Several prominent researchers have alleged that Twitter causes unhappiness among affluent politically- engaged 30-something-year-old individuals. You were hired by Twitter to prepare a defense against these allegations. You ran a randomized control trial: you selected a large sample of affluent politically-engaged 30-something-year-old individuals and split them randomly into two groups (control and treatment). You blocked access to Twitter for the individuals in the treatment group for some time Xi (measured in hours). You measured the levels of happiness of all individuals before and after the trial. You believe that the relationship between the change in the happiness level (yi) and the number of hours a person is separated from Twitter (li) is generated by the following data generating process: E(YX) = Bri. You also believe that the error of this regression is heteroskedastic and the skedastic function is quadratic: E((Yi - Bx;)?|x) = ye?. You consider four possible ways to estimate B and to construct the standard errors: 1n • Method 1: B1 = Li= my Use homoskedasticity-only s. e. n2=1 • Method 2: B2= 12h (). Use homoskedasticity-only s. e. • Method 3: B1 = 1 Liety 1 Use heteroskedasticity-robust s. e. • Method 4: B2 = 12-1(4). Use heteroskedasticity-robust s. e. (a) Discuss the validity of each method.
(b) Which of these methods do you expect the opposing side to use to establish the claim? Explain.
(c) (Which of these methods should you use for your defense to cast doubts on the results of the experiment? Explain.
(d) For your defense, will you use a two-sided or one-sided alternative? Why?
(e) Your model assumes that the intercept term of the data generating process is zero. Somebody told you that in this case it may be a good idea to transform your data first by removing the mean and run OLS on the transformed data: i. e. instead of regressing Yi on ti, you will be regressing (Yi - y) on (Ii – 7). Evaluate whether the proposed approach violates any of the OLS assumptions discussed