Instrumental Variables via Two-Stage Least Squares (IV/2SLS)
Also known as: instrumental variables, IV estimation, 2SLS, instrumental variable regression, Araç Değişken — İki Aşamalı EKK (IV/2SLS)
IV/2SLS is a two-stage estimation method that recovers the causal effect of an endogenous regressor by isolating the part of its variation driven by an external instrument. It is the workhorse identification strategy in modern applied econometrics, developed at length in Angrist and Pischke's Mostly Harmless Econometrics (2009).
Key highlights
- Recovers a consistent causal effect for an endogenous regressor where ordinary least squares is biased.
- Handles omitted-variable bias, reverse causality, and measurement error through a single, transparent identification strategy.
- Provides a clear diagnostic — the first-stage F-statistic — for judging instrument strength before trusting the estimate.
Intuition
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How it works
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When to use it
Use IV/2SLS when a key regressor is endogenous — correlated with the error term through omitted variables, simultaneity, or measurement error — so ordinary least squares would be biased, and you can defend an instrument that is both relevant and excludable. It applies to continuous or binary regressors in cross-sectional or panel data and needs a reasonable sample (at least about 100 observations) so the first stage is well identified. It is reliable only when the instrument is strongly correlated with the endogenous variable (first-stage F > 10) and affects the outcome solely through that variable; the exclusion restriction cannot be tested directly and must rest on theoretical argument.
Strengths & limitations
- Recovers a consistent causal effect for an endogenous regressor where ordinary least squares is biased.
- Handles omitted-variable bias, reverse causality, and measurement error through a single, transparent identification strategy.
- Provides a clear diagnostic — the first-stage F-statistic — for judging instrument strength before trusting the estimate.
- Weak instruments (first-stage F below 10) produce biased and inconsistent estimates that can be worse than ordinary least squares.
- The exclusion restriction — that the instrument affects the outcome only through the endogenous variable — cannot be tested directly and must be justified on theoretical grounds.
- Requires a fairly large sample (at least about 100 observations); with fewer the first stage is poorly identified.
Common pitfalls
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Applications
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Frequently asked
What makes a good instrument?
A good instrument satisfies two conditions: relevance — it is strongly correlated with the endogenous regressor, judged by a first-stage F-statistic above 10 — and the exclusion restriction — it affects the outcome only through that regressor. Relevance is testable; exclusion must be defended with subject-matter theory.
What is a weak instrument and why is it dangerous?
A weak instrument is only loosely correlated with the endogenous variable, signalled by a low first-stage F-statistic. It yields biased and inconsistent 2SLS estimates with badly behaved standard errors, sometimes worse than ordinary least squares. Stock and Yogo's thresholds are the standard guide for detecting it.
How is 2SLS different from ordinary least squares?
Ordinary least squares regresses the outcome directly on the predictors and is biased when a predictor is endogenous. 2SLS first replaces the endogenous predictor with the part of its variation explained by an instrument, then regresses the outcome on that cleaned version, removing the confounding to recover a causal effect.
What does the estimated effect represent?
With heterogeneous effects, 2SLS identifies a local average treatment effect — the average effect among the units whose behaviour the instrument actually shifts (the compliers) — not necessarily the effect for the whole population.
Sources
- 1.Angrist, J. D. & Pischke, J. S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.ISBN 978-0691120355
- 2.Stock, J. H. & Yogo, M. (2005). Testing for Weak Instruments in Linear IV Regression. In Identification and Inference for Econometric Models. Cambridge University Press.
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Cite this page
ScholarGate. (2026, June 1). Two-Stage Least Squares (2SLS). ScholarGate. https://scholargate.app/causal-inference/iv-2sls