# Detecting Identification Failure in Moment Condition Models

## TL;DR

This paper introduces a new method to detect identification failure in moment condition models using a quasi-Jacobian matrix, enabling robust inference regardless of the identification strength.

## Contribution

It proposes a novel quasi-Jacobian matrix approach and a simple chi-squared test for detection of identification failure in moment models.

## Key findings

- The quasi-Jacobian is asymptotically singular when identification fails.
- The test works for strong, semi-strong, and weak identification.
- Monte Carlo simulations and empirical application validate the method.

## Abstract

This paper develops an approach to detect identification failure in moment condition models. This is achieved by introducing a quasi-Jacobian matrix computed as the slope of a linear approximation of the moments on an estimate of the identified set. It is asymptotically singular when local and/or global identification fails, and equivalent to the usual Jacobian matrix which has full rank when the model is point and locally identified. Building on this property, a simple test with chi-squared critical values is introduced to conduct subvector inferences allowing for strong, semi-strong, and weak identification without \textit{a priori} knowledge about the underlying identification structure. Monte-Carlo simulations and an empirical application to the Long-Run Risks model illustrate the results.