Select and Ultimate Mortality Tables

Definition

A select-and-ultimate table is an actuarial mortality table structured by two dimensions: attained age and duration since a qualifying entry event. For disability insurance (DI) beneficiaries, the entry event is entitlement. The "select" period covers the first 10 years on the rolls, during which duration independently predicts mortality; after that is the "ultimate" period, where attained age alone drives the death probability.

Key Ideas

Standard age-only mortality tables are inadequate for populations defined by a qualifying entry event, because mortality conditional on recent entry is radically different from mortality conditional on long survival.
The standard notation is $q_{[x]+t}$ : the death probability for someone who entered at age $x$ and has survived $t$ additional years. $q_{[35]+0} \neq q_{[35]+7}$ , even though both describe someone now in their mid-30s or 40s.
The select period captures a biological/statistical reality: new entrants are acutely ill; survivors have already demonstrated relative resilience. This is sometimes called the "select effect" or "frailty selection."
After the select period, duration no longer adds predictive power and the table collapses to age-only ("ultimate") rates.
Frailty selection applies within early retirees too: Waldron (2001) first established that men claiming retired-worker benefits at exactly age 62 face $38\%$ greater odds of dying than age-65+ claimants — with a further discontinuity between exact-62 and men retiring just months later identifying a quasi-disability subgroup (workers too ill for continued employment but unable to qualify for DI, clustering at the first eligible claiming age). Waldron (2004) formalizes this as a three-group trichotomy. A benefit-optimization mechanism operates alongside quasi-disability: the shortest-lived workers self-select into the earliest claiming age because the actuarial reduction is implicitly favorable for those with below-average life expectancy. The question for any Social Security (SS) subpopulation is therefore never whether they are sick in absolute terms, but how their mortality compares to the reference population — exactly the question select-and-ultimate tables are designed to answer. The age-62 mortality discontinuity recurs in Fitzpatrick and Moore (2017).

How It Works

Structure

For each sex, Office of the Chief Actuary (OACT) produces a grid of death probabilities with:

Rows: age at entitlement ( $x$ )
Columns: duration on the rolls ( $t = 0, 1, 2, \ldots, 9$ for the select period; then age-only ultimate rates for $t \geq 10$ )

Each cell $q_{[x]+t}$ gives the probability of dying in the next year, conditional on: (a) having entered DI at age $x$ , (b) having survived $t$ years on the rolls, and (c) still being an active DI beneficiary (not recovered or converted to Old-Age and Survivors Insurance (OASI)).

Multiple-Decrement Environment

DI beneficiaries can exit in three ways — death, recovery, or conversion to retirement benefits at Full Retirement Age. The mortality tables are constructed in a multiple-decrement framework: $q_{[x]+t}$ is the probability of dying given survival in the DI program, with recovery and conversion treated as competing decrements. This means the tables condition on continued DI enrollment, not just survival.

The Select Effect, Quantified

Table 3 of Meseguer (2021) illustrates the magnitude directly, using life expectancy at two duration snapshots vs. the general population:

Age	Duration	Men (mortality ratio)	Women (mortality ratio)
50	Year 0	$8.5\times$	$9.9\times$
50	10+ yrs	$3.9\times$	$4.5\times$
35	Year 0	$\approx 18.5\times$	$\approx 30\times$

The gap between year- $0$ and year- $10{+}$ ratios is the select effect: roughly halving the excess mortality ratio over 10 years of survival. This does not mean beneficiaries got healthier — it means the sickest died earliest, leaving a progressively more resilient survivor pool.

OACT Methodology Evolution

Earlier studies (Nos. $74$ – $93$ , $1970$ s): 5-year select period — duration tracked for years $0$ – $4$ , then ultimate.
Later studies (Nos. $114$ – $125$ , $1990$ s onward): 10-year select period — duration tracked for years $0$ – $9$ , then ultimate. This change reflected empirical evidence that duration effects persisted beyond year $5$ .

This methodological shift makes direct cross-era table comparisons awkward; any apparent trend spanning the two eras must account for the change in select-period length.

Why It Matters

For program cost estimation: Using age-only tables for a DI-like population would systematically misstate costs. New entrant mortality is far higher than average beneficiary mortality; failing to track duration conflates these.
For interpreting mortality trends: When the paper reports "mortality improvement," it must be interpreted within duration bins — year- $0$ improvement vs. year- $10{+}$ improvement can trend differently and reflect different phenomena.
For policy: The select structure shows that the 5-month waiting period (which excludes claimants who die before entitlement) means year- $0$ mortality is slightly understated — the sickest claimants are never observed. See Period Mortality.

Period Mortality
DI Beneficiary Mortality
Office of the Chief Actuary
Eric Stallard — parallel multi-state Markov architecture for National Long-Term Care Survey (NLTCS) elderly disability; Stallard's disability-state-specific mortality rates use the same conceptual framework as OACT's select-and-ultimate tables, applied to the general elderly population rather than DI beneficiaries