Let indicate a recent birthday event, indicate a social gathering, and denote subsequent household COVID-19 infection. The standard instrumental variable conditions are:
- Instrument relevance: changes the probability or intensity of .
- Instrumental-variable independence: conditional on chosen baseline covariates, birthday timing is independent of unmeasured causes of infection and of the relevant potential outcomes.
- The exclusion restriction: affects only through the social gathering .
- For a local average treatment effect, instrumental-variable monotonicity excludes households that would hold a gathering without a birthday event but would suppress it because of one.
The usual consistency in causal inference, well-defined exposure, and absence of relevant interference in causal inference are also needed to interpret the result causally.
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