14
Stata Technical Bulletin
STB-48
might include labor income, income from investments and pensions, cash transfers, and so on. See Shorrocks (1982b) and Jenkins
(1995) for examples. ineqfac may also be applied to summarize and compare the riskiness of portfolios of wealth holdings:
has exactly the same form as the “beta coefficient” used in financial analysis.
Syntax
ineqfac facvars Wveight∖ [if exp∖ [in range] [, stats total (totvar) i2 ]
fweights and aweights are allowed.
Options
stats provides the means, standard deviations, and correlations of the factor components and totvar.
total (OoVvar) creates a new variable, totvar, equal to the sum of the factor components for each observation.
i2 summarizes inequality using 22 = GE(2) rather than CV.
Example
Let us consider how inequality in household money income, ybhc, is related to the income sources which comprise it.
I distinguish five factor components: labour, employment and self-employment earnings; invst, income from investments,
savings, and private pensions; socsecb, cash social assistance and social insurance benefits; other, other income; and deducts,
income taxes and social insurance contributions.
In general, each of the factor components may have negative or zero values. Examples of valid negative values are found
most commonly for deducts; we assume that taxes are treated as negative income. (If values of variables such as tax payments
are recorded as positive in the data, it is the responsibility of the user to create a suitably signed variable prior to using ineqf ac.)
Examples of zero values might occur for, say, labour, in observations where no one in the household does paid work, or for
socsecb, if no one in the household receives any social security benefits.
. ineqfac labour invst socsecb other deducts [fw=wgt], stats total(total)
|
Factor |
I |
100*s.f |
S_f |
100*m.f∕m |
CV_f |
CV_f/CV(Total) |
|
— |
— | |||||
|
labour |
I |
77.0372 |
0.6515 |
76.0261 |
1.0414 |
1.2314 |
|
invst |
I |
27.8958 |
0.2359 |
10.2059 |
4.3230 |
5.1116 |
|
socsecb |
I |
-5.4941 |
-0.0465 |
15.3310 |
1.1401 |
1.3481 |
|
other |
I |
1.0902 |
0.0092 |
2.1276 |
5.5795 |
6.5973 |
|
deducts |
I |
-0.5292 |
-0.0045 |
-3.6907 |
0.5312 |
0.6280 |
|
— |
— | |||||
|
Total |
I |
100.0000 |
0.8457 |
100.0000 |
0.8457 |
1.0000 |
Note: The proportionate contribution of factor f to inequality of Total,
s_f = rho_f*sd(f)∕sd(Total). S_f = s_f*CV(Total).
m_f = mean(f). sd(f) = std.dev. of f. CV_f = sd(f)∕ιιι-f.
Means, s.d.s and correlations for factors and total income
(sum of wgt is 5.5852e+007)
(obs=6468)
Variable ∣ Mean Std. Dev. Min Max
----------+----------------------------------------------------
|
labour |
I 220 |
.3662 |
229.4935 |
-223.1994 |
2754.562 |
|
invst |
I 29. |
58227 |
127.8837 |
-97.52 |
6747.25 |
|
socsecb |
I 44. |
43792 |
50.6651 |
0 |
335.534 |
|
other |
I 6.167069 |
34.40908 |
-151.0626 |
878.31 | |
|
deducts |
I -10. |
69765 |
5.68206 |
-45.04 |
0 |
|
Total |
I 289 |
.8558 |
245.1361 |
-123.9898 |
7740.044 |
|
I |
labour |
invst |
socsecb |
other deducts |
Total |
|
— | |||||
|
labour I |
1.0000 | ||||
|
invstI |
0.0120 |
1.0000 | |||
|
Socsecbl |
-0.5111 |
0.0179 |
1.0000 | ||
|
other I |
-0.0518 |
-0.0129 |
-0.0373 |
1.0000 | |
|
deducts I |
-0.2868 |
-0.0031 |
0.0826 |
0.0111 1.0000 | |
|
Total I |
0.8229 |
0.5347 |
-0.2658 |
0.0777 -0.2283 |
1.0000 |