July 1, 2014

Does it make sense?

From the Herald (via @BKDrinkwater on Twitter)

Wages have only gone up $34.53 annually against house prices, which are up by $38,000.

These are the findings of the Home Affordability Report quarterly survey released by Massey University this morning.

At face value, that first sentence doesn’t make any sense, and also looks untrue. Wages have gone up quite a lot more than $34.53 annually. It is, however, almost a quote from the report, which the Herald embeds in their online story

 There was no real surprise in this result because the average annual wage increase of $34.53 was not enough to offset a $38,000 increase in the national median house price and an increase in the average mortgage interest rate from 5.57% to 5.64%. 

If you look for income information online, the first thing you find is the NZ Income Survey, which reported a $38 increase in median weekly salary and wage income for those receiving any. That’s a year old and not the right measure, but it suggests the $34.53 is probably an increase in some measure of average weekly income. Directly comparing that to the increase in the cost of house would be silly.

Fortunately, the Massey report doesn’t do that. If you look at the report, on the last page it says

Housing affordability for housing in New Zealand can be assessed by comparing the average weekly earnings with the median dwelling price and the mortgage interest rate

That is, they do some calculation with weekly earnings and expected mortgage payments. It’s remarkably hard to find exactly what calculation, but if you go to their website, and go back to 2006 when the report was sponsored by AMP, there is a more specific description.

If I’ve understood it correctly, the index is annual interest payment for an 80% mortgage  on the median house price at the average interest rate, divided by the average weekly wage.  That is, it’s the number of person-weeks of average wage income it would take to pay the mortgage interest for a year.  An index of 30 in Auckland means that the mortgage interest for the first year on 80% mortgage on the median house would take 30 weeks of average wage income to pay. A household with two people earning the average Auckland wage would spend 15/52 or nearly 30% of their income on mortgage interest to buy the median Auckland house.

Two final notes: first the “There was no real surprise” claim in the report is pretty meaningless. Once you know the inputs there should never be any real surprise in a simple ratio. Second, the Herald’s second paragraph

These are the findings of the Home Affordability Report quarterly survey released by Massey University this morning.

is just not true. Those are the inputs to the report, from, respectively, Stats New Zealand and REINZ. The findings are the changes in the affordability indices.


Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »


  • avatar

    Is that 30 weeks of average income before or after tax? It’s an important distinction.

    3 years ago

    • avatar
      Thomas Lumley

      Before income tax; GST isn’t relevant. It makes about a 15% difference at the average wage, so about 4.5 weeks. That sort of issue is presumably why they just call it an index.

      3 years ago

      • avatar

        I realise we’re dealing with the realm of pure numbers here and the index only measures relativities. But it would be more meaningful if the index dealt with after tax incomes. After all, that’s the money people actually have to spend on their housing.

        3 years ago