*! version 1.0 30may2017
help FGT_CIdialog:

Title

FGT_CI -- calculates and decomposes Foster–Greer–Thorbecke (and standard) concentration indices

Syntax

FGT_CI depvar [indepvars] [if] [in] [weight], rankvar(varname) [options]

where depvar is the variable to calculate the Foster-Greer-Thorbecke (FGT) concentration index (CI) for with the observations ranked according to rankvar.
The FGT-CI can be decomposed according to indepvars and options can set the FGT transformation to apply, regressions to use for the decomposition, and complex survey bootstrap.
User-written commands twopm, concindc, and bsweights must be installed to use command FGT_CI.

Main
method(string) sets the type of CI to compute and decompose

cutoff(real) sets the threshold or ceiling value for the FGT transformation

power(real) indicates which FGT power to use

modpart1(string) specifies the model used in the first part of the decomposition model

modpart2(string) specifies the model used in the second part of the decomposition model

Complex survey bootstrap
boot_reps(integer) indicates the number of bootstrap repetitions

boot_seed(integer) sets the seed number for the bootstrap

strata(varname) indicates the strata variable

psu(varname) indicates the primary sampling unit

bsw_average(integer) pecifies the number of replications for the mean bootstrap

nosvy performs a simple bootstrap instead of a complex survey bootstrap

Display
noresults suppresses the estimation results

table(string) displays and saves an aggregate result table

table_opt(string) sets options for option table

Description

This command combines two of the most widely used measures in the inequality and poverty literatures: the concentration index (CI) and the Foster–Greer–Thorbecke (FGT) metric.
It does so by applying the FGT transformation to a variable of interest (depvar) and by calculating the CI of the transformed variable after ranking the observations according to a socioeconomic status variable rankvar.
The command also decomposes the resulting FGT-CI by means of a two-part model (TPM) to determine how the factors listed in indepvars are associated with overall socioeconomic inequality.
The command further decomposes the contribution of each factor to the overall socioeconomic inequality into the association of each factor with the dependent variable (obtained from the TPM regression) and its distribution according to socioeconomic status (computed with factor-specific CIs).
Also note that the command can be applied to calculate and decompose the standard CI as it is a special case of the FGT_CI when no threshold or ceiling apply.
The command saves its results in e().
User-written commands twopm and concindc must be installed to use command FGT_CI.

Options

Main

method(string) sets the type of CI to compute and decompose.
Value "standard" refers to CI of the untransformed dependent variable.
Value "threshold" refers to the FGT transformation defined above a cutoff value (e.g. body mass index above 30).
Value "ceiling" refers to the FGT transformation defined below a cutoff value (e.g. body mass index below 18.5).
Default value is "standard".

cutoff(real) is the threshold or ceiling value for the FGT transformation.
Default value is 0.
This option is inactive when the method is "standard".

power(real) indicates which FGT power to use.
Default value is 0 and negative values are not allowed.
This option is inactive when the method is "standard".

modpart1(string) specifies the model used in the first part of the decomposition model.
The syntax of user-written command twopm must be followed.
This is the model that applies when power equals 0.
Default is logit without any option.

modpart2(string) specifies the model used in the second part of the decomposition model.
The syntax of user-written command twopm must be followed.
This is the model that applies when method is "standard".
Default is reg without any option.

Complex survey bootstrap

boot_reps(integer) indicates the number of bootstrap repetitions.
Default value is 250.

boot_seed(integer) sets the seed number for the bootstrap.
Default value is 852015.

strata(varname) indicates the strata variable.

psu(varname) indicates the primary sampling unit.

bsw_average(integer) specifies the number of replications for the mean bootstrap.
Default value is 10.

Display

noresults asks the command no to display the estimation results.

table(string) displays an aggregate result table and saves it under the name imputed as a string.
If string is "", the table is neither displayed or saved.
If string is "nosave" the option only displays the table without saving it.
This option is only used when indepvars have been specified.
Default value is "".
User-written command esttab must be installed to use this option.

table_opt(string) adds options to option table.
The syntax of user-written esttab must be followed.

Stored results

FGT_CI saves the following results in e(b) and their corresponding bootstrapped variance-covariance matrix in e(V):

CIk gives the CI of each variable specified in indepvars with the observations ranked according to rankvar

eyex gives the elasticity of depvar according to each variable specified in indepvars

CIy gives the contribution of each variable specified in indepvars to the total FGT-CI, the residual CI unexplained by these variables, and total FGT-CI

CIy_fact gives the total contribution of each factor variable specified in indepvars to the total FGT-CI

Reference

Bilger M., E.J. Kruger, and E.A. Finkelstein, 2016.
Measuring Socioeconomic Inequality in Obesity: Looking Beyond the Obesity Threshold.
Health Economics 24(1), 75-85.

Author

Marcel Bilger, Laboratory of Health Econometrics, Signature Program in Health Services and Systems Research, Duke-NUS Medical School, Singapore.
Email marcel.bilger@duke-nus.edu.sg with "overfit.ado" as subject if you have any question, comment or suggestion regarding this stata user-written command.