Daniel
This page explains the methods used to derive the global, region, and country level poverty counts. The page is divided into six sections:
1. Acquiring household survey data:
2. Constructing welfare aggregates:
3. Generating survey estimates:
4. Calculating poverty and inequality:
5. Generating global and regional estimates:
6. Refernences:
Please cite this page as:
World Bank. 2020. “Poverty and Inequality Platform Methodology.” March 2020 version. Available at [link to follow].
For old versions of this page, please see [link to follow].
Daniel
Daniel
For developing countries, mostly 0fficial surveys used by the government for monitoring poverty. Occasionally surveys are dropped due to quality concerns with the survey design, welfare aggregate or auxilliary data. Decision made by GPWG, reason summarized in What’s New.
The data mostly come from household surveys, explain very briefly what a household survey is, that NSOs conduct them. EU-SILC and LIS for some countries, a subset of these based on admin data. Link to more country information (country methodology pages).
Daniel
Discuss within-country spatial coverage. Mention that non-national surveys are also available but not used for regional/global numbers (Argentina exception). Temporal coverage; often covers one year, ## Binned vs. micro data Daniel
Mention countries exclusevely relying on binned data.
Daniel
Mostly receive data through country engagement, poverty economist, processed and harmonized through GMD.
Daniel
Marta
Explain briefly each, advantages and disadvantages of each (PSPR 2018 annex has material on this). Explain how zero/negative incomes are treated.
Samuel
Explain that some countries use spatial/temporal deflation but not all. Explain what spatial temporal deflation means. Mention India/China/Indonesia. Explain decimal years and that for EU-SILC/LIS, the reported year is the year before the survey year.
Poverty estimates are based on household welfare aggregates that are constructed from income or consumption surveys. Consumption surveys are often the source of data for most developing countries and are conducted over a period of time, sometimes spanning two calendar years. The Gambia, for example, has a survey or decimal year as 2015.31, meaning that 69% of the months of the fieldwork fall in 2015 while 31% of the fieldwork months fall in 2016. By convention, the year that is reported is the floor of the decimal year (e.g. 2015 in the case of the Gambia mentioned above). For EU-SILC/LIS countries, the reported year is the year before the survey year.
Household welfare aggregates are adjusted for temporal and/or spatial price differences within surveys, but not in all cases. Household consumption expenditure could be converted into the prices of a particular month or the average price level observed in a survey year (e.g. with a consumer price index). Similarly, household consumption expenditure could be converted into the prices of a particular location (e.g. capital city) or the national average price level obtained from both rural and urban prices (e.g. with a spatial price index). China, India and Indonesia have rural/urban PPPs that are used to deflate household welfare aggregates to account for spatial price differences within these countries (more details in Section @ref(purchasing-power-parities-ppps). Sometimes, a spatio-temporal price index is used to jointly adjust for both spatial and temporal price differences (e.g. the household welfare aggregate from the survey conducted in Ghana (2016.75) is evaluated at 2013 Greater Accra regional prices). These temporal and/or spatial price adjustments are important for constructing welfare aggregates in real terms.
Daniel
Discuss the relevance of questionnaire design for the consumption aggregate (perhaps refer to some of the papers on the topic). Use the India MMRP/URP example (PSPR 2018 has material).
Andres
What it means to include it, when it is included. Use China/LAC examples to show the relevance.
Christoph and Samuel
Let’s put down the actual formulas we use here to convert binned data into distributions.
In addition to micro data, grouped data are used as another source of data for estimating poverty and inequality when micro data are not available (e.g. China data). Grouped data are consumption expenditure or income organized in graduated class intervals or bins (e.g. see Table 1 below).
Table 1: Size distribution of consumption expenditure in rural India, 1983
a. Monthly per capita expenditure in Rs |
b. P roportion of persons (%) | c. Mean monthly per capita expenditure in Rs | d. Cumulative proportion of population (\(p\)) | e. Cumulative proportion of consumption expenditure (\(L\)) |
|---|---|---|---|---|
| 0 – 30 | 0.92 | 24.84 | 0.0092 | 0.00208 |
| 30 – 40 | 2.47 | 35.80 | 0.0339 | 0.01013 |
| 40 – 50 | 5.11 | 45.36 | 0.085 | 0.03122 |
| 50 – 60 | 7.90 | 55.10 | 0.164 | 0.07083 |
| 60 – 70 | 9.69 | 64.92 | 0.2609 | 0.12808 |
| 70 – 85 | 15.24 | 77.08 | 0.4133 | 0.23498 |
| 85 – 100 | 13.64 | 91.75 | 0.5497 | 0.34887 |
| 100 – 125 | 16.99 | 110.64 | 0.7196 | 0.51994 |
| 125 – 150 | 10.00 | 134.90 | 0.8196 | 0.6427 |
| 150 – 200 | 9.78 | 167.76 | 0.9174 | 0.79201 |
| 200 – 250 | 3.96 | 215.48 | 0.957 | 0.86966 |
| 250 – 300 | 1.81 | 261.66 | 0.9751 | 0.91277 |
| 300 and above | 2.49 | 384.97 | 1 | 1 |
| All expenditure classes | 100.00 | 109.90 |
Source: Datt (1998)
Columns (d) and (e) in Table 1 are used as inputs to derive a Lorenz function. Of the many approaches in the literature that could be used, the general quadratic (GQ) Lorenz function and the Beta Lorenz function are two approaches that tend to estimate poverty and inequality fairly accurately. Due to its computational simplicity, the general quadratic (GQ) Lorenz function is preferred. For poverty and inequality measures, the following parameterized GQ Lorenz function is specified and estimated:
\[ L(1-L) = a(p^2-L) + bL(p-1) + c(p-L), \]
where \(p\) is the cumulative proportion of population, \(L\) is the cumulative proportion of consumption expenditure or income, and \(a\), \(b\), \(c\) are parameter estimates.
See Section @ref(calculating-poverty-and-inequality) below for the formulae used to estimate poverty and inequality measures for grouped data. For the details, see Datt (1998).
Daniel
Mention per capita assumptions, drawbacks of it, and why we are still assuming it.
Andres
Explain the comparaiblity database and link to it
Daniel
Samuel
Short paragraph summary of why CPIs are needed, which CPIs we use, and link to the CPI paper
Consumer price indices (CPIs) summarize the prices of a representative basket of good and services consumed by households within an economy over a period of time. Inflation (deflation) occurs when there is a positive (negative) change in the CPI between two time periods. With inflation, the same amount of rupees is expected to buy more today than in one year from today. CPIs are used to deflate nominal consumption expenditure of households, so that the well-being of households can be evaluated and compared between two time periods at constant prices.
The primary source of CPI data for PovcalNet updates is the IMF’s International Financial Statistics (IFS) monthly CPI series (Lakner et al. 2018). The simple average of the monthly CPI series is used as annual CPI series. When IFS data are missing, other sources of CPI data are obtained from the World Economic Outlook (WEO), National Statistical Offices (NSOs), and International Labor Organization (ILO), among others. For more details on the different sources of CPI data used for global poverty measurement, see Figure 1 of Lakner et al. (2018) and “What’s New” technical notes accompanying PovcalNet updates (e.g. the latest September 2020 PovcalNet Update: What’s New).
CPI series are expressed in the prices of the ICP reference year, currently 2011.
Samuel
Short paragraph summary of why PPPs are needed, which PPPs we use and link to the PPP paper
Purchasing power parities (PPPs) are used in global poverty estimation to adjust for relative price differences across countries. PPPs are price indices that measure how much it costs to purchase a basket of goods and services in one country compared to how much it costs to purchase the same basket of goods and services in a reference country, typically the United States. PPP exchange rates are preferred to market exchange rates for the measurement of global poverty because the latter overestimates poverty in developing countries, where non-tradable services are relatively cheap (i.e., the Balassa-Samuelson-Penn effect). The revised 2011 PPPs are currently used to convert household consumption or income aggregates, originally expressed in local currency units, into a common internationally comparable currency unit.
The PPP estimates published by the ICP are used for global poverty measurement. A few special cases are described in the following. PPPs are imputed for six countries, namely Egypt, Iraq, Jordan, Lao, Myanmar and Yemen, where there are concerns over the coverage and/or quality of the underlying ICP price collection (Atamanov et al. 2018, 2020a). To account for “urban bias” in ICP data collection, rural-urban PPPs are also imputed for China, India and Indonesia using official national PPPs, the ratio of urban to rural poverty line, and the urban share in ICP price data collection (Chen and Ravallion 2008, 2010; Jolliffe and Prydz 2015; F. H. Ferreira et al. 2016).
Samuel
Explain in one paragraph or so how the international poverty line was derived and link to the RCS and Ferreira et al. paper
The international poverty line (IPL) summarizes and converts into PPP-adjusted dollars the national poverty lines of a reference group of poorest countries in the world. Ravallion, Chen and Sangraula (2009) selected 15 poorest countries based on household final consumption expenditure per capita of countries around 2008 when the 2005 PPPs were released. The 15 poorest countries at the time were Ethiopia, Ghana, The Gambia, Guinea-Bissau, Mali, Mozambique, Malawi, Niger, Nepal, Rwanda, Sierra Leone, Chad, Tajikistan, Tanzania, and Uganda. An IPL of $1.25/day per person, expressed in 2005 PPP dollars, was determined as the mean of the national poverty lines of these countries. When the 2011 PPPs were released in 2014, the same 15 national poverty lines were used, but now converted to 2011 PPPs yielding an IPL of $1.88, which was rounded to $1.90 (F. Ferreira, Jolliffe, and Prydz 2015; F. H. Ferreira et al. 2016). When the 2011 PPPs got revised in 2020, the IPL was similarly updated but remains unchanged at $1.90 (Atamanov et al. 2020b; World Bank 2020).
Samuel
Explain how higher lines are derived and link to Jolliffe & Prydz paper
In addition to the IPL, the World Bank uses two higher poverty lines to measure and monitor poverty in countries with a low incidence of poverty. These higher lines, namely $3.20 and $5.50 in revised 2011 PPPs, correspond to the national poverty lines of countries the World Bank classifies as lower- and upper-middle income countries, respectively. Jolliffe and Prydz (2016) used “implicit national poverty lines” to derive global poverty lines, including the IPL and higher lines. Implicit national poverty lines are defined as the percentiles that correspond to the national poverty rates that countries report, regardless of differences in methodology. Implicit national poverty lines are retrieved from PovcalNet, which contains all the Word Bank’s consumption and income distributions denominated in 2011 PPP dollars per capita. Jolliffe and Prydz (2016) suggested a robust IPL estimate of $1.90 as the median of national implicit poverty lines for low income countries from their approach. They further proposed, as higher global poverty lines, $3.20 and $5.50 as the median values of implicit poverty lines corresponding to lower- and upper-middle income countries. These lines were originally defined in original 2011 PPPs, but have later been updated using the revised 2011 PPPs with virtually no changes observed (F. Ferreira, Jolliffe, and Prydz 2015; F. H. Ferreira et al. 2016).
Daniel
For micro data, the poverty and inequality measures briefly described below are mainly based on Haughton and Khandker (2009). For grouped data, the poverty and inequality measures are based on Datt (1998).
Aleksander and Samuel
In this subsectoin and the one below, let’s write the name of each measure in Povcalnet and provide formulas for how they are derived. The FGT formulas should be easily available online
Poverty headcount index: The poverty headcount index (\(P_0\)) is a measure of the proportion of the population that is counted as poor. The poverty headcount index is obtained from micro data with the following expression:\[ P_0 = \frac{1}{N} \sum_{i=1}^{N} I (y_i < z) \]
where \(N\) is the total population size, \(y_i\) is consumption expenditure or income of individual \(i\), \(z\) is the poverty line, and \(I(.)\) is an indicator function that takes on the value 1 if the bracketed expression is true or 0 otherwise.
Headcount: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_poverty_stats.R
For grouped data, the poverty headcount is obtained using the following expression:
\[ P_0 = - \frac{1}{2m}[n + r(b+2z/\mu)((b+2z/\mu)^2)-m)^{-1/2}], \]
where \(m\) = \(b^2 - 4a\), \(n = 2be - 4c\), \(r = (n^2 - 4me^2)^{1/2}\), \(e = -(a + b + c + 1)\), \(z\) is the poverty line, \(\mu\) is the mean consumption expenditure or income, and \(a, b, c\) are the parameter estimates of the GQ Lorenz function.
Poverty gap index: The poverty gap index (\(P_1\)) is a measure that adds up the extent to which individuals on average fall below the poverty line, and expresses it as a percentage of the poverty line. It is given as:
\[ P_1 = \frac{1}{N} \sum_{i=1}^{N} \frac{G_i}{z} \] with \(G_i = (z - y_i) × I (y_i < z)\), where \(G_i\) is defined as the poverty gap (i.e. poverty line (\(z\)) less consumption expenditure or income (\(y_i\))) of poor individuals; the gap is considered to be zero for everyone else. The poverty gap index shows the average minimum cost of eliminating poverty (relative to the poverty line) using targeted transfers, expressed as a percentage of the poverty line.
Gap: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_poverty_stats.R
For grouped data, the poverty gap index is obtained using the following expression:
\[ P_1 = P_0 - (\mu/z)L(P_0), \]
with all variables defined as before.
Poverty severity index: The poverty severity index (\(P_2\)) is a measure of the weighted sum of poverty gaps (as a proportion of the poverty line), where the weights are the proportionate poverty gaps themselves. It is given as:
\[ P_1 = \frac{1}{N} \sum_{i=1}^{N} \left(\frac{G_i}{z} \right)^2 \]
Also known as the poverty squared gap index, the poverty severity index accounts for inequality among the poor.
Severity: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_poverty_stats.R
For grouped data, the poverty severity index is obtained using the following expression:
\[ P_2 = 2(P_1) - P_0 - \left(\frac{\mu}{z}\right)^2 \left[aP_0 + bL(P_0) - \left(\frac{r}{16}\right)ln \left(\frac{1 - P_0/s_1}{1 - P_0/s_2}\right) \right] \]
where \(s_1 = (r- n)/(2m)\), \(s_2 = -(r + n)/(2m)\), and all other variables are defined as before.
The Watts index: The Watts index (\(W\)) is also an inequality-sensitive poverty measure that is given as:
\[ W = \frac{1}{N} \sum_{i=1}^{q} ln \left(\frac{z}{y_i} \right) \]
where \(N\) individuals in the population are indexed in ascending order of consumption expenditure (or income), and the sum is taken over \(q\) individuals whose consumption expenditure or income \(y_i\) falls below the poverty line \(z\). This formula applies for both micro and grouped data.
Watts: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_poverty_stats.R
Aleksander and Samuel
Can we get to the source code find out how the various other measures are calculated and list it here?
Gini coefficient: The Gini coefficient is derived from the Lorenz curve, which plots cumulative consumption expenditure (or income) share (on the y-axis) against cumulative population share (on the x-axis). A 45-degree line is defined over the Lorenz curve as a line of perfect equality. The Gini coefficient is the area between the line 45-degree line and the Lorenz curve. Let \(A\) be the area between the 45-degree line and the Lorenz curve, and let \(B\) be the area under the Lorenz curve. The Gini coefficient (\(Gini\)) is given as: \(\frac{A}{A + B}= 2A\) (since \(A + B = 0.5\)).
Formally, if \(x_i\) is a point on the x-axis, and \(y_i\) a point on the y-axis, then
\[ Gini = 1 - \sum_{i=1}^{N} (x_i - x_{i-1})(y_i + y_{i-1}). \]
When there are \(N\) equal intervals on the x-axis, the equation above simplifies to:
\[ Gini = 1 - \frac{1}{N}\sum_{i=1}^{N} (y_i + y_{i-1}). \]
The Gini coefficient ranges from 0 (perfect equality) to 1 (complete inequality).
Gini: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_gini.R
For grouped data, the Gini coefficient is obtained using the following expression :
\[ Gini = \frac{e}{2} - \frac{n(b + 2)}{4m} + \frac{r^2}{8m\sqrt{-m}} \left[\sin^{-1} \frac{(2m + n)}{r} - \sin^{-1}\frac{n}{r} \right] \text{if $m<0$} \]
\[ Gini = \frac{e}{2} - \frac{n(b + 2)}{4m} + \frac{r^2}{8m\sqrt{m}} ln\left[\text{abs}\left( \frac{2m + n + 2\sqrt{m}(a + c - 1)}{n - 2e\sqrt{m}}\right) \right] \text{if $m>0$} \]
with all variables defined as before.
Mean log deviation: The mean log deviation (MLD) belongs to the family of generalized entropy (GE) inequality measures. It is given as:
\[ MLD = \frac{1}{N} \sum_{i=1}^{N} ln \left(\frac{\bar{y}}{y_i} \right) \]
where \(N\) is the total population size, \(\bar{y}\) is the mean consumption expenditure or income per person, and \(y_i\) is consumption expenditure or income of individual \(i\). The mean log deviation has a minimum value of 0 (perfect equality) and has no upper bound. This formula applies for both micro and grouped data.
MLD: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_mld.R
Polarization: The polarization index (\(P\)) measures the extent to which the distribution of consumption expenditure or income is “spread out” and bi-modal. It is given as:
\[ P = \frac{2(\mu^* - \mu^L)}{m} \]
where \(\mu^*\) is the distribution-correction mean (i.e. \(\mu(1 - Gini)\)), \(\mu^L\) is the mean of the poorest half of the population, and \(m\) is the median. Like the Gini coefficient, the polarization index ranges from 0 (no polarization) to 1 (complete polarization). The polarization index is based on Wolfson (1994) and Ravallion and Chen (1996). This formula applies for both micro and grouped data.
Polarization: https://github.com/PIP-Technical-Team/wbpip/blob/master/R/md_compute_polarization.R
Nishant
Explain in a short paragraph the national accounts data used, countries where we use specific sources, and link to national accounts paper.
Nishant
Explain how/why we extrapolate, provide the formula, discuss the no-use of a passthrough rate (perhaps refer to relevant literature on this) and link to national accounts paper.
Explain the India exception.
Nishant
Explain how/why we interpolate and provide the two different interpolation formulas (in the national accounts paper).
Daniel
Marta
Explain the regions used and where the set of 218 countries comes from.
Marta
Explain the population data that we use.
Marta
Explain how we treat countries with missing data and derive the regional/global headcounts
Marta
Explain the coverage rule