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

51 Pages Posted: 26 Mar 2019 Last revised: 13 Mar 2023

See all articles by Magne Mogstad

Magne Mogstad

University of Chicago

Alexander Torgovitsky

University of Chicago

Christopher Walters

University of California, Berkeley - Department of Economics

Date Written: March 2019

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.

Suggested Citation

Mogstad, Magne and Torgovitsky, Alexander and Walters, Christopher, The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables (March 2019). NBER Working Paper No. w25691, Available at SSRN: https://ssrn.com/abstract=3359491

Magne Mogstad (Contact Author)

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Alexander Torgovitsky

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

Christopher Walters

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

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