Claims Inflation - a known unknown

Over the last year I worked with two colleagues of mine on the subject of inflation and claims inflation in particular. I didn't expect it to be such a challenging topic, but we ended up with more questions than answers. The key question and biggest challenge is to define what inflation, or indeed claims inflation actually is and how to measure it. We published a summary of our thoughts and findings in this month's issue of The Actuary.

Last year's discussion about the differences between the retail price index (RPI) and consumer price index (CPI) in the UK only exemplified the challenge. The economist Tim Harford illustrated the differences between the RPI and CPI with a simple example of price changes for a shirt and blouse in his Radio 4 programme More or Less. The radio podcast is still available from the BBC. Start listening after about 18 minutes into the show.

	# Inflation data example as presented by Tim Harford on 'More of Less'
	# http://downloads.bbc.co.uk/podcasts/radio4/moreorless/moreorless_20120817-1630a.mp3
	dat <- data.frame(shirt =c(year_1 = 20, year_2 = 25, year_3 = 20),
	blouse=c(year_1 = 25, year_2 = 20, year_3 = 25))
	dat
	# shirt blouse
	# year_1 20 25
	# year_2 25 20
	# year_3 20 25
	(yoyChange <- dat[-1,]/dat[-3,] - 1)
	# shirt blouse
	# year_2 0.25 -0.20
	# year_3 -0.20 0.25
	# Arithmetic average gives 2.5% inflation year on year
	apply(yoyChange, 1, mean)
	# year_2 year_3
	# 0.025 0.025
	geo_mean <- function(x) exp(mean(log(x)))
	# No inflation with the geometric mean
	apply(yoyChange + 1, 1, geo_mean) - 1
	# year_2 year_3
	# 0 0

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