  When observational data is available from practical studies and a directed
cyclic graph for how various variables affect each other is known based on
substantive understanding of the process, we consider a problem in which a
control plan of a treatment variable is conducted in order to bring a response
variable close to a target value with variation reduction. We formulate an
optimal control plan concerning a certain treatment variable through path
coefficients in the framework of linear nonrecursive structural equation
models. Based on the formulation, we clarify the properties of causal effects
when conducting a control plan. The results enable us to evaluate the effect of
a control plan on the variance from observational data.
