The Causal Interpretation of Two-Stage Least Squares with Multiple Instrumental Variables / Magne Mogstad, Alexander Torgovitsky, Christopher R. Walters.

Format:

Book

Author/Creator:

Mogstad, Magne.

Contributor:

National Bureau of Economic Research.

Torgovitsky, Alexander.

Walters, Christopher R.

Series:

Working Paper Series (National Bureau of Economic Research) no. w25691.

NBER working paper series no. w25691

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2019.

Summary:

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.

Notes:

Print version record

March 2019.