Global poverty monitoring has been brought to the forefront of the international policy arena with the adoption of the Millennium Development Goals (MDG) by the United Nations. The first MDG proposes reducing global poverty by the year 2015 and is stated as “halving the proportion of people with an income level below $1/day between 1990 and 2015” (United Nations, 2000). Progress towards attaining this MDG is monitored using global poverty estimates published by the World Bank and a number of independent scholars. The process is not only expensive (Moss, 2010) but also mired with conceptual, methodological, and data-related problems (Klasen, 2009).
Current estimates of global poverty proposed in the literature differ in magnitude as well as in the rate of change in poverty. Consider, for instance, Chen and Ravallion (2010) and Pinkovskiy and Sala-i-Martin (2009)—two studies that estimate global poverty using the international poverty line of $1/day (see Figure 1). Chen and Ravallion (2010) estimate that in 2005 nearly 26 percent of the population in the developing countries was poor, and the global poverty count fell by 520 million individuals since 1981. By contrast, Pinkovskiy and Sala-i-Martin (2009) estimate poverty to have been ten times lower in 2005, which implies a reduction of almost 350 million individuals since 1981. Although there is general agreement that global poverty has declined over the years, the estimated level of poverty and rate of poverty decline vary substantially across studies.
Figure 1Estimates of global poverty between 1981 and 2005
Notes: The poverty rates are not strictly comparable across studies because of differences in methodological approach (see Section II.B.).
This paper aims to contribute to the debate on global poverty not by providing a new set of estimates, but by addressing two important questions. First, we ask why estimates from different studies differ so much. As we unravel the various assumptions made by researchers, we show that global poverty estimates are simply not comparable across studies. For instance, they differ in terms of underlying data sources, number of countries included, welfare metric, adjustments to mean incomes, and statistical methods employed to estimate the income distribution. Given this variety of methodological choices, we arrive at our second question: Can we assess the impact of different approaches on the resulting poverty estimates? Since global poverty estimation requires making multiple assumptions simultaneously, we aim to isolate and assess separately the relative importance of each such assumption by undertaking a novel sensitivity analysis.
An important hurdle in estimating long-term trends in global poverty is the lack of high-quality, consistent survey data. The poor are those individuals whose income is less than or equal to some threshold set by the poverty line. If countries had complete information on every individual’s income then with an agreed-upon global poverty line, identifying the poor would be a straightforward exercise. However, there are severe data limitations.
Data on income is typically collected through household surveys (HS) of nationally representative samples. However, survey data are often available for periods far apart and suffer from a number of inconsistencies (regarding sampling and interviewing techniques, definitions of variables, and coverage) that render them incomparable across countries. Nonetheless, they are the sole source of information on the relative distribution of incomes in a country—that is, the shares of national income possessed by different population groups (quintiles, deciles). HS also provide estimates of mean income/consumption which are used to scale the income shares to obtain mean incomes by population group. A more readily-accessible and consistently-recorded source of information are national account statistics (NAS) which also provide aggregate income or consumption estimates and are available for most countries on a yearly basis.
A key methodological choice in estimating global poverty is whether to use data on mean income/consumption from HS or NAS or whether to combine data from the two sources. Some studies in the literature analyzed the sources of discrepancies between the levels and growth rates of income/consumption data from HS and NAS (Ravallion, 2003; Deaton, 2005). However these studies did not measure the precise effect of using HS and NAS data on global poverty levels and trends. In order to determine how sensitive global poverty estimates are to alternate data sources, we estimate global poverty by anchoring relative distributions alternately to HS and NAS estimates of mean income and consumption. This is our first sensitivity exercise.
The second sensitivity exercise concerns the choice of statistical method used to estimate income distributions from grouped data, that is, data on mean income or consumption for population groups (quintiles, deciles). We estimate global poverty by estimating each country’s distribution using different methods. These include the General Quadratic (GQ) and the Beta Lorenz curve, and the lognormal and Singh-Maddala functional forms for the income density function.2 In addition to these parametric specifications, we also consider the nonparametric kernel density method whose performance we assess in conjunction with four different bandwidths—a parameter that controls the smoothness of the income distribution.
As a benchmark, we follow the World Bank methodology to the extent possible and estimate global poverty in 1995 and 2005—the latest year for which data is available for many countries. Data on the relative distribution of income across population deciles is collected for 65 countries from the World Bank’s poverty monitoring website PovcalNet. Our sample covers more than 70 percent of the total world population and includes all countries for which both HS and NAS data are available in both years. Global poverty is estimated using international poverty lines ranging from $1/day to $2.5/day to provide further insight into how methodological choices impact poverty rates at different income cutoffs.
Our results are twofold. First, a large share of the variation in estimated poverty levels and trends can be attributed to the choice between HS and NAS as the source of data. Global poverty estimates vary not only in terms of the proportion of the poor, and correspondingly the number of poor, but also in terms of the rates of decline in poverty. Poverty estimates based on HS and NAS do not tend to converge in higher income countries. Second, the choice of statistical method used to estimate the income distribution affects poverty levels to a lesser extent. A comparison of poverty estimates across parametric and nonparametric techniques reveals that the commonly used lognormal specification consistently underestimates poverty levels. While there is little doubt that the proportion of poor declined between 1995 and 2005, our results underscore the fact that global poverty counts are highly sensitive to methodological approach.
The remainder of the paper is structured as follows. Section II consists of a review of the literature on global poverty. We explain the sensitivity analysis and introduce the data in Section III. In Section IV we discuss the sensitivity of global poverty estimates to methodological approach. Conclusions are presented in Section V. The statistical techniques used in the exercise are described in the Appendix.
II. Literature Review
There is a large and diverse body of literature on global poverty. We have compiled this literature in two broad categories. The first consists of studies discussing conceptual and methodological challenges in defining poverty; the second includes studies mainly focused on providing estimates of global poverty. There is considerable overlap between the two types, with some studies falling in both categories.
A. Conceptualizing Global Poverty
A number of conceptual issues, which we briefly review here, are at the core of global poverty analysis.3 Measuring poverty inherently involves choosing between alternate notions of poverty. The subjective approach defines poverty using an individual’s perception of own well-being and utilizes data from self-reported assessments of living conditions.4 Thus the subjective approach involves a value judgment as to what it means to be poor. By contrast, the objective approach defines poverty based on measurable indicators of well-being. Traditionally, global poverty has been defined in terms of deprivation in a single dimension, namely income or consumption. Global poverty has been measured either in absolute terms, using a pre-defined poverty line based on the cost of living (Chen and Ravallion 2001, 2004, 2010), or in relative terms by anchoring the poverty line to mean or median income levels (Nielsen, 2009; Ravallion and Chen, 2009). However based on Amartya Sen’s broader notion of capabilities (Sen 1976, 1993), recent efforts have been aimed at estimating global poverty using multiple dimensions. For instance, the United Nations Development Programme’s new multidimensional poverty index measures global poverty as a combination of deprivation in three dimensions using ten indicators of well-being (Human Development Report, 2010).
Within the objective approach, global poverty is defined in terms of an absolute income cutoff equal to $1/day or $2/day. The $1/day poverty line was introduced by the World Bank in 1990 and roughly corresponds to the average of the purchasing power parity (PPP)-adjusted national poverty lines of the 15 poorest countries in the world (Ravallion, Chen and Sangraula, 2009). This poverty line provides a conservative definition of global poverty and has been criticized for not capturing the real requirements of well-being (Klasen, 2009; Reddy and Pogge, 2010). The $1/day poverty line which was based on 1985 PPPs was revised to $1.08/day based on 1993 PPPs and $1.25 based on 2005 PPPs. Using this last update, Chen and Ravallion (2010) found that global poverty had previously been significantly underestimated.5 Critics have also noted that the PPP exchange rates used in global poverty monitoring are inadequate because they are designed for national income accounting purposes and do not reflect the consumption patterns of the poor. In a sensitivity analysis similar to ours, Ackland, Dowrick and Freyens (2008) found that PPP rates calculated using different methods led to large differences in global poverty counts. A similar conclusion was arrived at by Deaton and Dupriez (2011) who proposed alternative PPP rates based on the expenditure patterns of the poor.
In addition to these conceptual challenges, the exercise of measuring global poverty is fraught with empirical problems. Objective poverty estimates can be drawn either from HS or NAS income or consumption data—a key issue discussed in detail in the next section. Furthermore, Latin American and Central and East European countries collect data on income, whereas Asian, African, and Middle Eastern countries collect data on consumption (Chen and Ravallion, 2004). Both income and consumption variables suffer from substantial measurement error and combining data from income and consumption surveys poses comparability issues (Deaton, 2001, 2003). Data on consumption at the household level is converted to per capita simply by dividing total consumption by the number of household members, ignoring economies of scale in consumption or inequality in the intra-household allocation of resources.6 To date there is no global poverty assessment that tackles these issues.
B. Estimating Global Poverty
Table 1 provides a chronology of studies estimating (objective) global poverty levels. An early attempt in the 1970s was undertaken by Ahulwalia, Carter and Chenery (1979) who estimated poverty in 36 developing countries. Global poverty monitoring received an impetus from the World Bank in the 1990s with its efforts to compile cross-country distributional data. Ravallion, Datt and van de Walle (1991) estimated global poverty in 1985 using distributional data from 22 countries. Chen, Datt and Ravallion (1994) and Ravallion and Chen (1997) expanded the data coverage and measured poverty between the mid-1980s and the early 1990s. Chen and Ravallion (2001) was the first global poverty analysis that relied entirely on survey data. Chen and Ravallion (2004) provided poverty estimates going back to early 1980s and created PovcalNet—a web-based interactive tool providing access to distributional data across countries. As more information became available, studies such as Bhalla (2002) and Sala-i-Martin (2006) proposed alternative estimates. The most recent contribution is Chen and Ravallion (2010) who derived their poverty statistics over 1980–2005 from 675 nationally representative surveys in 115 developing nations.
|Global poverty studies||Years||No. of countries1||Database2|
|Ahluwalia, Carter, and Chenery (1979)||1975||25||World Bank Data Bank|
|Ravallion, Datt, and van de Walle (1991)||1985||22||World Bank|
|Chen, Datt, and Ravallion (1994)||1985-1990||40||World Bank/WDR|
|Ravallion and Chen (1997)||1987-1993||67||World Bank/WDR|
|Chen and Ravallion (2001)||1987-1998||83||World Bank|
|Bhalla (2002)||1950-2000||149||World Bank, PWT|
|Chen and Ravallion (2004)||1981-2001||97||World Bank|
|Sala-i-Martin (2006)||1970-2000||110||WIID, PWT|
|Pinkovskiy and Sala-i-Martin (2009)||1970-2006||191||PovcalNet|
|Chen and Ravallion (2010)||1981-2005||115||WIID, PWT|
Countries for which data is imputed are not included.
PWT: Penn World Tables; WDR: World Development Report; WIID: UNU-WIDER World Income Inequality Database.
Countries for which data is imputed are not included.
PWT: Penn World Tables; WDR: World Development Report; WIID: UNU-WIDER World Income Inequality Database.
Two recent studies on global poverty—Chen and Ravallion (2010) and Pinkovskiy and Sala-i-Martin (2009)—present remarkably different estimates of global poverty due to different methodological approaches. As summarized in Table 2, key differences include the scope of the analysis (developing world vs. world) and the fact that Chen and Ravallion (2010) estimate consumption poverty whereas Pinkovskiy and Sala-i-Martin (2009) focus on income poverty. The relative distributions in Chen and Ravallion (2010) are scaled with mean consumption levels from HS, whereas Pinkovskiy and Sala-i-Martin (2009) scale them with NAS per capita income (GDP). Finally, Chen and Ravallion (2010) use a mix of individual records and grouped data and estimate a parametric Lorenz curve, while Pinkovskiy and Sala-i-Martin (2009) rely solely on grouped data and estimate the distribution employing the lognormal parameterization.
|Methodological choice||Chen and Ravallion (2010)||Pinkovskiy and Sala-i-Martin (2009)|
|Type of countries||Developing countries||Developed and developing countries|
|No. of countries||115||191|
|No. of surveys||675||1,069|
|Source of data||HS1||NAS|
|Type of data||Unit and grouped data||Grouped data|
|Poverty line in 2005 PPP||$1.25/day to $2.5/day||$1/day to $10/day|
|Estimation technique||Lorenz curves (GQ)||Density functions (Log-normal, Gamma, Weibull)|
Adjusted NAS data is used when HS data is not available.
Adjusted NAS data is used when HS data is not available.
Thus, global poverty estimates in the literature not only differ in their use of HS or NAS as sources of data, but also in terms of coverage, type of data, choice of poverty lines, and estimation technique. Inherently estimates of global poverty from different studies are not comparable. In order to resolve this issue, we undertake a sensitivity analysis of global poverty estimates to two crucial choices, namely, the choice between HS and NAS as the source of data on well-being, and that between different estimation methods of the income distribution.
III. Sensitivity Analysis
In this section we explain how we obtain poverty estimates in the sensitivity analysis and describe the data upon which these estimates are based. Figure 2 shows a schematic representation of the sensitivity exercise. The first row in the figure shows the method by which the benchmark poverty level is estimated. The shaded boxes show the different parameters chosen to estimate poverty in the sensitivity exercise.
Figure 2Schematic representation of the sensitivity analysis
Notes: The grey-shaded boxes show parameters that were varied in the sensitivity analysis relative to the benchmark poverty estimate P1.
The poor are those individuals whose income is less than (or equal to) an income threshold called the poverty line. A broad class of poverty measures such as the Foster-Greer-Thorbecke (1984) poverty indices is then completely determined by three factors: the poverty line, the mean income/consumption level, and the relative distribution of income. The poverty level P1 in a country can be expressed as:
where z denotes the global poverty line,
Keeping all other parameters fixed, we first test how poverty estimates vary when mean consumption from HS
Unlike different poverty estimates available in the literature, P1, P2 and P3 are fully comparable with one another. They are computed by applying the same statistical technique—the GQ Lorenz curve (L1)—on the same distributional data (D) and differ only in terms of the means
Second, we analyze how the benchmark poverty P1 varies when we use the same poverty line, same consumption mean
by fitting a Beta Lorenz curve (L1) instead of the GQ Lorenz curve (L1), and poverty rates
by estimating income density using respectively the lognormal (F1) and the Singh-Maddala (F2) functional forms. In addition to these parametric specifications, we also estimate poverty rates by fitting nonparametric kernel density functions (K) with different bandwidths. The bandwidth is the parameter that controls the smoothness of the estimated distribution. We obtain poverty rates:
Poverty estimates P1, P4, P5, P6, P7, P8, P9 and P10 are directly comparable as they are based entirely on HS data and only differ in terms of the method employed to estimate the income distribution.
The sensitivity analysis is conducted by estimating poverty levels (discussed above) in 1995 and in 2005—the latest year for which data is available for a large number of countries.9 Our sample includes 65 developing countries and covers more than 70 percent of the total world population (see Table 3). Relative distributions (D) for population deciles are obtained from the World Bank’s PovcalNet database.10 These are scaled alternately to mean consumption from surveys
|Country||Initial year||Final year||Country||Initial year||Final year|
|Central African Republic||1993||2003||Nicaragua||1993||2005|
We treat the $1/day poverty line as the lowest cutoff and estimate poverty by gradually increasing the poverty line to $1.25, $1.45, $2 and $2.50/day (all expressed in 2005 PPP dollars). The rationale for using multiple poverty lines is to assess robustness to small changes in the international poverty line, with the range $1–$2.5/day representing roughly a 95 percent confidence interval for the $1.25/day cutoff (Chen and Ravallion, 2010). Poverty is computed as the absolute headcount (or number of global poor) as well as the poverty headcount ratio (or poverty rate), which is the ratio of the number of poor to the total population in the countries included in the sample.
A. Household Surveys vs. National Accounts Statistics
Household surveys are typically organized by national statistical agencies. These surveys collect information from sampled households on consumption expenditures and/or personal disposable income. As a result, HS-based consumption may suffer from flaws in survey design, lack of representativeness, recall bias, underreporting among the poor, and poor response rates among the wealthy.11 National Accounts Statistics-based private consumption expenditure is computed by subtracting net exports, investment, and government expenditure from national income. Although in principle preparing NAS according to the UN system of National Accounts should be standard exercise, in practice there is a great deal of heterogeneity as countries make ad-hoc adjustments to the data.
In Table 4 we report summary statistics for
|Max||Min||Mean||Sth. Dev.||Mean||Sth. Dev.|
B. Sensitivity to Household Surveys vs. National Accounts Statistics
We compute poverty estimates by alternately using
Figure 3 shows the effect of these alternate anchors on the global income distribution. The global distribution is obtained by using our three welfare metrics (
Figure 3Global income distribution anchored to alternate estimates of mean income/consumption
Source: Authors’ estimations.
|Headcount Ratio (%)|
|Absolute Headcount (millions)|
Between 1995 and 2005, the $1/day headcount ratio declined by 16 percent when estimated as P1 (from 29 to 24 percent), by 32 percent when estimated as P2 (from 5.9 to 1.7 percent), and by 72 percent when estimated as P3 (from 1.4 to 0.9 percent). The results confirm our prior that global poverty levels are higher when the welfare metric is HS consumption, lower when it is NAS consumption and least when it is per capita GDP. They also highlight the large extent to which the type of data used affects global poverty estimates. Poverty estimates vary significantly not only in terms of poverty headcount ratios, and correspondingly the total number of poor, but also in terms of the rate of decline in poverty.
Across Poverty Lines
The estimates also vary systematically across different poverty lines: as expected, poverty rates increase with higher poverty lines. However, the rate of poverty reduction is lower for higher poverty lines (with the exception of P2). While the falling trend of the headcount ratio is robust across the different thresholds, the number of poor has increased in some instances (for example, P1 estimate for the $2/day and $2.5/day poverty lines). The results are consistent with the increasing global poverty headcounts reported by Chen and Ravallion (2010) for the period 1981–2005. By contrast, P2 and P3 estimates consistently show a decline in the number of poor for all poverty lines, as shown in studies such as Pinkovskiy and Sala-i-Martin (2009), Sala-i-Martin (2006), and Bhalla (2002).
Across Income Levels
We explore whether country-level discrepancies in HS- and NAS-based poverty estimates vary with income level. Recall that P1 and P2 are estimated using the same method except that P1 is based on
Figure 4Ratios of consumption means and poverty estimates compared across income levels
Note: Cross-country and time series data for 1995 and 2005 have been pooled. In the second plot the poverty headcount ratios correspond to the $1.25/day poverty line. Per capita GDP is expressed in 2005 PPP dollars.
C. Estimation Methods
The second sensitivity exercise concerns the choice of statistical method used to estimate the income distribution from grouped data. Several statistical methods—both parametric and nonparametric—can be used for this purpose. Parametric methods are applied, for instance, to estimate the Lorenz curve of income inequality. We estimate the GQ and the Beta Lorenz curves, which are commonly used in global poverty analysis and perform well in estimating poverty for a wide range of unimodal income distributions (Minoiu and Reddy, 2009).
Parametric methods are also applied to estimate the income density function. While many functional forms have been proposed in the literature, only a few have been applied to global poverty measurement. We focus on the lognormal and Singh-Maddala functional forms. The lognormal specification has traditionally been used in poverty estimation though other functional forms often provide a better fit for income distributions (Bandourian, MacDonald, and Turley, 2003; Bresson, 2009). Besides the lognormal, Pinkovskiy and Salai-Martin (2009) used the Gamma and the Weibull distributions to assess the robustness of poverty estimates. However Pinkovskiy and Sala-i-Martin (2009) did not report poverty estimates based on different income distributions, but only the correlation coefficients between different poverty rates. By contrast, we report actual estimates of global poverty corresponding to each statistical method considered.
In addition to these parametric techniques we also employ a nonparametric estimation method. The nonparametric method consists of applying a kernel density estimator on grouped data and has the advantage that no functional assumption needs to be made regarding the underlying data generating process. Sala-i-Martin (2006) estimated global poverty using a kernel density function to approximate national income distributions. Kernel density estimation requires specifying additional parameters such as the bandwidth—the smoothing parameter—which can have a large impact on the resulting estimate if applied to grouped data rather than to individual records (Minoiu and Reddy, 2008). Hence in the sensitivity analysis we use four different bandwidths for the kernel density estimator. The bandwidths are optimal in the sense that they minimize the approximate distance between the true and the estimated distribution (see Silverman, 1986).
D. Sensitivity to Estimation Method
We undertake the sensitivity analysis of global poverty levels to estimation techniques by reverting back to the benchmark poverty level P1 which was obtained by fitting a GQ Lorenz curve. Keeping all other methodological choices unchanged, we employ different statistical methods and assess the variance in poverty estimates. Poverty rate P4 is based on Beta Lorenz curve, P5, P6 are based on the lognormal and Singh-Maddala density functions and P7 to P10 are based on nonparametric kernel densities (see Table 6).
|Lorenz Curve||Parametric Density||Nonparametric Density|
|Headcount Ratio (%) 1995|
|Headcount Ratio (%) 2005|
|Absolute Headcount (millions) 1995|
|Absolute Headcount (millions) 2005|
|Percent Change in the Headcount Ratio 1995-2005|
|Percent Change in the Absolute Headcount 1995-2005|
Overall poverty estimates based on different estimation methods are highly correlated, an observation also noted by Pinkovskiy and Sala-i-Martin (2009). In particular, poverty estimates based on nonparametric methods (P7 to P10) vary to a lesser extent than do poverty estimates drawn from parametric methods (P1, P4 to P6). Nevertheless, the observed variations in poverty estimates cannot be completely overlooked. For instance, poverty estimates for the $1/day poverty line range from 23.5 to 29 percent in 1995 and from 19.6 to 24.3 percent in 2005.
As shown in Table 6, the falling trend in the global poverty rate is robust across estimation methods. Between 1995 and 2005, the rate of decline in the headcount ratio varied between 12 and 17 percent for the $1/day poverty line and between 5 and 9 percent for the $2/day poverty line. Compared to the headcount ratio, however, the trend in the number of poor is more ambiguous. Between 1995 and 2005, the absolute headcount according to the $1/day poverty line is estimated to have declined anywhere between 24 million and 83 million depending on the technique used. Only for the $1/day cutoff did the absolute headcount decline in all instances. By contrast, for the intermediate cutoffs ($1.25/day and $1.45/day) the number of poor increased or decreased depending on the estimation method. Finally, for the two highest poverty lines ($2/day and $2.5/day) the number of poor in fact increased over 1995–2005 irrespective of the estimation method used.
Across Poverty Lines
Figure 5 plots poverty rates corresponding to different statistical techniques and different poverty lines. We find that for most poverty lines, the Singh-Maddala functional form consistently provides higher estimates of poverty (P6) whereas the Beta Lorenz curve (P4) and the lognormal distribution (P5) consistently yield lower estimates. A possible explanation is that the Beta parameterization provides a better fit at the higher end, while GQ does better at the low end of the Lorenz curve (Ravallion and Huppi, 1989). The lognormal parameterization leads to an underestimation of poverty relative to the well-performing GQ since it is too skewed to fit well real-world income distributions.
Figure 5Global poverty rates in 2005 estimated using different statistical methods
Note: Based on poverty estimates shown in Table 6.
Over the past decades, global poverty monitoring has gained significance in international policy-making, more so with the adoption of the Millennium Development Goals. However, measuring global poverty has proved to be a difficult exercise both conceptually and empirically. Estimates of global poverty in the literature vary substantially, partly due to the diversity of assumptions made by researchers. Inherently global poverty estimates in the literature are not comparable since it is impossible to isolate and assess separately the relative importance of each such assumption. In this paper we conducted a novel sensitivity analysis by proposing a step-by-step approach to assess the relative importance of different assumptions for global poverty estimates.
We have assessed the sensitivity of global poverty estimates in relation to two crucial choices, namely that between household survey and national accounts estimates of income or consumption, and that of estimation method of the income distribution. Our key finding is that poverty estimates vary markedly when they are based alternatively on data from household surveys versus national accounts. Although the decline in the global poverty rate between 1995 and 2005 is found to be robust across methodological approaches, the number of poor and the rate of poverty reduction differ significantly depending on the data source used. It is reassuring that global poverty rates vary to a lesser extent when estimated with different statistical methods.
The results of our sensitivity analysis suggest that assessing robustness to methodological choices is an important step in global poverty measurement. More broadly, our findings suggest that the debate on global poverty would benefit from efforts to improve data collection practices across countries and to compile individual records from surveys into public databases. Such improvements would increase confidence in estimates of global poverty.
AbdelkrimA. and J.-Y.Duclos2007 “DASP: Distributive Analysis Stata Package” PEP World Bank UNDP and Université Laval. Available on: http://dasp.ecn.ulaval.ca/.
AcklandR.DowrickS. and B.Freyens2008 “Measuring global poverty: Why PPPs matter” Australian National University Department of Economicsunpublished manuscript (Canberra: Australian National University).
AhluwaliaM. S.CartnerN. G. and H. B.Chenery1979 “Growth and poverty in developing countries” Journal of Development EconomicsVol. 6 pp. 299–341.
BandourianR.J. B.MacDonland and R. S.Turley2003 “A comparison of parametric models of income distributions across countries and over time” Revista EstadisticaVol. 55 pp. 164–165.
BhallaS.2002 “Imagine there’s no country: Poverty, inequality and growth in the era of globalization” Population StudiesVol. 55 pp. 263–279.
BourguignonF.2005 “Comment on ‘Measuring poverty in a growing world (or measuring growth in a poor world)’ by Angus Deaton” Review of Economics and StatisticsVol. 87 pp. 20–22.
BressonF.2009 “On the estimation of growth and inequality elasticities of poverty with grouped data” Review of Income and WealthVol. 55 pp. 266–302.
ChenS.DattG. and M.Ravallion1994 “Is poverty increasing in the developing world?” Review of Income and WealthVol. 40 pp. 359–376.
ChenS. and M.Ravallion2001 “How did the world’s poorest fare in the 1990s?” Review of Income and WealthVol. 47 pp. 283–300.
ChenS. and M.Ravallion2004 “How have the world’s poorest fared since the early 1980s?” World Bank Research ObserverVol. 19 pp. 141–169.
ChenS. and M.Ravallion2010 “The developing world is poorer than we thought, but no less successful in the fight against poverty” Quarterly Journal of EconomicsVol. 125(4) pp. 1577–1625.
DeatonA.2001 “Counting the world’s poor: Problems and possible solutions” World Bank Research ObserverVol. 16 pp. 125–147.
DeatonA.2003 “Household surveys, consumption, and the measurement of poverty” Economic Systems ResearchVol. 15 pp. 135–159.
DeatonA.2005 “Measuring poverty in a growing world (or measuring growth in a poor world)” TheReview of Economics and StatisticsVol. 87 pp. 1–19.
DeatonA.2008 “Income, health and well-being around the world: Evidence from the Gallup World Poll” Journal of Economic PerspectivesVol. 22(2) pp. 53–72.
DeatonA.2010 “Price indices, inequality, and the measurement of world poverty” American Economic ReviewVol. 100(1) pp. 5–34.
DeatonA. and O.Dupriez2011 “Purchasing power parity exchange rates for the global poor” American Economic Journal: Applied EconomicsVol. 3(2) pp. 137–166.
DeatonA. and M.Grosh2000 “Consumption” in M.GroshandP.Glewwe(eds.) Designing Household Questionnaires for Developing Countries: Lessons from Fifteen Years of the Living Standard Measurement Study (Washington: The Word Bank Group).
DeatonA. and V.Kozel2005 “Data and dogma: The great Indian poverty debate” World Bank Research ObserverVol. 20 pp. 177–199.
DhongdeS.2010 “Measuring global poverty” in R.Denemark(ed.) The International Studies Association CompendiumBlackwell PublishingUK.
FerreiraF. and M.Ravallion2008 “Poverty and inequality: The global context” in (eds.) W.SalverdaB.Nolan and T.SmeedingOxford Handbook of Economic InequalityOxford: Oxford University Press.
FosterJ.GreerJ. and E.Thorbecke1984 “A class of decomposable poverty measures” EconometricaVol. 2(81) pp. 761–766.
GibratR.1931Les Inégalités EconomiquesParis: Recueil Sirey.
HaddadL. and R.Kanbur1990 “How serious is the neglect of intra-household inequality?” The Economic JournalVol. 100 pp. 866–881.
HestonA.SummersR. and B.Atten2009Penn World Table Version 6.3 Center for International Comparisons of Production Income and Prices at the University of Pennsylvania. Available on: http://pwt.econ.upenn.edu/php_site/pwt_index.
Human Development Report2010The real wealth of nations: pathways to human development (United Nations Development Programme: New York)
JannB.2005kdens: Stata module for univariate kernel density estimation. Available on: http://ideas.repec.org/c/boc/bocode/s456410.html.
JannB.2007 “Univariate dernel density estimation” Boston College Department of Economics Statistical Software Component No. S456410 (Cambridge, MA: Boston College).
KakwaniN.C.1980 “On a class of poverty measures” EconometricaVol. 44 pp. 137–148.
KlasenS.2009 “Levels and trends in absolute poverty in the world: What we know and what we don’t” in (eds.) MackE.M.SchrammS.Klasen and T.PoggeAbsolute Poverty and Global JusticeLondon: Ashgate pp. 21–36.
MaddalaG. and S.Singh1976 “A function for the size distribution of incomes” EconometricaVol. 44 pp. 963–970.
MinoiuC. and S. G.Reddy2009 “Estimating poverty and inequality from grouped data: How well do parametric methods perform?” Journal of Income DistributionVol. 18(2) pp. 160–178.
MinoiuC. and S. G.Reddy2008 “Kernel density estimation based on grouped data: The case of poverty assessment” IMF Working Papers No. 183 (Washington: International Monetary Fund).
MistiaenJ. and M.Ravallion2003 “Survey compliance and the distribution of income” World Bank Policy Research Working Paper No. 295 (Washington: The World Bank Group).
MossT.2010 “What next for the Millennium Development Goals?” Global PolicyVol. 1 pp. 218–220.
NielsenL.2009 “Global relative poverty” IMF Working Paper No. 93 (Washington: International Monetary Fund).
PinkovskiyM. and X.Sala-i-Martin2009 “Parametric estimations of the world distribution of income” NBER Working Paper No. 15433 (Cambridge: The National Bureau for Economic Research).
PovcalNet. An Online Poverty Analysis Tool (Washington: The World Bank Group).
RavallionM.1996 “Issues in measuring and modelling poverty” Economic JournalVol. 106 pp. 1328–1343.
RavallionM.2003 “Measuring aggregate welfare in developing countries: How well do national accounts and surveys agree?” The Review of Economics and StatisticsVol. 85 pp. 645–652.
RavallionM. and S.Chen1997 “What can new survey data tell us about recent changes in distribution and poverty?” World Bank Economic ReviewVol. 11 pp. 357–382.
RavallionM. and S.Chen2009 “Weakly relative poverty” The Review of Economics and Statisticsforthcoming.
RavallionM.S.Chen and P.Sangraula2009 “Dollar a day revisited” World Bank Economic ReviewVol. 23(2) pp. 163–184.
RavallionM. and M.Huppi1989 “Poverty and under-nutrition in Indonesia during the 1980s” World Bank Agriculture and Rural Development Department Policy Planning and Research Working Paper No. 286 (Washington: The World Bank Group).
RavallionM.DattG. and D.van de Walle1991 “Quantifying absolute poverty in the developing world” Review of Income and WealthVol. 37 pp. 345–361.
ReddyS. and T.Pogge2010 “How not to count the poor” in (eds.) AnandS.SegalP. and StiglitzJ.Debates on the Measurement of Poverty. Oxford: Oxford University Press.
Sala-i-MartinX.2006 “The world distribution of income: Falling poverty and… convergence, period” Quarterly Journal of EconomicsVol. 121 pp. 351–397.
SenA.1976 “Poverty: An ordinal approach to measurement” EconometricaVol. 44 pp. 219–231.
SenA.1993 “Capability and well-being” in (eds.) A.Sen and M.NussbaumThe Quality of Life. Oxford: Clarendon Press.
ShorrocksA. and G.Wan2008 “Ungrouping income distributions” UNU-WIDER Discussion Paper No. 16 (Helsinki: World Institute for Development Economics Research).
SilvermanB. W.1986Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability 26. Boca Raton FL; London; New York: Chapman & Hall/CRC.
SzekelyM.LustigN.CumpaM. and J. A.Media-Guerra2004 “Do we know how much poverty there is?” Oxford Development StudiesVol. 4 pp. 523–558.
United Nations2000Millennium Summit Goals (New York: United Nations)
VillasenorJ. and B.Arnold1989 “Elliptical Lorenz curves” Journal of EconometricsVol. 40 pp. 327–338.
WandM.P. and M.C.Jones1995Kernel Smoothing. Chapman and Hall: London.
WIID (World Income Inequality Database)2008United Nations University World Institute for Development Economics Research (Helsinki).
Let x denote individual income, f (x) the income density, F (x)the cumulative density function (c.d.f.) and μ the mean income level in a country.
Lorenz Curve Estimation
The Lorenz curve is defined as the relationship between the cumulative proportion of the population and the cumulative proportion of income received when the population is arranged in an ascending order of income. The Lorenz curve
Parametric Density Estimation
In addition to estimating the Lorenz curve of income inequality, we estimate income distributions by specifying parametric functions. The lognormal function assumes that log-incomes are normally distributed with mean μ and variance σ2. The c.d.f. of the two-parameter lognormal distribution is given by
Nonparametric Density Estimation
Nonparametric methods impose no functional assumptions about the underlying data generating process. The standard kernel density estimator