Harnessing Genetic Variants for Local Average Treatment Effect Estimation

When multiple instruments are available, conventional instrumental variable estimators aggregate across heterogeneous margins of compliance, often yielding effects without a clear economic interpretation. This issue worsens when some instruments violate the exclusion restriction, as in settings using genetic variants. We propose a clustering-based plurality framework for instrumental variable estimation that addresses both instrument heterogeneity and invalid instruments. Rather than imposing a single causal parameter, our method groups instruments by similarity in the first stage and applies a plurality rule on subgroups with similar reduced-form relationships to identify locally valid subsets. This produces a set of margin-specific local average treatment effects instead of a single pooled estimate. We extend plurality-based identification to settings with non-mutually exclusive instruments, such as Mendelian Randomization designs. We illustrate the method in a two-sample Mendelian Randomization study of the effect of education on smoking. Results confirm a negative causal effect while revealing substantial heterogeneity across instrument-defined margins, masked by pooled IV approaches.