# ps7_sol - Department of Economics W3412 Columbia University...

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Unformatted text preview: Department of Economics W3412 Columbia University Spring 2010 SOLUTION TO Problem Set 7 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 Question I: 10.1 (a) Yes. The t-statistic for the coefficient on Experience is 0.031/0.009 = 3.44 > 2.58, so it is sign t the 1% level. ificant a (b) 0.712 + 0.031×10 = 1.022; ܲ (1.022) = 0.847 ݖ ெ௔௧௧௛௘௪ = ݎ ெ௔௧௧௛௘௪ = Φ (c) ௜௦௧௢௣௛௘௥ = 0.712 + 0.031×0 = 0.712; ܲݎ ஼௛௥௜௦௧௢௣௛௘௥ = Φ (0.712)=0.762 ݖ ஼௛௥ (d) ݖ ௃௘ௗ = 0.712 + 0.031×80 = 3.192; ܲݎ ௃௘ௗ = Φ (3.192) = 0.999. This is unlikely to be accurate because the sample did not include anyone with more than 40 years of driving experience. 10.2 (a) Yes. The t-statistic for the coefficient on Experience is 0.040/0.016 = 2.5 > 1.96, so it is nificant the 5% level. sig at ܲݎ ௔௧௧௛௘௪ ൌ 1 exp ሾെሺ1.059 0.040 ൈ 10ሻሿ ൌ 1 ൅ exp ሺെ1.459ሻ ൌ 0.811 ெ 1 ൅ ൅ 1 ܲݎ ஼௛௥௜௦௧௢௣௛௘௥ ൌ 1 1 ൅ exp ሾെሺ1.059 ൅ 0.040 ൈ 0ሻሿ ൌ 1 1 ൅ exp ሺെ1.059ሻ ൌ 0.742 (b) The shapes of the regression functions are similar, but the logit regression lies below the probit regression for experience in the range of 0 to 60 years. 10.3 (a) The t-statistic for the coefficient on Experience is 0.006/0.002 = 3 > 2.58, so it is significant evel. at the 1% l 0.774 + 0.006 × 10 = 0.836 ܲݎ ெ௔௧௧௛௘௪ = ܲݎ ஼௛௥௜௦௧௢௣௛௘௥ = 0.774 + 0.006 × 0 = 0.774 (d) The probabilities are similar except when Experience gets large (>40 years). In this case the LPM model produces nonsensical results (probabilities greater than 1.0). 10.4 (a) (b) Because there is only one regressor and it is a binary (Male), estimates for each model show the fraction of males and females passing the test. Thus, the results are identical for all models. 10.5 (a) = Φ (0.806 + 0.041 ×10 − 0.174 × 1 − 0.015 × 1 × 10) = 0.814 ܲݎ ஺௞௜௥௔ (b) ܲݎ ௃௔௡௘ = Φ (0.806 + 0.041 × 2 − 0.174 × 0 − 0.015 × 0 × 2) = 0.813 (c) No. The t-stat on the interaction term is − 0.015/0.019 = − 0.79. Since 0.79 < 1.64, it is not significant at the 10% level. Question II: Some U.S. states have enacted laws that allow citizens to carry concealed weapons. These laws are known as “shall-issue” laws because they instruct local authorities to issue a concealed weapons permit to all applicants who are citizens, mentally competent, and have not been convicted of a felony (some states have some additional restrictions). Proponents argue that, if more people carry concealed weapons, crime will decline because criminals are deterred....
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ps7_sol - Department of Economics W3412 Columbia University...

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