Micro and Macro Regressions
The AF measures can be used to analyse poverty determinants[245] for a household or person (henceforth we use the term ‘household') and for a population subgroup. We could study determinants of household or subgroup poverty in a micro and a macro context.
In what follows, the term ‘micro' refers to regressions where the unit of analysis is the person or household. The term ‘macro' refers to regressions where the unit of analysis is some spatial or social aggregate, such as a district, state, province, ethnic group, or country. Micro regressions are useful for describing the distinctive features of multidimensional poverty profiles across households (in a given country) or to understand their determinants of poverty. Macro regressions, on the other hand, are useful for studying the determinants of poverty at the province, district, state, or country levels. Both types of regressions use specific components of the AF measures. In the case of micro regressions, the focal variable is the (household) censored deprivation score. From the exposition of Chapter 5, we know that if the deprivation score of a household ci is equal to or greater than the multidimensional poverty cutoff (k), the household is identified as multidimensionally poor. This poverty status of a household is represented by a binary variable (indicator function) that takes the value of one if the household is identified as multidimensionally poor and zero otherwise.A natural question that arises is how to analyse the ‘causes' (in the sense of determinants) that underlie the (multidimensional) poverty status of a household. An intuitive way would be to model the probability of a household becoming multidimensionally poor or falling into multidimensional poverty. A crucial point should be noted here, which may be more particular to multidimensional notions of poverty than their unidimensional monetary counterparts: when modelling the probability of a household being in monetary poverty, various health- and education-related variables, which are not embedded in the monetary poverty measures, are used as exogenous variables.[246] In a multidimensional case, these exogenous variables may be used directly to construct the poverty measure and so the probability models at the household level, which include these as explanatory variables, are subject to a potential endogeneity issue.
For example, if among the explanatory variables we include an asset variable like car ownership, and if that indicator was also included among the ‘assets' indicator that appears in the multidimensional poverty measure, there will be an endogeneity issue in the model. A typical approach to deal with endogeneity is to use an instrumental variable, but often it is very difficult to find a valid instrument.[247] An alternative approach would be to restrain the set of explanatory variables of the household regression model to non-indicator measurement variables[248]—like certain demographic variables—or additional socioeconomic characteristics of the household. From such a perspective one would be interested in examining household poverty profiles. Sample research questions would be: are female-headed households more likely to be multidimensionally poor? Are larger households more prone to be multidimensionally poor? How does the probability of being multidimensionally poor vary by household size and composition, caste, or ethnicity?In the case of cross-sectional macro regressions, the focal variables are the Mα measures at the province, district, state, or country levels, or some other population subgroup or aggregate which leads to a proper sample size.[249] If the focus is on the Adjusted Headcount Ratio M0, the focal variables in a macro regression could comprise M0 or the intensity A and incidence H of multidimensional poverty. However, from Chapter 5 we know that H and A are partial indices that do not enjoy the same properties as the M0 measure. In this chapter we do not further consider regression models for A. Although H is also a partial index that violates dimensional monotonicity, we still discuss its analysis, given the prominence of existing studies using the unidimensional poverty headcount ratio.
As already noted, M0 and H are bounded between zero and one. In statistical terms, M0 and H are fractional (proportion) variables that lie in the unit interval. Their restricted range of variation limits the use of the linear regression model because these models assume continuous variables comprised between -∞ and +∞. A natural model to be considered is one that reflects the fractional nature of any of these two indices (see section 10.4).
10.2
More on the topic Micro and Macro Regressions:
- Micro and Macro Regressions
- CONTENTS
- THE RESEARCH QUESTION AND METHODS TO EXPLAIN INEQUALITY AND ITS CHANGE
- Distribution and Dynamics