The top and bottom quintiles (or fifths) of the income distribution tended to be more stable, the researchers found, with those in the highest quintile having a 72 per cent probability of remaining there the next year, while those in the lowest quintile had a 65 per cent chance of still being there the following year.
Over the whole seven years around half of those who started out in the highest quintile were still there at the end.
Likewise around half of those in the lowest quintile in 2002 were still there in 2009.
Mobility was greater among those in between.
The study defines low income as belonging to a household with an income less than 60 per cent of the median, before tax and when adjusted for the number of people in the household.
It found that between 23 and 25 per cent of the survey population were in the low income bracket each year.
But the "before tax" qualification is important. It does not adjust for the progressivity of the income tax scale or for Working for Families tax credits.
Other studies, based on a cross-sectional snapshot, have about 18 per of the population in the low income bracket, using the same 60 per cent of the median threshold but disposable or after-tax income.
Half the income survey population experienced low income for at least one year, a fifth for four years or more and 6 per cent for all seven years.
The data revealed a high degree of persistence or recurrence of low income, the researchers said.
Of those with a low income in year one, half had a low income in year seven and a quarter were in the low income bracket for all seven years.
The study distinguishes between low income and deprivation.
Deprivation is defined in terms of how often people answer yes to eight questions about such things as whether they have been forced to buy cheaper food in order to pay for other things they need, whether they have had to put up with feeling cold to save on heating costs, whether they have continued wearing shoes with holes in them, or whether they have had recourse to food banks. It was measured at three points of the survey.
About 12 per cent of the survey population were in deprivation at least once and 6 per cent were at each of three times it was tested.
Tracking the same people over time shows that twice as many people experienced low income at some stage as a snapshot survey at one point in time would indicate, 50 per cent against 25 per cent.
And it is a similar story for levels of deprivation. What the study does not tell us is how income mobility relates to life events, such as having a baby, getting divorced or retiring.
But it does give correlations between sub-groups of the population and low income or deprivation, and the persistence thereof.
If anything, it will underestimate those correlations because the more vulnerable groups were more likely to drop out of the study for one reason or another. The groups at greatest risk of persistent deprivation are sole parents and Maori.
Sole parents make up about 10 per cent of the population but 40 per cent of those in the persistent deprivation category. Maori are more than twice as likely to be persistently deprived as their share of the population would explain.
The young, those under 25, are also disproportionately represented.
Among the 16 per cent of the survey population with a persistently low income - that is, with a low income in at least five of the seven years surveyed - the groups which are over-represented are those over 65, Maori and other non-Europeans, those with low qualifications, sole parents and those not part of a couple.
Conversely those at least risk of low income are young adults, between 18 and 24, Europeans, university graduates, couples with children, and those living in Wellington.
Reflecting on the study the Treasury takes a glass-half-full approach.
While half the population experienced low income at least once over the seven years, 43 per cent of that group experienced it for only one or two of the seven years.
"A substantial proportion of those who had some experience of low income soon moved to relatively high incomes. Such short periods of low income are highly unlikely to be linked to deprivation," the Treasury said.
"The level of mobility already found in New Zealand raises the issue of whether the key focus of government is less upon supporting those in current low income and more on building resilience to resist becoming 'stuck'," it said.
It emphasises that low income and deprivation or material hardship are not the same thing.
"Despite low income, incidence of deprivation among over-65s is very low.
"In contrast, incidence of deprivation is strongest among sole parents, and mobility tends to be lowest."
Because of the potential inter-generational effects, sole parents should be a high priority for policy, the Treasury said.
No doubt Paula Bennett would say they already are.
But whether the welfare reforms are the right policy remains to be seen.
