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There seems nothing the British press likes more than a good house price story. Both the OECD and ‘The Economist’ studies quoted in The Telegraph recently use the house price to household income ratio as a consideration of affordability and sustainability of the market. Most often this is a ratio of average house prices to average incomes; I keep wondering if this ratio is itself a function of income? What follows is a first (and not that rigorous!) look at this idea.

To simplify I want to assume the top 1% of earners will consider the top 1% of houses and so forth down to the bottom 1% of earners who will be assumed to pay the bottom 1% of house prices. To approximate this I compare the percentiles of the two distributions. Of course, this is all a gross oversimplification but it does provides a tractable starting point and the results are certainly interesting.

For the income data I used the ready prepared figures from an excellent Guardian article published last year. The data is available here. The details on how the data is ‘equivalised’ are all on the Guardian site and in the original source. Let’s take a quick look at the percentiles of the income data:
It looks a bit different to the Guardian’s graph. I think this is because I’m looking at gross income instead of net.

The house prices took a little more work but fortunately the Land Registry has a complete record of house transaction prices. Here are the percentiles of their distribution between 2010-2011 (with the period chosen to match the income data):
To the naked eye the distributions look fairly similar and pretty much as we’d expect. To get a better sense of things we need to look at the ratios:
 Note: The 1% point is out of view at c. 23.
Whilst the ratio is fairly constant, at around 8, some variation is apparent. The interesting things are really happening at either end of the graph. At the low end perhaps there is some minimum price for which a house can reasonably be built, if the same hard minimum didn’t apply to household income at the low end the ratio would spike up as we observe here. From around 10% there is a steady increase in the ratio. I have two ideas: perhaps percentage of income available to spend on a house increases with income or perhaps the amount of ‘bubble’ in the market increases as one heads towards ‘prime investment opportunities’?!

As always, thanks for reading and I’d be grateful for your opinions!

For those interested please find the R code below or on github.