Therefore all the assumptions are exogeneity no

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Therefore, all the assumptions are exogeneity + no perfect collinearity + independent observations. B. Which of the above methods are equivalent? Methods I and II calculate the same test in two different ways. 4. (20) Consider a variable X2 that is the log of announced quarterly earnings for company XYZ. X3 is the log of expected quarterly XYZ earnings one day prior to the announcement. Suppose Y is the return on the XYZ stock on the day of the announcement. Assume that the stock prices move only if the announced earnings are above or below the expected earnings: (1) 0 , ) ( 2 , 3 , 2 2 1 > + + = β ε β β i i i i X X Y That is, the prior information is already priced-in. A. Explain why the regression , , 2 2 1 i i i X Y ε β β + + = usually fails to detect the connection between earnings and stock prices. Explain why the correlation between X2 and X3 is at fault in this case. Would you expect positive or negative bias in b2?
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The regression fails since it does not include X3. X3(expected earnings) are positively correlated with X2(earnings) leading to the omitted variable bias. Since β2 is positive, then the slope on X3, i.e. -β2, is negative. Correlation is positive. Negative times positive yields negative bias. B. Explain, how would you test the hypothesis that the prior information is in fact fully priced in (i.e. model (1) is correct) by F-test using the following regression model: i i i i X X Y ε β β β + + + = , 3 3 , 2 2 1 *
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