iv-regression-guide

npx skills add brycewang-stanford/Auto-Empirical-Research-Skills --skill iv-regression-guide --agent claude-code

Same command for any agent — swap --agent for codex, cursor, copilot.

# Instrumental Variables Regression Guide A skill for applying instrumental variables (IV) estimation to address endogeneity in regression models. Covers the logic of IV, two-stage least squares (2SLS), instrument validity tests, weak instrument diagnostics, and reporting standards. ## The Endogeneity Problem ### Why OLS Fails ``` Ordinary Least Squares assumes: E[u | X] = 0 (Regressors are uncorrelated with the error term) This assumption is violated when: - Omitted variable bias: A confound affects both X and Y - Simultaneity: X affects Y and Y affects X - Measurement error: X is measured with noise Consequence: OLS estimates are biased and inconsistent. No amount of data will fix this. ``` ### The IV Solution An instrumental variable Z satisfies two conditions: ``` 1. Relevance: Z is correlated with the endogenous regressor X Cov(Z, X) != 0 2. Exclusion: Z affects Y ONLY through X (not directly) Cov(Z, u) = 0 Z --> X --> Y Z -/-> Y (no direct path) ``` ## Two-Stage Least Squares (2SLS) ### How 2SLS Works ``` Stage 1: Regress the endogenous variable on the instrument(s) X = gamma_0 + gamma_1 * Z + controls + v Save the fitted values: X_hat Stage 2: Regress the outcome on the fitt