The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables
Christopher R. Walters
- American Economic Review (Forthcoming)
Empirical researchers often combine multiple instrumental variables (IVs) for a single
treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous,
a common justification for including multiple IVs is that the 2SLS estimand
can be given a causal interpretation as a positively-weighted average of local average
treatment effects (LATEs). This justification requires the well-known monotonicity
condition. However, we show that with more than one instrument, this condition can
only be satisfied if choice behavior is effectively homogenous. Based on this finding,
we consider the use of multiple IVs under a weaker, partial monotonicity condition.
We characterize empirically verifiable sufficient and necessary conditions for the 2SLS
estimand to be a positively-weighted average of LATEs under partial monotonicity. We
apply these results to an empirical analysis of the returns to college with multiple instruments.
We show that the standard monotonicity condition is at odds with the data.
Nevertheless, our empirical checks reveal that the 2SLS estimate retains a causal interpretation
as a positively-weighted average of the effects of college attendance among
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