Having written rather outspoken columns about conceptual errors in the Retail Prices Index and criticising the UK statistical authorities for ducking the challenge of rectifying these errors, quite a few people have asked for some numeric examples about the scale of the problem so they can understand better how it arises.
(People who want the real gory detail should look at professor Erwin Diewert’s report)
The first thing to note is that contrary to well-intentioned explainers such as this one from the BBC, or the otherwise-rather-good editorial in today’s Times newspaper, the problem in the calculation of the RPI is not to do with the difference between geometric averages and arithmetic averages. It is really about the deficiencies of one particular arithmetic average, the Carli index.
Don’t just believe me, play with this spreadsheet, (Price indices). I will also help you to use it with a few worked examples. The worked examples are extremes, but they serve to show the important biases of different ways of calculating inflation.