Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions
Abstract
In models estimated by (generalized) method of moments a test on coefficient restrictions can either be based on a Wald statistic or on the difference between evaluated criterion functions. From their correspondence it easily follows that the statistic used for testing instrument validity, the Sargan-Hansen overidentifying restrictions (OR) statistic, is equivalent to an exclusion restrictions test statistic for a nonunique group of regressor variables. We prove that asymptotically this is the case too for incremental OR tests. However, we also demonstrate that, despite this equivalence of test statistics, one can nevertheless distinguish between either the (in)validity of some additional instruments or the (un)tenability of particular exclusion restrictions. This, however, requires to be explicit about the adopted maintained hypothesis. It also highlights that recent warnings in the literature that overidentifying restrictions tests may mislead practitioners should not be directed towards the test, but to practitioners who do not realize that inference based on such tests is unavoidably conditional on the validity of particular just-identifying statistically untestable assumptions.
Acknowledgments
Most of this paper was written while I was enjoying hospitality as Visting Professor at the Division of Economics, School of Humanities and Social Sciences, Nanyang Technological University, 14 Nanyang Drive, Singapore 637332. Helpful comments by João Santos Silva on an earlier version of this paper and further suggestions by JEM co-editor Jason Abrevaya are gratefully acknowledged.
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Articles in the same Issue
- Frontmatter
- Research Articles
- Regression Discontinuity with Errors in the Running Variable: Effect on Truthful Margin
- A Simple Estimator for Dynamic Models with Serially Correlated Unobservables
- Selection of an Estimation Window in the Presence of Data Revisions and Recent Structural Breaks
- Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions
- Competing Risks Copula Models for Unemployment Duration: An Application to a German Hartz Reform
- Intercept Homogeneity Test for Fixed Effect Models under Cross-sectional Dependence: Some Insights
- Practitioner’s Corner
- Root-n Consistent Kernel Density Estimation in Practice
- Linear Model IV Estimation When Instruments Are Many or Weak
- Additive Nonparametric Instrumental Regressions: A Guide to Implementation
- Teaching Corner
- Teaching Size and Power Properties of Hypothesis Tests Through Simulations
Articles in the same Issue
- Frontmatter
- Research Articles
- Regression Discontinuity with Errors in the Running Variable: Effect on Truthful Margin
- A Simple Estimator for Dynamic Models with Serially Correlated Unobservables
- Selection of an Estimation Window in the Presence of Data Revisions and Recent Structural Breaks
- Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions
- Competing Risks Copula Models for Unemployment Duration: An Application to a German Hartz Reform
- Intercept Homogeneity Test for Fixed Effect Models under Cross-sectional Dependence: Some Insights
- Practitioner’s Corner
- Root-n Consistent Kernel Density Estimation in Practice
- Linear Model IV Estimation When Instruments Are Many or Weak
- Additive Nonparametric Instrumental Regressions: A Guide to Implementation
- Teaching Corner
- Teaching Size and Power Properties of Hypothesis Tests Through Simulations
