- "Each simulated observation has a treatment $T$, an outcome $Y$, and a set of covariates $X$ with distinct causal roles. Two covariates influence both the treatment and the outcome—these are the confounders. Two others affect only the treatment and serve as valid instruments. A final covariate affects only the outcome. The treatment and outcome errors are drawn from a correlated bivariate normal distribution, introducing endogeneity through their correlation parameter $\\rho$ . The treatment is exogenous and standard should regression recover the correct effect when $\\rho$ is low; while naive estimates are biased when $\\rho$ is high.\n",
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