2SLS with Multiple Treatments
Manudeep Bhuller () and
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We study what two-stage least squares (2SLS) identifies in models with multiple treatments and multiple instruments under treatment effect heterogeneity. Two testable conditions are shown to be necessary and sufficient for 2SLS to identify a positively weighted sum of individual treatment effects: monotonicity and no cross effects. For just-identified models, these conditions imply that (i) each instrument affects exactly one treatment choice and (ii) choice behavior can be described by single-peaked preferences (for ordered treatments) or by preferences where the excluded treatment is always either the best or the next-best alternative (for unordered treatments). For overidentified models, these conditions need to hold only on average across realizations of the instruments. The conditions are satisfied in a single-index threshold-crossing model under an easily testable linearity condition. We illustrate how our results can be used to assess the validity of 2SLS with multiple treatments in applications on the returns to educational choices and feedback effects in judicial decision-making.
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