### Simulating the Future

#### (Jan 13, 2015)

This blog has two aims: first, to describe how we go about simulation in the Projections Toolkit; second, to emphasize the important role a model has in determining the width of the confidence interval of the forecast.

We use US male mortality data for years 1970 to 2009 downloaded from the Human Mortality Database. Figure 1 shows the observed log mortality. Unlike UK mortality (which shows accelerating improvements in log mortality over the same period) the US improvement is perfectly well described by a straight line. We fit the simplest of models: $$y_j = a + b x_j + \epsilon_j$$, where $$x_j$$ is year $$j$$, $$y_j = \log(d_j/e_j)$$ with $$d_j$$ the observed number of deaths in year $$j$$ and $$e_j$$ the corresponding…