linarr: 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")

Arguments

Numerator variable (for gross pension income). One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector with only one TRUE value (length of the vector has to be th

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 or logical vector with only one TRUE value (length of the vect

Optional variable for unit ID codes. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector with only one TRUE value (length of the vector has to be the same as

weight

Optional weight variable. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector with only one TRUE value (length of the vector has to be the same as the column

age

Age variable. One dimensional object convertible to one-column data.table or variable name as character, column number or logical vector with only one TRUE value (length of the vector has to be the same as the column count of

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 or logical vector with only one TRUE value (

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

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 or logical vector with only one TRUE value (length of the vector ha

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 vec

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 or logical vecto

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 me

var_name

A character specifying the name of the linearized variable.

Value

A list with four objects are returned:
valueA data.table containing the estimated the aggregate replacement ratio.
linA data.table containing the linearized variables of the aggregate replacement ratio.

Details

The implementation strictly follows the Eurostat definition.

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 http://www5.statcan.gc.ca/bsolc/olc-cel/olc-cel?lang=eng&catno=12-001-X19990024882.

Examples

Run this code

data(eusilc)

dati <- data.table(IDd = 1:nrow(eusilc), eusilc)
dati$pl085 <- 12*trunc(runif(nrow(dati),0,2))
dati$month_at_work <- 12*trunc(runif(nrow(dati),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=dati, order_quant=50)
d$value

# 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=dati, order_quant=50)
dd

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