How to calculate inflation

RG2015

There was a discussion on another thread about inflation (see the link at the end of this post) and I learnt that there is a difference between the inflation rate and RPI (or CPI or CPIH).

As an example, the Dec-2020 CPI inflation rate, reported by the BBC and the ONS, was 0.6%. This is calculated as the Dec-2020 index divided by the Dec-2019 index, 109.2/108.5 = 0.64%

However, if I understand correctly, the 2020 Annual CPI inflation rate is 0.9%, based on the annual average index for 2020 compared with the same figure for 2019.

I think I understand the difference but would welcome any insights in layman's terms. I know that these various indices are just guides and that everyone has their own personal rate but am still interested in the official figures.

In addition, where these data are used to calculate other figures, such as allowable price or pension increases, which figures are used, the annual average or the 12 month index change?

https://forums.moneysavingexpert.com/discussion/6106986/regular-savings-accounts-the-best-currently-available-list/p314

eskbanker

To the best of my knowledge, pension increases are typically based on the 12 month index change rather than averages, with September's value often being used, i.e. CPI-linked increases applying from last month will be based on the increase in the index from September 2019 to September 2020 (108.5 to 109.1, so 0.55%), although the state pension increase may override this via the triple lock provisions.

Edit: NS&I use the same principle for their index-linked certificates, as per https://www.nsandi.com/files/asset/pdf/index-linked-savings-certificates-key-features.pdf

To calculate your index-linked growth, we multiply the value of your Certificate by the percentage increase (if any) in the CPI over the investment year. To calculate the percentage increase over your investment year, we look at the index at two points in time – two months before the start of the investment year, and two months before the end. (We use the index value from two months earlier because the index takes time to be compiled and published.)

masonic

RG2015 said:

However, if I understand correctly, the 2020 Annual CPI inflation rate is 0.9%, based on the annual average index for 2020 compared with the same figure for 2019.

I would say this is a questionable means to determine an inflation rate - taking a mean of the monthly figures for two calendar years and then determining the rate of inflation from those two derived mean values. What you get, I suppose, approximates the annual inflation rate for mid-2019 to mid-2020, but then attributing that to 2020 alone would be misleading.

The correct way of doing it is by calculating the ratio of Jan2021/Jan2020. Dec-Dec could also be valid.

GeordieGeorge

The right way to calculate it is to take the index at the end of the period and divide by the index at the start of the period.

There is no “average index”, the index is published for each month and the ratio of the end to the start gives you the effect of inflation over the period.

To give an example, if the inflation index was 1000 in Dec 2019 and 1020 in Dec 2020 then the rate of inflation was 2% for the year.

You’re conflating inflation measure with the calculation. There is more than one measure of inflation, with CPI and RPI being two of the most commonly used ones. They are different things, and ought not to be mixed together.

RG2015

This is what I have always thought. I am referring to posts on the other thread (p314) where some posters are referring to an inflation rate being different to RPI inflation. I am trying to understand what they are saying.

I am posting here as this discussion is a major digression from the main topic of that thread.

https://forums.moneysavingexpert.com/discussion/6106986/regular-savings-accounts-the-best-currently-available-list/p314

eskbanker

RG2015 said:

This is what I have always thought. I am referring to posts on the other thread (p314) where some posters are referring to an inflation rate being different to RPI inflation. I am trying to understand what they are saying.

Unless I'm misunderstanding polymaff's point (it wouldn't be the first time), it was that RPI is an index, but inflation relates to the rate of change of that index rather than the index itself, so it's inaccurate to say that "RPI is 2.4%" or "RPI is -0.5%", even if such terminology is often used lazily by the BBC and other media, and posters on here (including polymaff at the top of that page!) - "RPI inflation is 2.4% [over n months/years]" would be a more technically correct version.

polymaff's comment that 'the "RPI for 2009" started at 214.8 and ended at 213.7' does confuse me though, as these are the averages for 2008 and 2009, so I'd be more inclined to see things as you, masonic and GeordieGeorge do, i.e. using the actual starting and ending index values for 2009, so Dec 2008 212.9 and Dec 2009 218.0, for an RPI inflation rate of 2.4% over the 12 months of 2009.

RG2015

I am seeing some merit in this alternative method. If I was calculating my personal inflation rate for 2020, which would be more indicative? Comparing my expenditure in Dec 2020 with that in Dec 2019, or my total for 2020 with 2019?

All the index represents is expenditure in one month using a defined earlier month as the base of 100.

The effectiveness of the monthly comparison breaks down somewhat during periods of large and unusual monthly swings.

masonic

RG2015 said:

I am seeing some merit in this alternative method. If I was calculating my personal inflation rate for 2020, which would be more indicative? Comparing my expenditure in Dec 2020 with that in Dec 2019, or my total for 2020 with 2019?

All the index represents is expenditure in one month using a defined earlier month as the base of 100.

The effectiveness of the monthly comparison breaks down somewhat during periods of large and unusual monthly swings.

You are not comparing apples with apples. Your expenditure in Dec 2020 is not an index value. To determine your personal inflation index you'd need to take your total spending for 2020 and value everything in Dec 2020. To work out the inflation rate, you'd calculate the value in Dec 2019 and take a ratio. In reality that's too difficult (we don't have the resources of ONS), so have to use out of date pricing relating to when we actually spent on the goods or services. However, there is nothing to stop you creating a 'basket of goods/services' using the same methodology and keeping records of prices each month instead of using bank/credit card statements retrospectively.

The index does not represent expenditure in one month, it represents prices of everything at that point in time.

RG2015

It is easy to see how statistics can sometimes be misleading. It is also a shame (although understandable) that the conversation could not have been continued on the other thread. RPI inflation in 2009 was either 2.4% or -0.5% and that debate was not concluded.

masonic

It was 3.7% taking the Jan 2010 vs Jan 2009 figures, or 2.4% taking Dec 2009 vs Dec 2008. Inflation in the year to June 2009 was -1.6% and in the year to July 2009 it was -1.4%, because there was deflation between October 2008 and January 2009, but prices rose for the whole of the rest of 2009. The deflation really belongs to 2008 and balances out a period of high inflation earlier in 2008.

The rate of inflation for a particular calendar year is a fairly meaningless value. If you wish to calculate inflation for a specific period of time (for example, comparing returns to the rate of inflation), you should use the relevant monthly index values. However, if you wish to assess inflation over the long term or project it forwards, you should use more than a single calendar year as your time range.