Questions / Quant research, Regression & linear algebra
An instrument identifies a slope through a ratio
For a scalar linear model, a valid centered instrument Z has Cov(Z,Y)=0.6 and Cov(Z,X)=0.2. What is the population instrumental-variable slope?
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Answer: 3 slope
- The moment equation is Cov(Z,Y)−βCov(Z,X)=0. Solving gives β=0.6/0.2=3, provided the exclusion and exogeneity assumptions hold.
Interview shortcut. IV slope = Cov(Z,Y)/Cov(Z,X) = 0.6/0.2.
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