Don't cut corners

(Oct 7, 2014)

An important class of mortality-projection models is the Cairns-Blake-Dowd (CBD) family. These models are described in a landmark paper by Cairns et al (2009).  Three of the most important of the CBD models are M5, M6 and M7, as defined below for age \(x\) and calendar year \(y\):

M5 \(\log \mu_{x,y} = \kappa_{0,y} + \kappa_{1,y}S(x)\)
M6 \(\log \mu_{x,y} = \kappa_{0,y} + \kappa_{1,y}S(x) + \gamma_{y-x}\)
M7 \(\log \mu_{x,y} = \kappa_{0,y} + \kappa_{1,y}S(x) + \gamma_{y-x} + \kappa_{2,y}Q(x)\)

where:

\(\eqalign{S(x) &= \left(x - \bar x\right)\\ Q(x) &= \left(x - \bar x\right)^2-\hat\sigma^2\\ \hat\sigma^2 &= \displaystyle\frac{1}{n_x}\sum_{i=1}^{n_x} (x_i-\bar x)^2}\)

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Tags: cohort effect, Cairns-Blake-Dowd, CBD, M6 model, M7 model

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