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Solutions to assignment 2 of ecmt 463-100 spring 2008 course, focusing on regression analysis. It includes graded problems with explanations, coefficient interpretations, and predictions based on given data.

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Download ECMT 463-100 Spring 2008 Assignment 2 Solutions: Regression Analysis and more Assignments Introduction to Econometrics in PDF only on Docsity! 1 ECMT 463-100 Spring 2008 Raul Ibarra-Ramirez Solutions for Assignment 2 I. Required Part a) Graded Problems 1. Problem 5.7 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. (b) 3.2 ± 1.96 × 1.5 = 3.2 ± 2.94 (c) Yes. If Y and X are independent, then β1 = 0; but this null hypothesis was rejected at the 5% level in part (a). (d) β1 would be rejected at the 5% level in 5% of the samples; 95% of the confidence intervals would contain the value β1 = 0. 2. Problem E6.2 2. Estimated regressions used in question Model Regressor a b dist −0.073 −0.032 bytest 0.093 female 0.145 black 0.367 hispanic 0.398 incomehi 0.395 ownhome 0.152 dadcoll 0.696 cue80 0.023 stwmfg80 −0.051 intercept 13.956 8.827 SER 1.81 1.54 R 2 0.007 0.279 2R 0.007 0.277 (a) −0.073 (b) −0.032 (c) The coefficient has fallen by more than 50%. Thus, it seems that result in (a) did suffer from omitted variable bias. (d) The regression in (b) fits the data much better as indicated by the R2, 2,R and SER. The R 2 and 2R are similar because the number of observations is large (n = 3796). 2 (e) Students with a “dadcoll = 1” (so that the student’s father went to college) complete 0.696 more years of education, on average, than students with “dadcoll = 0” (so that the student’s father did not go to college). (f) These terms capture the opportunity cost of attending college. As STWMFG increases, forgone wages increase, so that, on average, college attendance declines. The negative sign on the coefficient is consistent with this. As CUE80 increases, it is more difficult to find a job, which lowers the opportunity cost of attending college, so that college attendance increases. The positive sign on the coefficient is consistent with this. (g) Bob’s predicted years of education = −0.0315 × 2 + 0.093 × 58 + 0.145 × 0 + 0.367 × 1 + 0.398 × 0 + 0.395 × 1 + 0.152 × 1 + 0.696 × 0 + 0.023 × 7.5 − 0.051 × 9.75 + 8.827 = 14.75 (h) Jim’s expected years of education is 2 × 0.0315 = 0.0630 less than Bob’s. Thus, Jim’s expected years of education is 14.75 − 0.063 = 14.69. 3. Problem E6.3 3. Variable Mean Standard Deviation Units growth 1.86 1.82 Percentage Points rgdp60 3131 2523 $1960 tradeshare 0.542 0.229 unit free yearsschool 3.95 2.55 years rev_coups 0.170 0.225 coups per year assasinations 0.281 0.494 assasinations per year oil 0 0 0–1 indicator variable (b) Estimated Regression (in table format): Regressor Coefficient tradeshare 1.34 (0.88) yearsschool 0.56** (0.13) rev_coups −2.15* (0.87) assasinations 0.32 (0.38) rgdp60 −0.00046** (0.00012) intercept 0.626 (0.869) SER 1.59 R 2 0.29 2R 0.23 The coefficient on Rev_Coups is −2.15. An additional coup in a five year period, reduces the average year growth rate by (2.15/5) = 0.43% over this 25 year period. This means the GPD in 1995 is expected to be approximately .43×25 = 10.75% lower. This is a large effect.

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