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Econ120BCh12

# Econ120BCh12 - Chapter 12 Answers 12.2 12.3 12.6 12.8 12.9...

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Chapter 12 Answers 12.2, 12.3, 12.6, 12.8, 12.9, 12.10 2. (a) When there is only one X , we only need to check that the instrument enters the first stage population regression. Since the instrument is Z X , the regression of X onto Z will have a coefficient of 1.0 on Z , so that the instrument enters the first stage population regression. Key Concept 4.3 implies corr( X i , u i ) 0, and this implies corr( Z i , u i ) 0. Thus, the instrument is exogenous. (b) Condition 1 is satisfied because there are no W ’s. Key Concept 4.3 implies that condition 2 is satisfied because ( X i , Z i , Y i ) are i.i.d. draws from their joint distribution. Condition 3 is also satisfied by applying assumption 3 in Key Concept 4.3. Condition 4 is satisfied because of conclusion in part (a). (c) The TSLS estimator is 1 ˆ ZY ZX s TSLS s using Equation (10.4) in the text. Since Z i X i , we have 11 2 ˆˆ . TSLS OLS ZY XY ZX X ss   3. (a) The estimator  2 1 101 2 ˆ ˆ ( n TSLS TSLS ai i n Y  2 ) i X is not consistent. Write this as

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Econ120BCh12 - Chapter 12 Answers 12.2 12.3 12.6 12.8 12.9...

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