ECON Introductory Econometrics Seminar 7

Transcription

1 ECON Introductory Econometrics Seminar 7 Stock and Watson EE11.2 April 28, 2015 Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

2 E b clear set more off clear all cd M:\pc\Desktop\courses\introductory_econometrics\seminar_7 // E b and E b set obs 19 gen edu=0 replace edu=_n-1 gen pred_log= 1/(1+exp( *edu)) gen pred_prob= normal( *edu) gen pred_lin= 0.035*edu twoway (line pred_prob edu) (line pred_log edu) Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

3 E b The shape of the regression functions are similar Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

4 E b In this case the LPM model produces nonsensical results (probabilities smaller than 0) Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

5 Empirical exercise E11.2: Data Smoking.dta is a cross-sectional data set with observations on 10,000 indoor workers. Smoking.dta is a cross-sectional data set with observations on 10,000 indoor workers. The data set contains information on whether individuals were, or were not, subject to a workplace smoking ban, whether or not the individuals smoked and other individual characteristics. We are going to investigate the effect of smoking bans on smoking behavior. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

6 Empirical exercise E11.2: Data Variable smoker smkban age hsdrop hsgrad colsome colgrad black hispanic female description =1 if current smoker, =0 otherwise =1 if there is a work area smoking ban, =0 otherwise age in years =1 if high school dropout, =0 otherwise =1 if high school graduate, =0 otherwise =1 if some college, =0 otherwise =1 if college graduate, =0 otherwise =1 if black, =0 otherwise =1 if Hispanic =0 otherwise =1 if female, =0 otherwise Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

7 Empirical exercise E11.2: Data use "Smoking.dta",clear summ Variable Obs Mean Std. Dev. Min Max smoker smkban age hsdrop hsgrad colsome colgrad black hispanic female Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

8 a) //a //estimated probability of smoking summarize smoker for all workers is the proportion of smoker in the sample Variable Obs Mean Std. Dev. Min Max smoker //estimated probability for all workers affected by smoking ban summarize smoker if smkban==1 Variable Obs Mean Std. Dev. Min Max smoker //estimated probability for all workers not affected by smoking ban summarize smoker if smkban==0 Variable Obs Mean Std. Dev. Min Max smoker Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

9 b) One way is to compute the diff between the means computed in part a): = We can estimate linear probability model to check whether difference is significant reg smoker smkban, robust Linear regression Number of obs = F( 1, 9998) = Prob > F = R-squared = Root MSE = Robust smoker Coef. Std. Err. t P> t [95% Conf. Interval] smkban _cons Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

10 c gen age2=age^2 regress smoker smkban female age age2 hsdrop hsgrad colsome colgrad black hispanic, robust Linear regression Number of obs = F( 10, 9989) = Prob > F = R-squared = Root MSE = Robust smoker Coef. Std. Err. t P> t [95% Conf. Interval] smkban female age age hsdrop hsgrad colsome colgrad black hispanic _cons Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

11 c Coefficient in multiple regression model is quite a bit smaller in absolute value, this indicates that the first coefficient suffers from omitted variable bias. Characteristics of workers that work in an office with a smoking ban differ from the characteristics of workers that work in an office without a smoking ban. For example, workers with a college degree are more likely to work in an office with a smoking ban than high-school dropouts, and college graduates are less likely to smoke than high-school dropouts Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

12 d We can compute the t-statistic: H 0 : β smkban = 0 H 1 : β smkban 0 t = = 5.27 t = 5.27 > 1.96 so the null hypothesis that the coefficient on smkban is equal to zero is rejected at a 5% significance level. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

13 e To test the hypothesis that the probability of smoking does not depend on education we have to test the following joint null hypothesis: H 0 : β hsdrop = β hsgrad = β colsome = β colgrad = 0 H 1 : at least one among β hsdrop, β hsgrad, β colsome, β colgrad is not equal to 0 test hsdrop=hsgrad=colsome=colgrad=0 ( 1) hsdrop - hsgrad = 0 ( 2) hsdrop - colsome = 0 ( 3) hsdrop - colgrad = 0 ( 4) hsdrop = 0 F( 4, 9989) = Prob > F = The pvalue = so the null hypothesis is rejected at a 1% significance level. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

14 e The omitted education category is Masters degree or higher Thus the coefficients show the increase in probability of smoking relative to someone with a masters degree or higher For example, the coefficient on colgrad is 0.045, so the probability of smoking for a college graduate is (4.5%) higher than for someone with a masters degree or higher. Similarly, the coefficient on hsdrop is 0.323, so the probability of smoking for a high school dropout is (32.3%) higher than for someone with a masters degree or higher. Because the coefficients are all positive and get smaller as educational attainment increases, the probability of smoking falls as educational attainment increases. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

15 f probit probit smoker smkban female age age2 hsdrop hsgrad colsome colgrad black hispanic, robust Iteration 0: log pseudolikelihood = Iteration 1: log pseudolikelihood = Iteration 2: log pseudolikelihood = Iteration 3: log pseudolikelihood = Probit regression Number of obs = Wald chi2(10) = Prob > chi2 = Log pseudolikelihood = Pseudo R2 = Robust smoker Coef. Std. Err. z P> z [95% Conf. Interval] smkban female age age hsdrop hsgrad colsome colgrad black hispanic _cons Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

16 f We can compute the t-statistic: H 0 : β smkban = 0 H 1 : β smkban 0 t = = 5.45 t = 5.45 > 1.96 so the null hypothesis that the coefficient on smkban is equal to zero is rejected at a 5% significance level. Very similar t-statistic as in the linear probability model. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

17 f test hsdrop=hsgrad=colsome=colgrad=0 ( 1) [smoker]hsdrop - [smoker]hsgrad = 0 ( 2) [smoker]hsdrop - [smoker]colsome = 0 ( 3) [smoker]hsdrop - [smoker]colgrad = 0 ( 4) [smoker]hsdrop = 0 chi2( 4) = Prob > chi2 = The pvalue = so the null hypothesis is rejected at a 1% significance level Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

18 g logit smoker smkban female age age2 hsdrop hsgrad colsome colgrad black hispanic, robust Iteration 0: log pseudolikelihood = Iteration 1: log pseudolikelihood = Iteration 2: log pseudolikelihood = Iteration 3: log pseudolikelihood = Iteration 4: log pseudolikelihood = Logistic regression Number of obs = Wald chi2(10) = Prob > chi2 = Log pseudolikelihood = Pseudo R2 = Robust smoker Coef. Std. Err. z P> z [95% Conf. Interval] smkban female age age hsdrop hsgrad colsome colgrad black hispanic _cons Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

19 g We can compute the t-statistic: H 0 : β smkban = 0 H 1 : β smkban 0 t = = t = > 1.96 so the null hypothesis that the coefficient on smkban is equal to zero is rejected at a 5% significance level. Very similar t-statistic as in the linear probability model. Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

20 g test hsdrop=hsgrad=colsome=colgrad=0 ( 1) [smoker]hsdrop - [smoker]hsgrad = 0 ( 2) [smoker]hsdrop - [smoker]colsome = 0 ( 3) [smoker]hsdrop - [smoker]colgrad = 0 ( 4) [smoker]hsdrop = 0 chi2( 4) = Prob > chi2 = log close Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

21 h, i. Mr.A (male, white, no hispanic, 20 years old, high school dropout) probability of smoking with no ban based on the probit results: Pr(smok = 1/smkban = 0) A = Φ( ) = Mr.A probability of smoking with smoking ban based on the probit results: Pr(smok = 1/smkban = 1) A = Φ( ) = effect of the smoking bans in the probabiliyt of smoking of mister A is a decrease of 6.2 % Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

22 h, ii. Ms. B (female, black, 40 years old, college graduate) probability of smoking with no ban based on the probit results: Pr(smok = 1/ban = 0) B = Φ( ) = Ms. B probability of smoking with smoking ban based on the probit results: Pr(smok = 1/ban = 1) B = Φ( ) = effect of the smoking bans in the probabiliyt of smoking of mister B is a decrease of 3.3 %. The effect of introducing the ban is different for different individuals Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

23 h, iii. linear probability model: Pr(smok = 1/smkban = 0) A = = Pr(smok = 1/smkban = 1) A = = Pr(smok = 1/ban = 0) B = = Pr(smok = 1/ban = 1) B = = the marginal impact of workplace smoking bans on the probability of an individual smoking is not dependent on the other characteristics of the individual. In both cases the bans reduces the probability of smoking by Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

24 h, iv. Logit model: 1 Pr(smok = 1/smkban = 0) A = = e ( ) Pr(smok = 1/smkban = 1) A = difference is Pr(smok = 1/ban = 0) B = Pr(smok = 1/ban = 1) B = difference is Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25

25 h,v linear probability model assumes that the marginal impact indipendent of other characteristics. probit and logit predicted marginal impact of workplace smoking bans on the probability of smoking depends on individual characteristics In this sense the probit and logit model are likely more appropriate, and they give very similar answers we can think of large impacts. For example, for people with characteristics like Mr. A the reduction on the probability is great than 6% (from the probit and logit models) Stock and Watson EE11.2 ECON Introductory Econometrics Seminar 7 April 28, / 25