In the Two-Stage Least Squares (2SLS) estimation procedure, what is the purpose of the first stage regression?

Question

BlackTom AI · Accepted Answer

Topic focus: 2SLS first-stage regression aims to address endogeneity by creating instrumented predictors.
Option 1: 'To obtain residuals that can be used to directly test the exogeneity of the instruments.' While residuals can be used in some diagnostics, the primary purpose of the first stage is not to produce residuals for exogeneity testing of instruments. This description confuses diagnostic testing with the core projection step.
Option 2: 'To generate predicted values (x̂) for the endogenous variable(s) that are uncorrelated with the structural error term.' This captures the essence of the first stage: project the endogenous variable on the instruments (and exogenous controls) to obtain fitted values that are purged of the endogenous component, thereby ensuring the second stage uses exogenous predictions. The resulting x̂ is then used in the second-stage regression to estimate the structural parameters consistently.
Option 3: 'To estimate the coefficients of the structural equation directly using OLS.' In 2SLS, the second stage uses OLS, but the first stage does not estimate the structural coefficients; its job is to produce x̂. Therefore this option misstates the role of the first stage in the two-stage process.
Option 4: 'To test for perfect multicollinearity among the instruments.' Testing for multicollinearity can be relevant in IV setups, but the first stage itself does not serve to test for perfect multicollinearity among instruments. Multicollinearity checks are diagnostic concerns, not the procedural aim of generating predicted endogenous values. This answer describes a diagnostic task rather than the core first-stage purpose.

In the Two-Stage Least Squares (2SLS) estimation procedure, what is the purpose of the first stage regression?

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