Flowing Data has a post about early retirement which provides an opportunity to highlight, yet again, the discontent of being averaged (Chapter 1 of **Numbers Rule Your World**).

The post comes with this chart. For each country and each gender, he compares the life expectancy and the average retirment age, the difference between which yielding the "number of years in retirement".

Unfortunately, one should be careful when taking the difference between two averages. This is because the population that underlies one average may not be the same one that underlies the other average.

The life expectancy is clearly an average over the entire population. Average retirement age, however, is almost certainly an average over people who live to at least retirement age. Thus, taking their difference doesn't make sense. What we need is the life expectancy of those people who at least live to see retirement.

The (somewhat) funny result of taking the difference of those averages can be seen in the case of Mexican men (the bottom blue bar). By this metric, the average years in retirement for Mexican males is essentially zero: they work till they die.

Another way to see that this metric can't work: if the average years in retirement is zero, then some will die after they retire while others will retire after they die! Retiring after death is quite literally captured when you substract the average retirement age from the average life expectancy!

***

By locating the right data, one can improve this analysis. What is needed is a life table. (one source is here). From this table, we can find for every age, the expected remaining life.

Take all the age groups above the retirement age, compute weights for each age group as a proportion of all remaining age groups, use these weights to compute the weighted average remaining life.

For Mexican males, this yields about 7 years, assuming the retirement age is indeed 75 as shown on the chart above.

P.S. See also the comments from the Flowing Data readers.

An alternative way of showing such data would be to use a box plot for the age at death and show retirement age on top of this. From a pure-gut-feel, the median shown in a box plot would be a more appropriate average than the mean for age. Maybe add a value of percentage of population who reach retirement.

I'd also prefer that the male / female were on the same axis to enable easier comparison

Posted by: Andrew Marritt | 05/12/2011 at 08:20 AM

+1 for plotting male and female in the same direction. I know these kind of "butterfly" plots are popular among people who study population metrics, but in truth, they make comparisons very difficult between the left and right wings of the chart.

Posted by: Jon Peltier | 05/12/2011 at 08:40 AM

Hmm, come to think of it, it makes sense. Since life expectancy is different in each country, retirement age also varied. Also, the measure of poverty must be considered. In some countries, retirement is simply not an option. Of course, every working class citizen's goal is to retire to a prosperous life, no matter what age.

Posted by: Neil Fiorenza | 05/30/2011 at 02:36 PM

Hmm, Neil is right when he said "every working class citizen's goal is to retire to a prosperous life, no matter what age." If you continue on working, it may mean two things: you either enjoy what you are doing, or you need money for a living.

Posted by: Frank Damon | 10/17/2011 at 01:17 PM