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In statistics and econometrics, the parameter identification problem is the inability in principle to identify a best estimate of the value(s) of one or more parameters in a regression. This problem can occur in the estimation of multiple-equation econometric models where the equations have variables in common. More generally, the term can be used to refer to any situation where a statistical model will invariably have more than one set of parameters that generate the same distribution of observations, meaning that multiple parametrizations are observationally equivalent. ==The standard example, with two equations== Consider a linear model for the supply and demand of some specific good. The quantity demanded varies negatively with the price: a higher price decreases the quantity demanded. The quantity supplied varies directly with the price: a higher price increases the quantity supplied. Assume that, say for several years, we have data on both the price and the traded quantity of this good. Unfortunately this is not enough to identify the two equations (demand and supply) using regression analysis on observations of ''Q'' and ''P'': of course one can not estimate a downward slope ''and'' an upward slope with one linear regression line involving only two variables. Additional variables can make it possible to identify the individual relations. 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. This ''Z'' might be consumers' income, with a rise in income shifting the demand curve outwards. This is symbolically indicated with the values 1, 2 and 3 for ''Z''. With the quantities supplied and demanded being equal, the observations on quantity and price are the three white points in the graph: they reveal the supply curve. Hence the effect of ''Z'' on ''demand'' makes it possible to identify the (positive) slope of the ''supply'' equation. The (negative) slope parameter of the demand equation cannot be identified in this case. In other words, the parameters of an equation can be identified if it is known that some variable does ''not'' enter into the equation, while it does enter the other equation. A situation in which both the supply and the demand equation are identified arises if there is not 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Parameter identification problem」の詳細全文を読む スポンサード リンク
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