You Can't Work Out Price Increases By Dividing Medians

If you have a market in which each of the goods are different and most don’t trade in any given period, you can’t calculate a growth rate by dividing two periods’ median observed prices. An example is residential property sales and rents.

The reason for this is obvious to people with even a modicum of numeracy: since in each period, most properties do not sell, the median sale from one period will not be the same property as the median sale from another period. The same applies to rents. If the region is small, say a suburb or postcode, the median sale or rental properties in each period can vary greatly in size and quality, given the small amount of data from which the medians would be calculated. They may not even have the same number of bedrooms.

Imagine comparing the weekly rental of a three bedroom house in 2010 with the 2011 weekly rental of a four bedroom house in the same suburb, but perhaps closer to a bus stop or the beach. You’d be pretty dumb to divide one by the other and believe that meant rents in the suburb had increased by that much over the course of 12 months.

But that’s exactly what happened in an article by Bronwen Gora in January 29’s Sunday Telegraph, which unfortunately I cannot find online. There is a table titled Biggest Rent Increases. It quotes median advertised rents from 2010 and 2011 in ten suburbs, then calculates the percentage rise, interpreting it as the percentage increase in actual rents in those suburbs.

The top three “increases” were Clovelly ($515 to $1300 = 152%), Bellevue Hill ($600 to $1400 = 133%) and South Coogee ($550 to $1200 = 118%).

Does anyone actually believe that rents in those suburbs have increased over 100% in 12 months? Any halfway decent journalist shouldn’t.

Even if Bronwen Gora and her editor don’t know much high school maths (which they evidently don’t), shouldn’t those figures ring alarm bells? Shouldn’t they have at the very least rung the data provider and said “There’s something wrong with this calculation. I don’t know what it is, but can you follow it up before I publish?”

That’s the minimum level of competence I’d expect from a journalist and certainly from an editor. If you don’t have the expertise to understand the error and its cause, at least have the nous to realise something about the numbers doesn’t smell right and follow it up.

Good property journalism requires some understanding of economics and finance, which in turn requires a grasp of mathematics: statistics, plus a bit of calculus and algebra to understand at least the qualitative parts of discussions of relationships between say, prices and interest rates. Things which are taught in all but the lowest level higher school certificate maths courses. Unfortunately, too many journalists mirror wider society in having completely forgotten whatever limited understanding of these skills they may have briefly gained at school.

This ignorance is a serious problem for modern, Western societies. It results in a large proportion of our population being unable to effectively participate in the new financial economy, because they do not understand it.

Now, back to the absurd “market analysis” which sparked this rant in the first place. What should be done to estimate the true rental increase from 2010 to 2011?

First, understand that since different properties are renting in each period, we’ll never know the exact increase in the same way as we can know the increase in the price of the same basket of groceries. That’s how many measurements are in real life: we can’t know the exact value or size or amount, but a bit of statistical analysis can give us an estimate which is sufficiently accurate for many purposes.

If there are at least say, 20 or 30 properties for rent in each period and we know things like their land size, number of bedrooms and bathrooms and whether they have a view, it is possible to make a statistical model which controls for these attributes as well as the date of the observation.

Then pool all the properties and use the statistical model to estimate 2011 rents for those which rented in 2010 and vice versa. That way, we’ll have either actual or estimated rental values for each property in 2010 and in 2011. To dampen statistical errors in the estimation, divide the sum of the 2011 rents by the sum of the 2010 rents. Subtract 1, multiply by 100 and that’s your percentage increase.

Because all statistical models have some estimation errors, the answer will necessarily be an approximation, but it will be close enough for most purposes. It certainly won’t say something ridiculous like 152%.

I got hold of the rental data for these suburbs and tried a very simple version of the above method. I got Bellevue Hill +6.8% and Clovelly +4.1%. A bit more believable?

South Coogee didn’t work so well and gave +15.2%. This was because there were many more high value properties renting in South Coogee in 2011 than in 2010. A better statistical model than I have time to construct would better control for this and give a lower figure.

I’m not saying I expect journalists to be capable of doing this type of analysis, or even to spend the time doing it if they could. But the data provider should be able to.

My point is that instead of parroting obviously useless and erroneous information, a competent journalist should have recognised that rent increases of over 100% in a year in well established suburbs of Australia’s largest city are clearly wrong and asked the data provider to provide the correct figures.

This is the level of understanding we should expect of the average adult citizen in a modern economy, so it’s certainly what we should expect of journalists writing articles for them.