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# ps8_sol - Department of Economics Columbia University...

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Department of Economics W3412 Columbia University Spring 2010 SOLUTION TO Problem Set 8 Introduction to Econometrics Prof. Marcelo J. Moreira and Seyhan E Arkonac, PhD for all sections Spring 2010 Question I: SW Exercises 12.1 (page 457) (a) The change in the regressor, ,1995 ,1985 ln( ) ln( ), cigarettes cigarettes i i P P from a \$0.10 per pack increase in the retail price is ln 2.10 ln 2.00 0.0488. The expected percentage change in cigarette demand is 94 0.0488 100% 4.5872%. The 95% confidence interval is ( 0.94 1.96 0.21) 0.0488 100% [ 6.60%, 2.58%]. (b) With a 2% reduction in income, the expected percentage change in cigarette demand is 0.53 ( 0.02) 100% 1.06%. (c) The regression in column (1) will not provide a reliable answer to the question in (b) when recessions last less than 1 year. The regression in column (1) studies the long-run price and income elasticity. Cigarettes are addictive. The response of demand to an income decrease will be smaller in the short run than in the long run. (d) The instrumental variable would be too weak (irrelevant) if the F -statistic in column (1) was 3.6 instead of 33.6, and we cannot rely on the standard methods for statistical inference. Thus the regression would not provide a reliable answer to the question posed in (a). Question II: 1. (a) Estimate the probability of smoking for (i) all workers (the full sample) (ii) workers affected by workplace smoking bans (iii) workers not affected by workplace smoking bans . sum smoker; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- smoker | 10000 .2423 .4284963 0 1 . sum smoker if smkban==1; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- smoker | 6098 .2120367 .4087842 0 1 . sum smoker if smkban==0; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- smoker | 3902 .2895951 .4536326 0 1

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(i) probability = 24.2% overall (ii) probability = 21.2% with smoking ban (iii) probability = 29.0% without smoking ban (b) What is the difference in the probability of smoking between workers affected by a workplace smoking ban and workers not affected by a workplace smoking ban? Use a linear probability model to determine whether this difference is statistically significant. . reg smoker smkban, r; Regression with robust standard errors Number of obs = 10000 F( 1, 9998) = 75.06 Prob > F = 0.0000 R-squared = 0.0078 Root MSE = .42684 ------------------------------------------------------------------------------ | Robust smoker | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- smkban | -.0775583 .008952 -8.66 0.000 -.0951061 -.0600106 _cons | .2895951 .0072619 39.88 0.000 .2753604 .3038298 ------------------------------------------------------------------------------ The probability of smoking is 7.8 percentage points less if there is a smoking ban than if there is not. The t -statsitic is -8.66 so the hypothesis that this difference is zero in population is rejected at the 1% significance level. (c) Estimate a linear probability model with smoker as the dependent variable and the following regressors: smkban, female, age, age 2 , hsdrop, hsgrad, colsome, colgrad, black, and hispanic. Compare the estimated effect of a smoking ban from this regression with your answer from 1(b). Suggest a reason, based on the substance of this regression, explaining the change in the estimated effect of a smoking ban between 1(b) and 1(c).
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