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# Chapter 9 Answers - Chapter 9 Answers 1 As explained in the...

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Chapter 9 Answers 1. As explained in the text, potential threats to external validity arise from differences between the population and setting studied and the population and setting of interest. The statistical results based on New York in the 1970’s are likely to apply to Boston in the 1970’s but not to Los Angeles in the 1970’s. In 1970, New York and Boston had large and widely used public transportation systems. Attitudes about smoking were roughly the same in New York and Boston in the 1970s. In contrast, Los Angeles had a considerably smaller public transportation system in 1970. Most residents of Los Angeles relied on their cars to commute to work, school, and so forth. The results from New York in the 1970’s are unlikely to apply to New York in 2002. Attitudes towards smoking changed significantly from 1970 to 2002. 2. (a) When Y i is measured with error, we have = + % , i i i Y Y w or = - % . i i i Y Y w Substituting the 2nd equation into the regression model β β = + + 0 1 i i i Y X u gives β β - = + + % 0 1 , i i i i Y w X u or β β = + + + % 0 1 . i i i i Y X u w Thus = + . i i i v u w (b) (1) The error term v i has conditional mean zero given X i : = + = + = + = ( | ) ( | ) ( | ) ( | ) 0 0 0. i i i i i i i i i E v X E u w X E u X E w X (2) i i i Y Y w = + % is i.i.d since both Y i and w i are i.i.d. and mutually independent; X i and ( ) j Y i j % are independent since X i is independent of both Y j and w j . Thus, ( , ), 1, , i i X Y i n = % K are i.i.d. draws from their joint distribution. (3) i i i v u w = + has a finite fourth moment given that both u i and w i have finite fourth moments and are mutually independent. So ( X i , v i ) have nonzero finite fourth moments. (c)The OLS estimators are consistent because the least squares assumptions hold. (d)Because of the validity of the least squares assumptions, we can construct the confidence intervals in the usual way. (e)The answer here is the economists’ “On the one hand, and on the other hand.” On the one hand, the statement is true: i.i.d. measurement error in X means that the OLS estimators are inconsistent and inferences based on OLS are invalid. OLS estimators are consistent and OLS inference is valid when Y has i.i.d. measurement error. On the other hand, even if the measurement error in Y is i.i.d. and independent of Y i and X i , it increases the variance of the regression error σ σ σ = + 2 2 2 ( ), v u w and this will increase the variance of the OLS estimators. Also,

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Chapter 9 Answers - Chapter 9 Answers 1 As explained in the...

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