From a policy perspective, in addition to measuring poverty we must perform some vital analyses regarding the transmission mechanisms between policies and poverty measures.
Issues we may wish to explore with a regression model include the determinants of poverty at the household level in the form of poverty profiles or the elasticity of poverty to economic growth, while controlling for other determinants.
We may also be interested in understanding how macro variables such as average income, public expenditure, decentralization, information technology, and so on relate to multidimensional poverty levels across groups or regions—and across time. Through regression analysis, we can partially study these transmission mechanisms by looking at the determinants of multidimensional poverty. In a regression model, we can account for the effect or the ‘size' of determinants of multidimensional poverty, which would not be possible with a purely descriptive analysis.Such analyses are routinely performed for income poverty using what we will term ‘micro' or ‘macro' regressions. As is explained below, the term ‘micro' refers to analyses in which the unit of analysis is a person or household; the term ‘macro' refers to analyses in which the unit of analysis is a subgroup, such as a district, a state, a province, or a country. This section provides the reader with a general modelling framework for analysing the determinants of Alkire-Foster poverty measures, at both micro and macro levels of analyses.
In general, in micro regressions, the focal variable to be modelled may be a binary variable denoting a person's status as poor (or non-poor) or a variable denoting the deprivation score assigned to the poor. In macro regressions, the focal variable to model is a subgroup poverty measure like the poverty headcount ratio or any other Foster-Greer-Thorbecke (FGT) poverty measure. As with regressions that model the monetary headcount ratio or the poverty gap, macro regressions with M0-dependent variables must respect their nature as cardinally meaningful values ranging from zero to one.
In these cases, a classic linear regression is not the appropriate model. The common assumptions of the classic linear regression fall short because the range of the dependent variable is bounded and may not be continuous or follow a normal distribution that is often assumed in linear regression models.Generalized linear models (GLMs), by contrast, are preferred as the data-analytic technique because they account for the bounded and discrete nature of the AF-type dependent variables. GLMs extend classic linear regression to a family of regression models where the dependent variable may be normally distributed or may follow a distribution within the exponential family—such as the gamma distribution, Bernoulli distribution, or binomial distribution. GLMs encompass models for quantitative and qualitative dependent variables, such as linear regression models, logit and probit models, and models for fractional data. Hence they offer a general framework for our analysis of functional relationships.[242]
This section presents the GLM as an overall framework in which to study micro and macro determinants of multidimensional poverty. Within this framework we are able to account for the bounded nature of the Adjusted Headcount Ratio M0 and the incidence H while modelling their determinants. We are also able to model these determinants for the probability of being multidimensionally poor.
This chapter is structured as follows. We begin by differentiating micro and macro regression analyses. For this purpose, we review the M0 measure of the AF class, its partial and consistent sub-indices, and the type of variables they represent in a regression framework. We then present the general structure and possible applications of the GLMs to AF measures. We begin with an exposition of linear regression models and how these extend to models for binary dependent variables—logit and probit—and fractional[243] data. We assume readers have some background in applied statistics and key elements of estimation and inference. Our exposition deals with cross-sectional data but could be easily extended to panel data.[244]
Before we begin, we should point out that the notation used in this chapter is self-contained. Some notation may duplicate that used in other sections or chapters for different purposes. When the notation is linked to discussions in other sections or chapters, it will be specified accordingly.
10.1