The name is absent

Stata Technical Bulletin

Subgroup poverty 'risk' = FGT.k(a)∕FGT(a) = S_k/v_k

The overall proportion of the population poor is 20.3% (as shown also by the xfrac output), the average normalized
poverty gap is 0.052, and the average squared normalized gap, 0.024. The decomposition shows that subgroup poverty status
is associated with average income, whichever index is used. For example, the group with the lowest average income, social
renters, also have the highest poverty rate. And those with the highest average income, owners with a mortgage, also have the
lowest poverty rate. Interestingly, however, average income among poor owners with a mortgage is lower than average income
among poor social renters, 74 pounds per week compared with 93 (and hence their poverty gaps are larger). This helps explain
why it is that although social renters’ poverty share is about one half according to the headcount ratio, FGT(0), it is rather
smaller when one moves to the measures sensitive to how poor people are (their poverty risks are also smaller). When one uses
the poverty gap measures, the poverty share and poverty risk of owners with a mortgage becomes markedly larger.

To illustrate use of the alternative poverty line specification, let us now work with money income ybhc (rather than eybhc
which is needs-adjusted), and suppose that the household type-specific poverty line is given by the former poverty line multiplied
by the household equivalence scale rate (hes_bhc). To get results exactly the same as shown above, one would simply type the
following:

. ge plinevar = 'z^z*hes_-bhc

. povdeco ybhc [fw=wgt], varplCplinevar) by(tenure)

Concluding remarks

The aim of this insert has been to make preparation of many common income distribution summary statistics a matter of
routine. These numerical summaries should usually be accompanied by graphical ones and it is hoped that glcurve, Jenkins
and Van Kerm (1999), should help with these.

The most notable omission from the program calculations presented here is systematic derivation of sampling variances for
key statistics (apart from those in geivars). This reflects the state of the income distribution literature; the required formulas
either do not yet exist or have only recently been developed. The treatment of different kinds of weights, and the interaction
of ‘self-weighting’ features with survey design aspects, raises several complicated issues in this context which have yet to be
resolved.

Nonetheless, it must also be said that conclusions drawn are likely to be at least as sensitive to other factors as to
sampling ones. For example, there are important consequences of choosing different equivalence scales, definitions of income
and income-receiving unit, and different treatments of rogue outliers and zero and negative incomes. Luckily, Stata is already
well-suited for examining these data issues.

Acknowledgments

This work forms part of the scientific research program of the Institute for Social and Economic Research, and was supported
by core funding from the University of Essex and the UK Economic and Social and Economic Research Council. The programs
are revisions and extensions of some presented at the 4th UK Stata Users’ Group meeting.

References

Atkinson, A. B. 1970. On the measurement of inequality. Journal of Economic Theory 2: 244-63.

Blackorby, C., D. Donaldson, and M. Auersperg. 1981. A new procedure for the measurement of inequality within and between population subgroups.

Canadian Journal of Economics XIV: 665-85.

Cowell, F. A. 1989. Sampling variance and decomposable inequality measures. Journal of Econometrics 42: 27-41

——. 1995. Measuring Inequality. 2d ed. Prentice Hall/Harvester-Wheatsheaf: Hemel Hempstead.

Department of Social Security. 1993. Households Below Average Income 1979-1990/91 HMSO, London.

Foster, J. E., J. Greer, and E. Thorbecke. 1984. A class of decomposable poverty indices. Econometrica 52: 761 -766.

Goldstein, R. 1995. sg31: Measures of diversity: absolute and relative. Stata Technical Bulletin 23: 23-26. Reprinted in Stata Technical Bulletin

Reprints, vol. 4, pp. 150- 154.

<<   <   14   15   16   17   18   19   20   >   >>