MULTIPLE CORRESPONDENCE ANALYSIS MCA
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E D I S I 0 2 T A H U N X V I I 2 0 1 1 gap
α=2 individuals receive higher weight the larger their poverty gaps are. For
α0 it satisfies monotonicity sensitive to the depth of poverty while if
α0 it satisfies transfer sensitive to the distribution among the poor.
In multidimensional context, distributional data are presented in a matrix size
, in which every typical element
corresponds to the achievement of individuali in dimensionj. Following Sen 1976, it is required
to identify the poor. The most common approach in the analysis is to define first a threshold level for each dimensionj,under
which a person is considered to be deprived. The aggregation of these thresholds can be expressed in a vector of poverty
lines
. In this way, whether a person is considered in deprived situation or not in every
dimension could be defined. This research computes poverty line using two-step FGT method as follows:
The non-normalised FGT index is estimated as: 3
where z is the poverty line and x
+
= maxx,0. The usual normalised FGT index is estimated as
4 The next decision is important to judge someone as
multidimensionally poor. A common starting point is to consider all those deprived in at least one dimension, also
called union approach. However, stricter criteria can be used, even to the extreme of requiring deprivation in all considered
dimensions, the so called intersection approach. According to Alkire and Foster 2008, this constructs a second cut-off:
the number of dimensions in which someone is required to be deprived so as to be identified as multidimensionallypoor.
This cut-off is named afterk. If
is the amount of deprivations suffered by individual i, then he will be considered
multidimensionally poor if .
Multidimensional poverty indicators are possibly heterogenous in the nature of quantitative indicators income, number of
assets or qualitative or categorical indicators ordinal, e.g. level of education and non-ordinal, e.g. occupation, geographical
region. This paper assumes variables are either quantitative or qualitative. A variable which has no meaningful ordinal
structure cannot be used as poverty or welfare indicator. The first step consists in defining a unique numerical indicator C as
a composite of the K primary indicators Ik, computable for each population unit Ui, and significant as generating a complete
ordering of the populationU. A composite poverty indicator C takes the value CiIik, k=1,K for a given set of elementary
population unit Ui.