Practice questions which I want to check some work with. Thank you!

In this section, show all work. Only partial credit will be given for correct answers if no explanations are provided. 1. (8 marks) Suppose you have data on wages () ) for the population who enrolled in an un- dergraduate program at University of Calgary and you know whether each individual has a BA degree (D.) (i.e. the population consists of college drop outs and college graduates). You regress wages (measured in Canadian dollars per hour) on the education (BA degree) dummy variable and get the following population regression function log(17) = 1.06 + 0.52D (a) Think of the model as a descriptive model. Interpret the estimated slope coefficient in this context. (b) Suppose a test was conducted, nationally, yesterday. Samson got information about the test scores for each individual (x2). He added the score as a conrol variable and he got the following results log(Y,) = 0.80 + 0.45D + 0.04x2. What can you tell about the causal effect of obtaining BA degree at U of C? 2. (5 marks) Suppose you have data on people's exercise habits (ezer, measured in average minutes per day) and their age at death (age, measured in years). Suppose now that you run a regression of age at death on exercise and find that age; = 65 + 0.lezer, + wi- (a) Thinking about the model in terms of causality, explain what it means that the slope coefficient is 0.1. (b) Do you think the omitted variable bias is negative or positive in this case (and please explain why)? If you got data on that variable and included that variable into the model, what would that do to the coefficient on exercise? 3. (15 marks) Suppose that you observe a random sample {(r;, y;)}, from the model Mi = Po + Bizi + wi- Suppose that this model satisfies the first four Gauss-Markov assumptions. Consider the slope estimator A = (EN,(a -3)w) / (EN(x -2)m ) where a = 2; (a) Show that #1 is linear. (b) Show that & is unbiased. (Hint for a) and b): you can treat both I, and 2, as nonrandom in your deviation because E(ulx) = 0)