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From |
"Stephen P. Jenkins" <stephenj@essex.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: poverty/inequality analysis |

Date |
Tue, 22 Jul 2008 11:55:21 +0100 |

===================================================== Date: Mon, 21 Jul 2008 15:27:02 -0400 From: "Austin Nichols" <austinnichols@gmail.com> Subject: Re: st: poverty/inequality analysis Lola and Stas: Given Lola's reference to survey data, I assumed she wanted to work with real income distributions, which are not lognormal (unfortunately for us programmers). Here's a silly example reducing the "poverty" rate (poverty line at 6.2 for no good reason) from 5% to 2% with either an increase in mean or a decrease in dispersion, holding the other constant: webuse psidextract, clear keep if t==7 g x=_n/100+5.6 in 1/300 kdensity lwage, at(x) g(d0) nogr g lw1=lwage+.2 kdensity lw1, at(x) g(d1) nogr sort lwage g add=-((_n-1)*2/594-1)*.2 g lw2=add+lwage kdensity lw2, at(x) g(d2) nogr line d0 d1 d2 x, sort xli(6.2) su lw* Note that the mean-preserving decrease in dispersion I used does generate some reranking. It so happens the same 12 people are poor under either transformation, but YMMV. No idea is that's the kind of thing Lola has in mind or not... Lola--you may also want to read (for conceptual background) "Trends in income inequality, pro-poor income growth, and income mobility" by Stephen P. Jenkins and Philippe Van Kerm in Oxford Economic Papers 2006 58(3):531-548. ===================================================== >>>>>>>>> Thanks for the plug, Austin. However, a paper that is perhaps more closely related to Lola's needs is "Accounting for income distribution trends: a density function decomposition approach", Journal of Economic Inequality, 3(1), April 2005, 43-61 (Stephen P. Jenkins and Philippe Van Kerm) "Abstract. This paper develops methods for decomposing changes in the income distribution using subgroup decompositions of the income density function. Overall changes are related to changes in subgroup shares and changes in subgroup densities, where the latter are broken down further using elementary transformations of individual incomes. These density decompositions are analogous to the widely-used decompositions of inequality indices by population subgroup, except that they summarize multiple features of the income distribution (using graphs), rather than focusing on a specific feature such as dispersion, and are not dependent on the choice of a specific summary index. Nonetheless, since inequality and poverty indices can be expressed as PDF functionals, our density-based methods can also be used to provide numerical decompositions of these. An application of the methods reveals the multi-faceted nature of UK income distribution trends during the 1980s." We decompose densities using a variation on the DiNardo-Fortin-Lemieux idea -- using elementary transformations to explore the impacts of changes in location, spread, and other distributional features -- what we call the three `S's of distributional change: * sliding: a ceteris paribus shift of the PDF along the income line; * stretching: a ceteris paribus increase in spread around a constant mean; and * squashing: a ceteris paribus disproportionate increase in density mass on one side of the mode. Stephen ------------------------------------------------------------- Professor Stephen P. Jenkins <stephenj@essex.ac.uk> Director, Institute for Social and Economic Research University of Essex, Colchester CO4 3SQ, U.K. Tel: +44 1206 873374. Fax: +44 1206 873151. http://www.iser.essex.ac.uk Survival Analysis using Stata: http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/ Downloadable papers and software: http://ideas.repec.org/e/pje7.html Learn about the UK's new household panel survey, the United Kingdom Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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