When is TSLS Actually LATE?

This paper asks: when does two-stage least squares (TSLS) with covariates actually estimate a local average treatment effect (LATE) — a non-negatively weighted average of causal effects for compliers only? The authors show that the answer is: almost never in practice.

The paper’s central theoretical result (Theorem 1) is that a linear IV estimand is weakly causal — meaning it cannot have the wrong sign relative to all underlying treatment effects — if and only if the IV specification has “rich covariates,” defined as the condition that the linear projection of the instrument onto the covariates, L[Z|X], equals the true conditional mean E[Z|X] at every covariate value. Saturated specifications (nonparametric covariate control) always satisfy rich covariates. Outside of two special cases — saturated covariates or an instrument that is mean-independent of covariates — rich covariates is an implicit parametric assumption that can fail.

Christine Blandhol | Macro Paper Warehouse

When is TSLS Actually LATE?