"Identification of Causal Effects with Multiple Instruments: Problems and Some Solutions"
Empirical researchers often combine multiple instruments for a single treatment using two stage least squares (2SLS). When treatment effects are heterogeneous, a common justication for combining instruments is that the 2SLS estimand can still be interpreted as a positively-weighted average of local average treatment effects (LATEs).
This justication requires the well-known monotonicity condition. However, we show that with more than one instrument, the monotonicity condition is only satised if the rates of substitution between distinct instruments are the same for all individuals. Based on this finding, we consider the use of multiple instruments under a weaker condition that does not require choice behavior to be homogenous. First, we show that the 2SLS estimand can still 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.