Definition of Identified / Identification: A parameter in a model is identified if and only if complete knowledge of the joint distribution of the observed variables gives enough information to calculate the parameter exactly.

If the model has been written in such a way that its parameters can be consistently estimated from the observables, then the parameters are identified. There exist cases (mostly obscure) where parameters are identified but consistent estimators are not possible.

A model is identified if there is no observationally equivalent model. That is, potentially observable random variables in the model have different distributions for different values of the parameter.

Formally:

Let h^* be a vector of unknown functions and distributions in an econometric model.

Let H denote a set which h^* is known to belong. H is defined by the model's restrictions.

Let P(h) denote the joint distribution of observable variables of the model for various elements of h in H. The distribution for the actual data will be assumed to be P(h^*).

Now, vector h^* is identified within H if for all h in H such that h<>h^* it is true that P(h)<>P(h^*).

Note: Linear models are either globally identified or there are an infinite number of observably equivalent ones. But for models that are nonlinear in parameters, "we can only talk about local properties." Thus the idea of locally identified models, which can be distinguished in data from any other 'close by' model. (Econterms)

Terms related to Identified / Identification:

• Locally identified