Categorical › Logistic regression

2SLS / IV regression

Two-stage least squares (instrumental variables) corrects for endogeneity — the standard remedy when a regressor is correlated with the error term.

What is 2SLS / IV regression?

When a regressor is correlated with the residual (endogenous), OLS is biased. 2SLS fixes this in two stages: (1) regress the endogenous variable on a set of instruments (variables correlated with the endogenous predictor but uncorrelated with the residual); (2) regress Y on the fitted values from stage 1. The resulting slope is consistent for the causal effect under the IV assumptions.

Valid instruments must satisfy: (a) relevance (correlated with the endogenous predictor — the weak-instruments F-test checks this; F > 10 is the Staiger-Stock cut-off), (b) exclusion (the instrument affects Y only through the endogenous predictor — untestable by data alone, must come from theory), and (c) ignorability (the instrument is as-good-as-randomly assigned).

Wu-Hausman tests whether the endogeneity correction was needed (significant ⇒ OLS biased). Sargan over-identification tests whether the instruments agree (significant ⇒ at least one instrument violates exclusion).

When should I use 2SLS / IV regression?

  • Observational studies where a key regressor is plausibly endogenous and you have a defensible instrument.
  • Mendelian randomization (genetic variants as IV for biomarkers).
  • Natural-experiment designs (geographic / temporal variation in policy as IV).

What data does it need?

Response + endogenous regressors + optional exogenous regressors + instruments (≥ # endogenous).

What does it report?

IV-adjusted β + SE + t + p + 95% CI per coefficient. Diagnostics: weak-instruments F, Wu-Hausman endogeneity, Sargan over-id (when applicable).

What does it assume?

  • Relevance: instruments correlated with endogenous regressor.
  • Exclusion: instruments uncorrelated with the residual.
  • Linearity in both stages.

How do I interpret the result?

Weak instruments F < 10 ⇒ 2SLS is biased toward OLS and the SEs are wrong. Report the F prominently.

2SLS SEs are larger than OLS SEs — efficiency cost of identification.

See also

References

  • Angrist & Pischke (2009). Mostly Harmless Econometrics, Ch. 4.