## Never Too LATE, Part 1

In a post on his blog, Cornell’s Tom Pepinsky discusses the frequent lack of discussion of local average treatment effects (LATEs) in the political science literature:

On two separate occasions I have been told by reviewers to “remove the discussion of the local average treatment effect” from a manuscript under review. One reviewer did not seem to understand what the LATE is. The other wrote something along the lines of “everyone knows what the LATE is, so get on with it.”

What’s a LATE? Suppose you wanted to test the claim that “breakfast is the most important meal.” You would randomly select, say, 50 subjects and randomly assign them to the treatment and control groups.

You would then instruct the subjects in the treatment group told to eat breakfast for the duration of the study, whereas you would instruct the subjects in the control group to skip breakfast for the same length of time.

At the end of the study period, you would compare the average value of some indicator of health for those in the treatment group with the average value of the same indicator of health for those in the control group. The difference between the mean indicator in the treatment and control group is the average treatment effect (ATE).

### ATE vs. LATE

A statistically significant difference between the two averages would be incontrovertible evidence that breakfast is important to health, right? Not so fast.

Some of the subjects in the treatment group might not be hungry on most mornings, so they might decide to skip breakfast even though you told them not to. Likewise, some of the subjects in the control group might be hungry on most mornings, so they might decide to eat breakfast even though you told them not to.

We call these people noncompliers, because they fail to comply with the experimenter’s instructions. Similarly, we call compliers those people who comply with the experimenter’s instructions, i.e., those subjects in the control group who skip breakfast, and those subjects in the treatment group who eat breakfast.

Because of noncompliers, what you would actually end up with is a local average treatment effect (LATE) rather than the ATE. Intuitively, the LATE is the ATE for those subjects who were (i) induced to eat breakfast because they are assigned to the treatment group, or (ii) induced to skip breakfast because they are assigned to the control group. In other words, the LATE is the ATE for the sub-population of compliers. Imbens and Wooldridge (2007) have a great (if a bit old) discussion here (link opens a .pdf).

Moreover, note that it is very often impossible to tell who the compliers and noncompliers are, so that it is often impossible to tell the ATE from the LATE.

On Thursday, I will give a specific example where, unlike Tom, I was actually encouraged to include a discussion of the LATE by a referee.