Stata Technical Bulletin
15
Unsurprisingly, labor earnings are by far the largest component of household income packages, comprising just over
three-quarters of total household money income. The next largest components are social security benefits (15% of total income)
and investment income (10%). Inequalities in investment income and other income are huge relative to that of the other factor
components (see the last two columns). However, inequality contributions tend to be more closely related to factor shares than
to factor inequalities or correlations.
According to the Shorrocks decomposition rule, labor earnings has the largest proportionate inequality contribution of all
the components, some 77% of total inequality. The second largest proportionate contribution is from investment income, 28%.
Observe that taxes and cash transfers have an equalizing effect on total inequality, though relatively small ones.
povdeco: Poverty indices, with decomposition by subgroup
povdeco estimates three poverty indices from the Foster, Greer and Thorbecke (1984) class, FGT(α), plus related statistics
(such as mean income among the poor). FGT(0) is the headcount ratio (the proportion poor); FGT(1) is the average normalized
poverty gap; FGT(2) is the average squared normalized poverty gap. The larger a is, the greater the degree of poverty aversion
(sensitivity to large poverty gaps). Optionally provided are decompositions of these indices by population subgroup. Poverty
decompositions by subgroup are useful for providing poverty ‘profiles’ at a point in time, and for analyzing secular trends in
poverty using shift-share analysis. Unit record (‘micro’ level) data are required.
A more detailed description is as follows. Consider a population of income-receiving units (persons, households or families,
and so on), i = 1,.. .,n, with income yi, and weight w,. Let fi = Wj∕JV, where N = W'=∣ ww . When the data are unweighted,
W, = 1 and N = n.
The poverty line is z, and the poverty gap for person i is max(0, z -yi). Suppose there is an exhaustive partition of the
population into mutually-exclusive subgroups к = 1,... .K.
The FGT class of poverty indices is given by
FGT(α)
= Σ^
i=l
(z-yi)∕z Ii
where Ii = 1 if yi < z and Ii = 0 otherwise.
Each FGT(α) index can be additively decomposed as
FGT (a)
∑ VfeFGTfe (α)
fe=ι
where vfe = JVfe/N is the number of persons in subgroup к divided by the total number of persons (subgroup population share),
and FGTfe(a), poverty for subgroup k, is calculated as if each subgroup were a separate population.
When subgroup decompositions are requested, povdeco also displays, for each k, the following additional subgroup summary
statistics: subgroup poverty share, S,fe = vfeFGTfe(a)∕FGT(a), and subgroup poverty risk, ⅛ = FGTfe (α)∕FGT(α) = S,fe∕vfe.
Typically one’s data are in one of two forms. In the first form, the money incomes for each income-receiving unit i, xi,
are equivalized using an equivalence scale factor, mi, so that yi = xi∕mi, and the poverty line is a single (common) value,
in the same units as equivalized income, z. This is the case discussed in the description. In the second form, incomes are not
equivalized, but there are different poverty lines depending on (for example) household type. Suppose the line for unit i is ¾.
Observe that if zi = z.r∏j, FGT poverty index calculations based on {yi, giv give exactly the same answers as calculations based
on {xi, zi}, i = 1,..., n. For the first form, use pline(#) to specify the single common poverty line, while for the second
form, use varpl Zzarr^) to specify the poverty lines.
Syntax
povdeco varname [wigght∖ [if exp [in range] , { pline(#) ∣ varpl(zvar) } [bygroup(tgrowpvαr)]
fweights and aweights are allowed.
The user must supply the poverty line value(s), either as a single number # in pline(#), or provide the variable name
containing the values as zvar in varpl Zzαrr^).