help for unemp (Version 1.0)Carlos Gradín (April 2014)

Measures of employment deprivation (unemployment) among households

unemp unempvar [weights] [if exp] [in range] , hid(hidvar) [ hsize(hsizevar) thao(#) format(%9.#f)
gamma(# [# ...]) alpha(# [# ...])
generate(newvar) decomp ]

fweights, aweights and iweights are allowed; see weights.

Description

unemp computes aggregate households' employment deprivation measures, which are sensitive to the distribution of employment among deprived households.

The program computes the family of FGT-type employment deprivation measures at the household level proposed in Gradín, Cantó, and Del Río (REHO 2014).

The measure first computes indices of employment deprivation for each household based on individual information on either unemployment (a dummy variable: 1 if unemployed, 0 if employed),
or underemployment (a continuous variable; i.e. relative gap in hours worked with respect to whished hours, ranging between 0 and 1).

Households deprivation indices can be saved as new variables using gen(newvar) with _subscripts indicating the value of gamma
(i.e. with gen(u), u_0, u_1, u_2... are created standing for household deprivation index for gamma=0, 1, 2 ...).
This could be useful to further analyze their distribution drawing kernel densities (see akdensity if installed)
or computing "employment deprivation curves" (similar to TIP curves in poverty analysis) (using glcurve if installed).

In a second step, the program aggregates households' employment deprivation indices across the entire target population in order to obtain a distribution-sensitive aggregate index of households' deprivation in employment.

By default, the aggregate index weights households by the number of economically active members (units are individuals) such as in official unemployment rates.

It is possible to weight each household by the number of members (whether in the labor force or not) or any other household-level variable using the hsize option. See examples below.

By default, a household is considered to be deprived in employment if any member has a positive gap (i.e. is unemployed or underemployed).
For restricting deprived households to be only those having a deprivation level (proportion of unemployed members or of hours, depending on how the gap was measured) greater than a given threshold (i.e .20, .50, ...),
use option thao(#), the default is thao(0). If thao(1), only households with all their members fully deprived contribute to aggregate deprivation.

Data requirements

Microdata are required with observations being individuals in the labor force (economically active). Information identiying the households they belong to is necessary too. unempvar is a variable containing individual unemployment gaps that can be either a dummy variable (1 if unemployed, 0 if employed)
or a continuous variable between 0 and 1 (i.e. indicating the relative gap in hours worked with respect to whished hours).
hidvar is the household identifier. Observations can be weighted by the number of households members (see example below). Individuals with missing values in unempvar or hidvar will not be used in calculations.

Reporting

* Aggregate measure of households' employment deprivation U() for the specified values of the parameters:

. gamma, for one or more nonnegative integer numbers (0, 1,2 3,...) specified in option gamma(integer [integer ...]), the default is to report gamma=0,1,2.

If unempvar is a dummy, the index does not vary with gamma, thus gamma(1) is recommended.

This parameter captures the sensitivity of household-level deprivation indices to variability of employment gaps across their members.

. alpha, for one or more nonnegative integer numbers specified in option alpha(integer [integer ...]), the default is to report alpha=0,1,2.

This parameter captures the sensitivity of the aggregate measure of households deprivation in employment to inequality of employment indices among deprived households.

* If option decomp is specified, the decomposition of the aggregate indices into deprivation incidence, intensity and inequality of employment among the deprived households is also reported.

Required Option

hid(hidvar) to indicate household identifier.

Other Options

gamma(integer [integer ...]) to indicate the values of gamma, the default is gamma(0 1 2).

alpha(integer [integer ...]) to indicate the values of alpha, the default is alpha(0 1 2).

thao(#) to set the threshold in employement deprivation (real value between 0 and 1). For thao<1, only those households with a deprivation (for gamma=1) larger than the threshold will be considered deprived in employment. For thao=1,
only fully deprived households are considered depived.
The default is thao(0) (i.e. a household with u_1>0 is considered deprived).

generate(newvar) to create new variables containing households' employment deprivation indices for different values of gamma.
If this option is combined with hsize, the variables created only take values for one observation per-household.

decomp to make the general decompoistion of the index for each aplha into incidence, intensity (alpha>0) and inequality (alpha>1) among deprived households.
It also computes the variance of individual households deprivation indices (u) and the coefficient of variation for 1-u in the case of alpha=2.

format(%9.#f) to change numeric format, the default is format(%9.4f).

hsize(hsizevar) to weight each household according to (hsizevar). (hsizevar) might be the number of household members. If hsizevar is the same for all households, then the aggregate measure weights each household equally, regardless of their size.

Saved results

Matrices:

r(unemp): aggregate employment deprivation measure, and main decomposition if option decomp specified

r(dec2): alternative decomposition for alpha=2 if option decomp specified

Scalars:

r(U_i_j): aggregate employment deprivation measures U() for gamma=i and alpha=j.

Inference

It is possible to obtain bootstrap standard errors with unemp using the returned scalars (see example below).

Examples

. use unemp.dta, clear

. desc

1. Households are weighted according to the number of people in the labor force:

With a dummy indicating unemployment status (the index does not vary with gamma, only gamma=1 requested)

. unemp unemployed [aw=w] , hid(hid) gamma(1)

With a variable indicating gap in hours, e.g. (whished-worked)/whished

. unemp hgap [aw=w] , hid(hid)

Saved results

. ret list

2. Households are equally weighted regardless of their size

. gen hs=1

. unemp hgap [aw=w], hid(hid) hs(hs)

3. Households are weighted according to their household size (i.e. including non economically active members)

. unemp hgap [aw=w], hid(hid) hs(hsize)

Generating household employment deprivation index

. unemp hgap [aw=w] , hid(hid) hs(hsize) gen(u)

. desc u_*

Computing employment deprivation curve (gamma=2) across the population of households with at leat one member in the labor force (including members not in the labor force)[ glcurve must be installed]

. gen mu_2=-u_2

. glcurve u_2 [aw=w*hsize] , sort(mu_2)

Estimating the density of household employment deprivation indices (gamma=1) across the target population [ akdensity must be installed]

. akdensity u_1 if u_1>0 [aw=w*hsize], at(u_1)

Changing default values of the parameters

. unemp hgap [aw=w] if country==1, hid(hid) hs(hsize) th(.2) gamma(0 1 2 3) alpha(1 2 3 4)

Specific rates:

Standard unemployment rate

. unemp unemployed [aw=w], hid(hid) g(1) a(1)

Unemployment rate of households heads (% households)

. unemp unemployed [aw=w] if head==1 , hid(hid) g(1) a(1)

Proportion of people whose household head is unemployed

. unemp unemployed [aw=w] if head==1 , hid(hid) hs(hsize) g(1) a(1)

Proportion of households with all economically active members unemployed

. unemp unemployed [aw=w], hid(hid) hs(hs) thao(1) g(1) a(1)

Proportion of people in households with all economically active members unemployed

. unemp unemployed [aw=w], hid(hid) hs(hsize) thao(1) g(1) a(1)

Decomposition

. unemp hgap [aw=w], hid(hid) hs(hsize) decomp

Bootstrapping U(), exmaple for alpha=2, gamma=0,1,2 [BC estimates for Confidence Interval]

cap program drop hhu

program def hhu

unemp hgap [aw=w], hid(hid) hs(hsize)

end

bootstrap r(U_0_2) r(U_1_2) r(U_2_2) if country==1, reps(10): hhu

estat bootstrap

Author

Carlos Gradín
<cgradin@uvigo.es>

Facultade de CC. Económicas

Universidade de Vigo

36310 Vigo, Galicia, Spain.

References

Gradín, C, Cantó, O., and Del Río, C.(2014), Measuring employment deprivation in the EU using a household-level index, Review of the Economics of the Household.

Also see

akdensity if installed; ; glcurve if installed