Weak Identification with Bounds in a Class of Minimum Distance Models

TL;DR

This paper develops a new inference method for minimum distance models that effectively combines bounds and weak identification, improving parameter estimation and inference in complex models.

Contribution

It introduces an identification-robust inference approach that incorporates bounds in minimum distance models, addressing a gap in existing weak identification methods.

Findings

Bounds improve inference in weakly identified models

Method applied successfully to latent factor and GARCH models

Empirical application demonstrates practical usefulness

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. This paper demonstrates the value of the bounds and identification-robust inference in a simple latent factor model and a simple GARCH model. This paper also demonstrates the identification-robust inference in an empirical application, a factor model for parental investments in children.