The study of identification has been clearly linked to the design of experiments. In a well-designed experiment the treatment group and the control group are similar in every aspect, except for the treatment. The difference in response may therefore be attributed to the treatment and the parameters of interest are identified. An extensive study of the identifiability conditions for the simultaneous equations models under various assumptions about the underlying structures was provided by Fisher. This chapter discusses the development of the subject since the publication of Fisher's book. It discusses the basic concepts of identification and some identifiability criteria for contemporaneoussimultaneous equation models under linear constraints. The chapter discusses criteria for models subject to nonlinear continuous differentiable constraints and covariance restrictions with special emphasis on the applications to errors in variables and variance components models. The Bayesian view on identification is also discussed in the chapter.
