Only 24 per cent of those in the bottom decile in 2002 were still there in 2009, according to a Treasury report.
Discussions of inequality and its links to poverty and deprivation need to be informed by moving pictures and not just a series of snapshots.
What really matters, surely, is not how much more dispersed or less tightly bunched incomes in the abstract have become over time, but what happens subsequently to the individual people who are in, say, the bottom decile when a particular survey is taken.
Are they still there a year later? Or seven years later?
That sort of information - longitudinal, in the jargon - is scant indeed in New Zealand's case.
There is some, however. The Treasury published a report two years ago based on analysis of the results of Statistics New Zealand's survey of family, income and employment (Sofie to her admirers) which ran between 2002 and 2009 and surveyed annually the same 18,000 or so people.
It is a pity the survey stopped then, after a period during most of which the economy was growing strongly.
When people were ranked each year by income, the survey found a degree of mobility over time that the Treasury considers "substantial" and "surprising to many".
"Only 24 per cent of those in the bottom decile in 2002 were also there in 2009," it says. By contrast, 46 per cent of those in the top decile in 2002 were still there seven years later.
Between the first and second years of the survey more than one in four had changed by at least two deciles of income and by the seventh year 47 per cent had. But 26 per cent were still in the same decile in 2002 and 2009.
Income levels give only limited information about a person's financial situation.
There is world of difference between an impoverished student who is acquiring the human capital that will give her a comfortable living later in life and a solo mother with years of welfare dependency ahead, or a superannuitant who is asset rich but income poor.
The Treasury report uses as its definition of low income one that is less than 60 per cent of the median pre-tax income that year.
Sofie found around a quarter of the population had a low income in any single year and that over the seven years half the population experienced low income at least once. For children under 9, people over 65 and Maori those ratios were higher.
"Conversely, 43 per cent of those who experienced low income experienced it for only one or two of the seven years covered by the survey," it said.
"A substantial proportion of those who had some experience of low income soon moved to relatively high incomes."
Sofie then compared experience of low income with deprivation, which it defines as a person reporting three or more indicators of lacking basic needs as measured using NZiDep, a set of questions developed by researchers at Otago University and the Family Centre Social Policy Research Unit.
It found only a "modest" link between low incomes and deprivation, with only a third of those who had seven years of low income having suffered deprivation in that period.
The Sofie survey put those deprivation questions to its respondents in 2005, 2007 and 2009.
It found that just over 12 per cent experienced some deprivation during the survey period.
"Of those in deprivation in the first survey (in 2005), 44 per cent were in deprivation when this was again measured in 2007 and 2009," it said.
"Very few people over 65 are in deprivation, suggesting their lower income is offset by having greater accumulated wealth.
"Secondly, it is striking that deprivation is so prevalent among sole parents that even though sole parents are a small proportion of the population, they still make up the majority of people in deprivation by family type."
That is unlikely to have changed.
The Ministry of Social Development's latest report of household incomes - which principally draws on a different (but at least ongoing) data source, Statistics New Zealand's annual household economic surveys - found a growing gap between benefit levels on the one hand and average wages, median household incomes and New Zealand Superannuation on the other.
Between 2007 and 2014 the average wage and NZ Super rose 12 per cent in real (CPI adjusted) terms but the DPB plus family assistance (one child) fell 2 per cent.
"While there is no evidence of growing income inequality in the population overall or between high-income households and the rest in the last two decades or so, there is evidence here that there is a growing gap between the incomes of those heavily reliant on the safety net provided by main working-age benefits, and the rest," the Ministry of Social Development report said.
The Treasury report says much of the debate about poverty moves quickly to income inequality as the key measure but it prefers a focus on material hardship and the mobility that enables someone to make the most of his or her life chances.
In light of the Sofie data it questions whether policies intended to support people with persistent low income are well targeted, if the real target is deprivation andthe correlation between the two isloose.
Policy should be careful not to lean against income mobility by creating disincentives to work, it says.
But it acknowledges that deprivation is most prevalent among sole parents, whose mobility tends to be lowest.
"Given the potential intergenerational effects this group should be a high priority for policy."
Few would quarrel with that.
The number of people on the sole parent support benefit is currently 74,000 - down 10.7 per cent on a year ago and down 17.6 per cent on its recent peak of just under 90,000 in December 2011.
But that still leaves, depending on the measure used, between 205,000 and 260,000 children living in poverty.