Robust Instrumental Variables Estimation
Also known as: Robust IV, Weak-instrument-robust IV, Robust 2SLS, Weak-instrument-robust inference
Robust Instrumental Variables estimation extends standard IV and two-stage least squares (2SLS) by guarding against weak-instrument bias and non-standard inference. Methods such as the Anderson-Rubin test, Limited Information Maximum Likelihood (LIML), and the Conditional Likelihood Ratio test provide valid confidence sets and hypothesis tests even when instruments are weak or only partially identified, making IV inference reliable in settings where standard 2SLS breaks down.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use Robust IV whenever you apply instrumental variables and face the possibility of weak instruments — signalled by a first-stage F below 10, or by a small sample relative to the number of instruments. It is also appropriate when you want confidence sets with guaranteed coverage regardless of identification strength, or when the number of instruments is large relative to the sample (many-instruments setting). Do not use standard 2SLS as a replacement — if you have strong instruments (F well above 10) and a single endogenous regressor, regular 2SLS already performs well, though LIML rarely hurts. Robust IV is not a substitute for finding better instruments: if instruments are completely irrelevant, no robust method can recover the parameter.
Strengths & limitations
- Anderson-Rubin confidence sets have correct coverage regardless of instrument strength, eliminating size distortions that plague 2SLS under weak identification.
- LIML and Fuller's estimator substantially reduce bias relative to 2SLS in many-instruments or weak-instruments settings while remaining consistent.
- Provides a diagnostic framework: first-stage F, Stock-Yogo critical values, and robust tests together clarify whether identification is strong enough for causal inference.
- CLR and LM tests achieve near-optimal power among weak-instrument-robust procedures, making them preferable to the conservative AR test when instruments are not entirely weak.
- Applicable to cross-sectional, panel, and time-series data wherever standard IV applies.
- When there are multiple endogenous regressors, weak-instrument-robust inference is more complex; the AR test loses power and joint confidence sets can be large.
- LIML can have fat-tailed finite-sample distributions with very many instruments, and Fuller's constant must be chosen carefully.
- Robust methods do not solve the fundamental problem of invalid instruments — if exclusion restrictions fail, all IV-based estimates are inconsistent.
Frequently asked
What makes an instrument 'weak'?
An instrument is weak when its partial correlation with the endogenous regressor is small. The Stock-Yogo rule of thumb is a first-stage F below 10; formal weak-instrument tests compare F to critical values that depend on the acceptable level of 2SLS size distortion or relative bias.
Should I always use LIML instead of 2SLS?
Not necessarily. With strong instruments and few regressors, 2SLS and LIML perform similarly. LIML's advantage is largest in many-instruments or weak-instruments settings. With genuinely strong instruments, 2SLS is standard and well-understood; switching to LIML adds little.
What is the Anderson-Rubin test and when should I use it?
The AR test inverts a reduced-form F-test to construct a confidence set for the structural parameter. Its key property is correct size regardless of instrument strength. Use it when the first-stage F is below Stock-Yogo critical values or when you want guaranteed coverage. With multiple endogenous regressors the AR test becomes conservative, and the CLR test is preferred.
Does robust IV fix invalid instruments?
No. Robust IV methods address weak identification but assume the exclusion restriction holds — that the instruments affect the outcome only through the endogenous regressor. If instruments are invalid (correlated with the error term), all IV estimates are inconsistent, robust or not.
How do I choose between AR, LIML, and CLR in practice?
Report the first-stage F and Stock-Yogo critical values first. With one endogenous regressor and weak instruments, the CLR test is near-optimal and preferred over AR. Use LIML or Fuller's estimator as the point estimate. With multiple endogenous regressors, consult Andrews, Stock, and Sun (2019) for the appropriate joint robust procedure.
Sources
- Stock, J. H., Wright, J. H., & Yogo, M. (2002). A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics, 20(4), 518-529. DOI: 10.1198/073500102288618658 ↗
- Andrews, I., Stock, J. H., & Sun, L. (2019). Weak instruments in instrumental variables regression: Theory and practice. Annual Review of Economics, 11, 727-753. DOI: 10.1146/annurev-economics-080218-025643 ↗
How to cite this page
ScholarGate. (2026, June 3). Robust Instrumental Variables Estimation. ScholarGate. https://scholargate.app/en/causal-inference/robust-instrumental-variables
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- 2SLS RegressionEconometrics↔ compare
- Difference-in-DifferencesEconometrics↔ compare
- Instrumental Variables in Health ResearchHealth Economics↔ compare
- Panel Data Instrumental VariablesCausal inference↔ compare