Wealth taxes are tricky things. Even leaving aside the complications in real-world applications that caused the OECD to recommend against them, wealth taxes have an additional pernicious effect. They destroy basic numeracy both in parties supporting them, and in parties opposing them.

For months, the Green Party has been campaigning for a wealth tax. It proposes a tax of 1% on the value of net wealth above $1 million and a 2% tax on net wealth above $2m. The tax would be comprehensive across all forms of wealth, barring exemptions for items not really worth the cost of valuing. Couples could split household assets, so the thresholds would be doubled for them.

The Greens argue, incorrectly, this tax would only affect the top 6% of wealthiest Kiwis. We will return to the Greens’ math problems shortly. The true number is far closer to 20% than to 6%.

This weekend, National retracted a campaign advertisement about the Greens’ proposed wealth tax because National had gotten the numbers wrong.

The ad warned that an Auckland couple with a mortgage-free house and holding Westpac’s recommended retirement savings would pay about $140 per week in wealth taxes. But National forgot that the wealth tax threshold doubles for a couple. Until one of those retirees is a widow or a widower, the wealth tax would not apply. But on that day, the threshold would cut in half as the assets transfer to the surviving spouse.

A more accurate ad could have warned that the tragedy of bereavement would be compounded by suddenly having to pay a wealth tax, or watching that tax accrue against the estate.

But the Greens’ numbers have their own problems. To go through those, we need a brief detour through basic wealth dynamics. It is a problem plaguing every iteration of wealth inequality surveys using static comparisons to make claims about what proportion of wealth is held by which proportion of people.

Wealth builds over time, and that matters for every question about wealth measurement.

Most people start life with little wealth. Taking on student loans to earn a higher income later on means beginning adulthood with a heavy net debt position, as education does not contribute to measured wealth on Statistics New Zealand’s balance sheets. As graduates move into employment, they begin paying down their student loan debt while (hopefully) building up savings. If they buy a house, they take on debt that has an offsetting and appreciating asset. Otherwise, they build up retirement savings.

Individual net wealth peaks shortly after retirement. Retirees then draw on those savings.

A cross-sectional snapshot of the country will reveal a lot of people with net debt, a lot of people with few net assets, and a few people with a lot of net assets. That, and the failure to account for the effects of New Zealand Superannuation, can make wealth distributions look more unequal than they really are. Even if every Kiwi followed exactly the same wealth trajectory, beginning with net debt and ending with the same retirement net worth, simple differences in ages would mean that a small proportion would be wealthy at any given time.

The Greens argue that only 6% of Kiwis would be subject to their wealth tax. But that seemed almost certainly to be based on a misleading cross-sectional snapshot. A reasonable proportion of today’s youth would be subject to the tax as they reach retirement. After prodding their representatives on Twitter more than a few times if they had checked what proportion of retirees might be subject to the tax, I decided to ask Statistics New Zealand instead.

I asked Stats to go back through the 2018 Net Worth Survey and sort net wealth holdings by age.

Without any sorting by age, the 2018 survey suggested 8% of individuals held net wealth in excess of $1m – so that was already rather higher than the 6% suggested by the Greens.

And, as expected, there was a severe age skew in the data. While only 1.5% of those aged 15-44 held a $1m in net assets, that proportion rose steadily for older age groups. Just over 18% of those aged 60-64 reported more than $1m in net assets, along with just under 18% of 65-year-olds. Wealth peaks among those aged 66-69 which means 21.8% of retirees would be liable for the wealth tax.

Among the 21.8% of those aged 66-69 and facing the wealth tax, 19.5% would be paying no more than $2000 per year as their net asset holdings were less than $1.2m. But 39% of retirees aged 66-69 facing the wealth tax, or 8.5% of all persons aged 66-69, would hit the 2% wealth tax rate as their net assets were above $2m.

These figures are based on estimates of individual wealth, where individuals tell Stats NZ surveyors what portion of any asset should count as theirs alone. Looking at households is more complicated because couples can split assets and because households come in all kinds of configurations.

But 24.5% of couple-only households with at least one person aged 66-69 hold net assets in excess of $2m – the wealth tax threshold for a couple. Among that group, the amount of tax owed by the median couple (half would owe more, half would owe less) would be $13,820 per year. A further 26% of couples in that age bracket would risk the wealth tax if they lost the ability to split their assets after a death.

The future is unpredictable. But if coming generations follow the same path as prior generations, it would be pretty reasonable to expect between a fifth and a quarter will be caught by the Greens’ proposed wealth tax, were it enacted. If the thresholds were not inflation adjusted over time, that proportion would rise substantially. House price inflation since the 2018 Statistics NZ figures will have substantially increased the proportion of retiring Kiwis subject to the wealth tax. And previous governments have not been keen on adjusting tax thresholds for inflation.

It may be perfectly fair for between a fifth and a quarter of Kiwis, predominantly retirees, to be potentially liable for a wealth tax during their lifetime. But the Greens have not advertised the tax on that basis. The party instead claims only 6% of Kiwis would pay the tax. By the figures provided by Statistics New Zealand, the real number is 8% and three times as many would wind up being liable for the tax during their lifetimes. That is, if they did not hire accountants and tax lawyers to reorganise their financial affairs in the meantime.

The first casualty of wealth taxes is basic numeracy. National failed to calculate the amount of the potential tax liability, but quickly corrected their error. And the Greens gave a rather misleading picture of who might be affected by a wealth tax. Labour and ACT, having so far ruled out a wealth tax, are on more solid ground.