{"id":155,"date":"2024-08-05T08:41:40","date_gmt":"2024-08-05T08:41:40","guid":{"rendered":"https:\/\/www.endogeneity.net\/?page_id=155"},"modified":"2026-04-04T14:36:45","modified_gmt":"2026-04-04T14:36:45","slug":"two-stage-least-squares-approach","status":"publish","type":"page","link":"https:\/\/www.endogeneity.net\/?page_id=155","title":{"rendered":"Two-Stage Least Squares Approach"},"content":{"rendered":"

Two-Stage Least Squares<\/strong><\/span><\/p>\n

Two-stage least squares is the most widely used instrumental variable estimator. It addresses endogeneity from omitted variables, simultaneity, and measurement error by replacing the endogenous predictor with its exogenously predicted component. It is best suited for models with a continuous predictor.<\/p>\n

How It Works<\/strong><\/p>\n

Step 1: First-Stage Regression<\/span><\/em><\/p>\n

Regress the endogenous predictor on the instrumental variable(s) and all exogenous controls and fixed effects from the outcome equation. Save the predicted values \u2014 these represent the variation in the predictor that is driven solely by the instrument and the exogenous controls, stripped of the endogenous component.<\/p>\n

Step 2: Second-Stage Regression<\/span><\/em><\/p>\n

Estimate the outcome equation, but replace the original endogenous predictor with the predicted values from the first stage. The instrument is excluded from this stage.<\/p>\n

Because the predicted values contain only exogenous variation, the second-stage coefficient estimates the causal effect free of endogeneity bias \u2014 provided the instrument is both strong and valid.<\/p>\n

Unlike the control function approach, 2SLS is a combined estimation procedure: both stages are estimated jointly, so standard errors are automatically corrected.<\/p>\n

Requirements<\/strong><\/p>\n