# Possible Causal Effects: Enumeration and Estimation

We consider the identification and estimation of total causal effects from observational data and background knowledge, under the assumption of no latent variables. The underlying causal graph may be partially known, and a maximally oriented partially directed acyclic graph (MPDAG) is used to represent this partial knowledge. In these settings, the causal effect might not be identified, and algorithms like IDA and joint-IDA have been proposed to estimate all the possible effects under linearity assumptions. In the first part of this talk, I will describe an algorithm that enumerates a collection of sub-MPDAGs such that the effect is non-parametrically identified on each of them. Such enumeration of possible causal effects is complete and minimal. In the second part, I will consider efficient estimation of an identified possible effect. For simplicity, I will assume that the data arise from a linear structural equation model with independent errors (not necessarily Gaussian). I will show that, a simple estimator in the form of iterated least squares, is the most efficient among all regular estimators that are based on the sample second moment (e.g., IDA and joint-IDA estimators). This talk is based on joint work with Emilija PerkoviÄ‡.