# Never Too LATE, Part 2

I began this discussion on Tuesday with an example in order to define the concept of local average treatment effect (LATE).

In the words of Imbens and Wooldridge (2007), LATEs are “average effects for subpopulations that are induced by the instrument to change the value of the endogenous regressors.”

What prompted my wanting to write about LATE is a post on Tom Pepinsky’s blog, where Tom 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.”

I wanted to offer a counterpoint. As part of the peer-review process leading to the publication of a recent article of mine in *World Development*, one of the referees specifically asked me to include a discussion of whether what I was estimating was an ATE or a LATE.

### LATE, and Cross-Study Comparisons

In my discussion, I briefly touched upon the fact that the estimation of LATEs made comparing results across studies very difficult, a point which I would like to reiterate here.

Indeed, imagine that you want to study the impact of a treatment* *D on some indicator of welfare Y. With observational data, because D is endogenous to Y, any observed correlation between Y and D is just that, and you cannot draw the conclusion that D causes Y.

But suppose you have an instrumental variable Z for D, and suppose that Z is a valid instrument for D when looking at the causal relationship flowing from D to Y.

Is your estimate the be all, end all of the relationship between D and Y? Not exactly. Indeed, suppose that three of your colleagues also decide to look at the relationship between D and Y, and that each and every one of them has a valid instrument Z1, Z2, and Z3.

Because each instrument induces subjects to take up treatment D in different ways, it is entirely possible that you and your colleagues come up with different estimates of the impact of D on Y, since each instrument yields a LATE. And if instruments Z, Z1, Z2, and Z3 are valid, there is usually no way to tell which of the four estimated impacts is closest to the ATE, which makes the comparison of results across studies very difficult.

This new paper by Peter Aronow and Allison Sovey Carnegie offers some hope. Here’s the abstract:

Political scientists frequently use instrumental variables estimation to estimate the causal effect of an endogenous treatment variable. However, when the treatment effect is heterogeneous, this estimation strategy only recovers the Local Average Treatment Effect (LATE). The LATE is an average treatment effect for one subset of the population: units that receive treatment if and only if they are induced by an exogenous instrumental variable. Typically, researchers are interested in the average treatment effect (ATE) for the entire population of interest. In this paper, we highlight the important distinction between these two estimands and develop a simple and intuitive method for estimating the ATE even when treatment effects are heterogeneous. We apply our method to two published experiments in political science in which we demonstrate that the LATE can differ considerably from the ATE.

Hi Prof. Bellemare, I just want to check my understanding about LATE: LATE is just an estimate of ATE based on the choice of instrument, right? Because people respond to different instruments differently, we don’t really know what the true effect of the endogeneous variable is. So are we assuming instrument variables can change the effective treatment groups?

Thank you for your comment and question, Chuhang! You are right: for every different IV, you will (in principle) get a different LATE. Different instruments don’t change the effective treatment groups in an experimental setting (the experimenter chooses who is assigned to each of control and treatment groups). In an observational (i.e., nonexperimental) context, however, the IV does change who takes up a treatment or not, and the LATE measures the ATE on compliers (i.e., those who change their treatment-taking behavior because of the IV).

I was looking around your site and noticed broken links. You might want to change it.

Feedback like yours is not helpful without specific examples. Oh, and you might want to be more creative in your spamming.