Problem 2. Wages and education. For this problem we will use the dataset PS2data (wages) . dta posted on bCourses. This dataset contains information on about 300 American workers. It includes their average monthly wage (wage), gender (male) and completed years of formal education (educ). You suspect (hope?) that people with higher educational attainment earn more on average. (a) Plot a scatter diagram of the average monthly wage against education level. Does it confirm your intuition? What differences do you see between individuals who did not complete high school and those that did? [Hint: use Stata's twoway command and overlay a linear fit using the Ifit graph option.] (b) Perform and OLS regression of wages on education. Be sure to include the robust option. Give a precise interpretation of least squares estimate of the intercept and evaluate its sign, size and statistical significance. Does its value make economic sense? Do the same for the least squares estimate of the slope. Does this slope estimate confirm the scatter plot above? (c) List the three OLS assumptions and give a concrete example of when each of those would hold in this context. Are these assumptions plausible in this context? (d) You are rightfully concerned whether education will, in fact, be rewarded in the labor market. You wonder if another year of education will yield an expected $100 more per month (which if discounted over a typical working lifetime at say, 5%, amounts to roughly a year at Berkeley). Test the following null hypothesis: Ho : B1 - 100 vs H1 : B / 100 (e) Let's now return to a familiar empirical question: do men and women carn the same amounts? As in part (a) above, generate a scatterplot of wage against the dummy variable male, and inscribe a linear fit. What is your answer to the question based on this graph? (f) Run an OLS regression of wage on male. Provide a precise interpretation of the slope. Do you believe you have found evidence of wage discrimination in this data, or is there another explanation for the differences? Explain. (g) As we did in problem set 1, perform a t-test of a difference in wages between men and women and report the t-stat and p-value. Compare the Stata output of that test with the regression results you got using the male dummy. To make the two results (in terms of t-stat and p-value) correspond, do you assume equal or unequal variance of men's and women's wages