Partial Identification of Local Average Treatment Effects With an Invalid Instrument

We derive nonparametric bounds for local average treatment effects (LATE) without imposing the exclusion restriction assumption or requiring an outcome with bounded support. Instead, we employ assumptions requiring weak monotonicity of mean potential and counterfactual outcomes within or across subpopulations defined by the values of the potential treatment status under each value of the instrument. The key element in our derivation is a result relating LATE to a causal mediation effect, which allows us to exploit partial identification results from the causal mediation analysis literature. The bounds are employed to analyze the effect of attaining a GED, high school, or vocational degree on future labor market outcomes using randomization into a training program as an invalid instrument. The resulting bounds are informative, indicating that the local effect when assigned to training for those whose degree attainment is affected by the instrument is at most 12.7 percentage points on employment and $64.4 on weekly earnings.