🤖 AI Summary
To address inaccurate parameter estimation and poor confidence interval coverage under weak identification, this paper proposes a robust inference method within the minimum distance framework that incorporates parameter boundary information. Methodologically, it unifies asymptotic theory for weak identification with limit distribution theory for parameters lying on boundaries, thereby constructing a boundary-constrained identification-robust estimation and inference system. The approach builds upon minimum distance estimation, integrated with factor model identification analysis and boundary-constrained inference techniques. Simulation studies and an empirical application to parental educational investment demonstrate that the method substantially improves confidence interval coverage—bringing it close to the nominal level—and enhances estimation precision under weak identification. It overcomes the failure of conventional methods near parameter boundaries and establishes a novel paradigm for weak-identification inference in structural models featuring inequality constraints.
📝 Abstract
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.