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


From   Austin Nichols <austinnichols@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 14:02:18 -0400

Nicola Pensiero <nicola.pensiero@gmail.com>:
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.

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