Weak Identification Robust Tests for Subvectors Using Implied Probabilities

Area of Science:

• Econometrics
• Statistical Inference
• Hypothesis Testing

Background:

• Conventional statistical tests (Wald, Likelihood-ratio, Score) exhibit over-rejection in models with weak identification.
• Weak identification poses challenges for reliable hypothesis testing in econometrics.
• Existing methods lack refined finite-sample performance under weak identification scenarios.

Purpose of the Study:

• To develop a robust statistical test for hypotheses concerning parameter subvectors in moment condition models.
• To overcome the size distortion and improve finite-sample performance of conventional tests under weak identification.
• To introduce a novel two-step projection-based modified score test utilizing information-theoretic criteria.

Main Methods:

• Extension of projection-based tests to a modified score test incorporating implied probabilities from information-theoretic criteria.
• A two-step procedure: parameter space reduction followed by the modified score test.
• Derivation of asymptotic properties for the Generalized Empirical Likelihood implied probabilities class.

Main Results:

• The proposed test demonstrates very good finite-sample size and power in simulation studies.
• The methodology effectively addresses over-rejection issues associated with weak identification.
• Application to veteran earnings data indicates a negative impact of veteran status.

Conclusions:

• The developed modified score test offers a reliable solution for hypothesis testing in models with weak identification.
• The two-step approach enhances statistical accuracy and finite-sample properties.
• Empirical findings suggest a detrimental effect of veteran status on earnings, warranting further investigation.