Date: April 5th 2017, 4 pm - 5 pm
Place: B705


The problem of partially identified parameters occurs when the most we can estimate from the observed data – even with infinite samples – is in the form of bounds for the parameters. The problem occurs naturally in some causal-inference applications, for example, in estimating causal interaction between two risk factors and in estimating direct treatment effects in a randomized trial with imperfect compliance. For observational studies, such as in econometrics or epidemiology, the latter is known as the problem of establishing a causal effect using the instrumental-variable or Mendelian randomization method. Such a causal effect is only partially identified under non-parametric model assumptions. Current procedures include linear programming to get the estimated bounds, plus bootstrapping to get confidence intervals. I will describe some examples, and a likelihood-based procedure that automatically yields the interval estimate from the flat region, and show some theory that allows us to construct confidence intervals from this non-regular likelihood.