Identification theory for high dimensional static and dynamic factor models

High dimensional factor models can involve thousands of parameters. The Jacobian matrix for identification is of a large dimension. It can be difficult and numerically inaccurate to evaluate the rank of such a Jacobian matrix. We reduce the identification problem to a small rank problem, which is easy to check. The identification conditions allow both linear and nonlinear restrictions. Under reasonable assumptions for high dimensional factor models, the small rank conditions are shown to be necessary and sufficient for local identification.