2SLS Multiple versus Single Instrumental Variable

Question

To address endogeneity, I was wondering whether it may be easier to find many instrumental variables that predict a single instrumental variable, rather than finding a single instrumental variable. My rational is that these multiple instrumental variables would be more loosely correlated and therefore easier to find than a single instrumental variable.

Answer 1

I do not think that it would be easier to justify several instrumental variables rather than one. The reason is that the validity of each instrumental variable has to be base on some causal story about the world. The more instrumental variables you have, the more complex your story has to be. But it might be the case that two instrumental variables are likely to be exogenous, but not very likely, but that the interaction between them is very likely to be exogenous, conditioning on both of them. There are several examples in the literature in social science of instrumental variables constructed as interactions between plausible exogenous and relevant variables.