It sometimes happens that the unobservable state vector of a linear dynamic model expressed in the state space is subject to known restrictions. Incorporation of this information into the Kalman filter procedure will increase the efficiency of estimation. It is shown that a simple augmentation of the measurement equation constrains the estimated state vector to obey the restrictions. The method applies whether the restrictions are time-invariant, time-varying, linear, or nonlinear. Copyright 1992 by MIT Press.

A bstract-A lack-of-fit test of model specification used by experimental statisticians but mostly unknown to econometricians is presented.The test is applicable in situations in which there are replicated observations on the dependent variable.In this paper the test is modified to allow for heteroskedasticity usually encountered when dealing with cross-sectional observations, and illustrated by an application to an earnings function estimated from a sample survey of Norwegian women.