Balke-Pearl nonparametric bounds for the average causal effect implemented in Stata

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 (bpboundsi only),
• models with a three category instrument,
• assuming a monotonic effect of Z on X.

Installation

To install, issue in Stata (in versions 13 and above):

net install bpbounds, from("https://raw.github.com/remlapmot/bpbounds-stata/master/") 

References

• 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