ps4_sol-1 - Introduction to Econometrics Professor Alexei...

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Introduction to Econometrics Professor Alexei Onatski Problem Set 4 – October 14 Problem 1) [ Stock and Watson5.1 ] (a) The 95% confidence interval for 1 β is { 5 82 1 96 2 21}, . that is 1 10 152 1 4884. .≤ . (b) Calculate the t -statistic: 1 1 ˆ 0 582 2 6335 ˆ SE( ) 2 21 act t −. = == . . . The p -value for the test vs. 01 0 H := 11 0 H :≠ is -value 2 ( | |) 2 ( 2 6335) 2 0 0042 0 0084 act pt =Φ− =Φ−. =×. =. . The p -value is less than 0.01, so we can reject the null hypothesis at the 5% significance level, and also at the 1% significance level. (c) The t -statistic is 1 1 ˆ (5 . 6 ) 022 0.10 ˆ SE( ) 2 21 act t −− . = . The p -value for the test :5 H . 6 = − vs. H . 6 ≠ − is -value 2 ( | |) 2 ( 0.10) 0.92 act = The p -value is larger than 0.10, so we cannot reject the null hypothesis at the 10%, 5% or 1% significance level. Because 1 5.6 = − is not rejected at the 5% level, this value is contained in the 95% confidence interval. (d) The 99% confidence interval for 0 is {520.4 2.58 20.4}, ± × that is, 0 467.7 573.0. ≤≤ Problem 2) [ Stock and Watson5.7 ] (a) The t -statistic is 3.2 1.5 2.13 = with a p -value of 0.03; since the p -value is less than 0.05, the null hypothesis is rejected at the 5% level.
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(b) 3.2 ± 1.96 × 1.5 = 3.2 ± 2.94 (c) Yes. If Y and X are independent, then β 1 =
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This note was uploaded on 12/20/2009 for the course ECON 1300 taught by Professor Natski during the Fall '09 term at Columbia.

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ps4_sol-1 - Introduction to Econometrics Professor Alexei...

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