SAMosa Takes

The arithmetic of counting the poor

Sep 16, 2016
By S. Subramanian
 
Economics  is a tricky subject, and economic measurement is just about the trickiest of its component elements. The judgements we make about the economy are (or should be) based on facts; and what we call ‘facts’ are overwhelmingly a product of measurement.
 
 This is true of our assessment – just by way of example – of the economy’s growth; of inflation; of population trends; of levels of unemployment; of the extent of economic inequality; of magnitudes of, and tendencies in, poverty; and indeed a host of other aspects of the economy’s functioning. What we make of the economy is thus hugely dependent on what we make of economic statistics. And what we can make of economic statistics, in turn, depends on the data which are available to us and on the basis of which the relevant statistics are constructed; on the quality and reliability of these data; and, importantly, on the interpretation which we do, and may, confer on the summary statistical measures we construct from the available data.
 
Concentrating only on the last-mentioned issue, it must be remarked that often enough there is a gap – which even (or perhaps especially) professional economists tend to miss – between how we ought to interpret economic indicators and how we actually end up interpreting them. Measurement is frequently perceived (or passed off) as being a routinely straightforward exercise which ought not to be burdened with the nuances of meaning and interpretation. The truth, unfortunately, is the very opposite of this disposition.
 
 Measurement, as it happens, is informed by a combination of common or garden ‘facts’, ethical values, ideological orientation, political perspective, and ambiguity of interpretation. This is what makes a seemingly simple and direct exercise an actually complex and challenging one. This also is why confident professional assessments of economic performance would benefit from a stance of uniformly greater humility in the pronouncement of these assessments – a humility that acknowledges the need for a clear statement of precisely what is being measured and how. A very simple example from the measurement of poverty should cast some light on this sentiment.
 
Suppose we observe that between two periods of time – let us call these period 1 and period 2 respectively – the proportion of the population with incomes less than a stipulated poverty line has declined from, say, 40 per cent to 30 per cent. Often, this finding is quite simply represented as ‘a decline in poverty over time’. Among various other things that are left out of this representation is the very simple one of why, even if poverty is to be measured by just counting the heads living in poverty, one must accept that the count is best captured by the proportion of the population in poverty. Why not, for instance, the absolute numbers of people in poverty? Why might this be important?
 
To see what is involved, let us consider some additional data on poverty and population counts for the hypothetical example I have just furnished. Suppose period 1 has 320 million poor people in a population of 800 million, and period 2 has 330 million poor people in a population of 1100 million. This is, of course, compatible (as noted earlier) with a decline in the headcount ratio (HCR) of poverty from 40 per cent in period 1 to 30 per cent in period 2. But notice also that the change described is compatible with an increase in the aggregate headcount (AH) of poverty from 320 million poor persons to 330 million poor persons over the two time periods under consideration. That is, there has been a decline in poverty according to one plausible measure of poverty (the HCR), and an increase, according to another (the AH). It appears that we cannot even be sure about the inter-temporal direction of change (leave alone the magnitude) of poverty, without further scrutiny.
 
At the least, and as the example just considered suggests, we must engage with the ‘meaning’ and the relative merits of the headcount ratio and the aggregate headcount. One difficulty with the HCR is the following. Suppose two out of four people are initially poor, so that the HCR in this situation is 50 per cent. Suppose further that two rich people now join this community, so that, with this change, we have two poor people in a population of six. Clearly, the HCR declines from 50 per cent to 33 per cent. By employing the HCR as our favoured poverty measure, we should diagnose a decline in poverty – even though nothing whatever has been done to alleviate the poverty of the two individuals initially in poverty! This amounts to a violation of what in the field of ‘population ethics’ is called the ‘Constituency Principle’ – a principle which requires that the ‘goodness’ of alternative states of affairs must be judged only from the standpoint of the interests of the relevant constituency in the two states. When we make poverty comparisons, the ‘relevant constituency’, presumably, is the community of poor persons. Yet, the HCR can pronounce a decline in poverty (as we have just seen) with no change in the poverty status of the community of poor persons.
 
At the same time, it seems reasonable to require that a measure of poverty should give some indication of the probability of encountering a poor person in a society. Let me call this requirement the ‘Likelihood Principle’. The HCR eminently satisfies the Likelihood Principle, just as the aggregate headcount (AH) measure obviously violates it: in the simple numerical example considered above, the probability of encountering a poor person in the society declines from 1/2 to 1/3, but the AH remains constant at 2.
 
So, what do we have? The HCR attractively satisfies the Likelihood Principle while unattractively violating the Constituency Principle, while things are just the other way around with the AH. Each measure has some virtue to commend it, but also some vice that detracts from it. This makes it difficult to rely entirely on any one or the other of the two measures. A ‘compromise candidate’ is one which is intermediate between the HCR and the AH, and which may be called an Intermediate Headcount (IHC) measure. Such a measure is given by the product of the two quantities – or, as in some formulations, as the square-root of the product of the two quantities, that is, ICH is just the square-root of the product of  HCR and AH.
 
Is this just some esoteric issue? Let us consider some World Bank data on global poverty according to its own calculations and given a global poverty line of $2.50 (in 2005 purchasing power parity.) Between 1981 and 2005, the global HCR declines from 75 per cent to 58 per cent; the AH increases from 2739 million poor persons to 3140 million; and the ICH is nearly unchanging, going from 45.3 million to 42.5 million. We are enabled to see now that our sense of what is happening to poverty is intimately guided by protocols of measurement that must be sensitive to ‘facts’, logic, and values – a proposition that is often not treated with the seriousness it deserves.
 
The Tribune, September 16, 2016

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