Compute an actuarial service table from a personnel panel

Builds a multiple-decrement service table: for each age (and any group_cols you supply), the number of survivors (lx), person- years of service (Lx, Tx), and expected remaining years of service (ex) for a synthetic cohort experiencing today's age-specific empirical decrement rates at every future age.

This chains estimate_decrement_rates()'s pooled, age-indexed rates across age – a different axis from the time-pooling that function already did. By default the rates are graduated first via smooth_decrement_rates(), since the chain below requires a complete, gapless, reasonably stable qx curve to produce a sensible result.

Usage

compute_service_table(
  personnel,
  age_col,
  status_col,
  personnel_id_col,
  ref_date_col,
  group_cols,
  radix = 1e+05,
  smooth = FALSE,
  span = 0.75,
  personnel_dt = NULL
)

Arguments

personnel: A data.table (or data.frame/tibble, coerced automatically) containing the personnel panel. Passed straight through to estimate_decrement_rates().
age_col: A single string naming the age column.
status_col: A single string naming the employment status column. The value "active" identifies the "stayed" outcome that the survival chain is built from.
personnel_id_col: A single string naming the personnel identifier column.
ref_date_col: A single string naming the reference date column.
group_cols: A character vector of additional columns (e.g. gender, service type) to compute a separate service table for, or NULL for a single table over the whole population.
radix: Numeric. The size of the synthetic starting cohort at the youngest observed age. Purely a normalizing constant – it cancels out of ex and does not represent real people. Defaults to 100000.
smooth: Logical. Whether to graduate the decrement rates via smooth_decrement_rates() before chaining. Defaults to FALSE: the raw pooled rates are chained directly, unless a group_cols stratum has an age gap, in which case compute_service_table() smooths reactively (with a warning) regardless of this setting, since the chain cannot run on a gappy age sequence. Set to TRUE to always smooth up front, including for noise reduction on strata that have no gap at all.
span: Numeric. Forwarded to smooth_decrement_rates() when smooth = TRUE. Defaults to 0.75.
personnel_dt: Deprecated. Use personnel instead.

Value

A data.table with one row per age / group_cols:

age_col, group_cols: As supplied.
px: Probability of remaining active from age x to x+1.
lx: Survivors at age x, out of radix at the youngest age: \(l(x) = radix \prod_{y<x} p(y)\).
lx_next: Survivors at age x+1: \(l(x) \cdot p(x)\).
Lx: Person-years of service between age x and x+1: \((l(x) + l_{next}(x)) / 2\) (trapezoidal approximation, assuming exits are spread uniformly across the year).
Tx: Total remaining person-years of service from age x onward: \(\sum_{y \ge x} L(y)\).
ex: Expected remaining years of service at age x: \(T(x) / l(x)\).

Details

This is a stationary-cohort summary, not a projection of your real workforce headcount. lx describe a hypothetical synthetic cohort that experiences today's cross-sectional age-specific rates at every future age – they are not a forecast of how many of your actual current employees will retire in each future calendar year. For that, the raw output of estimate_decrement_rates() (applied to your real current headcount by age, stepped forward through calendar time) is the right input, not this table.

Caveat. The literal string "active" is hardcoded as the status_col value the survival chain is built from – inherited directly from estimate_decrement_rates() and .compute_decrement_pair(), where the same caveat applies.

Examples

if (FALSE) { # \dontrun{
library(data.table)

personnel_dt <- data.table(
  personnel_id = c("P1", "P2", "P1", "P2"),
  ref_date = as.Date(c("2020-01-01", "2020-01-01", "2021-01-01", "2021-01-01")),
  age = c(60L, 45L, 61L, 46L),
  employment_status = c("active", "active", "pensioner", "active"),
  gender = c("M", "F", "M", "F")
)

compute_service_table(
  personnel_dt = personnel_dt,
  age_col = "age",
  status_col = "employment_status",
  personnel_id_col = "personnel_id",
  ref_date_col = "ref_date",
  group_cols = "gender"
)
} # }