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:

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

The original…

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

Excel's Limits

(Jun 27, 2014)

We have written in the past about some of the reasons why we don't use Excel to fit our models.  However, we do use Excel for validation purposes - fitting models using two entirely separate tools is a good way of checking production code.  That said, there are some important limits to Excel, especially when it comes to fitting projection models.  Some of these limits are rather subtle, so it is important that an analyst is aware of all of Excel's limitations.

The first issue is that Excel's standard Solver feature won't work with more than 200 variables, i.e. parameters which have to be optimised in order to fit the model.  This is a problem for a number of important stochastic projection models, as shown in Table 1. …

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Tags: Excel, Lee-Carter, APC, CBD

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