{"id":604,"date":"2017-08-30T17:04:06","date_gmt":"2017-08-30T15:04:06","guid":{"rendered":"http:\/\/abcabacus.org\/?page_id=604"},"modified":"2021-02-08T15:54:21","modified_gmt":"2021-02-08T14:54:21","slug":"annex-iii-useful-relationships-between-survivor-ratios-and-person-years","status":"publish","type":"page","link":"http:\/\/abcabacus.org\/?page_id=604","title":{"rendered":"Annex III: Miscellaneous"},"content":{"rendered":"


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\nAnnex III<\/title><\/p>\n<style type=\"text\/css\">code{white-space: pre;}<\/style>\n<div id=\"header\">\n<h1 class=\"title\">Annex III<\/h1>\n<\/div>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#annex-iii-miscellaneous\"><span class=\"toc-section-number\">1<\/span> Annex III: Miscellaneous<\/a>\n<ul>\n<li><a href=\"#abacus\"><span class=\"toc-section-number\">1.1<\/span> Abacus<\/a><\/li>\n<li><a href=\"#rules-of-thumb-splitting-factors\"><span class=\"toc-section-number\">1.2<\/span> Rules of thumb: Splitting factors<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#bibliography\"><span class=\"toc-section-number\">2<\/span> Bibliography<\/a><\/li>\n<\/ul>\n<\/div>\n<h1 id=\"annex-iii-miscellaneous\"><span class=\"header-section-number\">1<\/span> Annex III: Miscellaneous<\/h1>\n<p>This Annex assembles documentation and formulas not elsewhere covered.<\/p>\n<h2 id=\"abacus\"><span class=\"header-section-number\">1.1<\/span> Abacus<\/h2>\n<p>The Abacus population projection software of the United Nations Population Division used the following variant of the cohort-component model<a href=\"#fn1\" class=\"footnoteRef\" id=\"fnref1\"><sup>1<\/sup><\/a>. This implementation applies the split-migration option for all closed age groups, except the first one. For the first age group, half the migrants of this age group are added at the end of the projection period, that is without exposing them to the risk of dying.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-fec1368046e6fe603813d98e3ab70574_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_nP_x^{t + n} = {}_nP_{x - n}^{t + n}*{}_nS_{x - n}^{t.t + n} + {1 \over 2}\left( {{}_nM_{x - n}^{t,t + n}*{}_nS_{x - n}^{t.t + n} + {}_nM_x^{t,t + n}} \right);x = n,2n,...,z - n\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"582\" style=\"vertical-align: -4px;\"\/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-e211e48f888e154307a72296f438df64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_\infty P_z^{t + n} = \left( {{}_nP_{z - n}^t + {}_nP_z^t} \right)*{}_\infty S_z^{t,t + n} + {1 \over 2}\left[ {\left( {{}_nM_{z - n}^{t,t + n} + {}_\infty M_z^{t,t + n}} \right)*{}_\infty S_z^{t,t + n} + {}_\infty M_z^{t,t + n}} \right]\" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"582\" style=\"vertical-align: -11px;\"\/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-917f0aa37e32f1a6abeb3745cd24579e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_nP_0^{t + n} = {B^{t,t + n}}*{{{}_nL_0^{t,t + n}} \over {n*{l_0}}} + {1 \over 2}*{}_nM_0^{t,t + n}\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"298\" style=\"vertical-align: -8px;\"\/><\/p>\n<h2 id=\"rules-of-thumb-splitting-factors\"><span class=\"header-section-number\">1.2<\/span> Rules of thumb: Splitting factors<\/h2>\n<p>Preston, Keyfitz, and Schoen<a href=\"#fn2\" class=\"footnoteRef\" id=\"fnref2\"><sup>2<\/sup><\/a> (1972) suggested the following approximation for the separation factor for those less than 1 year of age: <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-3cc13186ab8fc805f93648f221f7b1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_1{a_o} = 0.07 + 1.7*{}_1{m_o}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"170\" style=\"vertical-align: -3px;\"\/>.<\/p>\n<p>Coale and Demeny introduced a system of regression coefficients to determine separation factors for age groups 0-1 and 1-5 (1963, 20; see also Coale et al. 1983, 20-21) that are anchored at values of <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-d944bcfb4cd165e8e621d45a9a74a9ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_1{q_0}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\"\/>, e.g the probability of dying between ages 0 and 1 (exact ages). Preston et al. adapted this approach to the age-specific mortality rates for age groups 0 to 1 (<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-e7761786916bcc1e1c58f073695730b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_1{m_0}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"30\" style=\"vertical-align: -3px;\"\/>) because this indicator seems to be more common in life tables constructions (2001, 47-48).<\/p>\n<p>I calculated a more realistic functional form of the <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-7aff5bdb8ae2595e3c7f1c992c6a9a02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_5{a_0}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"24\" style=\"vertical-align: -3px;\"\/> for the age group 0+5 based on the corresponding age-specific mortality rates for that age group (<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-eec2621b20f63d04d176cd7b28ae7da6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_5{m_0}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"31\" style=\"vertical-align: -3px;\"\/>). Employing the updated Coale\/Demeny Model Life Table prepared by the Population Division of the United Nations (UNPD 2015) for the “West” family of life tables, the following parameters were obtained:<\/p>\n<p>Males:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-cc093c5fba6e81a38fc22b8e52927397_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_5{a_0} = \left\{ {\matrix{ {{\rm{ - 0}}{\rm{.7427}}{}_5{{\rm{m}}_0}{\rm{ + 0}}{\rm{.9966}}} \hfill & {{}_5{m_0} \ge 0.06} \hfill \cr {{\rm{4768}}{\rm{.1*}}{}_5{{\rm{m}}_0}^3{\rm{ - 735}}{\rm{.36*}}{}_5{{\rm{m}}_0}^2{\rm{ + 38}}{\rm{.319*}}{}_5{{\rm{m}}_0}{\rm{ + 0}}{\rm{.2703}}} \hfill & {{}_5{m_0} < 0.06} \hfill \cr } } \right.\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"758\" style=\"vertical-align: -7px;\"\/><\/p>\n<p>Females<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/abcabacus.org\/wp-content\/ql-cache\/quicklatex.com-f132f2b5982a334e94171bc99e16afbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"{}_5{a_0} = \left\{ {\matrix{ {{\rm{ - 0}}{\rm{.8145*}}{}_5{{\rm{m}}_0}{\rm{ + 1}}{\rm{.1002}}} \hfill & {{}_5{m_0} \ge 0.06} \hfill \cr {{\rm{4825}}{\rm{.5*}}{}_5{{\rm{m}}_0}^3{\rm{ - 768}}{\rm{.63*}}{}_5{{\rm{m}}_0}^2{\rm{ + 40}}{\rm{.828*}}{}_5{{\rm{m}}_0}{\rm{ + 0}}{\rm{.3264}}} \hfill & {{}_5{m_0} < 0.06} \hfill \cr } } \right.\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"767\" style=\"vertical-align: -7px;\"\/><\/p>\n<h1 id=\"bibliography\"><span class=\"header-section-number\">2<\/span> Bibliography<\/h1>\n<p>Coale, Ansley J, and Paul Demeny. 1966. \u201cRegional Model Life Tables and Stable Populations.\u201d In <em>Regional Model Life Tables and Stable Populations<\/em>, 871. Princeton, NJ: Princeton University Press.<\/p>\n<p>Coale, Ansley J, Paul Demeny, and Barbara Vaughan. 1983. <em>Regional Model Life Tables and Stable Populations (Second Edition)<\/em>. <em>Studies in Population<\/em>. New York, NY; London, England: Academic Press. https:\/\/www.sciencedirect.com\/science\/book\/9780121770808.<\/p>\n<p>Pollard, A. H., Farhat Yusuf, and G.N Pollard (1990). Demographic Techniques. Third edition. Pergamon Press<\/p>\n<p>Preston, S., N. Keyfitz, and R. Schoen. 1972. Causes of Death: Life Tables for National Populations. New York: Seminar Press.<\/p>\n<p>Preston, Samuel H, Patrick Heuveline, and Michel Guillot. 2001. <em>Demography: Measuring and Modeling Population Processes<\/em>. Malden MA, USA; Oxford, UK: Blackwell Publishers.<\/p>\n<p>Swanson, D.A. and J.S. Siegel (2004) The Methods and Materials of Demography, Second Edition, Emerald Group Publishing.<\/p>\n<p>UNPD (2015). Extended Model Life Tables (Version 1.3). United Nations Population Division, New York. <a href=\"https:\/\/esa.un.org\/unpd\/wpp\/Download\/Other\/MLT\/\" class=\"uri\">https:\/\/esa.un.org\/unpd\/wpp\/Download\/Other\/MLT\/<\/a>.<\/p>\n<div class=\"footnotes\">\n<hr>\n<ol>\n<li id=\"fn1\">The Abacus projection software, programmed in FORTRAN, was in use up to the 2012 Revision of the United Nation’s global population projections.<a href=\"#fnref1\">\u21a9<\/a><\/li>\n<li id=\"fn2\">Cited from Siegel and Swanson (2004, p. 308, equation 13.5)<a href=\"#fnref2\">\u21a9<\/a><\/li>\n<\/ol>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Annex III Annex III 1 Annex III: Miscellaneous 1.1 Abacus 1.2 Rules of thumb: Splitting factors 2 Bibliography 1 Annex III: Miscellaneous This Annex assembles documentation and formulas not elsewhere covered. 1.1 Abacus The Abacus population projection software of the United Nations Population Division used the following variant of the cohort-component model1. This implementation applies … <a href=\"http:\/\/abcabacus.org\/?page_id=604\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> “Annex III: Miscellaneous”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":374,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-604","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/pages\/604","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/abcabacus.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=604"}],"version-history":[{"count":6,"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/pages\/604\/revisions"}],"predecessor-version":[{"id":745,"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/pages\/604\/revisions\/745"}],"up":[{"embeddable":true,"href":"http:\/\/abcabacus.org\/index.php?rest_route=\/wp\/v2\/pages\/374"}],"wp:attachment":[{"href":"http:\/\/abcabacus.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=604"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}