Non-parametric Analysis
When the form of the structural equations is unknown, an instrumental variable can still be defined through the equations:
where and are two arbitrary functions and is independent of . Unlike linear models, however, measurements of and do not allow for the identification of the average causal effect of on, denoted ACE
Balke and Pearl derived tight bounds on ACE and showed that these can provide valuable information on the sign and size of ACE.
In linear analysis, there is no test to falsify the assumption the is instrumental relative to the pair . This is not the case when is discrete. Pearl (2000) has shown that, for all and, the following constraint, called "Instrumental Inequality" must hold whenever satisfies the two equations above:
Read more about this topic: Instrumental Variable
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