Beware the Median

SPRC Newsletter No 82, November 2002, p.6-7.

Keywords: Distributional Economics; Social Policy

In their article Beware the Mean!, Peter Saunders and Tim Smeeding argue that median household is a superior reference point for establishing a poverty line than mean household income, concluding ‘Put bluntly, the use of a poverty line linked to mean poverty income produces excessively high poverty rates that tend to increase by more when poverty is rising but to fall by less when poverty is falling.’ The purpose of this note is to demonstrate that poverty lines based on a fixed proportion of the median income are subject to a fatal flaw, illustrating the consequences of the flaw with recent New Zealand experiences.

A fundamental requirement of any poverty line is that it should be policy neutral, that is a change in distributional policy should not change the line (although it may change the numbers above and below the line). The justification for this assertion is simple. Suppose a poverty line was dependent on distributional policy. Then the policy could deliberately reduce the poverty line, thereby reducing headcount poverty, without changing the material circumstances of the poor.

To illustrate the possibility, median income is policy dependent. In particular, tax and other income transfer policies mean it is possible to transfer income from those in the middle of the income to the rich (as we shall see this happened in New Zealand), where there is no change in national income (and hence average income). Such a transfer is unquestionably an increase in inequality, and does not affect the material standard of living of the poor. However the median income falls, and so a poverty line which uses the median as the reference income also falls. Thus headcount poverty falls.

So we have the following paradox with a median based poverty line: a policy which transfers income to the rich, reducing the incomes of those below them and decreasing their material standard of living, appears to result in a reduction in headcount poverty even though the poor experience no change (or even a reduction) in their material standard of living. (An (impractical) extreme would be to eliminate all headcount poverty based on a poverty line which is a proportion of median income by allocating all household income to the rich.)

Something like this happened in New Zealand in the late 1980s and early 1990s. Between 1981/2 and 1992/3, mean household real income fell 6.1 percent, largely as the result of neo-liberal policies which stagnated the economy. However the share in the top decile of households rose from 20.1 to 25.1 percent of all household income (so they experienced an increase in their real incomes of 17.0 percent while the real incomes of the bottom 80 percent of households fell by 14.7 percent). The Gini coefficient of inequality rose from .291 to .305. Not surprisingly the median income for the population fell more, some 19.2 percent over the eleven years. (Easton 1995)

The main distributional changes were the result of government policy. Income taxes cuts on top incomes (the top marginal tax rate was reduced from 66 percent to 33 percent) were paid for by higher taxes on those lower in the distribution, and by social security benefits cuts. There is plenty of evidence to suggest that their was a marked reduction in the quality of life of those at the bottom of the distribution, with a sharp rise in numbers using food banks as the most prominent.

The effect on head count numbers of these changes is predictable. If an absolute poverty level is used the numbers below the poverty line rose sharply (the population proportion rose 26.2 percent if the standard poverty line – based on the assessment of the 1972 Royal Commission on Social Security – is used). Headcount poverty based on the mean as a reference income rose modestly while those that used the median as a reference income fell (the population proportion fell by 18.3 percent for a poverty line based on 60 percent of median household income).

Extraordinarily, both the New Zealand Treasury and the neo-liberal New Zealand Business Roundtable used the median based headcount number to claim that the policies of the previous decade had been a success. They got little support from the poor.

Perhaps neither the median or the mean household income is satisfactory reference income for establishing a workable poverty line. My view is that there is a need to look outside the income distribution at the actual living standards of those on low incomes, and make a social judgement as to an appropriate income line which reflects the community judgements on poverty. Ideally it should be updated, perhaps every five years because any calibration exercise is costly. If it is necessary to make interim adjustments, changes in the mean income are likely to be more satisfactory than changes in the median income. However in my experience, if the mean income changes are large discussion is likely to get confused between changes in absolute incomes and changes in relative incomes. (If they are small, adjustment may be unnecessary.)

This does not resolve the problem which the Saunders-Smeeding paper addresses of international comparisons. A procedure which established a poverty level based on information from outside the available statistical distributions as discussed in the preceding paragraph is probably not practical, although given the existence of international price comparison data, some progress may be possible in the comparison of country poverty lines in real terms. The obvious options using the distributions themselves are the mean and the medians as discussed in the Saunders-Smeeding paper. Given that the median is not policy neutral we seem left with the mean.

We can deal simply the problem of the fact that the mean is higher than the median, and so generates more headcount poverty, by asking what is particularly sacred about using the relativity of 50 percent of the mean or median. On the basis of their Table 1, it looks as though typically 50 percent of the median equals about 45 percent of the mean. So why not set the standard poverty line at 45 percent of the household mean? (Better still, give the data for 40, 45 and 50 percent of the mean.)

This does not resolve the problem of changing mean incomes over time. The response depends upon the judgement one makes of the meaning of a poverty line. If the notion of poverty is intended to reflect some absolute standard of material comfort, the approach may be to identify a particular year (say 1992 which was a decade ago) and use the 45 percent (or whatever) of the mean of that year as an absolute poverty line thereafter. On the other hand if the notion is of a relative standard because the community judges the poor should share in its rising standards of living, then the poverty line should be 45 percent of the current year mean (or an average over surrounding years, if an adjustment for the business cycle is deemed necessary because the poor are entitled to greater income stability). With current computing power it is no great difficulty to provide all the data and leave specialists to chose for themselves, with a careful justification of their decision. Non-specialists might best use the 45 percent of mean income in a base year (even though it is a different proportion, say 43 percent, a decade later).

The final point to be made is the Luxembourg Income Study, which precipitated the Saunders-Smeeding paper, is a heroic venture in international comparative statistics, but the journey is a long one with many difficult obstacles to be overcome. (For instance how to incorporate the differing nationals of income in kind – health and education spending the most prominent – in international comparisons.) It may be that we are asking too much from the program at this stage to give us precise answers on international poverty comparisons. Yet as the Saunders-Smeeding paper shows, careful analysis can throw useful light on some international distributional trends.


Saunders P. & T. Smeeding (2002) ‘Beware the Mean!’ SPRC Newsletter, No 81, May 2002, p.1,4.

Easton, B.H. (1995) “Poverty in New Zealand: 1981-1993”, New Zealand Sociology, Vol 10, No 2, November 1995, p.182-213.