# pq1_ak - Practice Questions for Midterm 1 Answer Key...

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Practice Questions for Midterm 1 - Answer Key Introduction to Econometrics - Fall 2006 1. Recall that: corr X , Y XY X Y Note that Y 2 b 2 X 2 . Consequently, Y | b | X . Then: 1 X Y 1 | b | X 2 Next, XY E  Y E Y  X E X  E  a bX a bE X  X E X E  bX bE X X E X Then: XY bE  X E X X E X b X 2 As a result: corr X , Y XY X Y b X 2 | b | X 2 b | b | Note that if b 0, then b | b | 1 and if b 0, then b | b | 1 2. Solutions: a. The cumulative distribution of is: 012 3 Pr 0.20 0.70 0.95 1 Figure 1 shows the cumulative distribution of . 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.5 1 1.5 2 2.5 3 gamma F(gamma) Cumulative distribution for b. Given that Pr H 0 3 Pr H 0   3 0.05, we reject the null hypothesis. c. Given that Pr H 0 2 Pr H 0   2 Pr H 0   3 0.25 0.05 0.3, we cannot reject the null hypothesis. d. With respect to the mean :

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E 0 Pr   0 1 Pr   1 2 Pr   2 3 Pr   3 E 0 0.2 1 0.5 2 0.25 3 0.05 E 1.15 It’s biased . Regarding the variance : VAR E E  2 E 2 0 2 Pr   0 1 2 Pr   1 2 2 Pr   2 3 2 Pr   3 0 2 1 2 2 2 3 2 0.6275 3. Solutions: a. First, you are told that E u i inc i 0, so you know that the conditional mean assumption holds. Second, the observations edu i , inc i , i 1,. ..., n are obtained by simple random sampling, so they are i . i . d . Third, both the level of education and income are not constants, but they can take on only finite values, so it must be that 0 E edu i 4 and 0 E inc i 4 . The three least squares assumptions hold, so we know that 0 and 1 are unbiased and consistent estimator of 0 and 1 . Since we computed 0 and 1 from a large sample (5000 observations) we can also say that their distribution is approximately normal: 0 N 0 , 0 2 and 1 N 1 , 1 2 .
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## This note was uploaded on 07/28/2010 for the course ECON 410 taught by Professor Staff during the Fall '08 term at University of Wisconsin.

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pq1_ak - Practice Questions for Midterm 1 Answer Key...

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