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From |
Nicola Pensiero <nicola.pensiero@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: shift-share analysis (counterfactual) of inequality changes by subgroups using ineqdeco |

Date |
Wed, 13 Jun 2012 23:04:14 +0200 |

Thank you Austin Nichols, what I mean is to write the GE(1) index (theil index) distinguishing its within and between parts The Theil index GE(1) can be additively decomposed as GE(1)=GE_W(a) + GE_B(a) GE(1) = SUM [v_k^(1-a)] . [s_k^a] . GE_k(a)+ GE_B(a) My implementation of the within part is: =`v_`num''^0 * `s_`num''^1 * `GE_alpha1_`num'' where a=1, because Theil index assumes that a=1, which implies taking v locals to the zero power. My implementation of the between part is `v_`num''^0 * `s_`num''^1* log(`s_`num''^1) However, there is something odd about my implementation of the decomposition which results in inadmissible outcome values. Thank you for your support, Nicola Pensiero > Can you clarify what you mean by this? > > foreach num of numlist 1/30 { > local my_GE`num' = `v_`num''^0 * `s_`num''^1 * `GE_alpha1_`num'' + > `v_`num''^0 * `s_`num''^1* log(`s_`num''^1) > } > > Are you really taking v locals to the zero power? > This reduces to s_i*G_i + s_i*ln(s_i). > > On Wed, Jun 13, 2012 at 4:51 AM, Nicola Pensiero > <nicola.pensiero@gmail.com> wrote: >> Dear STATA users, >> my question is related to the shift-share analysis (counterfactual) of >> inequality changes by subgroups using the module ineqdeco. The problem >> is that the estimated counterfactual Theil (GE(1)) value is negative, >> which probably means that the implementation of the formula is wrong >> in some ways. >> >> I have households groups with a given income measured in two years >> (1977 and 2010). >> >> Given the quantities household type mean and population share of group >> x, I ask what would have happened to inequality (within and between >> groups) in year 2010 if the subgroup population share, v_k was the one >> of year 1977. >> >> >> My implementation of the counterfactual exercise is as follows. >> >> >> I saved the subgroup population share v_x from year 1977 >> >> ineqdeco income1977, by (group) >> foreach x of num 1/30 { >> local v_`x' = r(v_`x') >> } >> >> Then I saved the subgroup income share s_x and GE_k for year 2010. >> >> ineqdeco income2010, by (group) >> >> foreach x of num 1/30 { >> local s_`x' = r(theta_`x') >> } >> >> foreach x of num 1/30 { >> local GE_alpha1_`x' = r(ge1_`x') >> } >> >> >> Finally, I used the subgroup population share from year 1977 and the >> subgroup income share and GE_k from year 2010 in the calculation of >> Theil index GE(1). >> >> foreach num of numlist 1/30 { >> local my_GE`num' = `v_`num''^0 * `s_`num''^1 * `GE_alpha1_`num'' + >> `v_`num''^0 * `s_`num''^1* log(`s_`num''^1) >> } >> >> local my_GEglobal = `my_GE1' +........ `my_GE30' >> >> Thank you, Nicola Pensiero >> >> PS: the index should be decomposed in its within and between >> components as follows: >> >> GE = SUM [v_k^(1-a)] . [s_k^a] . GE_k(a) + GE_Between(a) >> where GE_B(a) is derived assuming every person within a given subgroup >> k received k's mean income, m_k. > > * > * 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/ * * 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/

**References**:**st: shift-share analysis (counterfactual) of inequality changes by subgroups using ineqdeco***From:*Nicola Pensiero <nicola.pensiero@gmail.com>

**Re: st: shift-share analysis (counterfactual) of inequality changes by subgroups using ineqdeco***From:*Austin Nichols <austinnichols@gmail.com>

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