IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Mortality projection
In the Lee-Carter model log m(x,t) = a(x) + b(x)k(t) + e(x,t), what does the parameter b(x) represent?
b(x) measures how sensitive the log mortality rate at age x is to changes in the period index k(t). Ages with larger b(x) improve faster. The average age pattern of log mortality is captured by a(x), not b(x).
- AThe average level of log mortality at age x over the fitting period
- BThe sensitivity of the log mortality rate at age x to changes in the period index k(t)Correct
- CThe projected value of the period index in future years
- DThe cohort effect for people born in year t minus x
- The variance of the random error at age x
Explanation
b(x) is the age-specific loading on the time index k(t). It shows how fast log mortality at age x moves when k(t) changes. The average level of log mortality is a(x), not b(x).
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