## Analysis of the Binary Instrumental Variable Model

Citations: | 1 - 0 self |

### BibTeX

@MISC{Richardson_analysisof,

author = {Thomas S. Richardson and James M. Robins},

title = {Analysis of the Binary Instrumental Variable Model},

year = {}

}

### OpenURL

### Abstract

We give an explicit geometric characterization of the set of distributions over counterfactuals that are compatible with a given observed joint distribution fortheobservablesinthebinary instrumental variable model. This paper will appear as Chapter 25 in Heuristics, Probability and Causality: A Tribute to Pearl’s seminal work on instrumental variables [Chickering andPearl1996;BalkeandPearl 1997] for discrete data represented a leap forwards in terms of understanding: Pearl showed that, contrary to what many had supposed based on linear models, in the discrete case the assumption that a variable was an instrument could be subjected to empirical test. In

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Citation Context ...Likewise ∑ ( ∑ j p(y =j, x=1 | z =1− j) < j ⇔ 1 < ∑ j p(y =j, x=1 | z =j). ) p(x=1 | z =j) − 1 25Thus (b1) fails if and only if (b2) fails. ✷ This equivalence should not be seen as surprising since [=-=Bonet 2001-=-] states that the instrument inequalities (a2) and (b2) are sufficient for a distribution to be compatible with the binary IV model. This is not the case if, for example, X takes more than 2 states. 6... |

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