  This paper deals with the problem of evaluating the causal effect using
observational data in the presence of an unobserved exposure/ outcome variable,
when cause-effect relationships between variables can be described as a
directed acyclic graph and the corresponding recursive factorization of a joint
distribution. First, we propose identifiability criteria for causal effects
when an unobserved exposure/outcome variable is considered to contain more than
two categories. Next, when unmeasured variables exist between an unobserved
outcome variable and its proxy variables, we provide the tightest bounds based
on the potential outcome approach. The results of this paper are helpful to
evaluate causal effects in the case where it is difficult or expensive to
observe an exposure/ outcome variable in many practical fields.
