The bpbounds command and its immediate form, bpboundsi, calculate the nonparametric bounds for the average causal effect (ACE) of Balke & Pearl (1997) for the all binary instrumental variable model (i.e. exposure/treatment X, outcome Y, and instrumental variable Z all binary).
The commands also calculate the bounds on the intervention probabilities; P(Y|do(X=0)), P(Y|do(X=1)); and the causal risk ratio.
The commands calculate these quantities for several extensions (Ramsahai, 2007 & 2008):
- bivariate/marginal data (
bpboundsionly), - models with a three category instrument,
- assuming a monotonic effect of Z on X.
To install, issue in Stata (in versions 13 and above):
net install bpbounds, from("https://raw.github.com/remlapmot/bpbounds-stata/master/") - Balke A, Pearl J. 1997. Bounds on treatment effects from studies with imperfect compliance. Journal of the American Statistical Association 92(439): 1172-1176. DOI: 10.1080/01621459.1997.10474074
- Ramsahai R. 2007. Causal Bounds and Instruments. In Proceedings of the Twenty-Third Annual Conference on Uncertainty in Artifcial Intelligence (UAI-07), 310-317. Corvallis, Oregon: AUAI Press. http://uai.sis.pitt.edu/papers/07/p310-ramsahai.pdf
- Ramsahai R. 2008. Causal Inference with Instruments and Other Supplementary Variables. Ph.D. thesis, Department of Statistics, University of Oxford. URL