Mostly Harmless Econometrics: An Empiricist’s Companion

Generalizing LATE

The LATE theorem applies to a stripped-down causal model where a single dummy instrument is used to estimate the impact of a dummy treatment with no covariates. We can generalize this in three important ways: multiple instruments (e. g., a set of quarter-of-birth dummies), models with covariates (e. g., controls for year of birth), and models with variable and continuous treatment intensity (e. g., years of schooling). In all three cases, the IV estimand is a weighted average of causal effects for instrument-specific compliers. The econometric tool remains 2SLS and the interpretation remains fundamentally similar to the basic LATE result, with a few bells and whistles. 2SLS with multiple instruments produces a causal effect that averages IV estimands using the instruments one at a time; 2SLS with covariates produces an average of covariate - specific LATEs; 2SLS with variable or continuous treatment intensity produces a weighted average derivative along the length of a possibly nonlinear causal response function.