Parameter identification problem

It is closely related to non-identifiability in statistics and econometrics, which occurs when a statistical model has more than one set of parameters that generate the same distribution of observations, meaning that multiple parameterizations are observationally equivalent.

For example, this problem can occur in the estimation of multiple-equation econometric models where the equations have variables in common.

In the graph shown here, the supply curve (red line, upward sloping) shows the quantity supplied depending positively on the price, while the demand curve (black lines, downward sloping) shows quantity depending negatively on the price and also on some additional variable Z, which affects the location of the demand curve in quantity-price space.

Hence the effect of Z on demand makes it possible to identify the (positive) slope of the supply equation.

In the situation described [without the Z variable], there clearly exists no way using any technique whatsoever in which the true demand (or supply) curve can be estimated.

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).