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Poverty and Inclusive Growth in the Light of the Quintile Income Statistic

9 December 2013

S. Subramanian

1 Introduction

It appears that the World Bank is planning to maintain and disseminate systematic information on a version of what Kaushik Basu (now a Vice-President of the World Bank) had some years ago advanced as the ‘quintile income statistic’. The quintile income—which we shall find convenient to refer to simply as Q—is just the average income of the poorest quintile (that is to say, poorest 20 per cent) of a population. The quintile income statistic is a very simple, but also very versatile, welfare indicator—one which can be employed to cast light, admittedly in a somewhat elementary way, on aspects of both income poverty and the ‘inclusiveness’ of growth. The World Bank aims to track, subject to the availability of data, country-specific performance with respect to the average income of the poorest 40 per cent of the population (rather than 20 per cent, as Basu had proposed in his original version of the statistic).

Notice that the quintile income, as well as the Bank’s proposed measure, are specific instances of a more general formula that pertains to the average income of the poorest x per cent of a population. As x goes toward 100, we move closer and closer toward that old work-horse summary indicator of welfare, the income per capita of a population. To ensure that some sensible distinction from per capita gross national product (GNP) is maintained, there is a case for pitching x ‘low’ rather than ‘high’. As such, one wishes the World Bank had stuck to Basu’s original recommendation of concentrating on the bottom 20 percent, instead of focusing on the bottom 40 percent. Having said this, it is nevertheless welcome that the Bank proposes to implement a version of the quintile income index, and, for specificity, it is this measure Q that I shall refer to in the rest of this article. In what follows, I shall attempt to describe as simply as I can how the Q statistic can be employed to reveal something about an economy’s poverty and dynamic inequality.

1.1 The poverty line

As is well known, extant protocols of money-metric poverty measurement follow what one may call the route of ‘identification-cum-aggregation’. The identification exercise is concerned with specifying an income ‘poverty line’ designed to distinguish the poor segment of a population from its non-poor segment. The aggregation exercise is concerned with combining information on the distribution of income and the poverty line in order to come up with a single real number which is supposed to signify the extent of poverty in the society under review. A particularly simple aggregate measure of poverty, and one which is very widely employed, is the so-called headcount ratio, or proportion of the population in poverty (that is to say, the proportion of the population with incomes or consumption expenditure levels below the poverty line).

It is important to recognize that the language of a ‘poverty line’ is ill-suited to treating income as anything but a means to an end—specifically the end of avoiding deprivation in the space of human functionings. After all, what is the common sense meaning of the term ‘poverty line’? Is it not a reference to that level of income which, when it is attained, enables an individual to escape deprivation? And what is deprivation, if not a failure to achieve certain ‘minimally satisfactory’ states of being and doing—such as the state of being reasonably well-nourished, reasonably mobile, reasonably free of disease and ignorance, reasonably sheltered against the forces of nature and climate, reasonably equipped to participate without shame in the affairs of one’s society, and so on? And if this is the case, surely the right way of going about fixing the poverty line would be to first make a list of human functionings in respect of which it is reasonable to insist that one should avoid deprivation in order to be counted non-poor; to identify the reasonable cost of achieving each reasonable level of functioning; and to add up all of these functioning-specific costs in order to arrive at the money-metric poverty line.

Notice now that there can be both inter-personal and ‘environment-’ or ‘context-dependent’ factors which can make for differences in the rate at which incomes (or resources in general) are converted into functionings. Thus, a pregnant or lactating mother will typically need more nutritional resources than a person who, other things equal, is not in this condition. Similarly, a physically handicapped person would typically need more resources to achieve the functioning of mobility than one who is not so handicapped. Apart from such individual heterogeneities, are also differences wrought by variations in the objective environment. Thus, a person living in unsanitary conditions without access to clean drinking water might be expected to require more food to achieve the same nutritional status as one whose absorptive capacity is not compromised by infected potable water. Similarly, a person living in a cold climate would require more resources to expend on protective clothing than one living in a temperate climate. We owe all of these insights to Amartya Sen who, many years ago, employed this line of argumentation to assert that poverty is best seen as an absolute concept in the space of functionings, but (and precisely because of variations across regimes in the ability to convert resources into functionings), as a relative concept in the space of resources (including income).

What is the implication of these seemingly arcane conceptual distinctions? The implication, it turns out, is of rather immediate pragmatic import. The line of discussion just pursued suggests that, ideally, one ought to have individual-specific money-metric poverty norms to take account of interpersonal variations in the ability to convert resources into functionings. This is scarcely feasible. More manageable might be to have ‘regime-specific’ poverty lines, to allow for differences across demographic groups, or space, or time. At a point of time, for instance, in a country like India, there might be a case for having at least district-specific poverty lines, based on spatial disaggregation. That would mean upward of 600 poverty lines in the country—not exactly a matter which is within the bounds of practical politics, unless there existed a functioning, permanent Poverty Estimation and Monitoring Bureau to do the job. The practical issue is this: for poverty comparisons to be meaningful, the poverty standard must be invariant across the contexts of comparison. But invariant in what space? In the space of functionings (which is compatible with variability in the space of resources), not in the space of real incomes or of commodity bundles.

Yet, in practice, the World Bank’s ‘dollar-a-day’ international poverty line preserves invariance in the space of real incomes, while India’s official poverty lines preserve invariance in the space of commodity bundles. Regrettably, the language of a ‘poverty line’—in terms of which incomes or resources are seen as a means to the end of avoiding deprivation in the space of functionings—is wholly incompatible with such postulated invariance of real incomes or commodity bundles. The resulting estimates of ‘poverty’ are, quite straightforwardly put, hard to interpret in any conceptually coherent or meaningful way. And the problem, I’m afraid, cannot simply be taken care of by impatient assertions regarding the unavoidability of some element of arbitrariness in the specification of an income poverty line.

2 Q

2.1 Q and money-metric poverty

Alternatively, one could abandon the ‘poverty line’ route to assessing money-metric poverty, and treat income as an end in itself. The notion of being in possession of income is, in such a view, treated as a desirable functioning to achieve, in and of itself. There is at any rate, in this construction, no ambiguity, or dissonance in the intended meaning of a notion and the use to which it is put. In such an event, one is enabled to get out of the ‘identification-cum-aggregation’ mould of poverty measurement and, instead, employ something like Kaushik Basu’s ‘quintile income statistic’ as a signifier of money-metric poverty. The idea, here, would be to track, monitor, and compare the average income of the poorest x per cent of a population across alternative regimes. The quintile income Q is a specific instance of a money-metric poverty indicator, pure and simple, and not least by virtue of its being a reflection of the income-performance of the income-poorest 20 per cent of a population.

One way in which the performance of Q over time for a given country (or for the world as a whole) can be evaluated is the following. Just as countries often set targets for the rate of growth of per capita GNP, so one can set rates of growth for Q. For some desired postulated rate of growth of Q over time, one can obtain a time-series of ‘warranted’ Qs—call these the corresponding Q* values—and obtain a time-series on the ratio of the actual quintile income (Q) to the ‘warranted’ quintile income (Q*) at each point of time. Increasing over-time ratios of greater than one would tell an encouraging story of declining over-time money-metric poverty; and just the opposite would be true for dwindling over-time ratios of less than one. Presumably, the targeted rate of growth of Q would be higher the lower the initial level of Q.

2.2 Q and inclusive growth

If we took a wholly relative view of inequality, we would say that inequality over time, in the presence of growth in per capita income, has remained unchanged when each person’s income has increased by the same proportion. If we took a wholly absolute view of inequality, we would assert over-time invariance in inequality when each person’s income has increased by the same amount. A ‘properly centrist’ view of inequality invariance might dictate that one-half of the product of growth should be distributed in the proportions that obtain currently (i.e., in the base year) and one-half should be distributed equally. Or, at a broader level of aggregation, we might wish for this outcome to hold at the level of quintiles. In assessing the ‘inclusiveness’ of growth over the past, say T years, we could proceed as follows. Suppose g to be the annual compound rate of growth of per capita income over the last T years. For each year t = 1,…,T, it is a simple matter, given g, to apply the ‘properly centrist’ formula just discussed in order to obtain the desired quintile specific average income levels in each year which will preserve over-time inequality-invariance.

so that the two trend lines together resemble a diverging fork starting together at unity in the base year, is a clear manifestation of non-inclusive growth, of rising dynamic inequality. This is a specific way in which the inclusiveness or otherwise of growth can be assessed, in terms of the over-time trends in the average incomes of the richest and the poorest deciles of a population.

3 Summary and conclusion

To summarize, even at the risk of some repetition, given the way the poverty line is often specified and treated, namely nominally as a means to an end but not substantively so, one is left with the view of an inappropriate use of language that characterizes the bulk of actual empirical work available on the identification issue in poverty measurement. The result, in my view, is that poverty statistics on magnitudes or trends—whether at the level of countries or at a global level—are often profoundly misleading. Rectification of standard practice would require that poverty be treated as an absolute conception in the space of human functionings, and as a relative conception—allowing for both interpersonal and contextual heterogeneities—in the space of incomes. This is a practically very difficult exercise to implement, but is the price that must be paid for treating income—in terms of the language of a ‘poverty line’—as a means to an end. Failing this, income could be treated as an end in itself, in which case the quintile income can be employed as a legitimate money-metric indicator of poverty. Over-time comparisons of the actual quintile income with reasonably targeted levels based on a normative growth rate should yield a picture of how money-metric poverty has fared over time. Suitable comparisons of the over-time performance of the average incomes of the richest and the poorest deciles over time—along lines discussed in the text—should yield a picture of the inclusiveness or otherwise of growth. In conclusion, I would say that there is a strong case for replacing dollar-a-day-type approaches to the estimation of money-metric poverty by a more straightforward ‘quintile income approach’, which can also be employed in order to pronounce judgment on whether or not growth in income has been ‘pro-poor’ or inclusive.

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Poverty and Inclusive Growth in the Light of the Quintile Income Statistic

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Blog Poverty and Inclusive Growth in the Light of the Quintile Income Statistic

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Poverty and Inclusive Growth in the Light of the Quintile Income Statistic