Full maximum likelihood estimation of dynamic demand models

The maximum likelihood estimation of dynamic demand models has usually been based on the likelihood function conditional on the first observations of the dependent variables. However, this neglects information which may be necessary for identifying the long-run structure. We formulate the full likelihood of a general dynamic demand model involving arbitrary lag orders, express its analytical derivatives in a relatively simple form, and propose a reparameterization which is always well-defined. The methodology is illustrated with a small empirical application, using the levels version of the CBS model proposed by Barten (1989) and annual British data on four commodities.