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

Short Answer

When there is a single instrument and single regressor, the TSLS estimator for the slope can be calculated as follows a. $\widehat { \beta } _ { 1 } ^ { T S L S } = \frac { s _ { Z Y } } { s _ { Z X } }$ .

b. $\widehat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { s _ { X Y } } { s _ { X } ^ { 2 } }$ .

c. $\widehat { \beta } _ { 1 } ^ { \text {TSLS } } = \frac { s _ { Z X } } { s _ { Z Y } }$ .

d. $\hat { \beta } _ { 1 } ^ { T L L S } = \frac { s _ { Z Y } } { s _ { Z } ^ { 2 } }$ .