarithms of the CPIs
4. Create a new column containing the partial sums of the logarithms (L1, L1+L2, L1+L2+L3...)
   
5. Do a linear approximation in Excel with the 1-24 column as x and the partial sums of the logarithms as y (the formulas are "SLOPE" and "INTERCEPT")
6. Calculate SLOPE*24 + INTERCEPT. This is the best approximation of the logarithm of the factor for two years.
7. Do the antilog (depends on what kind of logs you used).

 

[nomadreid]

Thanks, Svein. That sounds more reasonable.

 

[BWV]

Why calculate anything?
https://www.bls.gov/data/inflation_calculator.htm

But Svein is not correct - that calculation does not do a historical inflation adjustment. There is no need to calculate the slope unless you are looking for some kind of trend analysis for future prediction.

Here is the CPI-All Urban Consumers from 1910
http://www.usinflationcalculator.co...and-annual-percent-changes-from-1913-to-2008/

So the Dec 2017 value is 246.524 and Dec 2015 was 236.525

the two year factor is just 246.524/236.525 (or its inverse depending on which direction you are going)

to get an annualized rate just take (246.524/236.525)^(1/p)-1 where p is the number of years (in this case 2).

You can do the same thing going to logs which is often easier if doing this with code

 

[nomadreid]

Thanks, BWV. (Sorry for the delayed reaction.)