Chapter 5 presented the methodology for the Adjusted Headcount Ratio poverty index (M0) and its different partial and consistent sub-indices;
Chapter 6 discussed how to design multidimensional poverty measures using this methodology in order to advance poverty reduction; and Chapter 7 explained novel empirical techniques required during implementation.
Throughout, we have discussed how the index and its partial indices may be used for policy analysis and decision-making. For example, a central government may want to allocate resources to reduce poverty across its subnational regions or may want to claim credit for strong improvement in the situation of poor people using an implementation of the Adjusted Headcount Ratio. One is, however, entitled to question how conclusive any particular poverty comparisons are for two different reasons.One reason is that the design of a poverty measure involves the selection of a set of parameters, and one may ask how sensitive policy prescriptions are to these parameter choices. Any comparison or ranking based on a particular poverty measure may alter when a different set of parameters, such as the poverty cutoff, deprivation cutoffs, or weights is used. We define an ordering as robust with respect to a particular parameter when the order is maintained despite a change in that parameter.[215] The ordering can refer to the poverty ordering of two aggregate entities, say two countries or other geographical entities, which is a pairwise comparison, but it can also refer to the order of more than two entities, what we refer to as a ranking. Clearly, the robustness of a ranking (of several entities) depends on the robustness of all possible pairwise comparisons. Thus, the robustness of poverty comparisons should be assessed for different, but reasonable, specifications of parameters. In many circumstances, the policy-relevant comparisons should be robust to a range of plausible parameter specifications. This process is referred to as robustness analysis.
There are different ways in which the robustness of an ordering can be assessed. This chapter presents the most widely implemented analyses; new procedures and tests may be developed in the near future.The second reason for questioning claimed poverty comparisons is that poverty figures in most cases are estimated from sample surveys for drawing inferences about a population. Thus, it is crucial that inferential errors are also estimated and reported. This process of drawing conclusions about the population from the data that are subject to random variation is referred to as statistical inference. Inferential errors affect the degree of certainty with which two or more entities may be compared in terms of poverty for a particular set of parameters' values. Essentially, the difference in poverty levels between two entities—states for example—may or may not be statistically significant. Statistical inference affects not only the poverty comparisons for a particular set of parameter values but also the robustness of such comparisons for a range of parameters' values.
In general, assessments of robustness should cohere with a measure's policy use. If the policy depends on levels of M0, then the robustness of the respective levels (or ranks) of poverty should be the subject of robustness tests presented here. If the policy uses information on the dimensional composition of poverty, robustness tests should assess these—which lie beyond the scope of this chapter, but see Ura et al. (2012). Recall also from Chapter 6 people's values may generate plausible ranges of parameters. Robustness tests clarify the extent to which the same policies would be supported across that relevant range of parameters. In this way, robustness tests can be used for building consensus or for clarifying which points of dissensus have important policy implications.
This chapter is divided into three sections. Section 8.1 presents a number of useful tools for conducting different types of robustness analysis; section 8.2 presents various techniques for drawing statistical inferences; and section 8.3 presents some ways in which the two types of techniques can be brought together.
8.1