Econ 300 Fall 2016 Problem set 3 Due 10/18 Instructions: Please write/type your answers and hand in a hard copy before class starts. The total points for this problem set is 50. For STATA questions, paste codes/screenshot if relevant. 1. (Direction of bias) In order to improve performance, Chicago public schools decide to give bonus salary to teachers whose students achieve top 10 percentile of a standardized test. In order to evaluate if this bonus salary is effective in raising students' performance, one researcher runs the following regression: Avg_student_score=0+1Receive_Bonus+2School+3State+ a. Give two examples of omitted variables that may bias " b. Explain the direction of bias and the plausible stories leading to the bias 2. (Attrition) Seasonal affective disorder (SAD) is a mood disorder condition mostly common in winter. A randomized control trial is carried out to study whether light therapy is effective at treating SAD. The treatment group receive one more hour of sun exposure per day for a period of three months relative to the control group. The outcome is measured as a depression scale (0-5, 5 means very depressed) a. Specify the regression model you would run to evaluate this study b. Explain the condition when attrition causes no problem c. Assume people who are more seriously ill lack the perseverance of sticking to the treatment, and they drop out of the study more often in the treatment group than control. Will this type of attrition cause biased estimate? If so, explain whether it is an upward or downward bias and why. 3. (STATA) The exercise is based on the RAND Health Insurance Experiment we covered in class. Download the dataset ps3_rand.dta from blackboard. The dataset contains the following variables: The task is to create a balance table of demographic characteristics and pre-treatment outcome variables Part I Randomized control trial a. In this experiment, which group is control? which group is treatment? b. Generate the mean and S.D. for the variable educper separately for treatment and control groups. Do they look different? c. Perform a t-test on the difference in mean educper between treatment and control groups. Explain if these two coefficients are statistically different. (Hint: use the command ttest XX, by (XX). This is the codes for a two sample t-test with equal variance) d. Repeat c) for variables female, blackhisp, ghindx and cholest. Put all five variables (include educper) in a balance table. The table should contain only two columns. The first column shows means of all five variables for the control group. The second column shows the differences between treatment and control groups and standard errors for these differences. The s.e. are in parentheses. (Refer to the first two columns of the table below). Based on those t-tests, do you think the randomization is done properly? Explain. Part II Dummy variable trap a. We are interested in whether education affect pre-enrollment blood cholesterol. Run a simple regression of the blood cholesterol at enrollment on education. Does the sign of the coefficient make sense? Explain. b. Generate 3 dummy variables for education. Name them HS_dropout; HS_grad; college_or_above. HS dropouts have education under 12 years; HS grads have education between 12 and 16 (not including 16); and people with a college degree have education equal to or greater than 16. Paste your codes below. Show the summary statistics of three new variables. (Hint: the mean of all three variables should add up to 1) c. Regress the blood cholesterol at enrollment on two of the three education groups. Paste your codes and the regression results. Interpret three coefficients (including the coefficient of the constant term). d. Regress the blood cholesterol at enrollment on all three education group and omit the intercept.