The price tag for a top decile Auckland education is not $2m+

I meant to write a post on this a while back, when Corazon Miller wrote in the New Zealand Herald:

Parents wanting to send their children to some of Auckland's prestigious state schools may be forced to fork out more than $2m to buy a house in the zone, or more than $700 a week in rent - double the cost ten years ago.

Figures from property analysis site Relab.co.nz which analysed 33 Auckland school zones showed buying a home was more costly close to higher decile schools.

Topping the list were two decile nine school zones, Auckland Grammar and Epsom Girls Grammar - with median values topping $2m last year...

Relab marketing director Bill Ma said the figures showed parents what they should be budgeting for.

"The higher decile schools definitely come with a premium price."

Yes, homes in good school zones do have a premium for the school zone. But no, the premium is not the whole price. The reason is simple - if you weren't living in a house in the double Grammar zone, you'd have to be living somewhere else, and presumably that somewhere else is not free. To find out the actual premium for school zoning, you have to look at two otherwise-identical houses: one in the zone; and one outside the zone.

This relies on the concept of hedonic pricing - an idea that was first introduced by Irma Adelman, who sadly passed away in February. Hedonic pricing recognises that when you buy some (or most?) goods you aren't so much buying a single item but really a bundle of characteristics, and each of those characteristics has value. The value of the whole product is the sum of the value of the characteristics that make it up. For example, when you buy a house, you are buying its characteristics (number of bedrooms, number of bathrooms, floor area, land area, location, etc.). When you buy land, you are buying land area, soil quality, slope, location and access to amenities, etc.

In the case of Auckland, school zone is only one of many characteristics that make up the value of the house. And it is possible to separately identify and value those characteristics if you have good data, as my colleague John Gibson and his wife Geua Boe-Gibson did in this 2014 working paper using data on 8000 houses in Christchurch. They didn't look at school zones, but looked at the value of school outcomes (measured by NCEA pass rates), and found that a standard deviation increase in school performance raises house prices by 6.4%.

So overall, the 'price tag for a top decile Auckland education' won't be $2m or more. If we (generously) assumed that the premium was the difference between the $2.09 million median in the Auckland Grammar school zone mentioned in the article above, and the $1.05 million median across Auckland as a whole (as of today), then the premium is a little over $1 million. However, that wouldn't be correct, since the median house in the Auckland Grammar zone is clearly not the same as the median house across all of Auckland, as well as having access to different amenities (besides the school zone). So the premium for the Auckland Grammar zone is likely to be substantially lower than $1 million.