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Decrements: rates by benefit

Active decrements (other than retirement rates, mortality rates in U.S. Qualified and Canadian mode funding valuation assumptions, and termination rates in German mode assumptions) allow the option to specify "<rates by benefit>". In this case, one of the "standard" causes of decrement (i.e. termination, death, or disability) is subdivided into different sets of rates for different Benefit Definitions. This can be useful, for example,when different rates are assumed and different benefits are provided in the case of disability or death in the line of duty, as opposed to disability or death due to other causes. In addition, an option is available to apply the "<total decrement>" to a given benefit. The total decrement for a member will then be calculated as the sum of the unique rate tables for benefits for which the member is eligible according to the Benefit Definitions' selection expressions.

For example, consider a public pension plan covering both firefighters and police officers. The plan offers different benefits for these two classifications of participants, and furthermore, the plan offers different disability benefits for those who become disabled in the line of duty versus those who become disabled due to other causes. There is additionally a supplemental benefit available to all participants, regardless of employee classification or the type of disability decrement. The assumed disability rates in this situation could be input as follows:


Assuming that the Benefit Definitions with names beginning "Fire" have selection expressions excluding participants who are police officers, and similarly that the Benefit Definitions with names beginning "Police" have selection expressions excluding participants who are firefighters, the total disability rates for firefighters will be the sum of the tables enumerated as 1 and 3 in the screenshot above, and the total disability rates for police officers will be the sum of the tables enumerated as 2 and 3 in the screenshot above.


Note that if you specified under the Decrements topic that active decrements are not probabilities (i.e., either they should all be adjusted for competing decrements or only mortality should be adjusted for competing decrements), these tables will be summed into a total disability decrement before being adjusted for competing decrements. That is, the total disability decrement above (i.e., the sum of either tables 1 and 3 or tables 2 and 3) is the variable  referenced by the Decrements: rates vs. probabilities Technical Reference article, the absolute rate of decrement due to disability in a multiple decrement environment. The individual rate tables above are never adjusted prior to being summed into a total disability decrement. 
This actuarial assumption is mathematically identical to the following process, which does not use the "rates by benefit" functionality:
  1. Creating two disability rate tables representing total disability rates for firefighters and police officers, equal to the sum of tables 1 and 3, and 2 and 3, respectively.
  2. Varying disability rates by a coded database field, with the total disability rates applied separately to firefighters and police officers.
  3. Applying post-decrement probabilities to the first four benefits above. The post-decrement probability for the benefit "Fire: Line of duty" would be equal to the ratio of the rates in rate table 1 divided by the total disability rates for firefighters. The other three post-decrement probabilities would be analogous ratios of rates divided by the total applicable disability rates.