In a simultaneous equation system, the identification problem arises when it is not possible to uniquely determine the values of all the parameters in the system.

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This can happen when the number of equations is equal to or greater than the number of endogenous variables but less than the total number of parameters to be estimated. In other words, there are not enough independent equations to precisely estimate all the unknown parameters.

To decide whether an equation is identified, you can use the following rules:

Under-Identification: If the number of equations is less than the number of endogenous variables, the system is under-identified. This means there are not enough equations to uniquely determine the values of all parameters.
Exactly-Identification: If the number of equations equals the number of endogenous variables, the system is exactly-identified. In this case, there is just enough information to uniquely determine the values of all parameters.
Over-Identification: If the number of equations is greater than the number of endogenous variables, the system is over-identified. This situation can provide redundancy in information, and statistical techniques, such as instrumental variables or other econometric methods, may be used to estimate the parameters.

Identification is crucial for obtaining reliable estimates in simultaneous equation models. If a system is under-identified, it may not be possible to obtain unique parameter estimates. If it’s over-identified, additional statistical methods are often required to obtain efficient and consistent estimates.