Weak Identification with Bounds in a Class of Minimum Distance Models

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 (Andrews and Cheng (2012)) with parameter-on-the-boundary theory (Andrews (1999)). 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: estimating the effects of a randomized intervention on parental investments in children, where parental investments are modeled by a factor model.