- [[two-stage least-squares]] # Idea In [[causal inference]], endogenous variables are variables that are correlated with the error term (vs [[exogenous variables]]). They are determined from within our model. $ Y_{i}=\beta_{0}+A_{i} \beta_{1}+\epsilon_{i} $ If there is [[confounding variable|confounding]], $A_i$ and $\epsilon_{i}$ will be correlated, so $A$ is an **endogenous** variable, such that [[linear regression|OLS]] is inconsistent for the true $\beta_1$. [[instrumental variables|IV]] regression uses a single instrumental variable $Z$ to obtain a consistent estimate for $\beta_1$. # References - [12.1 The IV Estimator with a Single Regressor and a Single Instrument | Introduction to Econometrics with R](https://www.econometrics-with-r.org/12.1-TIVEWASRAASI.html) - [Two stage least squares - Instrumental Variables Methods | Coursera](https://www.coursera.org/learn/crash-course-in-causality/lecture/5B3AW/two-stage-least-squares)