Maximum Likelihood Estimation of Singular Equation Systems with Autoregressive Disturbances

Maximum likelihood estimation of equation systems with first-order autocorrelation should, in principle, take into account the first observation and associated stationarity condition. In the general case, this leads to computational difficulties compared with conventional procedures, which perhaps explains the failure of the latter to incorporate the initial observation. However, in a special case where the autoregressive process has only one parameter, which is widely used for single equation systems such as demand systems, taking the first observation into account is no more difficult than ignoring it. The paper presents empirical results of estimating a demand system with Canadian data which suggest that maximizing the full likelihood function can yield very different and more reasonable estimates than maximizing the conventional one.