Studies on the identification problem of the simultaneous economic models from viewpoint of unique determination of parameters (I)

Proceeding from the viewpoint that the parameters to be estimated should be uniquely determined, we definite the concepts of the distinction and identification of vectors such that under the basic assumptions of quite general nature, study the identification problem of the contemporaneous models and obtain a number of results. Among them, multicollinearity problem is treated as an identification problem. More noticeable in this paper is the idea of removing the usual assumption that no linear identities connect the exogenous variables. The one-step identification method and two-step identification are introduced. The usual major theorems about the identification for contemporaneous simultaneous models can be treated as special cases of our more general results. Also given in the paper are the concepts of almost identification and completely under identification. The proposal of the concepts of the distinction and identification of vectors is of great significance, in which the identification of economic models is abstractly included; further it has probability of linking up the relation between systems such as economic system, control system and biological system. In our following papers, we will study by using our viewpoints and methods the identification problems of the dynamic models (including the unstable ones), the nonlinear models, the error-shock models (also including the unstable ones) and obtain a number of theorems for the identification which are similar to contemporaneous models and are easy to verify.