help for welflossas (Version 1.0)Alicia Pérez-Alonso (March 2017)

Well-being (monetary) gain/loss measures and social welfare loss indices and curves associated with segregation using either disaggregated or aggregated data for the quantitative variable.

Disaggregated data: quantvar contains individual observations

welflossas unitvar groupvar quantvar [if] [in] [weight]
[,stats:(statname) thrincl:(#) nograph format:(%fmt)]

Aggregated data I: all individuals belonging to the same unit have the same value in quantvar

welflossas unitvar groupvar quantvar [if] [in] [weight]
[,aggregate: thrincl:(#) nograph format:(%fmt)]

Aggregated data II: a variable that contains an aggregated value for each unit is added from a
second dataset to existing individual observations from the dataset currently in memory

welflossas unitvar groupvar [if] [in] [weight]
[,aggregate: addstatus callfile:(filename1) callvar:(quantvar) saving:(filename2) thrincl:(#)
nograph format:(%fmt)]

stats() is available only for disaggregated data.

addstatus is available only for aggregated data.

fweights, aweights and iweights are allowed. iweights are not allowed by stats(median). See weight.

unitvar, groupvar, and quantvar must be numeric. Zero-values of quantvar are automatically changed to missing values by the program.
In case all observations of quantvar are missing for a specific value of unitvar, the program automatically excludes that value from the analysis.

Description

welflossas computes a family of indices measuring the well-being (monetary) gain/loss of a group associated with its segregation as proposed by Del Río and Alonso-Villar (2015) and Alonso-Villar
and Del Río (2016). welflossas also computes the FGT indices and produces the Social Welfare Loss curves as proposed by Del Río and Alonso-Villar (2017).

Microdata (individual observations) are required.

unitvar is a categorical variable identifying organizational units (e.g. occupations, census tracts, schools,...).

groupvar is a categorical variable identifying demographic groups (e.g. gender, race, gender x race,...).

quantvar is a quantitative variable (e.g. wage, status,...). Values of quantvar are either disaggregated or aggregated by unit (e.g. status by occupation).
Use the aggregate option for aggregated values. If these data come from an external source, specify also addstatus and its associated options.

If the nograph option is omitted, the default is to draw the Social Welfare Loss curves and the
decomposition of the per capita earning gap ratio (displayed only for disaggregated data).

Options

aggregate uses aggregated values by unit for quantvar at individual level, the default is to use disaggregated data.

addstatus performs a many-to-one merge on key variable unitvar; see [D] merge.

callfile:(filename1) is for use with addstatus; it specifies a valid filename1 that contains the using dataset.

callvar:(quantvar) is for use with addstatus; it specifies the name of quantvar in the using dataset.

saving:(filename2) is for (optional) use with addstatus; it stores the dataset currently in memory on disk under the name filename2.dta.

stats:(statname) specifies the statistic used to compute aggregated values of quantvar at unit level and within-unit for groups. Available statistics are mean and median. The default is equivalent to specifying stats(mean).
stats() requires disaggregated data because mean and median would produce the same output with aggregated data by unit (values of quantvar do not vary in within-unit for different groups).
If all values of quantvar are missing for a certain group within a unit, the value of the statistic for the whole unit is automatically imputed.

thrincl:(#) specifies a threshold z>=0 which determines the level of losses that would be considered when computing FGT indices and producing Social Welfare Loss curves using Psi_{0} index. thrincl(real 0) is the default.

nograph suppresses display of default graphs.

format:(%fmt) changes numeric format, the default is format(%9.4f).

Reporting

Notation: epsilon={0,1,2,3,4} is the constant elasticity of the assumed utility function that can be interpreted as a (relative) inequality aversion parameter in Psi_ indices.
alpha={0,1,2,3} is an inequality aversion parameter in FGT indices. See references below for some further notation and formulae.

Measures of well-being (monetary) gain/loss associated with segregation:

- Psi_{epsilon}, family of indices to quantify the well-being gain/loss of a group associated with its segregation.

Note that Gamma=Psi_{0} measures the monetary gain/loss of a group associated with its segregation.

Available only for disaggregated data:

- Omega_{epsilon}, the well-being gain/loss of a group due to within-unit status disparities with respect to other groups.

Note that Delta=Omega_{0} measures the monetary gain/loss of the group associated with within-unit status disparities with respect to other groups.

- WAD_{epsilon}, total well-being advantage/disadvantage (WAD) of a group: Psi_{epsilon} + Omega_{epsilon}.

- seg-EGap, contribution of segregation to the per capita earning gap ratio (EGap=WAD_{0}) of the group: Psi_{0}/WAD_{0}.

If option nograph is not specified:

- Decomposition of the per capita earning gap ratio (EGap) in terms of segregation (Gamma) and within-unit status disparities (Delta). The graph currently displayed is saved to disk under the name grEGap.gph.

Measures of social welfare loss associated with segregation:

- FGT_{alpha}, the Foster-Greer-Thorbecke (FGT) family of poverty indices adapted to measure the social welfare loss that the society experiences due to segregation.

Note that FGT_{0} is the headcount ratio, fraction of the population that belongs to groups that have well-being (monetary) losses associated with segregation.

If option nograph is not specified:

- WLAS_{epsilon}, Social Welfare Loss curves associated with segregation. The graph currently displayed is saved to disk under the name grWLAS.gph.

Each group's relative population share is also reported.

Saved results

welflossas stores the following matrices in r():

r(measures) : Measures of well-being (monetary) gain/loss associated with segregation

r(xywlas) : Coordinates of points on the WLAS curves

r(FGT) : FGT indices

r(share) : Population shares by group

Limits

This program makes use of tabulate to produce a two-way table of frequency counts for the variables unitvar (rows) and groupvar (columns).
The maximum dimension allowed for unitvar or groupvar is the maximum row or column dimension for tabulate (see limits).

Examples

Disaggregated data:

. use wlasdata.dta, clear

. welflossas occ1990 raceh hw [aw=perwt]

. ret list

. mat list r(xywlas)

. welflossas occ1990 raceh hw [aw=perwt], st(median) thr(15) nog

Aggregated data I:

. use wlasdata.dta, clear

Create a new variable (mhw) containing the weighted mean wage for each distinct occupation

. gen mhw=.

. qui levelsof occ1990, local(levels)

. qui foreach l of local levels {
summarize hw [aw=perwt] if occ1990 == `l', meanonly
replace mhw = r(mean) if occ1990 == `l'
}

. welflossas occ1990 raceh mhw [aw=perwt], ag

Aggregated data II:

. use wlasdata.dta, clear

. welflossas occ1990 raceh [aw=perwt], ag adds callf(wlas2data) callv(mhw) sav(wlas3data) nog

Author

Alicia Pérez-Alonso
<apereza@ucm.es>

Facultad de Estudios Estadísticos

Universidad Complutense de Madrid

Avda. Puerta de Hierro s/n, 28040 Madrid, Spain.

References

Del Río, C. and Alonso-Villar, O. (2017), Segregation and Social Welfare: A Methodological Proposal with an Application to the U.S., Social Indicators Research, forthcoming. DOI: 10.1007/s11205-017-1598-0

Alonso-Villar, O. and Del Río, C. (2016),
Local segregation and well-being, The Review of Income and Wealth. DOI: 10.1111/roiw.12224

Del Río, C. and Alonso-Villar, O. (2015),
The Evolution of Occupational Seggregation in the United States, 1940-2010: Gains and Losses of Gender-Race/Ethnicity Groups, Demography, vol. 52(3), pp. 967-988. DOI:10.1007/s13524-015-0390-5

Also see

localseg if installed; dicseg if installed