Partial Identification of Local Average Treatment Effects with an Invalid Instrument

We derive nonparametric bounds for local average treatment effects without requiring the exclusion restriction assumption to hold or an outcome with a bounded support. Instead, we employ assumptions requiring weak monotonicity of mean potential outcomes within or across subpopulations defined by the values of the potential treatment status under each value of the instrument. We illustrate the identifying power of the bounds by analyzing the effect of attaining a GED, high school, or vocational degree on subsequent employment and weekly earnings using randomization into a training program as an invalid instrument.