  We extend the constrained maximum likelihood estimation theory for parameters
of a completely identified model, proposed by Aitchison and Silvey (1958), to
parameters arising from a partially identified model. With a partially
identified model, some parameters of the model may only be identified through
constraints imposed by additional assumptions. We show that, under certain
conditions, the constrained maximum likelihood estimator exists and locally
maximize the likelihood function subject to constraints. We then study the
asymptotic distribution of the estimator and propose a numerical algorithm for
estimating parameters. We also discuss a special situation where exploiting
additional assumptions does not improve estimation efficiency.
