QUESTION 6 (Credit question - 25 marks) This question does not require a long exposition. Parts a, b and d ask you to pr

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Question 6 Credit Question 25 Marks This Question Does Not Require A Long Exposition Parts A B And D Ask You To Pr 1 (46.56 KiB) Viewed 62 times

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Question 6 Credit Question 25 Marks This Question Does Not Require A Long Exposition Parts A B And D Ask You To Pr 2 (66.02 KiB) Viewed 62 times

QUESTION 6 (Credit question - 25 marks) This question does not require a long exposition. Parts a, b and d ask you to provide some simple calculations (you must explain them) based on concepts/formulas that we have discussed extensively in the course. a) You want to estimate the model y = a + y2 + ε. Use the output below to show that the OLS estimator of y will be = 1.73. [Hint: Remember that the OLS estimator can be written as a ratio between a covariance and a variance. You can calculate them from the output below using the definition of correlation and standard deviation sum x y z Obs Mean Std. Dev. Variable Min Max X у 2 4,000 4,000 4,000 16.94809 59.3183 10.00008 4.171603 14.60061 2.057176 1.377411 4.820939 1.785265 32.18893 112.6613 16.65153 • corr Y Z (obs-4,000) у NK у Z 1.0000 0.2450 1.0000

b) We want to estimate the effect of y on x but x is potentially endogenous. We are therefore going to use z as an instrumental variable for x. Using the STATA output below and the result from part a), compute the IV estimator. (Hint: Remember that the IV estimator can be obtained by combining the reduced form and the first stage equations.] reg xz MS df Source SS Model Residual 4,000 255.35 0.0000 0.0600 0.0598 4.045 1 4177.89525 3,998 16.3616292 4177.89525 65413.7935 Number of obs F(1, 3998) Prob > F R-squared Adj R-squared Root MSE Total 69591.6887 3,999 17.4022727 Std. Err. t P>It! X Coef. 1959 Conf. Interval] z cons .4968572 11.97947 .0310932 3174444 15.98 37.74 0.000 0.000 .5578173 12.60184 .4358971 11.35711 c) Briefly state the two conditions required for a variable z to be a valid instrument for x d) Complete the missing values in the Stata's outcome below (indicated with rectangles A,B,C,D). Explain your calculations. [Hint for rectangle B: use the definition of the -statistic.] • reg Y2 X1 X2 df SS MS Source 330 83.21 0.0000 Model Residual 21.6685512 42.5747778 2 327 10.8342756 . 130198097 Number of obs F(2, 327) Prob > E R-squared Ad) R-squared Root MSE 0.3532 .36083 Total 64.243329 329 .195268477 Coef. t Std. Err. Y2 P>It! 1959 Conf. Intervall X1 X2 cons B .5125981 .0518867 .0697825 .0397344 .0443443 0.22 12.90 1.17 0.825 0.000 0.243 4344308 -.0353493 D .5907655 . 1391227