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

Magne Mogstad, Alexander Torgovitsky and Christopher Walters

No 25691, NBER Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C01 C1 C26 (search for similar items in EconPapers)
Date: 2019-03
New Economics Papers: this item is included in nep-ecm
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Published as Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, American Economic Association, vol. 111(11), pages 3663-3698, November.
Published as Magne Mogstad & Alexander Torgovitsky & Christopher R. Walters, 2021. "The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables," American Economic Review, vol 111(11), pages 3663-3698.

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Journal Article: The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables (2021)
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