The dataset SMOKE contains information on factors which determine an individual’
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Question
The dataset SMOKE contains information on factors which determine an individual’s smoking habits. The information includes on an individual’s race (a binary variable white equals one if individual is white and zero otherwise), age (age), income (income), years of education (educ), statewide smoking restrictions in restaurants (binary variable restaurn equal one if restaurants restrict smoking and zero otherwise), price of cigarettes (cigpric), and the number of cigarettes an individual smokes (cigs).
Use this dataset from http:/fmwww.bc.edu/ec-p/data/Wooldridge/smoke to estimate a linear probability (LPM) and probit model.
smoker= 0 + 1 lcigpric +2 educ + 3 age + 4 agesq + 5 income
+0 white + 1 restaurn + u
where smoker is a binary dependent variable equal to one if an individual smokes (cigs >=1) and zero otherwise, lcigpric is the log of cigarette prices, agesq is age2 and u is the error term. You need to create the binary dependent variable smoker.
Explain the difference in the estimated partial effects of lcigpric, educ, restaurn, and age for a 25 year old on the probability of smoking between the linear probability model and probit models. Calculate and interpret the average partial effect (APE), and partial effect at the average (PEA) for lcigpric, educ, restaurn, and age for a 25 year old in the probit model?
Hint: First test for heteroscedasticity for educ, income age agesq variables in the LPM model using hettest after regress.
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Then estimate both models with heteroscedasticity-robust standard errors using the option vce(robust) for both models.
Calculate the average partial effects for the probit model using the margins, dydx (*) command after probit.
Im having an unsually difficult time with this question, any help would be greatly appreciated
Explanation / Answer
Variable Definitions Variable Definition
smoker =1 if current smoker, =0 otherwise
smkban =1 if there is a work area smoking ban, =0 otherwise
age in years hsdrop =1 if high school dropout, =0 otherwise
hsgrad =1 if high school graduate, =0 otherwise colsome =1
if some college, =0 otherwise colgrad =1
if college graduate, =0 otherwise black =1
if black, =0 otherwise hispanic =1 if Hispanic =0 otherwise
female =1 if female, =0 otherwise.
1probability of smoking for all workers
2 . sum smoker
Variable Obs Mean Std. Dev. Min Max
smoker 10000 .2423 .4284963 0 1
3 . // Probability of smoking for workers affected by smoking ban
4 . sum smoker if smkban==1
Variable Obs Mean Std. Dev. Min Max
smoker 6098 .2120367 .4087842 0 1
5 . // Probability of smoking for workers not affected by smoking ban
6 . sum smoker if smkban==0
Variable Obs Mean Std. Dev. Min Max
smoker 3902 .2895951 .4536326 0 1
The partial effect of credit score on default probability is the amount that default probability goes up (or down) when credit score rises by one point and all other factors stay the same. Think about two people, one with a credit score of 650 and one with a credit score of 651. In all other respects (income, time on job, loan-to-value ratio, etc), they are identical. The one with the higher credit score will have a lower probability of default. The probability may only be a tiny, tiny bit lower since this is such a small difference in credit scores, but, because everything else is the same, it will be lower. This difference in default probabilities between a person with a credit score of 650 and a credit score of 651 but with everything else identical is the partial effect of credit score on default probability.
There are two complications, though. First, the difference in default probability between a person with a 650 score and a 651 credit score will not be the same as the difference in default probability between someone with a 750 and 751 credit score. Second, the 650 vs 651 difference in default probability will depend on their other characteristics. Two low income people, one with a 650 and one with a 651, may have a larger difference in default probability than two high income people, one with a 650 score and one with a 651.
To deal with these complications, we first calculate a personalized partial effect, the difference in default probabilities due to a one point increase in credit score, for each person in the sample. Then, we average over these personalized partial effects to give the average partial effect. This is called the "average partial effect" of credit scores on default probabilities.
The partial effect of credit score on default probability is the amount that default probability goes up (or down) when credit score rises by one point and all other factors stay the same. Think about two people, one with a credit score of 650 and one with a credit score of 651. In all other respects (income, time on job, loan-to-value ratio, etc), they are identical. The one with the higher credit score will have a lower probability of default. The probability may only be a tiny, tiny bit lower since this is such a small difference in credit scores, but, because everything else is the same, it will be lower. This difference in default probabilities between a person with a credit score of 650 and a credit score of 651 but with everything else identical is the partial effect of credit score on default probability.
There are two complications, though. First, the difference in default probability between a person with a 650 score and a 651 credit score will not be the same as the difference in default probability between someone with a 750 and 751 credit score. Second, the 650 vs 651 difference in default probability will depend on their other characteristics. Two low income people, one with a 650 and one with a 651, may have a larger difference in default probability than two high income people, one with a 650 score and one with a 651.
To deal with these complications, we first calculate a personalized partial effect, the difference in default probabilities due to a one point increase in credit score, for each person in the sample. Then, we average over these personalized partial effects to give the average partial effect. This is called the "average partial effect" of credit scores on default probabilities.
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