Identification region of the potential outcome distributions under instrument independence [report]

Toru Kitagawa
2009 unpublished
This paper examines identi...cation power of the instrument exogeneity assumption in the treatment e¤ect model. We derive the identi...cation region: The set of potential outcome distributions that are compatible with data and the model restriction. The model restrictions whose identifying power is investigated are (i) instrument independence of each of the potential outcome (marginal independence), (ii) instrument joint independence of the potential outcomes and the selection heterogeneity,
more » ... (iii) instrument monotonicity in addition to (ii) (the LATE restriction of Imbens and Angrist (1994)), where these restrictions become stronger in the order of listing. By comparing the size of the identi...cation region under each restriction, we show that the joint independence restriction can provide further identifying information for the potential outcome distributions than marginal independence, but the LATE restriction never does since it solely constrains the distribution of data. We also derive the tightest possible bounds for the average treatment e¤ects under each restriction. Our analysis covers both the discrete and continuous outcome case, and extends the treatment e¤ect bounds of Balke and Pearl (1997) that are available only for the binary outcome case to a wider range of settings including the continuous outcome case.
doi:10.1920/wp.cem.2009.3009 fatcat:kyj2szhcarhdtnosagr7uq6kf4