Nicholas Jewell on capture-recapture

Here we enjoy our last few moments with Nicholas Jewell. Most of the conversation is about one specific point: the leveraging effect of errors in determining overlaps between lists of war dead.

Let’s illustrate Nicholas’ point with an extremely simple example. For ease of exposition I will identify individual war deaths with numbers.

List 1 contains the following deaths – 1, 2 3

List 2 contains the following deaths – 2, 3, 4, 5

The two lists combined contain 5 unique deaths – 1, 2, 3, 4 and 5. 2 deaths appear on both lists – 2 and 3

The capture-recapture estimate for the total number of deaths is

(3 x 4)/2 = 6

Thus, we estimate that there is 1 death not captured on either list.

Now suppose we make a mistake in matching deaths across lists. In particular, we classify death 2 on list 1 as different from death 2 on list 2. This could happen if, for example, we match based on names but the name of death 2 is misspelled on one of the lists. Or maybe there is a coding error that gets the location of death 2 wrong on one of the lists.

This failure to match death 2 across the lists causes two separate problems with our estimate.

Mistake 1 we think that the two lists combined contain 6 unique deaths when, in reality, they only contain 5

Mistake 2 we think that only one death appears on both lists when, in reality, 2 deaths appear on both lists.

Our mistaken capture-recapture estimate is now

(3 x 4)/1 = 12

So our mistaken estimate exceeds the correct estimate by 6. 1 out of these 6 comes from mistake 1 while 5 out of the 6 come from mistake 2. This big effect of mistake 2 is the leveraging effect that Nicholas stresses.