A Unified Approach to Measuring Poverty and Inequality
the appendix includes tables and figures that may be useful in understanding some of the concepts and examples in the first two chapters.
The Income Variable Our discussion begins with the variable income, which may also represent consumption expenditure or some other single dimensional outcome variable. Data are typically collected at the household level. So to construct an income variable at the individual level, one must make certain assumptions about its allocation within the household. Using these assumptions, household data are converted into individual data that indicate the equivalent income level an individual commands, thereby taking account of household structure and other characteristics. One simplification is to assume that overall income is spread evenly across each person in the household. However, many other equivalence scales can be used. This adjustment enables comparisons to be made symmetrically across people irrespective of household or other characteristics. This simplification justifies the assumption of symmetry invoked when evaluating income distributions—whereby switching the (equivalent) income levels of two people leaves the evaluation unchanged. Additionally, it is assumed that the resulting variable can be measured with a cardinal scale that allows comparison of income differences across people.
The Data Income distribution data can be represented in a variety of ways. The simplest form is a vector of incomes, one for each person in the specified population. This format naturally arises when the data are derived from a population census. The population distribution may be proxied by an unweighted sample, which yields a vector of incomes, each of which represents an equal share of the population. It can also be represented by a weighted sample, which differentiates across observations in the vector in a prescribed way. For clarity, we will focus on the equal-weighted case here. Of course, a sample carries less information than does a full census, but the extent of the loss can be gauged and accounted for via statistical analysis. One further assumption must be made at this point: the evaluation method is
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