Econ HW

Problem Set 2 DUE: 2/17/2015 ECON300

1. Short questions

a. You run the following two models through OLS and record the !!:

Model A: ! = !! + !!!! + !!!! + ! → !!!

Model B: ! = !! + !!!! + !!!! + !!!! + ! → !!! Which is true: !!! ≥ !!! or !!! ≤ !!!? Give a one sentence explanation.

b. True or False: The homoskedasticity assumption is required for OLS estimates to be unbiased.

c. You estimate the following model using a sample of 100 observations.

! = !! + !!!! + !!!! + !!!! How many degrees of freedom does this model have? You must show your math.

2. The following random samples of 10 observations were taken from the same

population. You estimate the slope and intercept of the following model twice, once using each sample:

! = !! + !!! + ! Which sample do you think would yield a slope estimate with a smaller standard error? (In other words for which sample will !"(!!) be smaller, or alternatively, for which sample would you be most sure about your estimated slope?). Explain briefly.

(Sample 1) (Sample 2) HINT: While not necessary, it may help to think if you can say anything definitive about any of the ingredients in the numerator & denominator of the formula for the standard error:

!" !! = !!!!!!,! where !! ! = !!"!!! =

! !!! !!

!! !!!

!!!! = !! − ! !!!!! !!!!!!!!!!!!!!!!!!!! !

0 20

40 60

80 y

0 5 10 15 20 x

0 20

40 60

80 y

0 5 10 15 20 x

3. On average a baby born with a low birth weight is more likely to have health problems. According to the Centers for Disease Control (CDC): “Smoking during pregnancy can cause a baby to be born too early or to have low birth weight.” Suppose you are trying to uncover the relationship between the number of cigarettes smoked per day by pregnant mothers and the birth weight of their babies.

a. Use the dataset called PS2_BWGHT.dta (see instructions at the end of the

problem set for opening the dataset), to regress birth weight (variable bwght) against the number of cigarettes smoked per day (variable cigs):

!"#ℎ! = !!! + !!!"#$ + ! The results follow the sample regression line: !"#ℎ! = !!! + !!!"#$.

To do this in STATA, use the following command:

regress bwght cigs. What is the interpretation of !!, the estimated coefficient on cigs that you calculated with STATA? [HINT: Use the describe command to find out the units of the two variables]

b. Do you think the zero conditional mean assumption is satisfied in the

model that was estimated in part (a)? In other words, does ! !"#$ = ! ! = 0 ? Explain in 2-3 sentences.

c. Family income is a factor that we omitted from the model in part (a). The model should have been:

!!"#ℎ! = !!! + !!!"#$ + !!!"#$%& + !

In part (a) we omitted this relevant variable. Do you think this resulted in the estimate of !! in part (a) being biased? If so, in what direction do you think it was biased? [HINT: Use the table on the bottom of page 90 that we discussed in class]

d. EXTRA CREDIT. Luckily, family income is in the dataset. Try running

the model controlling for family income. How does the new estimated coefficient on cigs differ from what you calculated in part (a), and does this agree with your prediction in part (c)?

4. In a study relating college grade point average to time spent in various activities,

you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any activity is put into one of four categories, so that for each student, the sum of hours in the four activities must be 168 (total number of hours in a week).

a. In the following model:

!"# = !! + !!!"#$% + !!!"##$ + !!!"#$ + !!!"#$%&" + ! does it make sense to hold sleep, work, and leisure fixed, while changing study?

b. Explain why this model violates the No perfect collinearity assumption for

unbiasedness. (Hint: Remember perfect collinearity can happen when one independent variable is a linear combination of one or more of the other independent variables)

5. Suppose you are trying to uncover the relationship between education and wages, where education is measured with years of school completed and wage is measured by hourly wage. You know the population model is:

!"#$ = !! + !!!"ℎ!!" + !!!!"_!"# wage = hourly wage school = years of schooling completed ttl_exp = total years of work experience

a. Using the dataset nlsw_ps2.dta (see instructions at end of problem set for obtaining the dataset and inputting it into Stata) you run the model specified above. To do this in Stata run the following command after the dataset has been opened in the program:

regress wage school ttl_exp Report output. What is the interpretation of the estimated !!?

b. What if your dataset didn’t have a measure for total work experience so instead you ran this model:

!"#$ = !! + !!!"ℎ!!"

and obtained estimates !! and !!. Would you expect !! to be biased? If so, in what direction would you expect the bias to be? Show your work.

Instructions for opening an external dataset in Stata. If you are using a copy of Stata that is installed locally (like in a UIC lab), follow the following procedure to open the dataset: 1. Download the file from blackboard and save to your desktop.

2. Open Stata 3. In Stata, go to File, Open, and double click the downloaded file

If you are using a copy of Stata that you purchased from the UIC Webstore follow the following procedure to open the dataset:

1. Download the file from blackboard and save to your desktop. 2. Right click and copy the downloaded .dta or .do file 3. Open Stata 4. In Stata, go to File, Open, and create a new folder 4. Paste the file into the new folder, double click the file and it should open up.