Poverty and the Statistician

Presentation to the Wellington Statistics Group, 10 December, 2018

This year’s Child Poverty Reduction Act (CPRA) marks a major innovation in social policy. Politicians – here and overseas – have promised to eliminate child poverty at some date in the future. They never have and by the time the target date is reached the promisers have moved on and cannot be held to account.

This time the promise is embedded in an act of parliament. It does not actually say how the target will be attained but it proposes monitoring reductions in child poverty, regular reporting to parliament. It is not the first such act internationally. Britain passed a Child Poverty Act in 2010. There is a fascinating paper to be written comparing the two acts, especially as the British one has been running for eight years, But I leave that for another venue. This paper is about the underlying statistical base of the New Zealand act.

For, from a statistical perspective, it has some strange features Perhaps the oddest is that it does not discuss the concept of poverty despite it being central to the act.

It is true that there are numerous measures of poverty mentioned in the CPRA – I’ll come back to them – but a statistical measure is not a concept. Section 6 of the CPRA charges the Government Statistician with making decisions that define concepts and terms. It is extraordinary that Parliament has left a public official to define the most central issue in a piece of pioneering legislation.

There are difficulties defining the concept of poverty. In rich countries there are two quite different approaches. They are well illustrated by the 1972 Royal Commission on Social Security which identified the aims of the [social security] system as:

(i) First, to enable everyone to sustain life and health;

(ii) Second, to ensure, within limitations which may be imposed by physical or other disabilities, that everyone is able to enjoy a standard of living much like that of the rest of the community, and thus is able to feel a sense of participation in and belonging to the community.

(iii) Third, where income maintenance alone is insufficient (for example, for a physically disabled person), to improve by other means, and as far as possible, the quality of life available.

(Original’s italics.)

The first aim is consistent with a notion of an ‘absolute level of poverty’; the second aim defines a notion of ‘relative poverty’. (The third aim will come up as the presentation progresses.)

The Royal Commission saw the second aim of the system – that everyone should be able to enjoy a standard of living much like that of the rest of the community, and thus able to feel a sense of participation in and belonging to the community – as the basis of New Zealand social policy.

However, there are those who consider the first notion – of absolute poverty. with the state ensuring there is just enough to to sustain life and health – as the appropriate notion. This view appears regularly in the right wing blogosphere – imported from their US compatriots, I think. But it is also embedded in our existing social policy.

Recall that in the 1990 attack on the welfare state, the base social security benefit was cut from the level set by the Royal Commission to a much lower one. Except for a single lift in core benefits where there were children in 2014, its value adjusted for inflation has not been increased in the following 27 years. The clear implication is that subsequent governments have thought the level was adequate to sustain life and health while the recipients should not share in the benefits from rising prosperity. It enshrines an absolute poverty level.

In contrast, the level of New Zealand Superannuation was not cut in 1990 and its real level has been increased in line with rising real wages so that the elderly are expected to share the rising prosperity of the nation. This more European approach underpins relative poverty.

Probably the CPRA is intended to promote relative poverty. Yet there are some very ingenious people – like those who advised Ruth Richardson and Jenny Shipley – who could reinterpret the act’s undefined poverty line to an absolute poverty one. Certainly the act does not proscribe them from doing so and at various points it could be said to be introducing an absolute poverty notion as I’ll mention.

I am not going on to develop an elaborate definition of relative poverty here but instead talk about some of the treacherous issues arising when measuring poverty. I shall not do this by critiquing the CPRA, but by recalling my journey in research on poverty. What I am recounting here is set out in more detail in a memoir I am writing: Poverty, Inequality and Policy.

What definition of poverty am I using? In simple terms it is the 1972 Royal Commission’s approach of relative poverty with its crucial notion that people should be able to enjoy a standard of living much like that of the rest of the community, and able to feel a sense of participation in and belonging to the community. I have elaborated this notion in various ways, most importantly anchoring it in the philosophies of John Rawles and Amartya Sen.


When I returned from teaching in England in 1970 I chose distributional economics as my research topic, combining my interests in economic theory and statistical application.

It was a neglected field but had considerable practical applications. It was a huge field and I burrowed away. The question of poverty nagged at me. Almost all the useful income data was about individuals but poverty was a household phenomenon. Eventually I hit paydirt. The Department of Statistics ran a survey of household incomes and expenditure in 1973/4. It was the first such comprehensive data base.

Each household in the sample is asked to record its expenditures and income over the year, giving a ‘unit record’ for the household.

The income in the unit record is before tax, so I adjusted to an after-tax income including benefits. The disposable income is now transformed to an ‘adjusted equivalent income’ enabling the material standard of living of different size households to be compared, (I have more to say about this later;)

Next, we sneak in an important assumption: that the household shares its spending fairly. That is probably not quite true – for instance. Mothers will sacrifice their own wellbeing in order to support their children’s.

We then rank all the individuals in the sample, from those who have the lowest adjusted equivalent income to those who have the highest.

There is a detail here that is sometimes overlooked. The ranking is by individuals, not households. Ranking households can be misleading. For instance, it was recently mentioned to me that 40 percent of the poor were sole-parents and their children. Except they were counting households not individuals. Solo parent households are smaller than two-parent ones and there are many more poor individuals in two-parent households than in solo parent households.

We can now answer the following question. Suppose the poverty line is set at $X a year, then what proportion of the individuals are below that poverty line? Observe that if one has some characteristics of the individuals – say whether they are children – a poverty count can be done for the subgroup.

Couple of points for statisticians here. First sample sizes of some sub-groups in the Household Economic Survey means that there is high sampling variation and the estimates can jump around from year to year. That is the reason why the 2018 MSD report does not cover some subgroups which were considered in earlier reports. There is a need for the HES to over-sample some key groups.

Second, the method is essentially working with the cumulative frequency distribution of equivalent household incomes. The curve is steep in the range where the poverty lines fall. So even in the unlikely event of the commutative curve being accurately estimated, small changes in the choice of poverty line can result in large jumps of the numbers in poverty.

Despite these effects, known at the time, this method is broadly what I did, except I did not have access to the unit records. So I had to apply an estimated average tax rate in each category to get the disposable income; there was no alternative.

The relative poverty line I used was that judged by the Royal Commission on Social Security as the minimum to meet its second aim. (I called it the ‘Pensioner Datum Level’.) So I was not imposing my assessment of the poverty line but using an external and eminent social judgement.

My basic conclusion was that the following fell below the PDL

– 20 percent of persons over the age of 60, or 75,000 people;

– 25 percent of children, or  250,000 people;

– 20 percent of their parents, or  190,000 people;

– 5 percent of other adults, or  35,000 people;

a total of

– 18 percent of the population, or 550,000 people.

The estimate of over half a million below the chosen poverty line may be called a ‘Gee-whiz’ figure. It is great for headlines and shocking people but only offers some broad insights.

There was one salient conclusion. According to the RCSS judgement, poverty in New Zealand was a significant issue for a large number of people. There was no inherent reason why the figure was not lower, say 55,000, which perhaps the complacent would have thought reasonable. What the gee-whiz figure suggested was that New Zealand could not be complacent; that around one in five New Zealanders did not have an acceptable living standard. This was published in 1976; we are getting there.

As well as the conclusion that relative poverty was a major problem in New Zealand there were two other major takeaways. First, it was a pioneering approach in New Zealand. I was told in 1980 that New Zealand was in front of the international research effort, a lead we soon lost.

The approach was taken up by the Department of Statistics who developed a computer model based on the unit records I never had access to. The model, with improving quality of the data, has evolved into the standard workhorse for evaluating the household income distribution. The MSD annual report on households incomes uses this approach.

The second critical takeaway was that it refocused on who were poor. The conventional wisdom was that the poor were either beneficiaries or those unable to provide fully for their families because of special circumstances. What this estimate, based on survey evidence, showed was that the poor in New Zealand were (and are) mainly children and their parents, and that many of those parents were in households which were in receipt of near- and above-average wages. It would take a long time for this to become the conventional wisdom. This year’s legislation is surely the official imprimatur – 40 years later.

Household Equivalence Scales

The above account has skipped over some issues of interest to statisticians.

Recall that it is necessary to compare the effective spending power of different households. In practice, our households are compared by the numbers of adults and children. Importantly, we do not allow for the age of children though obviously their needs vary. For instance, an adolescent girl needs more food than her father; I do not discuss clothing allowances.

The studies use a Household Equivalence Scale. In principle it is a table which sets out the relative needs of a household with, say, A adults and C children, compared to a reference household of, say, two adults. In practice the table can be summarised by a simple mathematical function involving a couple of parameters. One parameter gives the relativity between the average adult and the average child; the other measures the household economies of scale, since a household with more people can make some savings compared to people living in separate households.

The immediate reaction of a statistician is that we could estimate the parameters, but that is not what happened. Rather, the standard HES we use. reflects a personal judgement for which there appears to be no systematic empirical evidence. The parameters were first set in 1978 and then changed in a 1988 for no clear reason. The 1988 household equivalence scale is the one used by the Ministry of Social Development and most poverty commentators, although the annual MSD report provides estimates for some other scales but they were not estimated either.

There is no guidance given in the current legislation about the choice of Household Equivalence Scale. The impression is that the drafters of the statute were not even aware there was a problem.

Fortunately, there have been empirical attempts to estimate an HES based on evidence. Stalwart statisticians included Harry Smith and Srikanta Chatterjee but the best New Zealand work was by Claudio Michelini of Massey University.

When I was working with Suzie Ballantyne on a short-lived HRC grant I had planned to estimate HESs. Fortunately Claudio took over the hard grind, estimating scientifically based equivalence scales from ‘preference-consistent extended linear expenditure systems’. Thus Claudio (and other econometricians) derived HESs from actual data – from the evidence of how people behave. Claudio and I discussed how his scale could be improved. He was keen to do so but, alas, he was struck down with a brain tumour in the middle of his project and so his work was never completed.

Does it matter? Many people see little difference when they look at the scales. But the small differences can matter a lot. For instance, if you used the Michelini scale rather than the official MSD scale, the relativity between those in single households and couples changes quite markedly.

You might think that by using the same Household Equivalence Scales as other economies gives them some integrity. Exactly wrong! Institutional arrangements matter. To see this, consider what would happen if the government abandoned free education and give each household the cash equivalent. Since their income would go up, each family would be less likely to be measured as in poverty. The paradox arises because the household equivalence scale should be adjusted for the additional schooling charges the household faces.

So arrangements in public supply of services, such as education and health, matter. Price changes, including the cost of servicing a mortgage, matter. It would be a miracle if a household equivalence scale which was correct in 1988 was as true thirty years later.

The different HESs give different estimates for the numbers below the poverty line – generally the Michelini numbers of poor are higher. The composition of the poor is also affected – the Michelini HES finds more poor children and their parents in multiple adult households than does the official MSD one.

Looking at the evidence makes me pretty sure that the assumed economies of scale effect is too strong. That would mean that the poverty line (and therefore recommended support) for large families is too low and any count of the poor in large households is underestimated. It gives policy an incentive to address poverty in small households, ignoring it in large ones where it is more serious.


Spending on accommodation is always a difficult issue. The problem arises because a family in exactly the same house may have quite different outgoings: they may be paying the market rent, or their rent may be subsidised, or they may own the house freehold and their outgoings may be just rates, insurance and maintenance, or they may own it with a mortgage so that on top of the freeholder’s outgoings there will be the debt servicing, and there are those who pay next to nothing because the house goes with the job or there is some family or trust arrangement.

The counsel of perfection is that the difference between outgoings and the market rent should be treated as additional income (or perhaps negative income). Applying the counsel is tricky. Suzie and I made good econometric progress and the indications were that it improved the statistical results. But Claudio did not stay around long enough to apply our approach to his HESs.

The alternatives have been either to ignore the housing outlay problem or to deduct the housing outlays from income. Both are proposed in the new CPRA.

The argument for ignoring it may be that income support should be adjusted for housing outlays as is done to some extent (e.g. via the accommodation supplement or subsidised state housing). At the aggregate level it is assumed that the impact of the heterogeneity will average out so the total in poverty is not affected. That is unlikely but the overall effect may be small. Even so, it is likely to lead to an undercount of those with heavy mortgage outgoings. Conversely, some of those who have lower outgoings may appear to be below the poverty line when they are actually a little better off.

Deducting housing costs from income might seem to be a good idea, although an economist bridles at deducting a spending flow from an income flow – it is like subtracting apples from oranges. Fastidiousness aside, the next step by the orthodoxy is astonishing: the same household equivalence scale is applied to income less housing costs as the one applied to total income.

But the standard HES, used where housing costs are included, has strong economies of scale arising from the cost savings that large households have in their housing bills. If the HES is correct for total income, it must be wrong for income less housing costs where there are not the same economies of scale. The consequence is that once more the incidence of poverty is under-represented in larger households. (The 2018 MSD reports uses a different OECD scale when adjusted housing costs are deducted, with lower economies of scale. It is not empirically based.)

In conclusion using the current arbitrary Household Equivalence Scale probably underestimates the poverty line and the numbers in poverty of the following:

– those in larger households

– those in households with adolescent children

– those with high housing costs arising from high mortgages or high rents

– those in households with workers with employment costs.

Choosing a Relative Poverty Line

Back in the mid-1970s, the Royal Commission judgement as to the relative poverty line, based on listening to the evidence submitted to it, was the best we had. With time, we try to find a better estimate.

In the 1990s, the Poverty Measurement Project asked focus groups of relatively poor people what they thought was the minimum adequate household expenditure for their households.

Unfortunately, the results were nonsensical – they seemed to suggest an individual adult would be satisfied with a negative income.

Eventually the Project abandoned the focus group approach and settled on a proportion of median equivalised household incomes. Where they got the notion from is unclear, although it is used in international comparisons, perhaps because it is tricky to calculate the top and the bottom of the income distribution. The median benchmark is central to the poverty indicators in the CPRA.

The median is the middle of the income distribution with as many above it as below it. Advocates argue over whether the percentage should be 50 or 60 of the median income. They do not provide much evidence for their opinions.

The weakness of a median income benchmark is illustrated by the following paradox. A median-income-based poverty line makes it possible for measured poverty to be reduced by taking income from those in the middle of the income distribution and giving it to those at the top. The income of the middle household falls and so does a median-income-based poverty line. Thus numbers of those measured in poverty are reduced even though there is no change in the living standards of the poor.

Suppose the median (middle) income is 100 units, and we use the 50 percent of median income poverty line, so anyone in a household below 50 units is in poverty. Now suppose the government rejigs the tax system in favour of the rich by raising taxes on those in the middle and using the proceeds to cut taxes at the top. Suppose the higher taxes on the middle reduced median income to 90 units from 100 units. The measured poverty level falls to 45 units and all the people in the 45 units to 50 units income range are no longer deemed to be in poverty.

This is not just a meticulous scholar-statistician generating a theoretical paradox. This actually happened when in the early 1990s, when the government redistribution transferred income to the rich. The Poverty Measurement Project reported the numbers in poverty fell. Any objective observer at the time saw plenty of evidence of rising deprivation. Yet the faulty poverty measure showed exactly the opposite. Both the Treasury and a right-wing think-tank, the Business Round Table, trumpeted the success of their pro-rich redistributive policies at reducing poverty.

It is not hard to switch to a mean benchmark: 60 percent of the median is would be 49 percent of the mean today. Before 1990 it would have been 54 percent. In effect the pro-rich tax changes in the late 1980s cut the relative poverty line by 10 percent if it was benchmarked by the median.

Not only is the mean easier to understand, has better statistical properties and is harder to manipulate, but it is also easier to forecast. A statistician is left bewildered when we use the median benchmark.

The 50 percent median seems too low, at least in terms of one case study in which I was involved. In 2012 I had the task of offering guidance to the Social Security Appeal Authority as to the income which would be sufficient to enable a particular family of Meg and her early-teenage daughter, Stacey, to attain an adequate standard of living. Since this involves judgement, I estimated ten different rates. One – based on American standards – was clearly too high but eight clustered around $540 p.w. In contrast, the family’s actual income was about $470 a week, so they needed a 15 percent boost (plus more for exceptional expenses).

There was a lower outlier, well away from the other eight estimates. It was the 50 percent median figure of $455 p.w. – much the same as what the family was actually receiving.

But the amount the family was receiving was clearly inadequate. There is an uninformed view that all the poor really need is financial advice. This family had gone to the local budget advisory service. The budget it prepared for them provided for food, housing, electricity, medical and educational costs, transport and phone. It left them with just $19 a week for everything else: clothing and footwear, entertainment, recreation, dental care, consumer durables, insurance, haircuts, presents, school trips and pets.

It was hard to conclude from the budget that the family had an adequate standard of living which would enable them to belong to and participate in society. The conclusion is reinforced by two instances.

To eke out their inadequate income the two skipped some of their medical needs, but the big saving was on food, usually only $40 to $80 a week, well below the level of $130 for the simple but nutritious meals recommended by the University of Otago Department of Human Nutrition. Meg and Stacey depended on chips. They knew it was not healthy but chips are the cheapest way to fill one’s belly, putting off hunger and leaving some cash for other necessities.

Second, not only was Stacey’s health compromised by poor nutrition, unhealthy housing and skipping some healthcare but she was excluded by not being able to afford to participate with her school friends in social events (while I was there she missed out on going with them to a gig). These compromised her education, as did the lack of funds for the ongoing charges schools place on today’s children. Stacey’s adulthood prospects were not good.

One concludes that a 50-percent-of-median poverty line is far below any relative poverty line the Royal Commission might have envisaged. Yet it is included among the indicators in the CPRA. But even were it to be struck out, the reference to a median benchmark remains treacherous.

Instructively, the British Child Poverty Act does not contemplate a 50 percent median poverty measure, mentioning only the 60 percent one. One has an uneasy feeling that the New Zealand legislation enables us to sneak back to an absolute poverty line, if a government wants.

Non-Income Measures of Poverty

The paradigm used in the CPRS was developed in the 1970s; can we progress? Then I used income because I did not have any other measure. In any case, supplementing income is the main means of dealing with poverty (although, as the Royal Commission’s third aim mentions, there are others).

In fact, back in the early 1970s there had been an attempt at an alternative approach. In 1974 David Ferguson led a DSW study of the living standards of the elderly, which was used to calibrate an appropriate public pension level for them. It is implicit in the analysis I did of Meg and Stacey.

From 2001 the MSD has been constructing a scale based on non-monetary indicators which will measure economic living standards. (Its acronym is ELSI). It was an early innovation in the now fashionable international effort to better measure wellbeing.

Essentially it involves asking a sample of households some 40 questions that relate to

– possessions (personal and household items),

– social participation activities (interaction with family and friends, holidays),

– degree of economising – including having no need for economising – across many areas (food, clothing, recreation, use of medical services),


– self-ratings (of the respondent’s standard of living, satisfaction with standard of living, and adequacy of current income to meet basic everyday needs).

From these are constructed the ELSI scale.

In principle the ELSI scale could be used as a measure for individual poverty identification but, practically, misleading responses to the questions could raise the amount one was entitled to. Essentially the ELSI is a research tool. (The MSD have moved onto a Material Wellbeing Index (MWI) and a deprivation index (DEP-17).)

Currently the MSD reports on the ELSI each year separately from its income report, but with attention to the relationship between the two. In principle one could use the ELSI scale to set a poverty line. Perhaps the CPRA refers to the ELSI in various places. But it still involves a judgement.

(Incidentally, there has been little serious statistical investigation of the data bases in either he Household Survey, the ELSI (or SOFIE discussed below) despite each having a rich statistical base. Fundamentally this is because an unwillingness to fund serious research into household incomes and poverty (although limited access to unit records has not helped.)

When I look at the set of questions I wonder whether they are over-dependent upon choices by middle-income middle-aged males. As far as I know, there has been no attempt to do a pre-survey asking people what they think should be asked.

I mention – this became very evident as I wrote my memoir – that one of the constant challenges I have had in my research work has been to ensure the distinctive features of women’s experience are recognised – a particularly important issue since more women than men are in poverty.

This is not an uninformed rant against male statisticians; rather it is a wish that there were more top-quality women social statisticians. There have been numerous places where I had to recognise women were different, but another example has arisen recently – period poverty. There is no relevant question in the ELSI questionnaire. How should it handle an issue which is clearly vital to some but not to everyone?

The same is true for children even if the poverty focus is on them. Earlier I mentioned mothers who make sacrifices to enhance their children’s wellbeing. Perhaps sometimes children do the same to protect the rest of the family.

An even bigger problem is that, as I mentioned with Stacey, deprivation now may affect future life chances. Here we are suing a wider conception based on, say, the RCSS’ notion, or that of Rawles or of Amartya Sen’s notion of ‘capabilities’ – which is a development – inhibition of life chances is clearly a serious part of the concept of poverty.

Sadly there is not a lot of data which enables the assessment of life chances. The New Zealand longitudinal studies did not collect a lot of economic material on the families involved. The recently reported MSD study which was interpreted by some to show that poverty caused criminality, It is based on evidence about families with nine month children. The confidence interval for prospects two decades out must be huge.

Just to complete the dynamics story, I mention the Survey of Family, Income and Employment (SOFIE) which enabled tracking household incomes over seven years. It showed many experience ups and downs which may mean they are below the income poverty line for only part of the time. However, some households remained recalcitrantly below the line through all seven years. Sadly, but as you might expect given the sad state of our social analysis, the valuable survey has been ended.


We conclude that the new legislation aiming to reduce child poverty has a poor quality statistical base but it is going in the right direction. Does it matter?

While low quality analysis is irritating to a professional statistician, the system envisaged in the CPRA can also be corrupted. Recall Gilling’s Law which states that the way the game is scored shapes the way the game is played. What if the scoring system is distorted?

Even if the poverty reduction game is played by people of goodwill, distorted outcomes are going to happen. I have mentioned how the system seems to be biased against households with more children. An even more egregious possibility is that, as I have explained, on some poverty measures one can get a reduction in measured poverty by tax cuts which favour the rich with no effect on the living standards of the poor. If one is competent, it is easy to think of many more ways of corrupting the outcome. I wont describe them; I am not applying for that job.

As in the case of the bias against large families, the poor quality outcomes may occur unintentionally. Consider the minister looking at various policy options each of which has the measured poverty reduction. The minister is likely to choose the one which gives the greatest measured reduction. Except it may not have the greatest impact on reducing poverty.

I regret having to come to such a sad conclusion. One wonders how we have ended up with such a mess. The answer may be the poor statistical skills of the social policy community.

The government has embarked upon a courageous course to reduce child poverty. The Child Poverty Reduction Act is a mix of visionary political leadership with inept social policy and analysis. Let us hope that leadership outweighs the inept.