This post presents a simple explanation of the concept of “local average treatment effects” in the context of instrumental variables estimation. I borrow shamelessly from the somewhat more advanced presentation in Imbens and Wooldridge’s lecture notes, which is a good place to look for further reading.
The basic idea underlying LATE is to acknowledge that different people (or different units more generally) generally have different causal effects for any given “treatment,” broadly defined. It is common to talk about “the” causal effect of, say, education on earnings, or interest rates on growth, or pharmaceuticals on health, but if different people respond differently to education or to medical treatments and different countries respond differently to macroeconomic interventions, it’s not clear what we mean by “the” causal effect. We can still talk coherently about distributions of causal effects, though, and we may be interested in estimated various averages of those causal effects. Local average treatment effects (LATEs) are one such average.
For concreteness, let’s suppose the government decides to lend a hand to empirical researchers by implementing the following goofy policy: a randomly selected group of high school kids are randomized to get an offer of either $0 or $5,000 to acquire a college degree. We wish to use this natural experiment to estimate “the” effect of getting a college degree on, say, wages. We collect data on all these folks comprised of: a dummy variable which equals one if person was offered $5,000 and zero if they were offered zero, a dummy variable which indicates the student actually received a college degree, and wages, .