1 · Why OLS fails
Endogeneity from omitted variables and simultaneity makes OLS biased and inconsistent.
Instrumental Variables & 2SLS
When OLS is biased by endogeneity, and how an instrument plus 2SLS rescues it.
Course overview
Learn Instrumental Variables & 2SLS interactively
This free course uses real Python and statsmodels in your browser. Work through the modules below with explanations, executable examples, interactive controls, and questions.
2 · Instruments
A valid instrument is relevant (moves x) and excluded (affects y only through x).
3 · Two-Stage Least Squares
Project x on the instruments, then regress y on the fitted x to recover a consistent β₁.
4 · Diagnostics
First-stage F flags weak instruments; over-identification tests probe exclusion.