The Problem of Identification Cont SEM....

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The Problem of Identification

The problem of identification means whether the structural parameters can be derived from reduced form parameters. The choice of estimation depends on the identification status of the model. The identification is used as advance strategy to check whether the structural parameters can be obtained from reduced form parameters. 

There are two possible situations.

1.      Exactly Identified

If all structural parameters can be retrieved in a unique manner from reduced form parameters, an equation is exactly identified. The reduced form parameters in this situation can be estimated using the indirect least squares (ILS) method.

2.      Un Identified

If all structural parameters cannot be uniquely determined from reduced form parameters, the equation is under identified.

Unidentified SEM can be further divide into two.

i.                    Over-identified

A model is considered to be over identified if it does not have a unique estimate for at least one structural parameter generated from reduced form parameters. Under identified.

ii.                  Under identified

A model is under identified if all structural parameters can not be derived from reduced form parameters.

The following example can be used to clarify the concepts of exactly and under identified:

$$

qd = a1 + b1 P + C1 Y + u1 → Demand Equationq

$$\begin{gathered} \text{ \\ qs = a2 + b2 P + C2 W + u2→Supply Equation} \end{gathered}$$

$$\begin{gathered} \text{ \\ <br>} \end{gathered}$$

$$\begin{gathered} \text{ \\ qd = qs → Equilibrium \\ } \end{gathered}$$