ECON 306 Homework 5 Creighton Mitchell ID 0874 CKM6071 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 a Finished 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 a Beta coefficient 1839249 p value 0 000 b In this case the beta coefficient represents the relationship amongst education and smoking Meaning that if you have 16 years of education you are 18 39 more likely to smoke than if you had less than 16 years of education c Create a frequency table for the smoke and hi ed variables The command in STATA is tabulate smoke hi ed a Finished smoking for high education d Calculate the probability that a person smokes if low education Calculate the probability for a Low education calculation 403 971 0 4150 b High education calculation 52 225 0 23111 e What is the relationship between the results for parts b and d a I see a good correlation in the table you see that if you have hi ed then you are less likely to smoke same as what we see in the percentage calculations in d f Calculate the odds that a low education person smokes Calculate the odds a high education person smokes Calculate the odds ratio a Low education 403 971 568 971 0 709507 b High education 52 225 173 225 0 30057 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 a I found that what we calculated in the odds ratio matched what we calculated in Stata using the logistic command When you subtract the low education odd from 1 you can check to see if we get our high education odds ratio that we calculated Which we did This coefficient means that the odds of smoking between low and high education individuals differs by the factor of 4236 which was found in Stata Part 2 a Generate a variable for the log of prices a Finished a Finished 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 a Coefficient for high education 252753 b Coefficient for low education 433757 i The coefficients tell us the story that any change in the price of cigarettes which is what we ran the regression for would say that the price affects the propensity to buy in high education individuals more than the low individuals In everyday terms this would make sense because price wouldn t impact people who are dependent on cigarettes because no matter what they will need the cigarettes Whereas the high education people who seemingly aren t as reliant on the cigarettes would have less of an issue finding an alternative if the price rises 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 a Finished 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 a log 252753 0 59730 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 a Coeff b P z b If the price of cigarettes increases by 1 all else equal then what will be the change in the odds a 252753 1 252753 252753 747247 approx 0 338245 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 a 0 338245 5 0 338245 1 691225 …