Something is peculiarly wrong with Auckland that stops it from building housing for its rapidly growing population at anything like the rate the rest of the country manages.

One of the factors, at least, retarding an adequate supply response is a chronic shortage of construction workers.

These are the takeaway messages from some careful research by Andrew Coleman for the Productivity Commission, and Ozer Karagedikli at the Reserve Bank, reported in a paper "Residential construction and population growth in New Zealand: 1996-2016".

The pair have trawled through population and building permits data for that period which divide New Zealand into 16 regions. They back out permits required to replace old houses and maintain existing dwellings; it is the marginal increase in housing they are interested in.

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When they plot new residential building permits per capita against population growth rates across those 16 regions, 15 of them cluster around a line with a gradient of one in three — one new dwelling for every three additional people.

The conspicuous outlier is Auckland. "Even though the population increased more in Auckland than in the rest of New Zealand put together, only half as many new dwelling permits were issued in Auckland as in the rest of the country, 153,000 versus 304,000." If it had built at the same rate as the rest of the country in response to population growth, there would be between 50,000 and 60,000 more homes in the city.

If [Auckland] had built at the same rate as the rest of the country in response to population growth, there would be between 50,000 and 60,000 more homes in the city.

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When they interrogate the data in a more subtle way, to allow for varying time lags between when the population goes up and when the buildings go up, the picture remains essentially the same: it amounts to a cumulative shortfall of 40,000-55,000 dwellings, equivalent to around 10 per cent of Auckland's housing stock.

These figures are at the high end of the range for such estimates. Officials' briefing to the incoming Minister of Housing, Phil Twyford, put the shortfall at 45,000. Auckland Council puts it at 40,000, and the recent Housing Stocktake estimates a shortfall of 28,000 over the past 10 years.

One possible explanation Coleman and Karagedikli consider is that builders in Auckland have been building unusually large houses.

The building permits data also provides information on the floor area of dwellings consented.

Nationwide, the average house built these days is about half as large again as in 1990. In Auckland, new builds smaller than 150 square metres have fallen from 68 per cent of the total then to 32 per cent now, while the share of those over 250sq m increased from 8 to 26 per cent.

Read more: Auckland's housing ranking nothing to celebrate

But Coleman and Karagedikli found that the data clearly show Auckland's housing shortfall — relative to the rest of the country — has not primarily been because Auckland builders specialised in large houses.

If Auckland had built unusually large houses, the average size of new houses in the city would be larger than those built in the rest of the country. In fact, at 177sq m, it was 6sq m smaller.

Although the size of new housing in Auckland mirrored trends in the rest of the country, more small dwellings, primarily apartments, were built in Auckland prior to 2005, Coleman and Karagedikli found.

"Auckland's housing shortfall was modest until 2005 but sharply accelerated when apartment building effectively ceased between 2008 and 2012."

Builders in regions with low population growth mainly had to alter the quality profile of the existing building stock, Coleman and Karagedikli said. "In contrast, builders in regions with large population increases had to cope with increased demand for larger houses from their incumbent populations, and the increased demand for houses across the whole quality distribution due to the influx of new people.

"The extent that the construction industry concentrated on one quality level rather than another ... reflects the differences between the cost of new housing and the second-hand price of old housing along the quality scale."

In other words, the combination of high prices resulting from a shortage of housing and capacity constraints in the building industry could encourage builders to concentrate on larger properties. But the drivers are the shortage and capacity constraints, not some unusual preference for McMansions on the part of Aucklanders.

Coleman and Karagedikli also look at the relationship between population growth and the composition of the workforce.

In regions whose population is static, builders are still needed to maintain and upgrade the existing housing stock and build things other than housing. By backing out that base level of demand for people in the building trades, they are able to figure out how many additional building workers are required to cope with population growth. So Tauranga needs 600 more construction workers than Dunedin, even though they now have similar populations.

On that basis, Auckland is about 9000 construction workers short of what it needs.

Whatever other factors may be constricting construction, a lot more builders will be needed.

Read more: Auckland housing: A foundation to build on

Coleman and Karagedikli leave it at that.

But diligent readers of this column may recall that a cursory analysis of the visa issuance statistics for the 2015-16 year (still the most recent tidy data available) showed that of the 193,000 work visas issued that year, only one in six was in the essential skills category. It was a similar proportion in the two previous years. The rest were for working holidaymakers, family members, seasonal horticultural workers and former foreign students.

But of the 32,000 essential skills visas, only one in four was a first-timer, implying a marginal increase of 8000 to the skilled workforce.

And a startlingly low proportion — 7 per cent, or 2233 to be precise — were classified as construction trades workers like carpenters, plumbers, plasterers, tilers and painters. If you include scaffolders and builders' labourers, the proportion rises to nearly 10 per cent.

So in a year when the net migration gain — excluding the comings and goings of New Zealand citizens, which can't really be regulated — was around 72,000, immigration contributed only a few hundred extra pairs of skilled hands to the construction workforce.

The conclusion has to be that the effect of immigration on the construction sector and the housing market was overwhelmingly on the demand, not the supply, side.

1996-2016:
Population increase
Auckland: 499,000
Rest of NZ: 462,000

Building permits issued
Auckland: 153,000
Rest of NZ: 304,000

Source: Andrew Coleman & Ozer Karagedikli