Two Stage Least Squares (2SLS)

Two-stage least squares (2SLS) is an instrumental variable estimator that first predicts an endogenous treatment from an instrument and then regresses the outcome on that prediction to estimate a causal effect.

2단계 최소제곱법(2SLS)은 먼저 도구변수로 내생적 처치를 예측하고 그 예측값에 결과변수를 회귀하여 인과효과를 추정하는 도구변수 추정법이다.

How do I estimate a causal effect when the treatment is endogenous or confounded by unobserved factors?

처치가 내생적이거나 관측되지 않은 요인에 의해 교란될 때 인과효과를 어떻게 추정하나요?

Two-stage least squares uses an instrument that shifts the treatment but affects the outcome only through the treatment, removing bias from unobserved confounding. It fits observational data with a credible instrument, and the first-stage F-statistic is reported to check instrument strength.

When to use Two Stage Least Squares (2SLS)

• A treatment correlated with unobserved confounders or measured with error
• A credible instrument such as distance, policy rules or lottery assignment
• Estimating a local average treatment effect for compliers

When to use something else

• No valid instrument exists but confounders are measured: use propensity score methods or regression adjustment
• Treatment effects are expected to vary with covariates: use an instrumental variable forest

Assumptions and requirements

• Relevance: the instrument is strongly correlated with the treatment
• Exclusion restriction: the instrument affects the outcome only through the treatment
• Independence: the instrument is as good as randomly assigned
• Monotonicity for interpreting the estimate as a local average treatment effect

What the analysis reports

• First-stage coefficients and F-statistic
• Second-stage (IV) coefficient with robust standard error
• Comparison with OLS estimate
• Durbin–Wu–Hausman endogeneity test
• Overidentification test when several instruments are used

How to report it

The instrument was strong (first-stage F = [value]), and the 2SLS estimate indicated that [treatment] increased [outcome] by [value] (SE = [value], p = [value]).

Related methods

• Instrumental Variable Forest
• Regression Discontinuity Design (RDD)
• Propensity Score Matching

Run Two Stage Least Squares (2SLS) on Quorant