# Chapter 4 Poverty measurement methodology

In its most basic form, poverty measurement refers to identifying those individuals or households that live below a predefined threshold of welfare. Such a threshold is generally known as a poverty line and the welfare aggregate that ranks the population from poorest to richest is usually measured on monetary terms like income or consumption expenditures. Given that SAR household surveys are consumption based, the rest of the book refers to “welfare aggregate” and “consumption aggregate” indistinguishably.

Many books, reports, and papers have been written regarding the best practices to construct welfare aggregates, calculate poverty lines, and estimate poverty. Thus, this chapter is in no sense an attempt to replace or summarize those resources. Instead, this chapter presents a brief explanation of the most important concepts, shows some technical examples in Stata on how to calculate poverty rates using SARMD, and showcases valuable resources with which the user should get familiar in order to understand poverty measurement properly.

## 4.1 Components of the consumption welfare aggregate

Household consumption surveys are the starting point in monitoring progress in poverty reduction and enhancing shared prosperity in any country. Ideally they should be not only available at reasonably frequent intervals, but also comparable over time (Serajuddin, Uematsu, Wieser, Yoshida, and Dabalen 2015a). Assuming we have computed comparable consumption expenditures at the household level, several spatial and temporal adjustments are necessary to take into account differences in costs of living across time and across countries.

The assumption of comparable household surveys is strong given the considerations explained in the introduction. Yet, in a general sense most consumption aggregates account for four basic components of expenditure: food, non-food, durables, and housing. Section 3 of Deaton and Zaidi (2002) provides a detailed explanation on how to estimate each of such components. In addition, valuable and applied insights about the general idea of constructing a welfare aggregate can be found in Lanjouw (2009). The takeaway of this exercise is to realize that the welfare aggregates from two different household surveys won’t ever be fully comparable because, by nature of the questionnaires, the subcomponents of each consumption aggregate will be different. In SARMD, the consumption aggregates used to measure well-being are provided by the National Statistics Office of each country, rather than being calculated by the SARTSD.

## 4.2 Additional factors that affect the welfare aggregate

First, a consumer price index (CPI) is necessary to measure by how much the general price level in a country has changed over time. Deflating all nominal expenditures to real expenditures allows to ensure that welfare comparisons between two periods are not being driven by inflation. Figure 4.1 displays how the CPI has changed for each country in South Asia over time.

Second, spatial price differences, typically between urban and rural areas, can also be large and it is important to take them into account. In South Asia, price levels for rural households are often lower than for urban households. The ideal way to control for spatial differences in prices is to use a Paasche or Laspeyres index to account for differences in the cost of living across space.

Third, it is necessary to convert expenditures to a common currency taking into account purchasing power. At present, data on purchasing power parity (PPP) comes from the International Comparison Program (ICP) collected in 2011, which is absent for Afghanistan. Purchasing power parities (PPPs) are the rates of currency conversion that equalize the purchasing power of different currencies by eliminating the differences in price levels between countries. The PPP between countries A and B measures the number of units of country A’s currency required to purchase a basket of goods or services in country A as compared to one unit of country B’s currency to purchase a similar basket of goods in country B. This indicator is measured in terms of national currency per US dollar and shown in the following table:

Country Currency ICP 2011
Afghanistan Afghan afghani NA
Bhutan Bhutanese ngultrum 16.96292
India Indian rupee 13.98707
Maldives Maldivian rufiyaa 10.67606
Nepal Nepalese rupee 25.75928
Pakistan Pakistani rupee 25.41426
Sri Lanka Sri Lankan rupee 42.21894

A fourth adjustment is dividing total household expenditure by some measure of the number of people in the household, and to assign the resulting per capita welfare measure to each household member as an individual. Later in the applications, we show how larger households typically have lower per capita expenditure levels than smaller households. In South Asia, the consequences of dividing total household expenditures by a greater number of individuals would not be complete without considering the extent of economies of scale within the household and a discussion of how much children and the elderly typically consume compared to adults.

## 4.3 Estimation of poverty

The FGT measures devised by Foster, Greer, and Thorbecke (1984) remain the most commonly used to measure poverty. They are define as:

$$$P_{\alpha}=\frac{1}{N}\sum^{N}_{i=1}I_{i}\left(\frac{\bar{u}-u_{i}}{\bar{u}}\right)^{\alpha}$$$

where N is the sample size, $$\bar{u}$$ is the scalar-valued poverty line, $$u_{i}$$ is the flow-based measure of welfare (income, expenditures, assets), $$I_{i}$$ is an indicator variable taking value one if $$u_{i} < \bar{u}$$ and zero otherwise, and $$\alpha$$ is a parameter reflecting the weight placed on the severity of poverty. Setting $$\alpha =0$$ yields the poverty headcount ratio $$P_{0}$$ (the share of a population falling below the poverty line). The higher order measures, $$P_{1}$$ and $$P_{2}$$, yield the poverty gap measure (the money metric measure of the average financial transfer needed to bring all poor households up to the poverty line) and the squared poverty gap (an indicator of the severity of poverty that is sensitive to the distribution of well-being among the poor). As we progress from $$P_{0}$$ to $$P_{1}$$ to $$P_{2}$$, the $$P_{\alpha}$$ measure gets more and more sensitive to extremely low incomes.

## 4.4 A technical example

The following lines of code show a simple example on how to calculate poverty rates in Stata using the SARMD and the GMD collections.


qui {
/*==================================================
USING SARMD
==================================================*/
cap datalibweb, country(PAK) year(2015) type(SARMD) clear
gen double welfare_ppp = welfare/cpi/ppp/365

/*==================================================
USING GMD
==================================================*/
cap datalibweb, country(PAK) year(2015) type(GMD) clear
gen double welfare_ppp = welfare/cpi2011/icp2011/365

/*==================================================
poverty measures
==================================================*/
local plines "1.9 3.2 5.5"
local wvar "welfare_ppp"
foreach pl of local plines    {
gen pl_=100*pl'' = pl'
forval a=0/2    {
gen fgta'_=100*pl'' = 100*((wvar'<pl')*(1-(wvar'/pl'))^a')
}
}

noi tabstat fgt0* [aw = weight], by(year) nototal
* tabstatmat
noi table year [aw = weight], c(mean fgt0_190 mean fgt0_320 mean fgt0_550 )
}
r; t=5.81 16:37:31

.
. qui {

Summary statistics: mean
by categories of: year (4 digit year of the survey)

year |  fgt0_190  fgt0_320  fgt0_550
---------+------------------------------
2015 |  3.941213  34.71227  75.41372
----------------------------------------

----------------------------------------------------------
4 digit   |
year of   |
the       |
survey    | mean(fgt0_190)  mean(fgt0_320)  mean(fgt0_550)
----------+-----------------------------------------------
2015 |       3.941213        34.71227        75.41372
----------------------------------------------------------
r; t=44.99 16:38:16
r; t=44.100 16:38:16

The variable welfare` contains the yearly nominal expenditures per capita in local currency. Once turned into daily 2011 USD (PPP), these values may be compared over time and between countries as in Figure 4.2. The area to the left of the US\$1.90 extreme poverty line represents the proportion of individuals living in extreme poverty.

### References

Deaton, Angus, and Salman Zaidi. 2002. Guidelines for Constructing Consumption Aggregates for Welfare Analysis. Washington, DC: World Bank Publications. http://ideas.repec.org/p/fth/priwds/192.html.

Foster, James, Joel Greer, and Erik Thorbecke. 1984. “A Class of Decomposable Poverty Measures.” Econometrica 52 (3): 761–66. https://EconPapers.repec.org/RePEc:ecm:emetrp:v:52:y:1984:i:3:p:761-66.

Lanjouw, Peter. 2009. “Constructing a Consumption Aggregate for the Purpose of Welfare Analysis: Principles, Issues and Recommendations Arising from the Case of Brazil,” January.

Serajuddin, Umar, Hiroki Uematsu, Christina Wieser, Nobuo Yoshida, and Andrew Dabalen. 2015a. Data Deprivation: Another Deprivation to End. The World Bank Policy Research working paper; no. WPS 7252. http://documents.worldbank.org/curated/en/700611468172787967/Data-deprivation-another-deprivation-to-end.