linarr {vardpoor}

Linearization of the aggregate replacement ratio

Description

Estimates the aggregate replacement ratio (defined as the gross median individual pension income of the population aged 65-74 relative to the gross median individual earnings from work of the population aged 50-59, excluding other social benefits) and computes linearized variable for variance estimation.

Usage

linarr(
  Y,
  Y_den,
  id = NULL,
  age,
  pl085,
  month_at_work,
  weight = NULL,
  sort = NULL,
  Dom = NULL,
  period = NULL,
  dataset = NULL,
  order_quant = 50,
  var_name = "lin_arr",
  checking = TRUE
)

Arguments

Y

Numerator variable (for gross pension income). One dimensional object convertible to one-column data.table or variable name as character, column number.

Y_den

Denominator variable (for example gross individual earnings). One dimensional object convertible to one-column data.table or variable name as character, column number.

id

Optional variable for unit ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number.

age

Age variable. One dimensional object convertible to one-column data.table or variable name as character, column number.

pl085

Retirement variable (Number of months spent in retirement or early retirement). One dimensional object convertible to one-column data.table or variable name as character, column number.

month_at_work

Variable for total number of month at work (sum of the number of months spent at full-time work as employee, number of months spent at part-time work as employee, number of months spent at full-time work as self-employed (including family worker), number of months spent at part-time work as self-employed (including family worker)). One dimensional object convertible to one-column data.table or variable name as character, column number.

weight

Optional weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number.

sort

Optional variable to be used as tie-breaker for sorting. One dimensional object convertible to one-column data.table or variable name as character, column number.

Dom

Optional variables used to define population domains. If supplied, linearization of at-risk-of-poverty threshold is done for each domain. An object convertible to data.table or variable names as character vector, column numbers as numeric vector.

period

Optional variable for survey period. If supplied, linearization of at-risk-of-poverty threshold is done for each survey period. Object convertible to data.table or variable names as character, column numbers as numeric vector.

dataset

Optional survey data object convertible to data.table.

order_quant

A numeric value in range \left[ 0,100 \right] for \alpha in the formula #'for at-risk-of-poverty threshold computation:

\frac{p}{100} \cdot Z_{\frac{\alpha}{100}}.

For example, to compute at-risk-of-poverty threshold equal to some percentage of median income, \alpha #'should be set equal to 50.

var_name

A character specifying the name of the linearized variable.

checking

Optional variable if this variable is TRUE, then function checks data preparation errors, otherwise not checked. This variable by default is TRUE.

Details

The implementation strictly follows the Eurostat definition.

Value

A list with four objects are returned:

• value - a data.table containing the estimated the aggregate replacement ratio.

• lin - a data.table containing the linearized variables of the aggregate replacement ratio.

References

Working group on Statistics on Income and Living Conditions (2015) Task 5 - Improvement and optimization of calculation of net change. LC- 139/15/EN, Eurostat.
Jean-Claude Deville (1999). Variance estimation for complex statistics and estimators: linearization and residual techniques. Survey Methodology, 25, 193-203, URL https://www150.statcan.gc.ca/n1/pub/12-001-x/1999002/article/4882-eng.pdf.

See Also

varpoord, vardcrospoor, vardchangespoor

Examples

library("data.table")
library("laeken")
data("eusilc")
dataset1 <- data.table(IDd = paste0("V", 1 : nrow(eusilc)), eusilc)
dataset1$pl085 <- 12 * trunc(runif(nrow(dataset1), 0, 2))
dataset1$month_at_work <- 12 * trunc(runif(nrow(dataset1), 0, 2))
    
# Full population
d <- linarr(Y = "eqIncome", Y_den = "eqIncome",
            id = "IDd", age = "age",  
            pl085 = "pl085", month_at_work = "month_at_work",
            weight = "rb050",  Dom = NULL,
            dataset = dataset1, order_quant = 50L)
d$value
    
## Not run: 
# By domains
dd <- linarr(Y = "eqIncome", Y_den = "eqIncome",
             id = "IDd", age = "age",  
             pl085 = "pl085", month_at_work = "month_at_work",
             weight = "rb050",  Dom = "db040",
             dataset = dataset1, order_quant = 50L)
 dd
## End(Not run)