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Knowing how many people live in households with income or consumption expenditure below the ‘poverty line’ has helped focus attention on the extent of poverty and has informed policymaking for fighting poverty. But how are poverty lines defined and calculated? This article first provides a theoretical definition, and then describes the main methods found in practice.

Poverty Lines in Theory

People in different circumstances – with different household sizes or demographic compositions or living in different places – naturally have different levels of economic welfare at the same level of income. They have different needs. A poverty line should reflect these differences. But how should that be done? To answer this question we must first define the conceptual ideal against which the methods found in practice are to be judged.

The poverty line for a given individual can be defined as the money the individual needs to achieve the minimum level of ‘welfare’ to not be deemed ‘poor’, given its circumstances. Everyone at the poverty line is taken to be equally badly off, and all those below the line are worse off than all above it. The next question is: what concept of ‘welfare’ should serve as the anchor for the poverty line? For economists the obvious answer is ‘utility’. A justification for utility-consistent poverty lines can be found by applying standard welfare-economic principles to poverty measurement (Ravallion 1994). These principles are that assessments of social welfare should depend solely on utilities, that people with the same initial utility should be treated the same way, and that social welfare should not be decreasing in any utility.

To formalize this definition, consider individual i with characteristics xi (a vector). The interpersonally comparable utility function is u(qi,xi). The quantity vector qi is utility maximizing, giving demand functions q(pi,yi, xi) at total expenditure yi and corresponding utility maximum, v(pi,yi,xi). The utility-consistent poverty line is the point on the consumer’s expenditure function corresponding to a common reference utility level. (As always, the monetary measurement of welfare requires a reference utility level.) The consumer’s expenditure function is e(pi, xi, u), giving the minimum cost of utility u when facing the price vector pi. Let uz denote the minimum utility deemed necessary to escape poverty. Consistency requires that this is a constant across all i. The money metric of uz defines the utility-consistent poverty lines:

$$ {z}_i^u=e\left({p}_i,{x}_i,{u}_z\right)\kern0.48em \mathrm{for}\kern0.24em \mathrm{all}\kern0.36em i=1,\dots n $$
(1)

This is closely related to a number of other economic concepts. Eq. (1) is ‘money-metric utility’ at a specific reference utility, interpretable as the poverty line in utility space. (Textbook treatments of money-metric utility functions – sometimes called ‘equivalent income functions’ – can be found in Varian 1978, and Deaton and Muellbauer 1980.) The value of \( {z}_i^u/e\left({p}_r,{x}_r,{u}_z\right) \) for reference individual r gives the ‘true cost-of-living index’ (see, for example, Deaton and Muellbauer 1980). The value of \( {y}_i/{z}_i^u \) is the ‘welfare ratio’ (Blackorby and Donaldson, 1987). On exploiting the properties of the expenditure function, Eq. (1) can be written in a more instructive form:

$$ {z}_i^u={p}_iq\left({p}_i,{x}_i,{u}_z\right) $$
(2)

Thus, the poverty line is the cost of a bundle of goods, namely, the vector of utility-compensated (Hicksian) demands, q(pi, xi, uz). This bundle can be interpreted as ‘basic consumption needs’.

Note that an absolute poverty line in terms of utility can have the properties of a relative poverty line in the income space, in that it rises with the mean income of a relevant reference group. This is possible if individual utility depends on both ‘own income’ and income relative to others in that reference group. In other words, the indirect utility function has the form, \( v\left({p}_i,{y}_i,{y}_i/{\overline{y}}_i^r,{x}_i\right) \) where \( {\overline{y}}_i^r \) is the mean income of the reference group(s); the poverty line takes the form \( {z}_i=z\left({p}_i,{\overline{y}}_i^r,{x}_i,{u}_z\right) \) (which solves \( {u}_z=v\left({p}_i,{z}_i,{z}_i/{\overline{y}}_i^r,{x}_i\right) \)). Thus, we can view poverty as absolute in the space of welfare, but relative in the space of commodities (paraphrasing Sen 1983). However, the extreme case in which the poverty line is a constant proportion of the mean (as used by poverty measures derived by Eurostat, for the European Commission) requires the seemingly implausible assumption that utility depends solely on relative income, given by the ratio of own income to the mean. By this measure, if all incomes increase by the same multiplicative factor then the proportion of people living below the poverty line will be unchanged. Cross-country comparisons of poverty lines suggest that relative income is valued more highly as mean income rises; in the poorest countries, absolute income levels are the dominant consideration, so then the poverty lines tend to have a low elasticity to the mean (Ravallion 1994, 1998). There is micro empirical evidence supporting this view, based on self-assessed welfare (Ravallion and Lokshin 2005).

For economists, utility is the obvious anchor for setting poverty lines, but it is not the only approach. Functioning-based concepts of welfare offer an alternative foundation for poverty lines. The approach can be characterized in the terms of Sen’s (1985) argument that ‘well-being’ should be thought of in terms of a person’s capabilities, that is, the functionings (‘beings and doings’) that a person is able to achieve. On this view, poverty means not having an income sufficient to support specific normative functionings. Utility – as the attainment of personal satisfaction – can be viewed as one such functioning relevant to well-being (Sen 1992, ch. 3). But it is possibly only one of the functionings that matter. Independently of utility, one might say that a person is better off if she is able to participate fully in social and economic activity.

From this starting point, a more general theoretical formalization of the definition of a poverty line can be proposed as follows. Let a person’s functionings be determined by the goods she consumes and her characteristics, giving the vector of functionings:

$$ {f}_i=f\left({q}_i,{x}_i\right) $$
(3)

where f is a vector-valued function. One can postulate that a person derives utility directly from her functionings. We can then interpret u(qi, xi) as a derived utility function, obtained by substituting (3) into the (primal) utility function defined over functionings.

Functioning consistency for a set of poverty lines requires that certain normative functionings are reached at the poverty line. Let fz denote the vector of critical functionings needed to not be deemed poor. These are normative judgements, just as uz is a normative judgment. Assume that there is a bundle \( {q}_i^c \) such that no functioning is below its critical value:

$$ {f}_z\le f\left({q}_i^c,{x}_i\right) $$
(4)

This yields the poverty lines: \( {z}_i^c={p}_i{q}_i^c \). There can be multiple solutions for \( {q}_i^c \). Two ways to pick a unique poverty line can be identified. The first is to define \( {z}_i^c \) as the minimum y such that (4) holds. Notice that one (or more) specific functionings will be decisive; that is, the functioning that is the last to reach its critical value as income rises. In this sense, the lowest priority functioning for the individual will be decisive. The alternative approach is to treat attainments as a random variable (that is, with a probability distribution) and take a mean conditional on income and other identified covariates, including group membership. Then poverty lines are deemed to be functioning consistent if fz is reached in expectation.

Implementing these concepts empirically requires that we solve two problems. The first can be called the referencing problem: what is the reference level of utility that anchors the poverty line (uz in Eq. 1)? It is tempting to say this choice is arbitrary, and to hope that it is innocuous. But the choice of the reference is far from arbitrary, and (in general) it affects the resulting poverty measure. This speaks to the importance of testing the sensitivity of poverty comparisons (such as between groups or over time) to the choice of reference, as it determines the level of the poverty line. Tests exist for the robustness of ordinal comparisons using stochastic dominance criteria; on this approach see Atkinson (1987) and Ravallion (1994).

The second problem is the identification problem. Even if we can readily agree on what the poverty line is in welfare space, there is a further problem in identifying the expenditure function in Eq. (1). Standard practice is to calibrate the parameters of the cost function from consumer demand behaviour. The problem is that individuals vary in characteristics, such as their size and demographic composition, which influence welfare in ways that may not be evident in consumer demand behaviour. Then there is a fundamental problem of identification (Pollak and Wales 1979; Pollak 1991).

Poverty Lines in Practice

The methods of setting poverty lines found in practice fall under two headings: objective poverty lines and subjective poverty lines.

Objective Poverty Lines

The main methods found in practice are the food-energy-intake (FEI) method and the cost-of-basic-needs (CBN) method. It is known that these methods give radically different results; using data for Indonesia, Ravallion and Bidani (1994) found virtually zero correlation between the regional poverty profiles (given the poverty rates across geographic areas) produced by these two methods. Since policy choices (such as in regional targeting) could depend critically on which method is used, it is important to probe carefully into the choice.

The FEI method can be interpreted as a special case of the functioning-based approach described above. The specialization is to focus on just one functioning, namely food-energy intake. The method finds the consumption expenditure or income level at which food-energy intake is just sufficient to meet predetermined food-energy requirements for good health and normal activity levels. (Such caloric requirements are given in WHO 1985, for example.) To deal with the fact that food-energy intakes naturally vary at a given income level, the FEI method typically calculates an expected value of intake at given income. Figure 1 illustrates the method. The vertical axis is food-energy intake, plotted against income (or expenditure) on the horizontal axis. A line of ‘best fit’ is indicated; this is the expected value of caloric intake at given income (that is, the nonlinear regression function). By simply inverting this line, one finds the income z at which a person typically attains the stipulated food-energy requirement. This method, or something similar, has been used often, including by Dandekar and Rath (1971), Osmani (1982), Greer and Thorbecke (1986), and Paul (1989), and by numerous governmental statistics offices. It is often found in practice in developing countries.

Poverty Lines, Fig. 1
figure 1624figure 1624

The food-energy intake method of setting poverty lines

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One concern about this method is that the resulting poverty lines need not be consistent in terms of utility or capabilities more generally (Ravallion 1994; Ravallion and Lokshin 2006). Consider first how FEI poverty lines respond to differences in relative prices, which can of course differ across the subgroups (such as regions) being compared in the poverty profile and over time. For example, the prices of many non-food goods relative to food are likely to be lower in urban than in rural areas. This will probably mean that the demand for food and (hence) food-energy intake will be lower in urban than in rural areas, at any given real income.But this does not, of course, mean that urban households are poorer. The relationship between food-energy intake and income will shift according to differences in tastes, activity levels and publicly provided goods. There is nothing in the FEI method to guarantee that these differences are ones that would normally be considered relevant to assessing welfare. Indeed, it is quite possible to find that the ‘richer’ sector (by the agreed metric of utility) tends to spend so much more on each calorie that it is deemed to be the ‘poorer’ sector. That has been found to be the case in studies of the properties of FEI poverty profiles for Indonesia (Ravallion and Bidani 1994) and Bangladesh (Ravallion and Sen 1996; Wodon 1997).

Problems also arise in comparisons over time. Suppose that all prices increase, so the cost of a given utility must rise. There is nothing to guarantee that the FEI-based poverty line will increase. That will depend on how relative prices and tastes change; the price changes may well encourage people to consume cheaper calories, and so the FEI poverty line will fall. Wodon (1997) gives an example of this problem in data for Bangladesh. The FEI poverty line fell over time even though prices generally increased. The potential utility inconsistencies in FEI poverty lines are worrying when there is mobility across the subgroups of the poverty profile, such as due to inter-regional migration. For example, it is possible that a process of economic development through urban sector enlargement, in which none of the poor are any worse off and at least some are better off, would result in a measured increase in poverty.

The CBN method stipulates a consumption bundle deemed to be adequate for ‘basic consumption needs’, and then estimates its cost for each of the subgroups being compared in the poverty profile. This is the approach of Rowntree (1901) in his seminal study of poverty in York, England, in 1899, and there have been numerous examples since, including the official poverty lines for the United States (Orshansky 1963; also see Citro and Michael 1995). Some form of functioning consistency is assured by construction, since various valued functionings are essentially the starting point for defining ‘basic consumption needs’. The poverty bundle is typically anchored to food-energy requirements consistent with common diets in the specific context. However, allowances for non-food goods are also included, to assure that basic non-nutritional functionings are assured.

The CBN method is utility consistent if the right bundle is used, corresponding to the relevant points on the utility-compensated demand functions (Eq. 2). However, there is nothing to guarantee that the bundles of goods built into CBN poverty lines lie on the compensated demand functions, at the (common) reference level of utility. Thus it is important to have some way of assessing a set of CBN poverty bundles. Ravallion and Lokshin (2006) propose an approach to testing the utility consistency of CBN poverty lines across households with common preferences using Samuelson’s (1938) theory of revealed preference. However, this can be applied only within subgroups deemed to have common preferences. In practice utility functions can vary, due to differences in climate, for example.

In some cases a complete vector of normative (food and non-food) goods is set, as in Russia’s poverty lines (Ravallion and Loskhin 2006). However, it is more often the case that only food needs are set, based on nutritional requirements. To include an allowance for non-food needs, a common practice is to divide the food poverty line by some budget share for food. For example, the US poverty line assumes a food share of one third, so the total poverty line is three times the food line (Orshansky 1963). However, the basis for setting a food share is rarely transparent. Why use the average share, as in the US line? Whose food share should be used?

Arguably, a more appealing approach is to set an allowance for non-food goods that is consistent with demand behaviour at (or in a region of) the food poverty line. Ravallion (1994) proposes two methods. The first divides the food component of the poverty line by the mean food share of households whose actual food spending is in a neighbourhood of the food poverty line. The second method uses mean non-food spending of households whose total sending is in a neighbourhood of the food poverty line. Ravallion argues the first method gives a reasonable upper bound to the allowance for non-food needs while the second gives a lower bound.

Subjective Poverty Lines

There is an inherent subjectivity and social specificity to any notion of ‘basic needs’, including nutritional requirements. Psychologists, sociologists and others have argued that the circumstances of the individual relative to others influence perceptions of well-being at any given level of individual command over commodities. (Runciman 1966, provided an influential exposition, and supportive evidence. Also see the discussions in Easterlin 1995, and Oswald 1997.) By this view, ‘the dividing line … between necessities and luxuries turns out to be not objective and immutable, but socially determined and ever changing’ (Scitovsky 1978, p. 108).

Subjective poverty lines have been based on answers to the ‘minimum income question’ (MIQ), such as the following (paraphrased from Kapteyn et al. 1988): ‘What income level do you personally consider to be absolutely minimal? That is to say that with less you could not make ends meet.’ (This can be thought of as a special case of Van Praag’s 1968, ‘income evaluation question’, which asks what income is considered ‘very bad’, ‘bad’, ‘not good’, not bad’, ‘good’, ‘very good’.) One might define as poor all whose actual income is less than the amount they give as an answer to this question. However, this would almost certainly lead to inconsistencies in the resulting poverty measures, in that people with the same income, or some other agreed measure of economic welfare, will be treated differently. Clearly an allowance must be made for heterogeneity, such that people at the same standard of living may well give different answers to the MIQ, but must be considered equally ‘poor’ for consistency. Past empirical work has found that the expected value of the answer to the MIQ conditional on actual income tends to be an increasing function of actual income. (Contributions include Groedhart et al.1977; Danziger et al.1984; and Kapteyn et al.1988.) Furthermore, past studies have tended to find a relationship such as that depicted in Fig. 2, which gives a stylized representation of the regression function on income for answers to the MIQ. The point z* in the figure is an obvious candidate for a poverty line; people with income above z* tend to feel that their income is adequate, while those below z* tend to feel that it is not. We can call z* the ‘social subjective poverty line’ (SSPL).

Poverty Lines, Fig. 2
figure 1625figure 1625

The social subjective poverty line (z*)

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It is recognized in the literature that there are other determinants of economic welfare which should shift the SSPL, such as family size and demographic composition. Indeed, the answers to the MIQ are interpretable as points on the consumer’s expenditure function at a point of minimum utility (Eq. 1). Under this interpretation, subjective welfare assessments provide a means of overcoming the well-known problem of identifying utility from demand behavior alone when household attributes vary (Kapteyn 1994).

While the MIQ has been applied in a number of OECD countries, there have been few attempts to apply it in a developing country. There are a number of potential pitfalls. ‘Income’ is not a well-defined concept in most developing countries, particularly (but not only) in rural areas. It is not at all clear whether one could get sensible answers to the MIQ. The qualitative idea of the ‘adequacy’ of consumption is a more promising one in a developing-country setting, and (arguably) many developed counties.

Pradhan and Ravallion (2000) propose a method for estimating the SSPL based on qualitative data on consumption adequacy, as given by responses to appropriate survey questions. Instead of asking respondents what the precise minimum consumption is that they need, one simply asks whether their current consumptions are adequate. This provides a multidimensional extension to the one-dimensional MIQ. The SSPL is the level of total spending above which respondents say (on average) that their expenditures are adequate for their needs. For empirical implementation, the probability that a sampled household will respond that its actual consumption of each type of commodity is adequate can be modelled as a probit regression. Under certain technical conditions, a unique solution for the subjective poverty line can then be obtained from the estimated parameters of the probit regressions for consumption adequacy. Pradhan and Ravallion provide empirical examples for Jamaica and Nepal; the SSPL gave a similar overall poverty rate to preexisting objective poverty lines for both countries, though the structure of the poverty profile was different in some respects: for example, while the objective poverty lines implied that larger households tended to be poorer, this was not the case with the subjective approach.

Subjective data also offer a test of objective poverty lines, by regressing selfrated welfare on income normalized by the poverty line plus the variables that went into the construction of the poverty line, which should be jointly insignificant if those lines accord with subjective welfare. This approach is outlined in Ravallion and Lokshin (2002) and illustrated using Russia’s poverty lines.

See Also