ECON 306 - Homework 5
Don’t lose points - read these instructions carefully!
· Carefully answer each of the questions below.
· You need to show your work, not just the final answer
· Please make sure your work is legible & each problem and step are properly numbered/lettered in order
· You can write or type your answers for the questions
· Please put your name and PSU ID number at the top of the 1st page
· You may use as many sheets of paper as you need.
· If you did parts by hand:
o Scan your entire document (including the parts you typed and the parts done by hand)
o Save the file on your computer (.PDF is the only acceptable format)
o Merge the separate PDFs into one file using a service such as (PDFMerge!)
§ Failure to submit a single file will result in points being deducted
o Upload it to the CANVAS dropbox for this homework assignment.
· If you typed everything:
o Save the file on your computer (.PDF is the only acceptable format) and then upload it to the CANVAS dropbox for this homework assignment.
o Be sure your assignment is all on one file. Failure to submit a single file will result in points being deducted
· Pages must be scanned in proper order
The following problems will require a lot of calculations in STATA. It will generate many pages of output. Here is how your should organize it. The first pages should contain your answers to all the questions, along with showing any key algebraic equations or explanations you need to use along the way. After that, include the output from the regressions you executed in support of your answers. (You are encouraged to save paper and economize here, you may print this section with a small font, double-sided and/or with 2-up format.) Last, include a copy of the DO file that contains the commands you asked STATA to execute. Be sure you organize these in a way that will be clear to the reader.
For the following, use robust standard errors in all regressions/logits. (The language is “, robust” at the end of the command.)
Problem 1
In the dataset Smoker, there is information on 1196 males from the United States. Data from this sample includes the variables:
smoke= 1 for smokers, and 0 for nonsmokers
age=age in years
educ= number of years of schooling
income= family income
pcigs= price of cigarettes in the individual’s state
Part 1)
a) Generate a dummy variable “hi_ed” that is a 1 if a person has 16 or more years of education.
b) Estimate a linear regression (which in this context is called a linear probability model (LPM)) for the binary variable smoke on the independent variable hi_ed. Report the beta coefficient on the dummy variable and its p-value. In words, express what the beta coefficient means in this case.
c) Create a frequency table for the smoke and hi_ed variables. The command in STATA is tabulate smoke hi_ed.
d) Calculate the probability that a person smokes if low education. Calculate the probability for smoking for high edcuation.
e) What is the relationship between the results for parts b and d?
f) Calculate the odds that a low education person smokes. Calculate the odds a high education person smokes. Calculate the odds ratio.
g) Estimate the logistic regression (logistic command) for smoke and hi_ed. Confirm that this equals the odds ratio. In words, express what the odds ratio coefficient means in this case.
Part 2)
a) Generate a variable for the log of prices
b) Estimate the logistic regression for smoke on lpcigs when hi_ed=0. Then, calculate the predicted values for Y. The command to do this is “predict yhat_0.” Repeat for when hi_ed=1, and also create a predicted value variable yhat_1.
c) Compare the coefficients for the two models. In words, explain what the model is saying about the impact of lpcigs for the two different education groups.
d) Create a graph of the predicted values for the two versions. Use the following syntax: twoway (line yhat_0 lpcigs, sort) (line yhat_1 lpcigs, sort), legend(label(1 "low ed") label(2 "hi ed"))
e) For a low education person, if the price of cigarettes doubles, the by approximately how much this change the odds of smoking? (Remember the interpretation of a log variable. A doubling is a change of 100%.)
Part 3)
a) Run a logit regression (stata command logit) for smoke on all the independent variables: age, educ, pcigs, income. Report the coefficients and p-values. This Model 1. Remember, for logit, (rather than logistic), the coefficients have not been exponentiated.
b) If the price of cigarettes increases by $1 (all else equal), then what will be the change in the odds of smoking?
c) If the price of cigarettes increases by $5 (all else equal), then what will be the change in the odds of smoking? (Here’s a hint: If you think this will be 5x as large as in part b, you are wrong. Close, but wrong.)
d) Create an interaction variable of educ and income. Run another logit regression, adding this interaction to Model 1. Report the coefficients and p-values. This is Model 2.
e) What differences strike you about Model 1 and Model 2? In particular, note how the significance levels of the variables of educ and income have changed now that the interaction is included. In a clearly articulated paragraph (or two) give a thoughtful answer as to what you think must be going on. (This is not easy. Take your time and think hard about it.Your answer should contain two parts. First, talk about what the coefficients of the Model 2 regression are implying. Second, try and come up with an intuitive/economic hypothesis for why we are observing these results.)