Price, volume, and bid–ask spread may respond to the same unobserved news. A regression slope can then be precise without identifying the effect the researcher wants. Endogeneity changes the coefficient's probability limit; robust standard errors cannot repair that change. This lesson derives the bias term and explains when valid instruments can identify a slope through IV or two-stage least squares.
Learning objectives. By the end of this note you should be able to:
- define endogeneity and show the plim bias term for OLS;
- distinguish simultaneity, omitted variables, and measurement error;
- state relevance and exclusion; write just-identified IV and 2SLS;
- explain weak-instrument danger and why HC/HAC cannot repair endogeneity.
In this lesson
- When OLS is inconsistent
- Instruments and 2SLS
Before you start
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