Sunday, 13 October 2013

UK House Prices vs. Household Incomes

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 provide 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.


  1. Very interesting, one important point - in some markets including uk there is a significant percentage of foreign buyers, i wonder how much they affect the results

    1. That's true and certainly one of the largest assumptions is this 'closed' market in which the householders are assumed to be the sole buyers. I note this is an issue with the generally published single ratios too.

  2. inverse y-axis label in in 3rd plot

  3. Dear Joe, Perhaps the answer is an omitted variable, wealth, and this one is in turn associated more than proportionally with income.

  4. The ratio in the third picture does not make sense to me because the income and the price in the same percentile interval can be from different samples. I would suggest do the ratio for each sample. One should not compute Mr. White's income / Mr.Black's price!

  5. -- Most often this is a ratio of average house prices to average incomes

    Well, no. Economists have for decades known that mean is a lousy measure of central tendency with skew distribution such as wealth or income. Median to median is the proper way to do that. OTOH, the mainstream media use "average" without asking what the stat really is, so it could be OK. Doubt it, though.

  6. Percentiles of disposable income increase at a higher rate than those of household income. More the disposable income higher the investment and hence higher house prices.

  7. This is interesting. Where are all these figures of 5 times earnings coming from. 8x looks very high in comparison to what the media report.

    It would be interesting to see this on a historic basis...maybe not across the entire spectrum of household incomes, just for the 50th percentile of incomes v 50th percentile of houses.

    I'd not worry too much about the impact of foreign buyers....its mainly in London and probably accounts for the RHS of your custom ratio. You could just lop off the tails.

  8. Nice graphs and interesting data...... certainly at the upper end its safe to assume that borrowing levels are also higher (i.e. can borrow 4-5x salary v's perhaps banks being more rigidly 3-4x salary at lower end) which means house price purcahses / incomes ratio increases at that end, but also the upper end data (i.e top 1%) is likely to be more heavily influenced by the London market whereby there is indeed more of a "bubble" (albeit thats not to imply its unsustainable !) and therefore people tend to have to 'stretch' their house price/income ratio in order to buy, compared to lower income bands.

  9. To what extent does housing benefit prop up house prices?

    If Local Authorities only released housing benefit in exchange for equity in the property and realised that equity at the 50% level, what effect would this have on the market?