Summer 2004 - Jeon's Class - Exam 1

# Summer 2004 - Jeon's Class - Exam 1 - Economics 120B...

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Economics 120B Name: _________________________ Professor Yongil Jeon August 11, 2004 Student ID#: _________________________ Exam 1: Econometrics 120B 1. (5 points) An example of a randomized controlled experiment is when a. All households receive a tax rebate in one year but not the other. b. one U.S. state increases minimum wages and an adjacent state does not, and employment differences are observed. c. random variables are controlled for by holding constant other factors. d. some 5 th graders in a specific elementary school are allowed to use computers at school while others are not, and their end-of-year performance is compared holding constant other factors. Answer : d 2. (5 points) Most economic data are obtained a. through randomized controlled experiments. b. by calibration methods. c. through textbook examples typically involving ten observation points. d. by observing real-world behavior. Answer : d

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2 EXAM #1, ECON 120B, Summer 2004 3. (20 points) Show that the two alternative formulae for the slope are identical: (Note that 1 n i i X nX = = ) 1 22 1 1 1 n ii i n i i X YX Y n X X n = = = 1 2 1 () ( n i n i i ) X XY Y XX = = In addition, the STATA gives the following definition for the regression slope it estimates: ∑∑ == = n i n i i i n i n i i n i i i i X X n Y X Y X n 11 2 2 1 ) ( ) )( ( Prove that this formula is also the same as those given above. Answer : Let’s start with the first equality. The numerator of the right-hand side expression can be written as follows: 1 1 1 ( ) ( ) nn n n n i i i iii i i i i i i i X XYY X YY X X Y X YX YY Xn Y X = = = −= −−+ = + Y X nXY nXY nXY Y X nXY =− + . (Note that 1 n i i X nX = = .) Multiplying out the terms in the denominator and moving the summation sign into the expression in parentheses similarly yields 2 1 n i i 2 X nX = . Dividing both of these expressions by n then results in the left-hand side fraction.
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## Summer 2004 - Jeon's Class - Exam 1 - Economics 120B...

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