Document(s) 8 of 20

Three major issues arise in the estimation and in the use of poverty lines. First, we must define the space in which well-being is to be measured. As discussed in Chapter 1, this can be the space of utility, incomes, "basic needs", functionings, or capabilities. Second, we must determine whether we are interested in an absolute or in a relative poverty line in the space considered. Third, we must choose whether it is by someone's "capacity to function" or by someone's "actual functioning" that we will judge if that person is poor. We consider first the issue of the choice between an absolute and a relative poverty line.

6.1 Absolute and relative poverty lines

An absolute poverty line can be interpreted as fixed in any one of the spaces in which we wish to assess well-being. Conversely, a relative poverty line would depend on the distribution of well-being (including the utilities, living standards, functionings or capabilities) found in a society and would therefore vary across societies. Considerable controversy exists on whether absoluteness or relativity is a better property for a poverty threshold. Most analysts would probably agree that a poverty threshold defined in the space of functionings and capabilities should be absolute (but even on this there is no unanimity). An absolute threshold in these spaces would, however, generally imply relativity of the corresponding thresholds in the space of the commodities and in the level of basic needs required to achieve these functionings.

There are two main reasons for this. First, the relative prices and the availability of commodities depend on the distribution of incomes. For instance, as a society initially develops, rising numbers of people need to travel to work and to trade, without first being able to afford the costs of private transportation. Because of increasing returns to scale in the provision of public transportation, the affordability and accessibility of public transportation usually also first increases during that development stage. As societies become richer on average, however, their citizens start making increasing use of private forms of transportation, a phenomenon which causes a fall in the supply and availability of public transportation, leading to an increase in its relative price. This makes the capacity to travel (arguably an important capacity) more or less costly, depending on the state of economic development.

Second, not to be deprived of some capability may require the absence of relative deprivation in the space of some commodities. In support of this, there is Adam Smith's famous statement that the commodities needed to go without shame (an oft-mentioned basic functioning) can be to some extent relative to the distribution of such commodities in a society:

By necessaries I understand not only the commodities which are indispensably necessary for the support of life, but whatever the custom of the country renders it indecent for creditable people, even of the lowest order, to be without. A linen shirt, for example, is, strictly speaking, not a necessary of life. The Greeks and Romans lived, I suppose, very comfortably though they had no linen. But in the present times, through the greater part of Europe, a creditable day-laborer would be ashamed to appear in public without a linen shirt, the want of which would be supposed to denote that disgraceful degree of poverty which, it is presumed, nobody can well fall into without extreme bad conduct. Custom, in the same manner, has rendered leather shoes a necessary of life in England. The poorest creditable person of either sex would be ashamed to appear in public without them. In Scotland, custom has rendered them a necessary of life to the lowest order of men; but not to the same order of women, who may, without any discredit, walk about barefooted. In France they are necessaries neither to men nor to women, the lowest rank of both sexes appearing there publicly, without any discredit, sometimes in wooden shoes, and sometimes barefooted. Under necessaries, therefore, I comprehend not only those things which nature, but those things which the established rules of decency have rendered necessary to the lowest rank of people. (Smith 1776, Book 5, Chapter 2)

Sen (1985), reinforces this by distinguishing clearly the two dimensions of capabilities and commodities:

I would like to say that poverty is an absolute notion in the space of capabilities but very often it will take a relative form in the space of commodities and characteristics (Sen 1985, p.335).

This view is in fact also consistent with the World Bank's influential definition of poverty, which says that poverty is the inability to attain a minimal standard of living (World Bank 1990). This minimal standard consists of

of nutrition and other basic necessities and a further amount that varies from country to country, reflecting the cost of participating in the everyday life of society. (World Bank 1990, p. 26)

This has led some writers (particularly in developed countries) to conclude that attempts to preserve some degree of absoluteness in the space of commodities are untenable:

In summary, it does not seem possible to develop an approach to poverty measurement which is linked to absolute standards. While some analysts are uneasy with relativist concepts of poverty on the grounds that they are difficult to comprehend and can be seen as somewhat arbitrary and open to manipulation, no real practical alternative to relativist concepts exists. (Saunders 1994, p. 227)

6.2 Social exclusion and relative deprivation

Complete relativity of the poverty line in the space of commodities would nevertheless draw poverty analysis very close to the analysis of social exclusion (as exemplified by Rodgers, Gore, and Figueiredo 1995 at the International Labor Organization) and relative deprivation (as propounded for instance by Townsend 1979). Social exclusion entails "the drawing of inappropriate group distinctions between free and equal individuals which deny access to or participation in exchange or interaction" (Silver 1994, p.557). This includes participation in property, earnings, public goods, and in the prevailing consumption level (Silver 1994, p.541). Relative deprivation focuses on the inability to enjoy living standards and activities that are ordinarily observed in a society. Townsend (1979) defines it as a situation in which

Individuals, families and groups in the population (...) lack the resources to obtain the types of diet, participate in the activities and have the living conditions and amenities which are customary or at least widely encouraged or approved, in the society to which they belong, (p.30)

Equating absolute deprivation in the space of capabilities with relative deprivation in the space of commodities can, however, be a source of confusion in poverty comparisons. First, it tends to blur the operational and conceptual distinction between poverty and inequality. Second, it can hinder the identification of "core" or absolute poverty in any of the spaces. The identification of core poverty is, indeed, probably the most important input into the design of public policy in developing countries. Third, although the ethical appeal of Sen's capability approach has variously been invoked to justify the use of an entirely relative poverty line in the space of commodities, Sen himself does not accept this:

Indeed, there is an irreducible core of absolute deprivation in our idea of poverty, which translates reports of starvation, malnutrition and visible hardship into a diagnosis of poverty without having to ascertain first the relative picture. Thus the approach of relative deprivation supplements rather than supplants the analysis of poverty in terms of absolute dispossession (Sen 1981, p. 17)).

Furthermore,

(...) considerations of relative deprivation are relevant in specifying the 'basic' needs, but attempts to make relative deprivation the sole basis of such specification is doomed to failure since there is an irreducible core of absolute deprivation in the concept of poverty (Sen 1981, p.17).

Given the measurement difficulties involved in estimating relative poverty lines that correspond to absolute poverty lines in the space of functionings and capabilities, analysts often find most transparent to use the space of living standards as the space in which to define an absolute threshold. If this is done, however, it must subsequently be admitted that the procedure will imply a set of thresholds in the space of functionings and capabilities that depend at least partly on the conditions of the society in which an individual lives. Indeed, for a given absolute level of living standard in the space of commodities, an individual's capabilities are generally relative, that is, they depend on his social and economic environment, at least for functionings such as shamelessness and participation in the life of the community.

6.3 Estimating absolute poverty lines

Methodologies for the estimation of poverty lines have been most developed in the context of the fulfillment of basic physiological needs. Although such methodologies have often been set in a welfarist framework, they also matter for the basic needs, functioning or capability approaches since these approaches are also concerned with basic physiological achievements. These methodologies have recently been most often applied to developing country contexts.

6.3.1 Cost of basic needs

The estimation of the "cost of basic needs" (CBN) usually involves two steps. First, an estimation is made of the minimal food expenditures that are necessary for living in good health; we will denote this by z_F. Second, an analogous estimate of the required non-food expenditures, Z_NF, is computed and added to z_F to yield a total poverty line, Z_T We consider now in some detail each of these two steps.

6.3.2 Cost of food needs

The first step in the computation of a global poverty line is usually to estimate a food poverty line. The determination of a food poverty line generally proceeds by asking what amount of food expenditures is required to achieve some minimal required level of food-energy intake (or nutrient intake, such as proteins, vitamins, fat, or minerals. Early examples of the application of this approach include Rowntree (1901) and Orshansky (1965). A basket of food commodities is designed or estimated by "food specialists" such as to provide those minimally required levels of food-energy intake. The cost of that basket yields the food poverty line zF.

To illustrate how this exercise can be carried out in practice, consider Figure 6.1, which plots consumption x₁(p) and x₂(p) of two goods, goods 1 and 2, over a range of percentiles p. For simplicity, Figure 6.1 supposes that good 1 is "income-inelastic" (x₁(p) is constant) but that the consumption of good 2 increases with the rank in the distribution of income (it is income elastic). The idea then is to select a combination of x₁(p) and x₂(p) that provides a given level of minimal calorie intake. For the purposes of this illustration, assume that this minimum energy intake is 3000 calories per day, and that 1 unit of good 1 and 2 provides 2000 and 1000 calories each respectively. Also assume that each unit of good 1 and 2 costs q$.

The cheapest way to achieve the minimum calorie intake would be to consume only of good 1, since good 1 is the most calorie-efficient (we can think of good 1 as "cereals" and good 2 as "meat"). Indeed, each calorie provided by the consumption of good 1 costs q$/2000, whereas each calorie provided by the consumption of good 2 costs twice as much, that is, q$/1000. 1.5 units of good 1 (1.5 units *2000 calories/unit =3000 calories) would then be required for the minimal energy intake to be met, and zF would then equal 1.5q$.

This, however, would suppose a food commodity basket that no individual in Figure 6.1 would be observed to consume. Even at the very bottom of the distribution of income, individuals consume indeed at least some of good 2 at the expense of a diminished consumption of the more calorie-efficient good 1. We should presumably take this information into account if we wished to respect at least to some extent the cultural and culinary preferences of those whose well-being we aim to evaluate. This raises the obvious question of which preferences we should consider. Note that the preferred ratio of good 2 over good 1 increases continuously with p in Figure 6.1. For convenience, denote that ratio by ρ(p) = x₂(p)/x₁(p). Simple algebra then shows that the cost of attaining the minimum calorie intake is given by zF(p) = 3q$(1 + ρ(p))/(2 + ρ(p)), where zF(p) indicates that zF depends on the rank p of those whose preferences we use to build the commodity basket and to compute the food poverty line.

Figure 6.1 plots zF(p) and shows that it is not neutral to the choice of p. Using the preferences of the poorest, we obtain zF(p = 0) = 1.8q$, but if we use the preferences of the median population, we get zF(p = 0.5) = 2.1q$. This is in fact just one example of a more general standard observation in the literature on poverty lines that the choice of reference parameters matters for the estimation of poverty lines. In Figure 6.1, the farther are the preferences ρ(p) from the most calorie-efficient choice, the more costly is the estimated food poverty line zF(p). Arguably, the preferences ρ(p) should be those of the individuals that are close to the total poverty line, but this is a (partly) circular argument since ρ(p) is itself a determinant of that total poverty line. In practice, an arbitrary value of p is often chosen, reflecting some a priori belief on the position of those at the edge of the total poverty line. A more common (though arguably less commendable) procedure is to compute and use an average value of x₂(p)/x₁(p) over a range of p, such as the bottom 25% or 50% individuals of a population.

Figure 6.1: Engel curves and cost-of-basic-needs baskets

Even if we were to agree on the position p at which we wish to observe preferences such as ρ(p), there still remains the awkward fact that preferences will often vary significantly even at this given value of p. Said differently, there are in practice many different actual consumption patterns for a group of "typical poor". One solution is simply to ignore these differences and estimate the typical poor's average consumption patterns. Following this line of argument, consumption expenditures on various food items are regressed against income and the estimated parameters of these regressions are then used to predict the consumption patterns of the "typical poor". These regressions have often been parametric — assuming for instance that expenditures on cereals and meat are globally quadratic or log-linear in total expenditures. It is unlikely, however, that such parametric forms fit appropriately at all income levels, low and high alike. A better statistical procedure would probably be to regress consumption expenditures non parametrically on total expenditures, which would allow for a better fit of the preferences of those around the "typical poor".

An additionally important issue then is whether variations in culinary tastes and food habits across socio-economic characteristics should be taken into account. If no account of such variations are taken, then we can choose as a reference group that group whose diet minimizes food cost while providing the minimum required level of food-energy intake. This would typically generate an unreasonably low level of expenditures for many other groups, with an implied dietary basket of food commodities that could again be very different from those they typically consume.

If, however, full account of diversity in culinary tastes were to be taken, a serious risk would exist of overestimating the poverty lines of those individuals and groups of individuals with a greater taste for expensive foods (e.g., of higher quality or better taste). This is commonly the case, for instance, for urban households, who customarily have more sophisticated culinary tastes than rural dwellers (for the same overall living standards), and have also greater access to a larger variety of imported and expensive foods. This procedure would then assign greater poverty lines to urban versus rural individuals. It would also mean that the utility equivalents of individual food poverty lines would depend on the peculiarities of the individuals' food preferences. This would generally lead to inconsistent comparisons of well-being across urban and rural inhabitants, and would exaggerate the degree of poverty in the urban as compared to the rural areas.

We can illustrate this using Figure 6.2. Figure 6.2 shows baskets of two food commodities, x₁ and x₂, with three food budget constraints of total food consumption equal to Y0, Yl, and Y2 (these total budgets are expressed in units of x₁). Figure 6.2 also shows a "minimum calorie constraint", along which the total calories provided by the consumption of x₁ and x₂ equal the required minimum level of calorie intake. If no account whatsoever were taken of preferences, Y0 would yield the food poverty line. But along the food budget constraint Y0, there is only one point which meets the minimum calorie constraint (the point at which x₁ = Y0 and x₂ = 0, and it is of course unlikely that individuals will choose a food basket to be precisely at that corner. An individual with preferences U0 and budget Y0, for instance, would not locate himself on the minimum calorie constraint. It is only with the more generous budget constraint Y1 that this individual will consume the minimally required level of calorie intake, as shown on Figure 6.2.

But not all individuals will necessarily choose to be "calorie-sufficient" even with a total food budget of Y1. Individuals with greater preferences — as in the case of U2 — for the less-calorie efficient good x₂ will not choose a food basket on or above the minimum calorie constraint. Individual with preferences U2 will instead need Y2 to be calorie-sufficient. Yet, whether individuals with preferences U1 and budget Y1 are just as well off as individuals with preferences U2 and budget Y2 is debatable. Such would be the assumption, however, if we used two distinct poverty lines Y1 and Y2 for the two different tastes.

As mentioned above, such comparability assumptions are often implicitly made in practice when individuals living in different regions, rural or urban for instance, are assigned different poverty lines for reasons independent of differences in needs or prices. As illustrated in Figure 6.2, this supposes that an individual with "sophisticated" preferences (an urban dweller who has been accustomed to food variety) needs a higher budget to be as "well off" as an individual with less expensive preferences (a rural dweller who is content with eating basic food types). Probably more convincing, however, would be the view that U2 with Y2 in Figure 6.2 provides greater utility and well-being than U1 with Y1. Assigning different poverty lines Y1 and Y2 would then lead to inconsistent and biased poverty estimates.

Minimally required food expenditures can also be (and are often) adjusted for differences in climate, sex, or age, when such differences impact on needs rather than on tastes (as we discussed above). These expenditures can also be adjusted for variations in activity levels, although activity levels depend on the level of one's well-being, and thus on one's poverty status. Activity-level adjustments would thus generate a poverty line that evolves endogenously with the standard of living of individuals, a slightly awkward feature for comparing poverty.

6.3.3 Non-food poverty lines

The subsequent step is usually to estimate the non-food component of the total poverty line. The most popular method for doing this is simply to go straight to an estimate of the total poverty line by dividing the food poverty line by the share of food in total expenditures. The intuition behind this is as follows. The larger the food share in total expenditures, the closer the food poverty line should be to the total poverty line. Therefore, the smaller should be the necessary adjustment to the food poverty line (the closer to 1 should be the denominator that divides the food poverty line). Indeed, dividing ZF by ZF/ZT (the food share) gives ZT. The problem of which food share to use is of course an important issue. It is a problem analogous to the one discussed above on what the food basket should be for computing a food poverty line. Popular practices vary, but often make use of:

Figure 6.2: Food preferences and the cost of a minimum calorie intake

A- the average food share of those whose total expenditures equal the food poverty line;

E: 18.4.5

B- the average food share of those whose food expenditures equal the food poverty line;

E: 18.4.3

C- the average food share of a bottom proportion of the population (e.g., the 25% or 50% poorest).

In addition to this, another popular method

D- adds to zF the non-food expenditures of those whose total expenditures equal ZF

E: 18.4.7

To see how methods A, B and D work and differ from each other, consider Figure 6.3. Figure 6.3 shows (predicted) total expenditures against various levels of food expenditures. The regression can be done parametrically, but a generally better approach would be to predict total expenditures using a non-parametric regression on food expenditures.¹ On each of the two axes is shown the level of the (previously estimated) food poverty line zF. These two levels meet at the 45 degree line.

As indicated above, method A makes use of the average food share of those whose total expenditures equal the food poverty line. Total expenditures equal the food poverty line, zF, at point E on Figure 6.3. The food share at point E is given by the inverse of the slope of the line OE that goes from the origin to point E. The total poverty line according to method A is therefore given by the height of a line OE that extends to just above a level of food expenditures zF. This gives the vertical height of point A as the total poverty line according to method A.

Method B makes use of the average food share of those whose food expenditures equal the food poverty line. Those who consume zF in food are located at point B on Figure 6.3. Their food share is given by the inverse of the slope of the straight line that would extend from point O to point B. Hence, dividing zF by that food share brings us back to point B, which is therefore the total poverty line according to method B.

¹ DAD: Distribution|Non-Parametric Regression.

The total poverty line according to method B is more generous than that according to method A since the food share used for B is lower than that used for A. Indeed, method A focusses on the food share of a rather deprived population: those who, in total, only spend the food poverty line. Method B focusses on the food share of a less deprived population: those who, on food only, spend the food poverty line. Since food shares tend to decline with standards of living, method B's food share is usually lower than method A's.

Finally, method D considers the non-food expenditures of those whose total expenditures equal zF. As for method A, these individuals are found at point E on Figure 6.3. Their non-food expenditures are given by the length of line EG on the Figure. Adding these non-food expenditures to zF yields a total poverty line given by the height of point D.

The choice of methods and food shares and the estimation of the non-food poverty lines is rather arbitrary, and the resulting estimate of the total poverty line will also be somewhat arbitrary. Moreover, and perhaps more worryingly, some of the estimates will also vary with the distribution of living standards, as in the case of method C where the food share is an average over a range of individuals. To avoid inconsistencies in poverty comparisons, it would therefore seem preferable to use the same food share across the distributions being compared, and to use methods that do not make estimates overly dependent on a particular distribution of living standards.

6.3.4 Food energy intake

A slightly different method for estimating poverty lines that is popular in the literature is the so-called Food-Energy-Intake (FEI) method. Estimates of observed calorie intakes are first computed and then graphed against observed (total or food) expenditures. The analyst then estimates the expenditures of those whose calorie intake is just at the minimum required for healthy subsistence. When these expenditures are on food, this provides a food poverty line, which can then be used as described above in Section 6.3.3 to provide an estimate of a global poverty line. When the expenditures are total expenditures, the FEI method provides a direct link between a minimum calorie intake and a total poverty line².

E:18.4.1

Figure 6.4 illustrates how this method works. The curve shows the level of expenditure (measured on the vertical axis) that is observed (on average) at a given level of calorie intake (shown on the horizontal axis). The curve is increasing and convex, since calorie intake is usually expected to increase at a diminishing rate with food or total expenditures. Above zk, the minimum calorie intake recommended for a healthy life, we read z, the food or total poverty line according to the FEI method.

²DAD: Distribution|Non-Parametric Regression.

As just exposed, the FBI method may appear straightforward and simple to implement. A number of conceptual and measurement problems are hidden, however, behind this apparent simplicity. Note for instance that the line traced on Figure 6.4 is the expected link between expenditure and calorie intake; there is in real life a significant amount of variability around this line. How are we to interpret this variability? If it is due to measurement errors, then we may perhaps ignore it. If it is due to variability in preferences, then we may wish to model the calorie-intake-expenditure relationship separately for different groups of the population, as is often done in practice, for urban and rural areas for instance. As in the cost-of-basic-needs method, however, we then run the risk of estimating higher poverty lines for those groups that have more expensive or more sophisticated tastes for food. This would lead to inconsistent comparisons of well-being and poverty, as discussed in Section 6.3.2.

To compute expected expenditure (given the variability of actual observed spending) at a given calorie intake, we can estimate the parameters of a parametric regression linking expenditures to calorie intake. Again, the regression is often postulated to be log-linear or quadratic. This parametric specification supposes, however, that the functional relationship between expenditures and calorie intake is known by the analyst, up to some unknown parameter values. This is unlikely to be true everywhere, especially for those far from the level of calorie intake of interest (e.g., those at the lower and upper tails of the distribution of spending and calorie intake). In such cases, the parametric procedure will make the estimated expenditure poverty line affected by the presence of "outliers" that are relatively far from the minimum level of calorie intake. This procedure will then generate a biased estimator of the "true" poverty line. A more flexible and arguably better approach would be to estimate the link between expenditures and calorie intake non parametrically.

6.3.5 Illustration for Cameroon

To see whether differences in some of the methodologies described above can matter, consider the case of 1996 Cameroon. Table 6.1 shows the result of estimating food, non-food and total poverty lines for the whole of Cameroon and for each of its 6 regions separately. Note that the figures are in Francs CFA adjusted for price differences, with Yaoundé being the reference region. The food poverty line was estimated using the FEI method at 2400 calories per day per adult equivalent. A non-parametric regression using DAD was performed for the whole of Cameroon and separately for each of the 6 regions. The lower non-food poverty line was obtained (non parametrically) using method D in section 6.3.3, and the upper non-food poverty line using method B. Again, the relevant regressions were carried out for the whole of Cameroon and separately for each of its 6 regions.

As can be seen, the link between calorie intake and food expenditures varies systematically across regions. Expected food expenditure at 2400 calories per day is significantly higher in urban areas (Yaoundé, Douala and Other cities) than in the rural ones. In Douala, for instance, a household would need 408 Francs CFA per day per adult equivalent to reach an intake of 2400 calories per day. In the Highlands, no more than 170 Francs CFA would on average be needed. The link between food and total expenditures also varies across Cameroon's regions. Combined with the different estimates for the food poverty lines, this leads to very significant variations across regions in the total poverty lines. Using method D, a lower total poverty line of 589 Francs CFA is obtained for Douala, but that same poverty line is only 235 Francs CFA for the Highlands. Note also that the choice of method B vs method D has a very significant impact on the estimate of the total poverty line. For the whole of Cameroon, the lower and the upper total poverty lines are respectively 373 and 534 Francs CFA, a difference of 43%.

Unsurprisingly, these large differences across regions and across methods have a large impact on national poverty estimates and on regional poverty comparisons. This is illustrated in Table 6.2, which shows the proportion of individuals underneath various poverty lines for various indicators of well-being. "Calorie poverty" (first line) is relatively constant across Cameroon. In the whole of Cameroon, 68.1% of the population was observed to consume less than 2400 calories per day per adult equivalent. This proportion varies between 59.9% (for Other cities) and 86.5% (for Forests) across regions. Roughly the same limited variability and the same poverty rankings appear when food poverty is estimated using for each region its own food poverty line (third line). However, when a common food poverty line is used to assess food poverty in each region (second line), national poverty stays roughly unchanged at around 69% but urban regions now appear significantly less poor than the rural ones. For instance, the poverty headcount in Douala (42.0%) is now only half that of the Highlands (82.5%).

The rest of Table 6.2 confirms these lessons. When a common poverty line is used to compare the regions, rural areas are significantly poorer than urban ones. When region-specific poverty lines are used, these differences are much reduced, and the regional rankings are often even reversed. For example, using a common lower total poverty line (fourth line), the Highlands have a head-count ratio more than three times that of the urban regions. When regional lower total poverty lines are used instead, the Highlands become prominently the least poor of all regions. Setting common as opposed to regional poverty lines can thus have a crucial impact on poverty rankings and the setting of subsequent poverty alleviation policies. The choice of a lower as against an upper total poverty line also makes a difference. For the whole of Cameroon, the proportion of the Cameroonian population in poverty increases from 43.9% to 68.0% when we move from a common lower total poverty line (fourth line) to a common upper total poverty line (sixth line). Clearly, this changes significantly one's understanding of the incidence of poverty in Cameroon.

These results also implicitly warn that the choice of well-being indicators is not neutral to the identification of the poor. In our context, this is because the correlation between calorie intake, food expenditure and total expenditure is imperfect. Table 6.3 indicates, for example, that in bidimensional poverty analyses using any two of these three indicators of well-being, around 20% to 25% of the population is characterized as poor in one dimension but non poor in the other. In the first part of 6.3, we note for instance that 11.2% of the population would be judged poor in terms of calorie intake but not poor in terms of food expenditure. Conversely, 9.6% of the population would be deemed non poor in terms of calorie intake but poor in terms of food expenditure. These proportions are slightly higher for the other bidimensional poverty analyses, which compare food with total expenditure poverty, and calorie with total expenditure poverty, respectively.

6.4 Estimating relative and subjective poverty lines

6.4.1 Relative poverty lines

There are two other popular methodologies for the estimation of poverty lines. The first deals with purely relative poverty lines, which, as we saw above, can be useful to determine the commodities needed for "living without shame" and for participating in the "prevailing consumption level". A relative poverty line is typically set as a somewhat arbitrary proportion of the mean or of some income quantile (often the median). Clearly, such a poverty line will vary with the central tendency of the income distribution, and will not be the same in constant terms across space and time. One possibly awkward feature of the use of a relative poverty line approach is that a policy which raises the income of all, but proportionately more those of the rich, will increase poverty, although the absolute incomes of the poor have risen. Conversely, a natural catastrophe which hurts absolutely everyone will decrease poverty if the rich are proportionately the most hurt³.

E:18.3

Another possibly awkward feature of the use of relative poverty lines is that an improvement in the absolute incomes of some of the poor, with no change

³DAD: Poverty|FGT Index.

Table 6.1: Estimated poverty lines in Cameroon according to different methods (Francs CFA/day/adult equivalent), for the whole of Cameroon and separately for its 6 regions

Table 6.2: Headcount according to alternative measurement methods and for different regions in Cameroon (% of the population)

Table 6.3: Distribution of the poor according to calorie, food and total expenditures poverty (% of the population)

in the incomes of the others, may in fact increase poverty. To see why, let η and ς be small positive values and let an income distribution be defined as Q(p) + η(p), with

and with η set initially to 0. Choose z = λμ. The un-normalized FGT index is then given by

Note that , which also says that the relative poverty line λμ increases with an increase in ς. We may then check how increases in η affect overall poverty, for a small ς. For the headcount index, we find

which says that the headcount necessarily increases whenever someone's income increases, regardless of whether that person is poor or rich. When α > 0,

The term A on the right-hand side of (6.4) is positive: an increase in incomes increases the relative poverty line and thus tends to increase poverty. When p0 > - F(λμ), the increase in income is beneficial to the rich: the term B is then nil, and poverty then necessarily increases with η. When p₀ < F(λμ), the increase in income benefits some of those below the poverty line, and this increase in their absolute living standards explains why the term B is then negative. Whether it is sufficiently negative to offset the positive term A depends 1) on how far below the poverty line these poor are, and 2) on the value of the ethical parameter α. Hence, even with α > 0, relative poverty may increase when growth is beneficial to the poor⁴.

E:18.3

6.4.2 Subjective poverty lines

An alternative poverty line methodology relies uses subjective information on the link between living standards and well-being. One source of information comes from interviews on what is perceived to be a sound poverty line, using a question found for instance in Goedhart, Halberstadt, Kapteyn, and Van Praag (1977):

We would like to know which net family income would, in your circumstances, be the absolute minimum for you. That is to say, that you would not be able to make both ends meet if you earned less, (p.510)

The answers are subsequently regressed on the incomes of the respondents. The subjective poverty line is given by the point at which the predicted answer to the minimum income question equals the income of the respondents. The basic intuition for this is that unless someone earns that poverty line, he will not truly know that it is indeed the appropriate minimum income needed to "make both ends meet".

This method is illustrated in some detail on Figure 6.5. Each point represents a separate answer to the above query, namely, the minimum income judged to be needed to make both ends meet as a function of the actual income of the respondents. The filled line shows the predicted response of individuals at a given level of income. For low income levels, this predicted minimum subjective income is well above the respondents' income. The predicted minimum subjective income increases with actual income, but not as fast as income itself. Those with below z* answer that they need more than their own income. Those with income above z* answer that they need on average less than their own income. At z*, which is also where the 45-degree line crosses the line of predicted minimum subjective income, that predicted minimum subjective income equals actual income. The subjective poverty line would therefore be estimated here as z*.

One difficulty with the subjective approach is the sensitivity of poverty line estimates to the formulation of the interview questions. Another problem comes from the considerable variability in the answers provided, even within groups of relatively socio-economically homogeneous respondents. The presence of this variability is apparent on Figure 6.5 with points sometimes quite far away from the predicted response line. This variability has some awkward consequences. On Figure 6.5, for instance, an individual at point a is someone who would be judged poor according to the subjective income method since his income falls below z*. An individual at a feels, however, that his income exceeds the minimum income he feels to be needed (point a is to the right of the 45-degree line). He would therefore feel that he is not poor. Conversely, someone at point b feels that he is poor, since his reported minimum income exceeds his actual income, but he would be judged not to be poor by the subjective poverty line method.

⁴DAD: Poverty|FGT Index.

How, therefore, ought we to interpret this variability? Is it due to measurement errors? If so, then we may probably best ignore it. Is it rather that the link between living standards and true well-being varies systematically even within homogeneous groups of people? If so, then we might not want to use incomes or other direct or indirect indicators of well-being to classify the poor and the non poor. Instead, we should take individuals at their word on whether they declare themselves to be poor or not. But then, this would clearly raise important practical and incentive problems for the design and the implementation of public policy.

6.4.3 Subjective poverty lines with discrete information

An alternative approach to estimating subjective poverty lines is to ask respondents whether they feel that their income is below the poverty line, without directly asking what the value of that poverty line should be. Answers are coded 0 or 1 — according to whether respondents feel that they are poor or not — alongside the respondents' incomes. The estimate of the poverty line is that which best reconciles the distribution of those answers with that of the respondents' incomes.

This is illustrated in Figure 6.6. Each "dot" is an observation of whether a respondent of a certain income level felt poor (1) or not (0). The working assumption is that respondents compare their income to a common subjective poverty line z*. z* is unobserved and must be estimated. One estimation procedure for z* would be to maximize the likelihood that the respondents' declarations of poverty status correspond to that which would be inferred by comparing z* to their incomes. Said differently, the estimator of z* would minimize the likelihood of observing observations within the ellipses of Figure 6.6. Not everyone with an income below z* says that he is poor; conversely, not everyone above z* says that he is not poor. These "classification errors" would be explained by measurement and/or misreporting errors. Hence, on Figure 6.6, there are "false poor" and "false rich", as shown within the ellipses at the bottom left and at the top right of the Figure. Again, this would run into difficulties if individual preference or need heterogeneity were the true explanation for the "classification errors".

6.5 References

The literature on the estimation of poverty lines is both significant and varied. Note that there is often a sharp distinction in tone and in content between those works which focus on poverty in less developed countries and those which address poverty in more developed economies.

Early reviews of the literature include Goedhart, Halberstadt, Kapteyn, and Van Praag (1977) and Hagenaars and Van Praag (1985). An excellent and comprehensive recent review can be found in Ravallion (1998b) — this chapter has been much influenced by it. Greer and Thorbecke (1986) has been influential in establishing the FEI method of estimating a poverty line. A method based on "basic needs budget" is described in Renwick and Bergmann (1993). The differential effects for poverty measurement of choosing FEI vs CBN methods for estimating poverty lines can be found inter alia in Ravallion and Bidani (1994) and in Wodon (1997a).

Barrington (1997), Fisher (1992), Glennerster (2000) and Orshansky (1988) provide critical reviews of the literature on the setting of the official poverty line in the United States.

The consequences and the issues that surround the choice between absolute and relative poverty lines are discussed in Blackburn (1998) (on the empirical sensitivity of poverty comparisons to that choice), de Vos and Zaidi (1998) (on whether poverty lines should be country specific), Foster (1998) and Zheng (1994) (on the consequences for the choice of poverty indices), and Fisher (1995) and Madden (2000) (on the empirical income elasticity of poverty lines).

Subjective methods for setting poverty lines are discussed and explored in de Vos and Garner (1991) (for comparisons of results between the US and the Netherlands), Pradhan and Ravallion (2000) (on perceived consumption adequacy), Stanovnik (1992) (for an application to Slovenia), Van den Bosch, Callan, Estivill, Hausman, Jeandidier, Muffels, and Yfantopoulos (1993) (for a comparison across 7 European countries), Blanchflower and Oswald (2000) (for reported levels of happiness in Great Britain and in the US), and Ravallion and Lokshin (2002) (for perceptions of well-being in Russia).

Figure 6.3: Food, non-food and total poverty lines

Figure 6.4: Expenditure and calorie intake

Figure 6.5: Subjective poverty lines

Figure 6.6: Estimating a subjective poverty line with discrete subjective information

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