Two-Stage Least Squares (2SLS / IV) Regression
Two-Stage Least Squares (Instrumental Variables) Regression · Also known as: two-stage least squares, 2SLS, instrumental variables regression, IV regression, İki Aşamalı En Küçük Kareler (2SLS/IV)
Two-Stage Least Squares is a two-step instrumental-variables estimator that addresses endogeneity, the situation where a regressor is correlated with the error term. In the first stage the endogenous regressor is predicted from instrumental variables, and in the second stage the structural equation is estimated using those predictions. It is a central tool in applied econometrics, developed in textbook treatments such as Angrist and Pischke (2009).
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When to use it
Use 2SLS when a regressor is endogenous (correlated with the error term) and you have at least one valid instrument: a variable that is correlated with the endogenous regressor but uncorrelated with the structural error. It suits continuous or binary outcomes on cross-sectional or panel data and needs a reasonably large sample (about 100 observations or more), because its properties are asymptotic. The instruments must be strong, judged by a first-stage F-statistic above 10, and when there are more instruments than endogenous regressors a Sargan/Hansen overidentification test should support their validity. With LATE assumptions the estimate can be read as a local average treatment effect.
Strengths & limitations
- Delivers consistent coefficients when an endogenous regressor would bias ordinary least squares.
- Provides a transparent two-step route to instrumental-variables estimation that is easy to communicate and diagnose.
- Handles cross-sectional and panel data with continuous or binary regressors, and supports a local average treatment effect (LATE) interpretation.
- With weak instruments (first-stage F below 10) the 2SLS estimator can be even more biased than OLS.
- In small samples (n < 100) the asymptotic justification fails and serious finite-sample bias appears.
- Validity hinges entirely on the instrument being both relevant and exogenous, which cannot be fully tested and must be argued from theory.
Frequently asked
What makes an instrument valid?
A valid instrument must satisfy two conditions: relevance, meaning it is correlated with the endogenous regressor (a first-stage F above 10), and exogeneity, meaning it is uncorrelated with the structural error and affects the outcome only through the regressor. Relevance is testable; exogeneity must be argued from theory.
What is a weak instrument and why is it dangerous?
A weak instrument explains very little of the endogenous regressor, signalled by a first-stage F-statistic below 10. With weak instruments the 2SLS estimator becomes badly biased, sometimes more so than the OLS estimate it was meant to fix, and its standard errors become unreliable.
When should I prefer OLS over 2SLS?
If there is no genuine endogeneity, or if your instrument is weak (first-stage F < 10) or the sample is small (n < 100), OLS is often the safer choice. 2SLS trades efficiency for consistency, so it only pays off when endogeneity is real and a strong, valid instrument exists.
What is the Sargan/Hansen overidentification test for?
When you have more instruments than endogenous regressors (an overidentified model), the Sargan or Hansen J test checks whether the extra instruments are jointly consistent with the exogeneity assumption. A rejection signals that at least one instrument is invalid.
Sources
- Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press. ISBN: 978-0691120355
How to cite this page
ScholarGate. (2026, June 1). Two-Stage Least Squares (Instrumental Variables) Regression. ScholarGate. https://scholargate.app/en/econometrics/two-stage-least-squares
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.
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