Instrumental Variables and Two-Stage Least Squares

When trading volume and spreads are jointly determined, the regression needs variation in volume that is unrelated to the unobserved liquidity shock. An instrument supplies that variation: it moves the endogenous regressor but has no direct path to the structural error. Two-stage least squares (2SLS) uses the instrument-predicted component of the endogenous variable. The method is powerful precisely because its assumptions are demanding; a weak or invalid instrument does not provide a softer version of causal identification.

• state relevance, exclusion, and the rank/identification requirement;
• write the just-identified IV estimator and the general 2SLS projection form;
• execute the two conceptual stages without using first-stage standard errors in the structural regression;
• interpret an IV coefficient as the effect identified by instrument-induced variation;
• explain the efficiency cost and weak-instrument danger of IV.

1. What makes an instrument valid?
2. IV and the two stages
3. Identification, endogeneity tests, and weak instruments