only a variable Z entering the demand equation but not the supply equation, but also a variable X entering the supply equation but not the demand equation: supply: demand: with positive bS and negative bD. Here both equations are identified if c and d are nonzero. Note that this is the structural form of the model, showing the relations between the Q and P. The reduced form however can be identified easily. Fisher points out that this problem is fundamental to the model, and not a matter of statistical estimation: More equations More generally, consider a linear system of M equations, with M > 1. An equation cannot be identified from the data if less than M − 1 variables are excluded from that equation. This is a particular form of the order condition for identification. (The general form of the order condition deals also with restrictions other than exclusions.) The order condition is necessary but not sufficient for identification. The rank condition is a necessary and sufficient condition for identification. In the case of only exclusion restrictions, it must "be possible to form at least one nonvanishing determinant of order M − 1 from the columns of A corresponding to the variables excluded a priori from that equation" (Fisher 1966, p. 40), where A is the matrix of coefficients of the equations. This is the generalization in matrix algebra of the requirement "while it does enter the other equation" mentioned above (in the line above the formulas). See also Identifiability, the related problem in statistics Errors-in-variables model#Linear model Instrumental variable#Identification Set identification References ("A classic and masterful exposition of the subject", , p. 31) Further reading External links by Mark Thoma Estimation theory