The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables

Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When effects are heterogeneous, common justification including IVs is that the 2SLS estimand can be given causal interpretation as positively weighted average of local (LATEs). This requires well-known monotonicity condition. However, we show with more than one instrument, this condition only satisfied if choice behavior effectively homogeneous. Based on finding, consider use under weaker, partial We characterize empirically verifiable sufficient and necessary conditions to LATEs monotonicity. apply these results an empirical analysis returns college instruments. standard at odds data. Nevertheless, our checks reveal estimate retains attendance among complier groups. (JEL C26, I23, I26, J24, J31, R23)