When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows:
A) $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z Y } } { S _ { Z x } }$
B) $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { X Y } } { S _ { X } ^ { 2 } }$
C) $\hat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { S _ { Z X } } { S _ { Z Y } }$
D) $\hat { \beta } _ { 1 } ^ { \text {TSLS} } = \frac { S _ { Z Y } } { S _ { Z } ^ { 2 } }$

Question

Quizplus · Accepted Answer

In this case, the TSLS estimator for the slope is calculated by dividing the covariance between the instrument and the dependent variable by the covariance between the instrument and the regressor. This can be represented by the formula (covariance between instrument and dependent variable) / (covariance between instrument and regressor). Option A is the correct formula for this calculation.

When There Is a Single Instrument and Single Regressor, the TSLS