The Identification Region of the Potential Outcome Distributions under Instrument Independence

This paper examines the identifying power of instrument exogeneity in the treatment effect model. We derive the identification region of the potential outcome distributions, which are the collection of distributions that are compatible with data and with the restrictions of the model. We consider identification when (i) the instrument is independent of each of the potential outcomes (marginal independence), (ii) the instrument is independent of each of the potential outcomes jointly (joint independence), and (iii.) the instrument is independent of each of the potential outcomes jointly and is monotonic (the LATE restriction). By comparing the size of the identification region under each restriction, we show that joint independence provides more identifying information for the potential outcome distributions than marginal independence, but that the LATE restriction provides no identification gain beyond joint independence. We also, under each restriction, derive sharp bounds for the Average Treatment Effect and sharp testable implication to falsify the restriction. Our analysis covers discrete and continuous outcome cases, and extends the Average Treatment Effect bounds of Balke and Pearl (1997) developed for the dichotomous outcome case to a more general setting.

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