(Requires Appendix Material)The Relationship Between the TSLS Slope and the Corresponding

question 18

Multiple Choice

(Requires Appendix material) The relationship between the TSLS slope and the corresponding population parameter is:

• A) \(\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }\)
• B) \(\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }\)
• C) \(\left( \hat { \beta } _ { 1 } ^ { T SLS } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z }) ^ { 2 } \right. }\)
• D) \(\left( \hat { \beta } _ { 1 } ^ { \text {TSLS } } - \beta _ { 1 } \right) = \frac { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( X _ { i } - \bar { X } \right)u _ { i } } { \frac { 1 } { n } \sum _ { i = 1 } ^ { n } \left( Z _ { i } - \bar { Z } \right) \left( X _ { i } - \bar { X } \right) }\)

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