Measuring Poverty: Some Problems

Social Policy Journal of New Zealand, November 1997 (9), p.171-179. (1)

Keywords: Distributional Economics; Social Policy;

While it is easy to be compassionate over the magnitude and situation of the poor, it is not in their interest for researchers to be as equally sentimental in the analysis and measurement of poverty. Estimates which are not developed rigorously may be misleading, and may be so in a way which could be used against the interests of the poor. Where an estimate of the numbers of the poor is overly generous, the resolution of reducing poverty appear excessively expensive, and may delay the facing up to the issues. Wrong assessments of the composition of the poor may result in policy targeting the wrong groups. Thus policies based on faulty data are likely to be inefficient and wasteful, and in the end to be manipulated against the interests of the poor.

Thus it is incumbent on social scientists to scrutinize the work on poverty, to ensure that it is seeking high standards of analytical rigor. A recent paper by Stephens, Waldegrave and Frater (Stephens et al, 1995 – henceforth SWF) provides a useful basis to do this, albeit some of the problems it raises appear elsewhere.

Focus Groups

SWF reports the use of focus groups (selected groups of people with chosen characteristics) as a means of identifying a poverty line by asking their judgement as to the minimum adequate household expenditure for a household of one adult and three children, or of two adults and four children. The households came from Porirua, and there is little guidance as to how representative the sample is or, for that matter, how the households were selected. This paper does not propose to investigate this issue. Insofar as there are systematic differences between ethnic groups and between household compositions, or between household income strata, there are serious problems of interpretation, and useful policy conclusions are difficult to infer.

SWF also note that the focus group conclusions could be sensitive to the precise way in which the groups are managed, and questions posed. (p.90-92) Again this is not pursued here, except to note that the issues have not yet been investigated by the Project. Related is the need to apply the method using facilitators independent of the Project to assess the extent of experimenter bias. At this point we simply use the raw scores to draw attention to some further problems with the conclusions – implicitly assuming that the method itself is valid.

Unfortunately the raw scores are not published, indicative of an approach which is almost totally bereft of statistical analysis. However Table 4 of SWF includes averages for various subgroups. If we assume there is no systematic differences between the subgroups (a point raised a couple of paragraphs ago), and assuming that there are 65 observations in the original sample, we can estimate the standard error of the estimated means as $5.70 p.w. in the case of the $471 p.w. for two adult, two children households (i.e. 1.2 percent of the mean), and $6.45 p.w. in the case of the $386 p.w. for the one adult, two child household (i.e. 1.7 percent of the mean). (2)

Does this error matter? From Easton (1995c), we observe that in 1992/3 the change of the poverty line from $14050 p.a. (in 1991/2 dollars) to $13050 p.a. (that is by 7.1 percent), reduces the numbers in poverty (i.e. the headcount measure) from 16.3 percent to 13.2 percent, or 19 percent. (3,4) On this basis the Project estimate of the number in poverty in New Zealand has an inaccuracy of between 6 and 9 percent (using a 95 percent confidence interval), assuming the very favourable assumptions apply, including ignoring potential systemic bias such as the accuracy of the cumulative frequency curve based on the household survey, and of the household equivalence scales.

So sampling does not seem to be the major source of inaccuracy. Instead, observe how the focus groups consider a household with an extra adult and child requires only an extra $85 a week. It is not hard from the data to calculate that the focus groups think that an extra child costs $301 p.w. a week and an extra adult costs negative $216 p.w. (5) These figures are clearly nonsensical. The problem cannot be readily resolved by assuming strong economies of scale.

SWF identify the problem, (p.96-97) but they do not make the obvious point. It is difficult to believe that the addition of one adult and one child into the household (of one adult and two children) adds only an extra $85 p.w. in additional minimum necessary expenditure. The two estimates do not seem consistent. (6)

Suppose we adjust the SWF data by a household equivalence scale (HES). SWF use the Jensen-1988 scale, of which more will be said shortly. In which case the minimum adequate income for two adults and three children was $471 p.w. according to the direct estimate, while it was $537 p.w. adjusting the estimate of the one adult and two children figure ($386) to two adults and three children, using the Jensen-1988 HES. (7) The $66 p.w. gap is considerably greater than the standard errors of the differences between the estimated averages. The focus group approach results in a estimated difference of about a 14 percent between two procedures which ought to give the same outcome. The inaccuracy of the poverty number estimates as a result will be over 30 percent.

Relating the Focus Group Estimates to the National Distribution

The focus groups estimate a “minimum adequate household expenditure” on a weekly basis. which can be grossed up to annual expenditure. In order to keep it consistent with the standard literature the line is converted it to the standard household size of two adults, using the Jensen-1988 HES. This gives a figure of $14,895 p.a. for a two adult household based on the 2 adult, 3 child focus group average and $16,995 p.a. for a two adult household based on the 1 adult, 2 child focus group averages.

By way of comparison, the standard RCSS-BDL (Royal Commission on Social Security Benefit Datum Line) – the poverty line based on the recommendation of the 1972 Royal Commission on Social Security for a standard benefit in 1990/1 prices was $14,585 p.a., which is within the margin of error of the estimate based on two adults and three children, and making the SWF claim that the BDL Is “no longer appropriate” contradictory. (p.89)

To estimate the changing level of the poverty line over time, SWF backdates the focus group assessments to 1990/1 using the Consumer Price Index. (p.99) This is the same method used for updating the RCSS-BDL, but they also flirt with other methods, which are much more problematic.

In particular much is made of a proposed poverty line in relation to the median household income (adjusted for composition) – especially the setting of the poverty line at 50 percent and 60 percent of the median. This is a deeply flawed notion.

Table 1: How the A Median Based Poverty Line Gives Contradictory Results with Increased Inequality

Before Tax
After Tax
1 1 1
2 2 1
3 3 2
4 4 3
5 5 4
6 6 5
7 7 7
8 8 8
9 9 12
Mean 5.0 5.0
Median 5.0 4.0
Poverty Line
50% of Median
2.5 2.0
Households Below
Poverty Line
1,2 1
Percent Below
Poverty Line
22.2 11.1

Consider a nation of nine households, numbered 1 to 9, and conveniently each in receipt of the same amount of income as the household number. (Table 1) The middle household is number 5, its income is 5, which is the population median (and mean). Suppose we set the poverty line as 50% of the median, which gives a line of 2.5. Households 1 and 2 are below the poverty line and so 2 out of 9 (22%) of households are in poverty.

Now suppose the government raises taxes on the three middle households (4,5,6), lowering their income in each case by one unit, and gives the additional three units to the richest household (9). There has been an unequivocal increase in inequality. Yet the income of the middle household has fallen to 4, and so 50% of the median has fallen to 2. Now there is only one household below the poverty line, and so the incidence of poverty has halved. According to a poverty line based on a proportion of median incomes, transferring income from middle to rich households, both increases inequality and reduces the incidence of poverty. A median based poverty line is anti-poor, because it can be used to justify policies which increase inequality and yet give the appearance of reduced poverty.

This is not just a theoretical possibility. Table 7 of SWF shows the median falling 17.1 percent between 1983/4 and 1992/3, while the mean falls only 5.4 percent. This divergence is not only from policy changes which have tended to advantage the rich relative to those in middle incomes (e.g. the substantial reductions in top tax rates), but there are also changes in the income distribution over time. (Easton 1996a)

The falling median leads to foolish conclusions if a median based poverty line is used. Figure 3 from Easton (1995) not included here shows the numbers in poverty according to three definitions of the poverty line: the standard RCSS-BDL, one which is adjusted with changes in mean income, and one which is adjusted with changes in median income. The graph confirms Table 8 of SWF. Because the median income is falling so quickly, the proportion of people below the median based poverty line has fallen since 1980/1. While this conclusion may give comfort to anti-poor advocates of the reforms, it an obvious nonsense in the light of the actual experiences of the poor. Not surprisingly the more rational poverty lines, related to an absolute level or mean income, give a result more consistent with reality – poverty has on the whole been rising, especially sharply in the 1990 to 1992 period.

As SWF says, it is not at all obvious that the surveyed focus groups think of their poverty line in relation of median income (if they think of a median at all). SWF seem to have confused two issues. It is true that any line nominated by the focus groups will be some proportion of the median equivalent income, and indeed any other income statistic no matter how irrelevant (such as the Kuwaiti per capita GDP). However that does not mean the proportion has any significance whatsoever or that, in particular, the proportion is likely to be constant over time.

SWF point out the particular percentage of the median may change each year (p.89,90.109) but they give no indication how it might change, and indeed use exactly the same percentage for their Table 8 for the period from 1983/4 to 1992/3, giving the impression that a constant ratio is appropriate for long periods, even if the distribution of income is varying. Certainly some commentators using their approach have used the constant percentage assumption to conclude that poverty was falling over the period. (e.g. Barker 1996a,b; Kerr 1996a,c), This suggests that at the very least SWF have failed to emphasize the inappropriateness of the constant percentage assumption. And if the percentage is not constant over a reasonable period of time, why use it with the implication that the median is some sort of base parameter for indexation.

The indexing problem is nicely illustrated by the SWF paper itself. The focus groups gave a figure of $14,985 p.w. and $16,995 p.w. in 1990/1 prices. SWF uses these figures for the 1990/1 poverty lines. That makes them 51 percent and 58 percent respectively of the 1990/1 median of $29,942. (SWF Table 7) However the same poverty lines are 54 percent and 62 percent of the 1992/3 median. If SWF had projected the focus group averages back to 1981/2 (which is but a minor generalization of what SWF does on page 99), the proportions would have been 46 percent and 53 percent. The SWF method is generating a plethora of confusing figures, leaving the policy maker to select arbitrarily whichever suits the prejudice. (8)

The Household Equivalence Scales (HES)

Many of the problems with of the household equivalence scale used by SWF – the Jensen-1988 scale – are well known and documented. (Brashares & Aynsley 1990, Easton 1980b, 1995b, Perry 1995). The most serious issue is that an HES needs to have an empirical basis, which will be related to local conditions, and cannot be dependent upon foreign studies. For instance, different patterns of prices affect the HES. This is evident from the conversion of the scale HES based on New York expenditure patterns and prices, which Cuttance (1974) used in his pioneering study of poverty in New Zealand, and the same expenditure patterns in New Zealand prices. (Easton 1973) Children became relatively cheaper, and the household economies of scale were stronger. The New Zealand HES needs to be based upon domestic prices and domestic expenditure patterns.

Changes over time will also alter a local HES. The relativity between children and parents will be affected by the level of educational fees, and the pattern of user charges for health care, while changes in housing assistance by the state will affect the strength of household economies of scale. Use of a non-empirically derived scale such as the Jensen ones, or ones based on overseas studies, is clearly unsatisfactory.

SWF raise a further – and wider – criticism: “it is thus debateable as to whether equivalence scales appropriate for all incomes should be used at the low end of the income distribution.” (p.97) Unfortunately the rest of the paragraph confuses household composition with household income, so other than raising the point SWF contributes nothing. One is left with the feeling that because their focus group estimates with different family size cannot be reconciled with any sensible account (above), they find it easier to blame the HES tool, than the workmanship. In any case having raised the point, SWF ignore it, and within a few pages are uncritically using the Jensen-1988 HES – as will be shown in the next section – wrongly.

This section focuses on the problem of the non-empirical content of the Jensen HESs and the sensitivity of results to parameters which cannot not be verified. Easton (1995b:94) simplified the discussion to comparing the five available New Zealand HESs (two of which are due to Jensen) to two parameters, and noted that the Jensen-1988 had the highest household economies of scale – that is large households have lower per capita costs.

This has an interesting effect on the poverty line for the reference two couple household, given one derived form the focus groups which were larger households. dealt with larger ones. Table 2 shows how as the scale factor gets reduced (giving stronger economies of scale) the poverty line for the reference household rises (e.g. the fall in the scale factor for the Jensen scale form 1.77 to 1.58 raises the poverty line from 266 to 297. The effect is less clear with the other comparisons, because they have other obscuring assumptions.

Table 2: Reference Household Poverty Line for different HES
Base: 2 Adults and 3 Children = $471 p.w: Reference Household: 2 Adults

HES Scale
Poverty Line
Jensen-1978 1.77 266
Jensen-1988 1.58 298
Easton-1973 1.65 286
Easton-1980b 1.81 260
Smith-1989 1.90 248
(RCESS-BDL) n.a. 280

Source: See Easton (1995b)

The poverty line for the reference household is thus very sensitive to the choice of HES and/or the household on which it is based. In particular the use of the Jensen-1988 HES results in the highest poverty line under the SWF approach.

Does this matter when, for instance, a headcount poverty measure is made? We do not know. (9) Although Brashares (1993) argues that different equivalence scales will give broadly equivalent income distributions, an inspection of the evidence she cites (Rutherford et al 1990) suggest otherwise. The very steepness of the cumulative distribution in the relevant range means quite small differences may lead to substantial changes in the headcount estimate.

Moreover, a different HES will give a different composition of the poor. In particular those with high economies of scale (such as Jensen-1988) will underestimate the numbers of people in large households relative to those in small households, compared to an HES in which there are low household economies of scale. The policy implications could be enormous. That Jensen-1988 has been the scale that has been used in so much policy analysis, may explain one of the reasons why so little attention has been paid to the poverty problems of larger households. Since these tend to contain children, policy towards income support of children has probably suffered.

In the case of SWF, unless they can find a valid justification for the use of the Jensen-1988 HES, their headcount numbers are subject to yet another source of inaccuracy, and their estimates of the composition of the poor in Table 6 of SWF are probably misleading.

Adjusting for Housing

SWF rightly recognize that such is the variability of housing circumstance – especially between renter and home owner (and with and without mortgage), ideally there should be an adjustment for it. There are two obvious ways. The value of owner occupied housing can be imputed in, so that all households are put on a rental equivalent base with the homeowner receiving an imputed income for their more favourable situation (because of lower outlays). (Easton 1995a); or, Housing expenses can be netted out, so that only non-housing expenditure (or a hybrid concept of income less housing expenditure) is assessed.

Neither approach is ideal, but having access to unit records SWF chose the second. Unfortunately they made a dreadful error, which makes their results invalid. After deducting housing expenditure the residual is scaled by the Jensen-1988 HES. Now the Jensen-1988 HES is based on a notion which includes housing expenditure. The scale would only apply to non-housing expenditure (or the hybrid notion), if housing expenditure was a constant proportion of expenditure (or income) independent of housing composition. It is not. One of the major sources of economies of scale is that per capita housing requirements fall as the household gets larger.

An example for SWF illustrates this, albeit perhaps in an exaggerated way. (10) SWF’s Table 3 gives the minimum adequate household expenditure as assessed by Maori households for 2 Adults, 3 Children Households and 1 Adult, 2 Children Households. The respective totals are $475 p.w. and $374 p.w. The ratio between the two of 1.27 is an implicit HES ratio for the household composition pair. The figures for non-housing expenditure are $325 p.w. and $224 p.w., giving the implicit HES ratio for non-housing expenditure of 1.45, substantially higher than the HES ratio for the expenditure including housing. Thus the implicit HES without housing has much weaker economies of scale than the HES with housing.

It is not obvious how to adapt the Jensen scales, since they are not based on empirical evidence. The Easton-1980 and the Smith-1989 scales could have been estimated on a non-housing basis, but were not, and so cannot be used in this context. However the Easton-1973 scale can be adapted. Its scale factor rises from .64 with housing to .98 without. That is according to this HES the main household economies of scale derive from housing. (12) (1.00 would mean there are no household economies of scale.)

What is the consequence of applying an HES which includes housing expenditure, instead of an HES which excludes it, where the latter is more appropriate? The effect will be to exaggerate the role of housing in the expenditure patterns of individuals, and increase the proportion of the population below the poverty line. which is exactly what SWF report. However the likelihood is that this phenomenon is yet another consequence of the faulty application of statistical techniques rather than reflecting some actual reality. It is interesting that the only application of the first housing adjustment (i.e. imputing back income) did not markedly change the numbers in poverty but – not surprisingly – it did change it composition. (Easton 1994)


This note has considered a number of aspects of recent poverty research. The basic paradigm of the research was established by the end of the 1970s. (13) (Easton 1980a) Except for direct access to household unit data and the use of models such as ASSET and TAXMOD to process the data, (14) there has not been a lot of genuine progress in the use of the paradigm since then. Thus we have learned little new about poverty despite a lot of effort, too often without much understanding of the underlying paradigm. For instance most of the claims of SWF, may be true, but they are not proven as the result of the application of rigorous quantitative methods.

The one major significant innovation in recent years is that we are now able to trace the distribution of adjusted household income, and hence poverty lines over a number of years since 1980/1. (Mowbray 1993, Krishna 1995, Easton 1995b,c) The next major innovation may come from quasi-unit record data, based on combining three households to protect confidentiality, but which maintain much of the characteristics of a household record.

1. I am grateful for some suggestions from the referee.
2. SWF report there has been 130 focus groups, including this carried out by John Cody and David Robinson (1993). (p.96) It is not clear whether that data is included in their final estimates. The most generous assumption is that it has, and the samples are of equal size.
3. The reason why the poverty numbers are more proportionally inaccurate than the poverty line is because the gradient of the cumulative frequency function of the numbers below each income level is in excess of 2 in this region – that is its graph is steep.
4. Increasing the level from $14050 to $15050 (i.e. by 7.1 percent) increases the proportion in poverty from 16.3 percent to 23.3 percent, or the numbers by 43 percent. The different up and down figures reflects the cumulative frequency function not being near linear in this range.
5. 2A + 3C = 471 (eq.1)
A + 2C = 386 (eq.2)
A + C = 85 (eq.3 =eq.1-eq.2)
C = 301 (eq.4 = eq.2-eq.3)
A = -216 (eq.5=e.3-eq.4)
6. One is reluctant to think that such practical people in the focus group could make such an assumption without some external pressure. Once again this raises the issue of systemic biases in the research design.
7. The HES for one adult and two children is 1.75 (a 1 adult household being set at 1), and for a two adult three child family is 2.43. ($386 x (2.43/1.75) = $537.)
8. As discussed in Easton (1980a) and subsequently, my view is that the RCSS-BDL needs to be recalibrated, and in the interim should be adjusted for medium term (but not cyclical) changes in mean income levels.
9. An optimist might note the proportion is a ratio in which both the numerator and the denominator are adjusted by the same HES, and hope that the HES averages out to give substantially the same proportion irrespective of the HES chosen. Because both involve aggregations of various composition households, we cannot be sure.
10.The focus group assumes the same housing outlay for on each household combination. Implicitly they assume that the minimum necessary adequate size bedroom for one adult is the same size as for two adults, and that the minimum adequate size bedroom space for two children is the same as for three children, and that the two extra people do not require any additional living space.
11. Jensen-1988 gives 1.39.
12. The figures come from reworking the original worksheets, which are held by the author.
13. There was even early focus group research. (Faber et al 1980)
14. Pioneered by the Department of Statistics and Suzanne Snively (1986,1987,1988).

Barker, G. (1996a) Income Distribution in New Zealand, Institute of Policy Studies, Wellington.
Barker, G. (1996b) “Poverty on the Decline”, City Voice, October 17.
Brashares, E. (1993) “Assessing Income Adequacy in New Zealand”, New Zealand Economic Papers, 27(2), p.185-207.
Brashares, E. & M. Aynsley (1990) Income Adequacy Standards for New Zealand, The Treasury, Wellington.
Cody, J. & D.Robinson (1993) What is an Adequate Income, Unpublished Report.
Cuttance, P. (1974) Poverty Among Large Families in New Zealand, MSS Thesis, University of Waikato, Hamilton.
Easton, B.H. (1973) A Needs Index, Mimeograph, University of Canterbury.
Easton, B.H. (1980a) “Poverty in New Zealand”: Five Years After, Paper for the Conference N.Z. Sociological Association, 1980.
Easton, B.H. (1980b) “Three New Zealand Household Equivalence Scales”, New Zealand Statistician, p.25-31.
Easton, B.H. (1995a) Lower Incomes in Wellington City: A Report, Report for the Wellington City Council.
Easton, B.H. (1995b) “Poverty in New Zealand: 1981-1993”, New Zealand Sociology, Vol 10, No 2, November 1995, p.182-213.
Easton, B.H. (1995c) “Properly Assessing Income Adequacy in New Zealand”, New Zealand Economic Papers, 29(1), 1995, 89-102.
Easton, B.H. (1996a) “Distribution”, in A. Bollard, R. Lattimore, & B. Silverstone (eds) A Study of Economic Reform: The Case of New Zealand, North Holland.
Easton, B.H. (1996b) “Ignoring Economic Losses”, City Voice, October 10.
Easton, B.H. (1996c) “Letters”, City Voice, October 24.
Fabre, M., J. Ketchel, & B. Otto (1980) Family Circumstances Study: Preliminary Report, Community Studies Centre, Otago University, Dunedin.
Jensen, J. (1978) Minimum Income Levels and Income Equivalence Scales, Department of Social Welfare, Wellington.
Jensen, J. (1988) Income Equivalences and the Estimation of Family Expenditures on Children, Department of Social Welfare, Wellington.
Kerr, R.J. (1996a) “Sharing Economic Gains”, Evening Post, September 23.
Kerr, R.J. (1996b) “Escape routes from Poverty”, Evening Post, September 24.
Kerr, R.J. (1997c) “Letters”, City Voice, October 24.
Krishnan, V. (1995) “Modest but Adequate: An Appraisal of Changing Household Income Circumstances in New Zealand”, Social Policy Journal of New Zealand, No 4, July 1995, p.76-97.
Mowbray, M. (1993) Incomes Monitoring Report: 1981-1991, Social Policy Agency, Wellington.
Perry, B. (1995) “Between a Rock and a Hard Place: Equivalence Scales and Inter-Household Welfare Comparisons”, Social Policy Journal of New Zealand, Issue 5, December 1995, p.142-162.
Rutherford, S., A. Khan, M. Rochford, & G. Hall (1990) Equivalent Income, Research Report Series Number 11, Research Section, New Zealand Department of Social Welfare, Wellington.
Snively, S.L. (1986) Evaluating the Budget’s Distributive Influence on Household Incomes, Mimeo, Wellington.
Snively, S.L. (1987) The 1981/2 Government Budget and Household Income Distribution New Zealand Planning Council, Wellington.
Snively, S.L. (1988) The Government Budget and Social Policy, Paper prepared for the Royal Commission on Social Policy, Wellington.
Smith, H. (1989) An Attempt to Derive New Zealand Equivalence Scales Using Unit-Record Data from the Household Expenditure and Income Survey, Working Paper 1989/5 Department of Statistics, Wellington.
Stephens, R., C. Waldegrave, P. Frater (1995) “Measuring Poverty in New Zealand,” Social Policy Journal of New Zealand, Issue 5, December 1995, p.88-112.