Identification and Lack of Identification - Sargan, J. D. (Econometrica, 1983)
THIS PAPER IS INTENDED to stress the distinction between the conditions for lack of identification in models linear with respect to the variables but nonlinear in the parameters in the sense originally defined by Fisher [2], and the less numerous set of conditions required for first order lack of identification. The latter set of conditions involve only the first derivatives of the coefficients as functions of the parameters. It is argued that if the model suffers from first order lack of identification, it will generally be the case that the usual estimators are consistent, although not asymptotically normally distributed. In a leading special case the asymptotic distribution is discussed, and the simulation of a simple model illustrates the extent to which this asymptotic distribution approximates the actual finite sample distribution.