Project the endogenous regressor
The first stage regresses the endogenous regressor on the instruments and exogenous controls. Its fitted values represent the component explained by those variables.
Applied mathematics / English
Two Stage Least Squares - an introduction
Ben Lambert · YouTube · 8:24
YouTube · Ben LambertOriginal video
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Introduce two-stage least squares for an endogenous regressor and explain why instrument quality matters.
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0:00Project the endogenous regressor3:00Use the first-stage fitted values6:00More instruments are not automatically betterLearning script
Generated from the video's visuals and explanation; not verbatim speech.
The first stage regresses the endogenous regressor on the instruments and exogenous controls. Its fitted values represent the component explained by those variables.
The second stage uses those fitted values in place of the endogenous regressor in the structural regression. Validity requires instrument exogeneity and sufficient relevance; ordinary second-stage standard errors alone are not generally the correct 2SLS uncertainty estimate.
The lesson warns that weak or redundant instruments can harm finite-sample behavior. Claims of improved efficiency need valid instruments and the corresponding model assumptions; first-stage strength should be assessed.
Knowledge cards
Use the first-stage fitted values
The second stage uses those fitted values in place of the endogenous regressor in the structural regression. Validity requires instrument exogeneity and sufficient relevance; ordinary second-stage standard errors alone are not generally the correct 2SLS uncertainty estimate.
More instruments are not automatically better
The lesson warns that weak or redundant instruments can harm finite-sample behavior. Claims of improved efficiency need valid instruments and the corresponding model assumptions; first-stage strength should be assessed.
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- Least squares ApplicationAt 0:00
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The first stage regresses the endogenous regressor on the instruments and exogenous controls. Its fitted values represent the component explained by those variables. The second stage uses those fitted values in place of the endogenous regressor in the structural regression. Validity requires instrument exogeneity and sufficient relevance; ordinary second-stage standard errors alone are not generally the correct 2SLS uncertainty estimate. The lesson warns that weak or redundant instruments can harm finite-sample behavior. Claims of improved efficiency need valid instruments and the corresponding model assumptions; first-stage strength should be assessed.
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