Identification of Causal Effects with Multiple Instruments: Problems and Some Solutions

Magne Mogstad, Alexander Torgovitsky, Christopher R. Walters

NBER Working Paper No. 25691
Issued in March 2019
NBER Program(s):Labor Studies Program, Technical Working Papers

Empirical researchers often combine multiple instruments for a single treatment using two stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple instruments is that the 2SLS estimand can still be interpreted 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 instruments under a weaker, partial monotonicity condition. This condition is implied by standard choice theory and allows for richer heterogeneity. First, we show that the weaker partial monotonicity condition can still suffice for the 2SLS estimand to be a positively-weighted average of LATEs. We characterize a simple sufficient and necessary condition that empirical researchers can check to ensure positive weights. Second, we develop a general method for using multiple instruments to identify a wide range of causal parameters other than LATEs. The method allows researchers to combine multiple instruments to obtain more informative empirical conclusions than one would obtain by using each instrument separately.

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Document Object Identifier (DOI): 10.3386/w25691

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