]Use that data set in BEAUTY. DTA , which contains a subset of the variables (bu

Question

]Use that data set in BEAUTY. DTA, which contains a subset of the variables (but more usable observations than in the regression) reported by Hamermesh and Biddle (1994).

i.Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as having above average or below average looks?

ii.Test the null hypothesis that the population fractions of the above average looking women and men are the same. (Hint: estimating a simple linear probability model is easiest.)

Now estimate the model

separately for men and women, and report the results in the usual form. In both cases, interpret the coefficient on behavg.

Is there convincing evidence that women with above average looks earn more than women with average looks? Explain.

v.For both men and women, add the explanatory variables educ, exper, exper2, union, goodhlth, black, married, south, bigcity, smallcity, and service. Do the effects of the “looks” variables change in important ways? Explain.

Explanation / Answer

Answer:

I use Stata commands to answer these questions

i. Using command “count if female ==1” and “count if female ==0”
Total females = 436 and total males = 824.

Now using command “count if abvavg ==1 & female == 1”, we get females with above average looks which is 144. Using “count if abvavg ==1 & female == 0”, we get males with above average looks which is 239.

Fraction of females with average looks = 144/436 and Fraction of males with average looks = 239/824

Total of people with above average looks can be found using command “count if abvavg==1” which is 383. Total of people with below average looks can be found using command “count if belavg==1” which is 155. Thus more people are rated as having above average looks.

ii.

Let us run the below code to form a new variable.
maleabavg represents males with above average looks and femaleabavg represents females with above average looks

gen maleabavg = 0
replace maleabavg =1 if abvavg == 1 & female ==0

gen femaleabavg = 0
replace femaleabavg =1 if abvavg == 1 & female ==1

We can now run a proportions t-test to see if their fractions are same or not.
prtest maleabavg == femaleabavg

Under   Ho: diff = 0 [i.e. prop(maleabavg) - prop(femaleabavg)   = 0 ].

The p-value is 0.000 i.e. null can be rejected. P-value of prop(femaleabavg) > prop(maleabavg) is 1.000 i.e. it is not statistically significant.

iii.
Now we also code the males and females with below average looks.

gen malebeavg = 0
replace malebeavg =1 if belavg == 1 & female ==0

gen femalebeavg = 0
replace femalebeavg =1 if belavg == 1 & female ==1

We may now estimate effect of looks on wage separately for male and females.

Regression 1 code on females: reg lwage femaleabavg femalebeavg

Lwage = 1.729114 – .5579231 femalebeavg – .3866561 femaleabavg
All estimates are significant at all level of significance.

Regression 2 code on males: reg lwage maleabavg malebeavg

Lwage = 1.60928 + .0758578 malebeavg + .2305978 maleabavg
Except the coefficient on malebeavg, all are significant.

H0: b1 = 0 against H1: b1 < 0
Null hypothesis means that below average looks has no effect on logwage whereas b1< 0 means that below average looks has negative effect on the logwage, everything else being held constant.

The coefficient on belavg for male (here malebeavg) is positive i.e. percentage change in wage has a positive association with a male with below average looks. The coefficient on belavg for female (here femalebeavg) is negative i.e. percentage change in wage has a negative association for a female with below average looks.

p-value of b1 for men = 0.229 while p-value of b1 for women = 0.000.

iv. Yes. The coefficient of below and above average looking women is negative as shown earlier. However, the coefficient of above average looking females is less than below average looking females. That can be taken as an evidence that women with above average looks earn more than women with average looks.

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