  When parameters are weakly identified, bounds on the parameters may provide a
valuable source of information. Existing weak identification estimation and
inference results are unable to combine weak identification with bounds. Within
a class of minimum distance models, this paper proposes identification-robust
inference that incorporates information from bounds when parameters are weakly
identified. The inference is based on limit theory that combines weak
identification theory with parameter-on-the-boundary theory. This paper
demonstrates the role of the bounds and identification-robust inference in two
example factor models. This paper also demonstrates the identification-robust
inference in an empirical application, a factor model for parental investments
in children.
