metadata: authors: 0: author: Ravallion,Martin
count: Bangladesh
docna: 0: docna: The challenging arithmetic of poverty in Bangladesh
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Rural Settlements,Industrial Economics,Poverty Impact Evaluation,Poverty Monitoring & Analysis,Economic Growth,Agricultural Growth and Rural Development,Inequality,Poverty Assessment,Poverty Diagnostics,Poverty Lines,Small Area Estimation Poverty Mapping
teratopic: Poverty Reduction
abstracts: cdata!: The arithmetic of poverty in Bangladesh
            is challenging from a number of perspectives. Counting
            Bangladesh's poor is difficult to do with seemingly
            tolerable precision, even just to get some idea of whether
            recent efforts to alleviate poverty have succeeded. But that
            is only the beginning of the challenge. The details of how
            to find resources, and design and implement effective
            policies - the arithmetic of poverty alleviation in
            Bangladesh - pose a severe challenge to policy analysts,
            governments, and the international community. This paper
            aims to offer a critical assessment of recent evidence
            relevant to these issues. It addresses the following three
            questions: (i) Has poverty decreased in Bangladesh during
            the 1980s? (ii) How responsive is poverty in Bangladesh to
            economic growth and changes in relative inequalities? (iii)
            What are the prospects for poverty alleviation through
            currently anticipated economic growth in Bangladesh? The
            paper takes a close look at some recent data suggesting that
            the problem of poverty in Bangladesh may be diminishing
            quite rapidly. It offers an empirical assessment of how much
            impact on poverty in Bangladesh is expected from economic
            growth, and from changes in overall inequality.
geo_reg_key: 517198,517212,517191
repnme: repnme: The challenging arithmetic of poverty in Bangladesh
display_title: The challenging arithmetic of
            poverty in Bangladesh
listing_relative_url: /research/1991/02/700072/challenging-arithmetic-poverty-bangladesh
topicv3: Economic Growth m1326241 471,Poverty m1326687 695,Poverty Measurement and Analysis m1326941 707,Population, Aging and Health m1327736 640,Rural Development m1504505 2667
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Poverty Reduction
origu: Policy, Research & Ect Affairs
no_of_pages: 37
author_keys: 0: author_key: 99002
model_extractions: **Policy, Research, and External Affair**

# **World Development Report**

# WPS **586**

- This paper a product of the Agricultural Policies Division, Agriculture and Rural Development Departmentwas prepared as a background paper for the _1990 World Development Report_ on poverty. The paperdrawson results from aPRE researchproject,Policy Analysis and Poverty: Applicable Methods and Case Studies. Copies are available free from the World Bank, 1818 H Street NW, Washington DC 20433. P;ease contact the World Development Report office, room S 13-060, extension 31393 (3' pages).

Did poverty increase in Bangladesh in the 1980s? How responsive is poverty in Bangladesh to economic growth and changes in relative inequalities? What are the prospects for poverty alleviation through currently anticipated economic growth in Bangladesh?

Ravallion addresses these questions using a narrow definition of poverty, whereby a person is judged to be poor if he or she resides in a household the income of which does not allow a consumption level that permits adequate nutrition. He concludes:

* The recent evidence of a decline in absolute numbers of poor in Bangladesh in the 1980s is unconvincing. The rate of growth in real per capita consumption of 10 percent a year implied by the underlying household spending surveys is too high to be believed. One cannot assume that the national accounts are accurate, but their implied growth rate of about 0.5 percent a year is more plausible. Assessments of growth in the 1980s consistent with national accounts data (using household surveys only to measure _relative_ inequalities) suggest that the proportion of the population deemed to be poor has remained fairly stable in recent years - while absolute numbers of poor have increased.

* Per capita growth rates in Bangladesh have been below average for South and Southeast Asia in the 1980s, and few observers expect this to change in the 1990s.

* The growth rates needed to prevent an increase in the absolute numbers of poor in Bangladesh, or to attain any given rate of poverty reduction, are higher than similar calculations have suggested would be needed for some other low-income countries in Asia. At a widely assumed poverty line for Bangladesh, the growth rate of real consumption per capita must be at least equal to the rate of population growth before the absolute numbers of poor can start to fall appreciably without a shift in relative inequalities. Such a growth rate has not been achieved in recent times, but is expected over the next 10 years or so by some observers.

* Recent growth in Bangladesh has been relatively low in a country where it needs to be relatively high to avoid an increase in the number of poor.

* Certain changes in relative inequalities could, in principle, wipe out poverty alleviation through growth. It appears that a fairly substantial change would be needed to do so for the simple headcount index of poverty in Bangladesh. However, other measures of - poverty which reflect changes in living standards of the poorest - will be more sensitive to how equitable the growth process is in the near future.

* Any poverty alleviation strategy for Bangladesh should strongly encourage domestic policy reforms and international assistance that not only enhance the rate of growth but also ensure that its benefits are shared widely.

Thc PRE Working Paper Series disseminates the findings of work under way in the Bank's Policy, Rcscarch, and Extemal Affairs Complex. An objcctive ofthe serics is to get thesc findings out quickly, cven if presentations arc css than fully p)lish.d. The findings, intcrpretations, and conclusions in these papers do not necessarily represent official Bank policy.

Produced bv PRE Editorial Services
The Challenging Arithmetic of Poverty in Bangladesh* by Martin Ravallion

# Table of Contents

|I.|Introduction|1|
|---|---|---|
|II.|Has Poverty Increased or Decreased in Bangladesh<br>During the 19809?|2|
||Some Recent Evidence|2|
||An Alternative Assessment|5|
|III.|Growth, Inequality, and Poverty|11|
||Methodological Issues<br>Prospects for Poverty Alleviation through Growth|11<br>13|
|IV.|Conclusions|18|
|Appen|dix|21|
|Footn|otes|24|
|Refer|ences|26|
|Table|s|28|
|Figur|es|31|

Backcroind paper for the _World Development Report 1990._ The paper draws on results of Research Project 675-04, "Policy Analysis and Poverty: Applicable Methods and Case Studies", funded through the World Bank's Research Committee, and based in the Agricultural Policies DIvision. The author is grateful to Gaurav Datt for assistance with the calculaticns reported here, and to Gaurav, Raisuddin Ahmed, James Sackey, Lyn Squire, Dominique van de Walle, and participants at the Bangladesh Development Forum 1989 for helpful comments on an earlier draft. Address for correspondence: Martin Razallion, Room N8-045, World Bank, 1818 H Street NW, Washington DC 20433, USA.
1

# I. **Introduction**

The arithmetic of poverty in Bangladesh is challenging from<sup>a number of</sup> perspectives. Counting Bangladesh's poor is difficult to<sup>do with seemingly</sup> tolerable precision. even just to get some idea of whether recent efforts to alleviate poverty have succeeded. But that is only the beginning of the challenge. The details of how we muster resources, and design<sup>and implement</sup> - - effective policies the arithmetic of poverty alleviation in Bangladesh pose a severe challenge to policy analysts, governments, and<sup>the international</sup> community.

The aim of this paper is to offer a critical assessment of recent evidence relevant to these issues. I hope to throw light on three main questions: i) Has poverty decreased in Bangladesh during the 1980s? ii)<sup>How</sup> responsive is poverty in Bangladesh to economic growth and changes in relative inequalities? iii) What are the prospects for poverty alleviation through currently anticipated economic growth in Bangladesh?

I shall restrict attention to a narrow definition of "poverty", whereby a person is judged to be poor if (and only if) he or she resides in a household whose income does not permit attainment of a pre-determined consumption bundle, as judged necessary for the fulfillment of certain basic consumption needs, most importantly (in this context) adequate nutrition. There are aspects of individual welfare which this definition cannot capture, such as access to publicly provided goods; the cleanliness of drinking water, for example, matters to one's standard of living, but it is unlikely to be reflected well in consumption or income, as usually measured. Nor does the definition have anything to say about how consumption is actually distributed within the household. But the narrow definition of poverty used here probably
2 does capture much of what does matter to individual living standards<sup>in</sup> - Bangladesh most importantly the adequacy of household<sup>food entitlements -</sup> and it is at least a tractable definition for empirical<sup>analysis. Probably</sup> for this reason, it has been the most common definition<sup>in past studies of</sup> poverty in Bangladesh, as elsewhere.

The following section takes a close look at some recent data<sup>suggesting</sup> that the problem of poverty in Bangladesh may be diminishing<sup>quite rapidlv.</sup> In section III, I will offer an empirical assessment of<sup>now much impact on</sup> poverty in Bangladesh we might expect from economic growth, and from changes in overall inequality. Section IV offers some conclusions.

# II. Has Poverty Increased or Decreased in Bangladesh During the 1980s?

Estimates from various surveys during the 1970s indicated a<sup>rising</sup> prevalence of poverty in Bangladesh (Muqtada, 1984; ILO, 1985; Islam<sup>and Khan,</sup> 1986; Rahman, 1986; Alamgir and Ahmed, 1988). Has this<sup>trend reversed in the</sup> 198Os?

# Some Recent Evidence

The Bangladesh Bureau of Statistics (BBS) has recently published estimates of poverty for various years in the 1970s and 80s. Using the Household Expenditure Surveys (HES), BBS (1988b) give estimates<sup>of the</sup> absolute number, and proportion of the population, that<sup>were unable to attain</sup> a caloric intake of at least 2122 calories per person per day (a<sup>popular</sup> poverty line for Bangladesh; also see Alamgir, 1978). These<sup>estimates appear</sup> to have been based on a comparison of actual household expenditure<sup>with an</sup>
3 estimated expenditure needed to reach<sup>this caloric requirement, though the</sup> details of estimation are unclear from<sup>the information given in BBS (1988b).</sup> The BBS results show a substantial decrease<sup>in the proportion of the</sup> rural population who were deemed poor,<sup>from 83% in 1973/74 to 74% in i981/82,</sup> then dropping quite sharply to 51% in<sup>1985-86. The estimates show a similar</sup> (though less dramatic) contraction in<sup>the prevalence of urban poverty. While</sup> the BBS figures suggest that the absolute<sup>numbers of poor increased during the</sup> 1970s, a sharp decline in rural areas<sup>during the 1980s is indicated, though</sup> this was partly mitigated by an increase<sup>in the numbers of poor in urban</sup> areas. Nonetheless, the BBS figures<sup>show an impressive recent record in</sup> poverty alleviation, with aggregate numbers<sup>of poor declining from 67 million</sup> in 1981/82 to 51 million in 1985/86.

Skeptics have pointed to a number of problems<sup>in comparing BBS's</sup> Household Expenditure Surveys over time.<sup>For one thing, there are differences</sup> in sample coverage; for example, while<sup>the 1981/82 HES surveyed about 9,500</sup> households (0.05 percent of the population),<sup>this dropped to just 3,800 (0.02</sup> percent) for the 1985/86 HES. There<sup>have also been some changes in the</sup> questionnaire used, with implications<sup>for the measurement of household incomes</sup> and consumptions, such as in the methods used<sup>for imputing the value of food</sup> consumption from own production.

So there are good reasons to ask: How robust<sup>is this seemingly excellent</sup> recent record on poverty alleviation<sup>to possible inconsistencies over time in</sup> the underlying household expenditure surveys,<sup>on which the estimates of</sup> poverty have been based?.

One possible clue can be obtained from<sup>an alternative source of data on</sup> aggrega-e incomes and consumpZion,<sup>namely Bangladesh's national accounts (NA).</sup>
4 It cannot **assumed** Lhat the national accounts are more accurate, but dram.iatic discrepancies with that source would clearly be worrying. The national accounts may not provide a better estimate of average consumption than the HES, but (given the aforementioned changes over time in HES methodology), the NA series is probably a better basis for comparing consumption aggregates across time daring the 1980s.

Table 1 gives my estimates if real consumption per capita in Bangladesh based on both the HES and the NA. For urban areas, I have used the Consumer Price Index (CPI) for middle income groups in Dhaka, while for rural areas I have used the average CPI for rural areas. Consumption f om NA is estimated from the "World Tables" (World Bank., 1988).1 The results in Table 1 reveal substantial divergence between the HES and NA means for 1983/84 and (even more so) 1985/86, though the two sources are in close accord for 1981/82.2 However, for the purposes of comparing poverty levels over time, the more disturbing observation from Table 1 is the discrepancy in growth rates between the two data sources. The national accounts suggest that real consumption per capita grew at the compound annual rate of 0.5% over the period 1981/82-1985/86; the household expenditure survex' on the other hand implies a compound annual growth rate of 9.9%, which would have been _ne of the highest recorded for any country in the world over this (generally difficult) period, or at other times for that matter. While the NA mav well be underestimating the true rate of growth, it is very hard to believe the rate of growth implied by the HES.
5

# **An Alternative Assessment**

Overestimation of the gl.;wth rate in real consumption will lead to overestimation of the rate of poverty reduction. To help assess hcw much overestimation may be involved, I have calculated measures of poverty by two methods. One relies exclusively on the HES (following conventional practice), while the other uses information on mean consumption from the NA to supplement the data on relative inequalities from HES. The latter method illustrates a new and potentially iseful methodology for other purposes, so some elaboration is called for. The idea is that one derives formulae for the poverty measures of interest as functions of the mean of the distribution, ard a set of other parameters describing the Lorenz curve, which summarizes all relevant information about relative inequalities. The latter parameters are estimated econometrically. From these formulae one can then estimate the poverty measure that would be obtained if the mean changed, holding the Lorenz curve constant; thus one can estimate the poverty levels that would hold if the mean was that obtained from NA, rather than HES, holding -he Lorenz curve constant.<sup>3</sup> The Appendix gives details.

We should be clear about the purpose of these calcula:,ions. Their aim is not to come up with the "best" measure of the magnitude of poverty in Bangladesh, or even a "better" one than that used by BBS. Rather, the objective is to test the robustness of the BBS estimates of how poverty has changed in Bangladesh during the 1980s.

Various measures of poverty will be considered, aiming to embrace the range of possible value judgments on this issue. The proportion who are poor, or "headcount index of poverty", implicitly treats all of the poor identically; no distinction is made amongst the 50-60 million poor in
6 Bangladesh in terms of the depth of their poverty. And it is plain from at least casual observation that the poor are not all equally poor. So I shall also consider two alternatives to the headcount index, both of which are members of the Foster, Greer and Thorbecke (FGT) (1984) class of additively decompoEable poverty measures, each member of which is identified by a nonnegative parameter a. The headcount index is also a member of this class. The hree FGT measures used here are: (i) The headcount index of poverty given by the percentage of the population living in households with average consumptions below the poverty line; this is the FGT measure for a - 0. While this is a simple measure to interpret, it has the disadvantage that it is entirely insensitive to changes below the poverty line; for example, a poor person may become poorer, but measured poverty will not change.

(ii) The Doverty gaR measure, defined as the consumption deficit of the poor as a proportion of the poverty line divided by the population size; this is the FGT measure for a - 1. Thus, letting g=(z-y)/z denote the proportionate poverty deficit of a person with income or consumption y below the poverty line z, and setting g-O for the non-poor, the FGT poverty gap measure is simply the arithmetic mean of g over tne whole population. The measure is then also equal to the average poverty deficit of the poor times the headcount index of poverty.

(iii) The distributionally sensitive FGT measure, whereby, instead of weighting the various poverty deficits of the poor equally (as in the previous measure) they are weighted by the deficits themselves. The resulting measure is then simply the mean of the squared proportionate poverty deficits i.e., a = 2. This measure satisfies the main axioms ftcr a desirable poverty measure
**7**

found in the theoretical literature<sup>(for a recent survey see Foster, 1984),</sup> including Sen's (1976, 1981) Transfei<sup>Axiom which requires that when income is</sup> transferred from a poor person<sup>to someone who is poorer measurei poverty</sup> decreases, Neither measures<sup>(i) nor</sup><sup>**(ii)**satisfy this condition. It alsohas;</sup> advantages over a number of<sup>alternative distributionally sensitive measures,</sup> such as the Sen index. For example,<sup>the FGT measure is additively separable;</sup> aside from the advantages of<sup>that property for constructing decompositionsof</sup> poverty ("poverty profiles"),<sup>it implies that when any subgroup of the</sup> population becomes poorer, aggregate<sup>poverty will also increase, ceteris</sup> paribus (Foster and Shorrocks,<sup>1987).</sup> We do not have any alternative<sup>data to the HES when estimating the</sup> distribution of consumption in<sup>Bangladesh arcund the mean. So I have little</sup> choice but to assume that the<sup>Lorenz curve from the HES is correct at each</sup> date. It should, however, be<sup>noted that one possible explanation for the high</sup> HES means for the later years<sup>is an undersampling of poor households,which</sup> would also lead to a bias in<sup>the Lorenz curve.</sup> Figures 1 and 2 give the estimated<sup>Lorenz curves and Gini indices for</sup> Bangladesh, for urban and rural<sup>areas respectively, over the three HES years.</sup> The rost notable point here is<sup>how 'ittle relative inequalities have changed</sup> within the rural sector; the Lorenz curves<sup>for these three years are virtually</sup> indistinguishable, and Gini indices<sup>are identical to two decimal places.</sup> Changes in overall inequality<sup>have been primarily due to changes in inequalitv</sup> within the urban sector, and inequality<sup>between sectors. A decline in</sup> inequality in urban areas after<sup>1981/82 is indicated, though it did not</sup> continue after 1983/84. The<sup>same pattern holds for inequality between sectors</sup> (as measured by the urban/rural<sup>disparity in ,means) though doubts have been</sup>
a cast on the accuracy of the sample means for the later dates, as discussed above. Inequality is higher (in terms of the Lorenz dominance criterion) in the urban sector for all three years.

A further complication arises concerning the BBS poverty lines. Nominai monetary equivalents of the BBS caloric poverty lines are available.<sup>4</sup> However, there are substantial discrepancies between the implied rates of inflation and those indicated by the aforementioned CPIs, for both urban and rural areas. The BBS poverty lines are of about 15% lower real value in 1981/82 than the two later years, in terms of the CPI bundle of goods.5 It might be argued that the CPI bundle of goods is inappropriate lor adjusting a caloric poverty line. But the BBS poverty lines also have increasing purchasing power in terms of food (using the food component of the Dhaka middle income CPI), and also in terms of the nain sources of calories, rice and wheat (using open market prices). While, as a general rule, one may allow the possibility of poverty lines with different real purchasing power, reflecting changing social standards over time (or in different countries), the validity of doing so in this particular context is far from obvious.

For the purpose of this investigation, I have preferred to use poverty lines with constant purchasing power, as indicated by the CPI. The poverty lines used are a consumption per capita of Tk 200 for rural areas, and Tk 300 for urban areas, in 1981/82 prices. These are approximately equal to the BBS poverty lines for 1981/82.6 I shall refe. co these as the "BBS 1981/82 poverty lines". To test the sensitivity of ths results to this choice, I shall also give results for lower poverty lines, set at three quarters of the above levels. All calculations are based on the distributions of consumption
9 expenciture per person for each year; these can be readily calculated<sup>from the</sup> data given in BBS (1986, 1988 a,b).

Each of the above poverty measures can niow be derived as a function of the poverty lines, the parameters of the Lorenz curve, and the means. (See the Appendix for further details). Table 2 gives the estimates obtained for all three of these measures, using both the HES and NA means from Table 1, and the 1981/82 BBS poverty line. I have assumed that the 1981/82 mear,s from the HES are correct; since the two means are very close nationally for that year, there is no obvious reason to doubt that assumption, and this also has<sup>the</sup> acvantage Df allowing us to maintain the urban/rural breakdown. (The national accounts are not dissagregated by urban/rural areas). To maintain that breakdown, I have alsc assumed that the .A consumption growth rates reported in Tab'le 1 hold for both urban and rural sectors. Figure 3 summarizes the results for the headcount index, and the absolute numbers of poor.

The following observations can be -ide on the results in Table 2: (i) The estimates of mean consumption per capita based on the HES imply sharply falling poverty levels over the period, as claimed by BBS (1988b), and, indeed, at an even higher rate of decline than they had suggested. This reflects the fact that the BBS poverty lines have increasing real purchasing power over the period, putting upward pressure on their estimates of poverty (though insufficient to eliminate the downward bias due to thkeir apparent overestimation of growth rates). Using the BBS 1981/82 poverty lines and HES means, absolute numbers of poor decline from 66 million persons in 1981/82 to 37 million in 1985/86. The estimates of poverty based on the HES Lorenz curves and the consumption means derived from NA do not, however, confirm this trend. The headcount index fell slightly from 1981/82 to 1983/84 in both
10 urban and rural , eas, but this was followed by a deterioration from<sup>1983/84</sup> to 1985/86. On balanice, the headcount index changed little over the period. Ab,solute numbers of poor in Bangladesh rose from 66 million to 72<sup>million in</sup> 1985/86.

(ii) The same basic pattern is found for the lower poverty line, though the decline **In** the number of poor, as estimated solely from the HES, is now even more dramatic: while 43 million people did not attain three-quarters of the BBS poverty line in 1981/82, this falls to only 14 million in 1985/86. The growth rate estimates from NA, on the other hand, indicate an<sup>increase to</sup> 46 million in 1985/86.

(iii) The poverty gap measures reported in Table 2 follow a similar pattern to the headcount indices. The consumption deficit of the urban poor normalized by the total urban population represented 22% of the poverty line in 1981/82; for rural areas the proportion is slightly higher, at 25%.7 Another way of interpreting these figures is to consider the magnitude of the poverty gap as a proportion of mean consumption of all households. The aggregate poverty gap of the urban sector represents 21% of that sector's mea. consumption in 1981/82; for rural areas it represented 28% of mean consumption. Roughly a one quarter increase in national consumption would be needed to eliminate poverty in Bangladesh, if that increase could be perfectly targeted at the poor. That is a big "if"; later I shall discuss the problem of reaching the poor when suchi perfect targeting is not feasible.

(iv) The distributionally sensitive measure of poverty (a=2) indicates a modest overall improvement during the period using the NA means, though, again, the rate of improvement is very considerably less than that implied by the unadjusted HES.
11 (v) The HES also suggests that urban poverty levels exceeded rural levels after 1981/82. This is surprising. The result is not confirmed by the alternative estimates based on the means from NA. All of these comparisons of urban and rural poverty levels may be, however, highly sensitive to the assumed cost-of-living differential (of about 50%) between sectors implicit in the BBS poverty lines for 1981/82. I have no basis for properly evaluating that assumption.

# III. Growth. Inequality, and Poverty

# Methodological Issues

There has been much debate about whether poverty is best alleviated by promoting economic growth, or by reducing economic inequalities. The level of poverty can be thought of as a function of mean consumption, the poverty line, and the inequality of consumption around that mean, as embodied in the Lorenz curve. An increase in the mean, holding the Lorenz curve and poverty line fixed, will unambiguously decrease any well behaved poverty measure, Following recent practice, I shall refer to such an increase in the mean as "distributionally neutral growth". Note that this requires an equiproportional. increase at all levels.

Certain shifts in the Lorenz curve will also reduce poverty, holding the rean constant. If the Lorenz curve shifts such that the share of any poor household increases, with the corresponding loss being incurred by any non- poor person, then the outcome is unambiguous poverty must fall. However, there is little one can say in general about the qualitative effect on poverty of a reduction in inequality;<sup>8</sup> for example, while a small transfer from
12 someone at the poverty line to someone below it will reduce inequality, it will increase the headcount index of poverty.

One can readily calculate the response of poverty measures to small distributionally neutral changes in the mean. Noting that the headcount index is simply the point on the cumulative distribution function corresponding to the poverty line, any distributionally neutral increase in the mean will have the same effect on the headcount index as a decrease in the poverty line of the same proportion. The point elasticity of the headcount index to distributionally neutral growth is thus given by the elasticity of the distribution funcUion evaluated at the poverty line. This fact appears to be well known. Though the analytics are slightly more complicated, computationally simple formulae for the effects of distributionally neutral growth can also be derived for all other members of the FGT class of poverty measures discussed above.<sup>9</sup> We would also like to get some idea of how sensitive poverty is to certain changes in overall inequality. Kakwani (1989) has suggested one convenient way of doing so, which assumes that the new Lorenz curve (after the - change in inequality) is given by L(p) 3(p-L(p)) where L(p) is the old Lorenz curve and 3 is a number measuring the proportionate increase in the Gini index. Roughly speaking, this assumes that the Lorenz curve shifts by a constant proportion of the difference between each income group's actual share and the share that it would have if there were equality. Thus the reduction in inequality can be said to occur at "all levels". Using this assumption, one can readily calculate the point elasticity of any of the FGT poverty measures with respect to the overall Gini index, holding the mean of the distribution constant.
13 There is no a priori reason why we need be confined to the rather simple stylizations of "distributionally neutral growth", or Kakwani's assumption of a proportionate shift in the Lorenz curve. The use of a point elasticity is also restrictive, when the changes involved are not small. By explicitly modelling the Lorenz curve, one can estimate the effect on poverty of any discrete shifts in either the mean, or the Lorenz curve, or any combination of the two. The results of the previous section illustrated how this can be done for discrete changes in the mean (due to measurement error in that case, though changes due to distributionally neutral growth can be modelled the same way). Explicit shifts in the Lorenz curve can **also** be simulated. Ravallion and Huppi (1989) discuss the methodology and give examples for Indonesia.

However, in applying these ideas to the Bangladesh data, I shall concentrate solely on point elasticities estimated from the 1981/82 HES. It would certainly be of interest to study further the change in poverty in - Bangladesh over time for example, using the various decomposition formulae - in Ravallion and Huppi (1989) but the doubts about comparability of the HES daca for other years must lead one to seriously question any results of such an exercise. All is not lost though, as there is still someching that can be learnt about the possible effects of growth on poverty by examining the distribution for only one year.

# Prospects for **Poverty Alleviation through Growth**

Table 3 gives my estimates of the point elasticity of each poverty measure to distributionally neutral growth in Bangladesh, as well as the elasticity with respect to an increase in the Gini coefficient, assuming the proportional Lorenz curve shift described above.
14 The headcount index of poverty in Bangladesh responds to distributionallv neutral growth with an elasticity of about unity, using the BBS poverty line for 1981/82. For example, an annual growth rate in mean consumption per capita of two percent, and at the same rate across the whole distribution, would reduce the proportion of the population who are poor by about two percent per year. This elasticity is lower than those recently estimated for some other countries; Datt and Ravallion (1989) estimate that the elasticity of the headcount index of poverty to distributionally neutral growth is -2.2 in India (based on 1983 data), and Ravallion and Huppi (1989) obtain an elasticity of -2.1 using Indonesian data for 1984. The elasticities to distributionally neutral growth are higher (in absolute value) for the alternative measures, and highest for the preferred (distributionally sensitive) measure; this was also found in the studies for other countries mentioned above.

The growth elasticity can be sensitive to the choice of poverty line.<sup>10</sup> The elasticity based on the lower poverty line in Table 3 is close to the value of about two obtained for other countries in the above studies. The lower poverty line generates headcount indices which are a good deal closer to the figures for India and Indonesia, and so it appears that much of the difference between these countries in growth elasticities is accountable to the fact that the proportion of poor (as judged by the usual local poverty lines) is higher in Bangladesh.

The headcount index of poverty is found to be quite unresponsive to changes in the Gini index of inequality, and rural poverty is actually found to increase slightly with decreases in the Gini for the implicit BBS poverty line; the latter finding reflects the fact that the rural poverty line is
**15**

slightly above the rural mean consumption for 1981/82. As one would expect, the distributionally sensitive poverty measure is far more responsive to changes in overall inequality.

It should be recalled, however, that the change in the Gini coefficient postulated here is associated with a specific shift in the Lorenz curve, whereby inequality falls across the whole -ange of the distribution. A reduction in inequality which is concentrated more amongst the poorer half (say) would naturally have a stronger impact on a distributionally sensitive assessment of aggregate poverty.

The results in Table 3 can be used to calculate the distributionally neutral growth rates which would be needed to achieve any specified targets for poverty alleviation in Bangladesh. This uses the fact that the rate of change in poverty over time is given by (to a first order approximation) the product of the growth rate in mean consumption per capita and the elasticity of poverty with respect to the mean.

For example one may ask: What is the minimum growth rate in mean consumption that would be needed to reduce the aggregate number of the poor in Bangladesh, without altering relative inequalities? To a first-order approximation, the answer is simply the ratio of the population growth rate to the elasticity of the headcount index with respect to the mean, as reported in Table 3. Since the growth elasticity is found to be about one using the BBS poverty line, we can identify a simple rule-of-thumb: Unless the rate of growth in aggregate real consumption is at least twice as high as the rate of population growth, the absolute number of poor in Bangladesh will increase. Some caveats should, however, be noted:
**16**

(i) The growth elasticity of poverty is likely **to chiange** over time; thln elasticity is a function of **the** mean (as well as the Lorenz curve parameters) aiid its derivative wvith respect to the mean can be readily calculated. Tab.1 3 gives the log derivatives in the mean for both elasticities (the formulae are given in Ravallion and Huppi, 1989). The absolute elasticity of the h1adcouiit index to distributionally neutral growth in Bangladesh is an

**i:'*)** 'Sing functionl of the mean. Thus, with growth in the mean, the ninill!uil! gr-owth rate needed to alleviate poverty (in terms of absolute numbers of poor) will start to fall. However, this effect turns out to be quantitatively Smil' **J OIle** pe:.ce:.t increase in the mean will increase the absolute growth elasticity of the headcount index by only about .0001 (Table 3). Note also th it growth will lead to an increase in the elasticity of poverty with resi, to the overall Giri (Table 3); the proportionate poverty alleviation effects ,f reduction-s in overall inequality will increase with growth in irean coa'sul;unn tion, rhough, arain the quantiltative effect is not found to be 1 a .Xable 3%

ii) It should also be recalled that this rule -of-thumlb assu:lmes thit 'ro:h is dal:rI})`utionaillv neutral; literally speaking, that is quite rarti x'.er _.cc_ it is instructive to note that the Loreniz cur-ve in Bangladesh has : ,. dli--it overt ime (FiMo,ures 1 and 2), and thlw h.oao an i . ;e,s Vi rlnv unrc;-ponsive to at least 'proportionail' shitts . lhus, th above no. - eo - nallb maN still give quite a good approx lllationi, given the type of growt' observed over recent times. (iii) The above calculation inay be rather sensitive to the choice of ' poverty line, and that choice is always likely to be somewhat arbitrary. A-t three-qua:ters of the BBS poverty line, the ahsolute elasticity to growth is
**17**

**found to be higher (Table** 3). A **rate of distributionally**<sup>**neutral growth**of</sup> **1. 3% per annum would be sufficient to prevent an increase in**<sup>**the number**of</sup> people below three-quarters of the BBS poverty line, at the current popula'Iw growth rate.

Over the last decade or so, Bangladesh has not achieved a rate of gro in real national income or consumptio in excess of twice the rate of population growth. The compound annual growth rate of real GDP was 4.4% o'v.the period 1972 to 1987; the population growth rate over **the** same period was 2.4% (World Bank, 1988). So, extrapolating from recent trends, a corlntirlur increase in the number of people below tlhe BBS poverty line must be ainticipated.

More encouragingly, however, some observers are currently projecting tvrate of growth in real GDP per capita in Bangladesh over the next ten years:. e::ceed that of the 1980s. It maay not be unreasonable to expect a distributionallv neutral growth rate in consumptionI per capita of at leas-;! current rate of population growth, anld, hence, stahl e or slightlv falil g :.u:.i;ers of poor in Bangladesh between now and 2000. A het.teperformance s .;ouid appear to be unlikely under current external and do:nestic CoI:di _:i(ouS_ . If a per capita **annu.al** growth rate of 2.4% can be achiev,kd _wir.ou_ adverse shitf"s in rela:ivineq'alities, or an increacse in tVh ra t population growth, then absolutIe rnurbers of poor in BaIg Iadlsh will s **_:ah_** i i (or fall slightly if one prefers to use a lower poverty line). The hoadcol-. index of poverty will fall at roughly the same rate, while the poverty gap measuie and the distributionally sensitive measure will fall at about 5% and 6% per year respectivelv.
18 One can also use the results of Table 3 to estimate the deterioration in overall inequality which would be sufficient to eliminate the otherwise desirable effect of growth on poverty in Bangladesh. The headcounc index of poverty will not be very sensitive to growth associated with an increase in inequality, assuming that this entails a proportionate shift in the Lorenz curve, as discussed above. It would take a 13% annual increase in the Gini index to eliminate the desirable effect of a 2.4% growth rate on the headcount index of poverty, using the lower poverty line.<sup>11</sup> This would imply a substantial increase in the Gini index, from 0.27 to 0.50 over five years. It would clearly take a highly inequitable growth process to undercut the desirable impact of growth on the proportion of poor in Bangladesh.

However, that conclusion is not robust **to** the choice of poverty measure. One finds that, for the distributionally sensitive FGT poverty measure, an increase in the Gini coefficient of only 4.1% per year would be sufficient to wipe out the effect on poverty of a 2.4% annual growth rate in mean consumption. This would be equivalent to an increase in the Gini from 0.27 to 0.33 over five years, which is not inconceivable. Thus, even seemingly small deteriorations in overall equity associated with growth can substantially impede progress in alleviating the most severe extremes of poverty in Bangladesh.

# IV. Conclusions

The recent evidence of a decline in absolute numbers of poor in Bangladesh during the 1980s is unconvincing. The rate of growth in real consumption per capita of 10% per year implied by the underlying household expenditure surveys is too high to be believed. While i_ should not be
19 assumed that the national accounts are accuratt, their implied growth rate of about 0.5% per year is more plausible.<sup>Assessimiints</sup> of growth during the 1980s consistent with national accounts data<sup>**(only**using the household surveys to</sup> measure relative inequalities) suggest<sup>that the proportion of the population</sup> deemed to be poor has remaired fairly stable<sup>over recent years, while absolute</sup> numbers or poor have increased.

Per capita growth rates in Bangladesh<sup>have been below the average for</sup> South and South-East Asia in the 1980s,<sup>and few observers expect this to</sup> change in the 1990s. Furthermore, the growth<sup>rates needed to prevent an</sup> increase in the absolute numbers of poor<sup>in Bangladesh, or to attain any given</sup> rate of poverty reduction, are higher<sup>than similar calculaticns have suggested</sup> would be needed for some other low-income<sup>countries in Asia. At a widely</sup> assumed poverty line for Bangladesh,<sup>the growth rate of real consumption per</sup> capita has to be at least equal to<sup>the rate of population growth before the</sup> absolute numbe of the poor can start to fall appreciably<sup>without a shift in</sup> relative inequaiities. Such a growth rate<sup>has not been achieved in recent</sup> times, but it is expected over the next<sup>ten years or so by some observers. By</sup> contrast, India and Indonesia will only<sup>require a per capita growth rate of at</sup> least half the rate of population growth<sup>to further reduce the numbers of poor</sup> assessed bv local poverty lines; both countries<sup>have done a good deal better</sup> than this over the last 10 years, and<sup>that is expected to continue. Recent</sup> growth in Bangladesh has thus been relatively<sup>low in a country where it needs</sup> to be relatively high to avoid an increase<sup>in the number of poor.</sup> Certain changes in relative inequalities<sup>could, in principle, wipe out</sup> povertv alleviation through growth. It appears<sup>that a fairly substantial</sup> distributional change would be needed<sup>to do so for the simple headcount index</sup>
20 of poverty in Bangladesh, which I find to be quite insensitive to stylized changes in overall inequality.

Currently anticipated growth in Bangladesh is likely to have a larger proportionate impact on other measures _of_ poverty, including measures which attach higher weight to the poorest of the poor, and measures which use a lower poverty line. These measures will also be more sensitive to any associated deterioration--or improvement--in overall equity. Only if one is content to focus attention solely on the "not-so-poor" moving across the poverty line, can one reasonably dismiss concerns about how equitable the process of growth will be in the near future. International assistance and domestic policy reforms which not only enhance the rate of growth, but also ensure that its benefits are shared widely, should be strongly encouraged as pait of a poverty alleviation str;fegy for Bangladesh.
**21**

# **Apgendix**

This appendix summarizes the various<sup>formulae used in the paper's</sup> calculations. The FGT class of<sup>poverty measures Pa used in sections 2 and 3</sup> can be written as: where f(y) denotes the probability<sup>density function of income y, and z is</sup> the poverty line. Following Kanbur<sup>(1987) and Kakwani (1989) it is readily</sup> verified that the elasticity of<sup>Pa with respect to the mean of the</sup> distribution of y, holding the<sup>Lorenz curve constant, is given by</sup> Under Kakwani's (1989) assumption<sup>about the shift in the Lorenz curve, the</sup> elasticity with respect to the<sup>Gini index, holding the mean#constant, is</sup> given by:
22 Since (like most researchers) I do not have access to<sup>the unit</sup> record data for Bangladesh. simulation is required<sup>to estimate the above</sup> poverty measures from the published grouped data.<sup>Simulated distributions</sup> are also required for estimating the poverty measures<sup>based on NA means</sup> reported in Section 2. For these purposes I have<sup>used Kakwani's (1989)</sup> parameterization of the Lorenz curve: which is the cumulative proportion of total income or consumption<sup>he.d by</sup> the poorest p proportion of the population. The parameters a, 7<sup>and6are</sup> positive, (if neither 7 nor _6_ exceed unity then the<sup>Lorenz curve is convex),</sup> and _e_ is a random error. The Lorenz parameters themselves<sup>are estimated by</sup> OLS for each state/sector from the following regression: All simulations are at Ee = 0. Given the mean and Lorenz<sup>function, the</sup> distribution function is fully characterized noting that<sup>the slope of the</sup> generalizea Lorenz curve, L'(p),U=x, is simply the inverse of the distribution function p=F(x). In earlier work on Indonesian data, the Kakwani parameterization was found to give a better fit<sup>than some obvious</sup> alternatives (namely the original Kakwani-Podder specification and elliptical Lorenz curves), at least in the crucial lower half of the distribution (Ravall on and Huppi, 1989).

The method of calculating the poverty measures then follows Datt and Ravallion (1899). For completeness I summarize the method<sup>here. Since</sup> L'(PO) = _z/Ik,_ (A6) implies that:
23 which is solved numerically for<sup>Po (using Newton's method). The poverty</sup> gap measure P1 can be written<sup>as</sup> where B(k,m,n) = _f_ pm- (l-p) dp. The FGT measure for a = 2 is 0 evaluated as follows. From<sup>the definition of P</sup> 2<sup>we know that</sup> Thus, given (p, a, 7, _6),_ the FGT poverty measures<sup>for any poverty line are</sup> calculated from (AB), (A9)<sup>and (AIO). The probability densities at the</sup> poverty line (as required<sup>for calculating %) are readily estimated using</sup> the fact that f(z) = l/(#LC(PO)).<sup>All of the above calculations can be</sup> performed using SAS.
24

# Footnotes

1. Consumption was estimated by combining W'orld Bank estimates of the share of consumption in GDII, with the Bank's estimates of CDP per capita at 1980 prices, converted to 1981/82 prices using the implicit GDP deflator (all necessarv data are containied in World Bank, 1988). Calendar figures were then converted to a two year moving average for comparison with the HES.

_2._ It appears that average income may well have been underestimated in 1481/82, with important implicationis for comparisons with the earlier surveys kOsmani, 1989). However, the same bias is not evident in the 1981/82 consumption data.

3. There are other applications of this idea; for example, Ravallion and Huppi (1989) use the same method to deriv3 a decomposition of observed changes in poverty between two dates into effects due to growth in the mean, holding the Lorenz curve constant, and the effect **of** shifts in the Lorenz curve. a4. BBS nominal poverty lines appear to have been constructed by graphing mean calorie intake against mean income based on grouped data and using this graph to find the income level at which households typically attain the predetermined caloric norm. There is nothing to guarantee that the poverty line so determined will have constant purchasing power in terms of any relevant bundle of goods, or correspond to any given reference "utility" level.

a1

|Real values of BBS||||
|---|---|---|---|
|poverty lines|1981/82|1Q83/84|1985/86|
|Urban Nominal|300|439|519|
|Real (CPI Dhaka)|300|364|353|
|KCpI food)|300|361|348|
|**\Rc_)**|360|367|376|
|Rural Nominal|192|300|331|
|Real (CPI rural)|192|252|235|

Although my rural poverty line is slightly higher than the BBS poverty line quoted in note 2 above, it actually gives a closer fit to the BBS (1988b) estimates of the rural headcount index for 1981/82, using the published grouped data and the Lorenz curve parameterization (Appendix). But one should not be too concerned about accuracy in choice of a poverty line in this context, given the level of accuracy of other relevant inputs to the calculations, such as the grouped data, the original survey data, and the
25 underlying caloric requirement. We are,<sup>at best, talking about rough orders</sup> of magnitude.

7. When normalized by the number of poor (w..ich<sup>gives the original versiorl of</sup> the poverty gap measure, as discussed in Sen,<sup>1976, for example), the poverty</sup> gaps represented 36% of the pove-ty line<sup>in urban areas and 34% in rural</sup> areas.

8. By a "reduction in inequality" I mean<sup>here any unambiguously upward shift</sup> in the Lorenz curve.

9. Following Kanbur (1987) and Kakwani (1989);<sup>see the Appendix for further</sup> details.

10. The condition required for the elasticity<sup>of the headcount index in the</sup> mean to be independent of the poverty line is<sup>quite restrictive. The</sup> elasticity will only be invariant to the poverty<sup>line if its value is equalto</sup> one plus the elasticity of the probability<sup>density function of consumption</sup> evaluated at the poverty line. This follows<sup>straightforwardly from the formula</sup> given in the Appendix.

11. This is given by the growth rate times the ratio<sup>of the growth elasticity</sup> to the Gini elasticity in Table 3. I have<sup>only used the lower povertyline</sup> for this calculation, given the perverse effect<sup>of changes in the Gini index</sup> on the headcount for the higher line, associated with the fact that it is above mean consumption for rural areas, as<sup>discussed above.</sup>