Glossary of economics research
Results of search for identification follow:
identification:
A parameter in a model is identified if and only if complete knowledge of the
joint distribution of the observed variables would be 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, as shown in
this discussion drawn from the elegant paper of
Gabrielsen (1978).
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.
"An identification problem occurs when a specifed set of assumptions
combined with unlimited observations drawn by a specified sampling process
does not reveal a distribution of interest." -- Manski, Charles F.
"Identification problems and decisions under ambiguity: empirical
analysis of treatment response and normative analysis of treatment
choice" Northwestern University Department of Economics and Institute for
Policy Research, September 1998, p. 2
Source: The New Palgrave: Econometrics, p 96; and Gabrielsen,
1978
Contexts: econometrics
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