Working Paper: NBER ID: w25691
Authors: Magne Mogstad; Alexander Torgovitsky; Christopher R. Walters
Abstract: 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 show that the 2SLS estimate retains a causal interpretation as a positively-weighted average of the effects of college attendance among complier groups.
Keywords: Instrumental Variables; Two-Stage Least Squares; Causal Interpretation; Monotonicity Condition; Heterogeneous Treatment Effects
JEL Codes: C01; C26
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| monotonicity condition (D11) | causal interpretation of 2SLS estimates (C20) |
| multiple instruments (C36) | restriction on choice behavior (D01) |
| partial monotonicity (D81) | causal interpretation of 2SLS estimand (C20) |
| unobserved heterogeneity (C21) | causal interpretation of 2SLS estimand (C20) |
| 2SLS estimates (C20) | causal interpretation among complier groups (C22) |
| unconditional correlations between treatment and instruments (C26) | verify causal interpretation of 2SLS estimand (C20) |