Identification problem

With the identification problem is referred to in the statistics , especially in econometrics , the fact that one, several or all equations of a model can not be clearly identified, as several numerical specifications of the parameters represent a solution to the system.

It cannot then be found out which specification corresponds to the true structure of the model. The various specifications are equivalent to observation . This occurs above all when an equation contains all model variables, since it can then be produced as a linear transformation from the other equations.

Identifiability

A structure is identifiable when no other structure has the same reduced form , i.e. H. if the parameters of the structural form can be clearly deduced from parameters of the reduced form .

Possible solutions

Identification can be achieved either by adding more model variables or by excluding variables from individual equations. In this way the equations are linearly independent .

example

The model

{\ displaystyle y_ {1t} = \ alpha x_ {1t} + \ beta x_ {2t}}

{\ displaystyle y_ {2t} = \ omega y_ {1t} + \ gamma x_ {1t} + \ delta x_ {2t}}

{\ displaystyle y_ {3t} = \ xi y_ {1t} + \ phi x_ {1t} + \ psi x_ {3t}}

would not be identified because one can not decide for given observations which of the variables y one has now estimated. However, it would be identified if each equation contained a variable that is not contained in the others: ${\ displaystyle x_ {1,2}}$

{\ displaystyle y_ {1t} = \ alpha x_ {1t} + \ beta x_ {2t} + z_ {1}}

{\ displaystyle y_ {2t} = \ omega y_ {1t} + \ gamma x_ {1t} + \ delta x_ {2t} + z_ {2}}

{\ displaystyle y_ {3t} = \ xi y_ {1t} + \ phi x_ {1t} + \ psi x_ {3t} + z_ {3}}

Identification criteria

There are already two identification options from the example: counting criterion and ranking criterion

The counting criterion is usually sufficient. It says: G-1 model variables must be excluded from each of the G equations, then each equation and thus the model is identified. In the above example, G-1, i.e. two variables each, would have to be excluded. In the unidentified case, the second equation only excludes , the third only . ${\ displaystyle y_ {3}}$ ${\ displaystyle y_ {2}}$

In the modified case, the second equation excludes such as and and the third equation excludes such as and . The model is thus identified. ${\ displaystyle y_ {3}}$ ${\ displaystyle z_ {1}}$ ${\ displaystyle z_ {3}}$ ${\ displaystyle y_ {2}}$ ${\ displaystyle z_ {1}}$ ${\ displaystyle z_ {2}}$

literature

Peter von der Lippe: The identification problem in econometrics . In: University of Duisburg-Essen, Faculty of Economics (Ed.): Contributions to the discussion . No. 127 , July 2003 ( IDEAS entry with download option [accessed on January 28, 2011]).