Harnessing Genetic Variants for Local Average Treatment Effect Estimation

When multiple instruments are available, conventional instrumental variable estimators aggregate across potentially heterogeneous margins of compliance and may yield effects that lack a clear economic interpretation. The problem is compounded when some instruments violate the exclusion restriction, as is common in certain empirical contexts such as those using genetic variants as instrumental variables. We propose a clusteringbased plurality framework for instrumental variable estimation that jointly addresses instrument heterogeneity and invalid instruments. Rather than imposing a single common causal parameter, our approach groups instruments according to similarity in first-stage and applies a plurality rule on subgroups with similar reduced-form to identify locally valid subsets. This yields a collection 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 where all individuals are exposed to all genetic variants. We illustrate the method in a twosample Mendelian Randomization analysis of the causal effect of educational attainment on smoking participation. Our results confirm a negative causal effect of education on smoking that remains robust under pleiotropy-robust estimators, while revealing substantial heterogeneity across instrument defined margins that is masked by pooled IV approaches. The framework provides a unified way to interpret and validate high-dimensional instruments in the presence of both treatment effect heterogeneity and potential violations of exclusion.