Tashkent institute of finance “Statistics and econometrics” department subject of econometrics phd jumayev Akbar Makhmudovich

The identification problem

• It is said to be exactly identified if unique numerical values of the structural parameters can be obtained.
• It is said to be overidentified if more than one numerical value can be obtained for some of the parameters of the structural equations.
• If this cannot be done, then wesay that the equation under consideration is unidentified, or underidentified.

The identification problem

• Rule for Identification
• If we denote as M-number of endogenous variables in the model, D-number of endogenous or predetermined variables in the model, the rule for identification states follow:

If D=M-1, equation is exactly or just identified

If D

If D>M-1, equation is overidentified

To illustrate the Rules for Identification, let us consider next examples.

• Example 3.

This model has two endogenous variables P and Q and no predetermined variables. To be identified, each of these equations must exclude at least M − 1 = 1 variable. Since this is not the case, neither equation is identified.

• Example 4.
• where It – income of the consumer
• In this model, Q and P are endogenous and I is exogenous. Applying the order condition given in Eq. (1), we see that the demand function is unidentified. On the other hand, the supply function is just identified because it excludes exactly M−1=1 variable It.

Example 5.

• (5)
• (6)
• wherePt-1 – price lagged one period
• Given that Pt and Qt are endogenous and It and Pt−1 are predetermined, Eq. (5) excludes exactly one variable Pt−1 and Eq. (6) also excludes exactly one variable It. Hence each equation is identified by the order condition. Therefore, the model as a whole is identified.

• Example 6.
• In this model Pt and Qt are endogenous and It, Rt, and Pt−1 are predetermined. The demandfunction excludes exactly one variable Pt−1, and hence by the order condition it is exactlyidentified. But the supply function excludes two variables It and Rt, and hence it is overidentified. As noted before, in this case there are two ways of estimating β1, the coefficientof the price variable.