4Notice the difference between under- and overidentification. In the former case, it is impossible to obtain estimates of the structural parameters, whereas in the latter case, there may be several estimates of one or more structural coefficients.
748 PART FOUR: SIMULTANEOUS-EQUATION MODELS
in a system of simultaneous equations. But these examples also show how time-consuming and laborious the process can be. Fortunately, it is not essential to use this procedure. The so-called order and rank conditions of identification lighten the task by providing a systematic routine.
To understand the order and rank conditions, we introduce the following notations:
M = number of endogenous variables in the model m = number of endogenous variables in a given equation K = number of predetermined variables in the model including the intercept k = number of predetermined variables in a given equation
A necessary (but not sufficient) condition of identification, known as the order condition, may be stated in two different but equivalent ways as follows (the necessary as well as sufficient condition of identification will be presented shortly):
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