When instruments are only weakly correlated with the endogenous regressor, 2SLS can be badly biased and its usual inference misleading — even in large samples. These slides recap 2SLS, show by simulation how weak identification distorts estimates and test sizes, cover testing the identification assumption, and work through the quarter-of-birth (returns to schooling) application where the problem became famous. This topic connects directly to Dr Grant's published research on identification-robust inference.
What these materials cover
- Recap of 2SLS and its identifying assumptions
- Finite-sample and asymptotic behaviour of 2SLS under weak/unidentified instruments
- Simulation evidence: bias and size distortion
- Testing the identification assumption in practice
- Empirical application: quarter of birth as an instrument for schooling
Download
Free to download and use for personal study. Written for my own university teaching; shared here as evidence of teaching style and depth.
Lecture slides: IV with weak/unidentified instruments (PDF)
Who this is for
MSc and PhD students whose empirical work relies on IV, and anyone assessing whether a first stage is strong enough to trust 2SLS inference.
Working on this topic?
Send the module topic list, the problem set and where you're stuck. A free consultation diagnoses whether the difficulty is definitions, derivations or software output — and proposes a plan.
Related free resources
- Cross-Section Econometrics — full study-note hub
- Instrumental variables and weak instruments — study note
- Identification-robust inference with singular variance — linked to Dr Grant's research
- Research: the Generalised Anderson–Rubin papers
- All teaching materials — notes, exercises and solutions
One-to-one help
For help with this material — or the module it belongs to — see PhD econometrics support or econometrics tuition. The first consultation is free, with no obligation.
Free worked video lectures: @economaths on YouTube.