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.

The results show that demand decreases with prices.They indicate that if we take a household with particular characteristics and vary only the marginal price a negative relationship holds between quantity and price.While this approach is less informative than that of section 1I, table 4 supports the downward sloping demand curve results rather than those produced in the Rosen framework and does not make any assumptions regarding the household's utility function. IV. ConclusionThis paper develops estimates of the demand for electricity in Medellin, Colombia using a method which exploits the information implicit in constrained maximization subject to a convex, but segmented linear, budget set.The estimates seem adequate statistically, fall within the accepted range of parameter estimates, and show a consistent pattern whereby richer consumers have absolutely larger price and income elasticities than do the poor.Their veracity is enhanced by similar results developed using a generalised Heckman method due to Vella (1990).This contrasts sharply with the results obtained when the standard Rosen method is applied to the same data.The formation of instruments which linearise the budget constraint was incapable with these data of identifying the downward sloping demand curve from the upward sloping supply curve.

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.