Question
Consider a market with two groups of customers. The individual inverse demand for customers in group one equals: P1 = 20 - q1. The individual
Consider a market with two groups of customers. The individual inverse demand for customers in group one equals: P1 = 20 - q1. The individual inverse demand for customers in group 2 equals: P2 = 20 - 2q2.The marginal cost of production is constant and equal to $2/unit. Assume an equal number of customers in each group. For purposes of the exercise, assume that there is one customer in each group. Assume that the market is served by a single firm with no entry.
3. You are concerned about omitted variable bias in the regressions of Question 1. For that reason, you decide to regress ln(wage) on all other variables in the dataset and use this model as a benchmark.
(a) Report a 95% confidence interval for the estimated slope parameter of educ (3 points), explain the relationship between the confidence interval and hypothesis testing (4 points), and test the hypothesis that one year of additional education would increase hourly wage by 12% (4 points).
(b) Assuming there is no omitted variable bias, discuss the estimated coefficient on female in the benchmark model. In particular, explain what the estimated coefficient on female means on hourly wage (3 points), compare the effect of being female and the effect of one year of additional education (2 points), and discuss whether it is statistically significant or not (2 points).
(c) Using the estimation results of the benchmark model, test the hypothesis that the hourly wage is not affected by the geographic location. Explain how you reach your conclusion. (Hint: use package car.)
(d) Using the estimation results of the benchmark model, test the hypothesis that the wage differential associated with African American is equal to the wage differential associated with Asian American. Explain how you reach your conclusion. (Hint: use package car.)
(e) How would you modify the benchmark model to estimate the effects on hourly wage of one additional year of education separately for each gender (4 points). How do the effects of education differ between the genders and is the difference statistically significant? (3 points) (f) Keoka is an African American woman, working in a metropolitan area. After she obtained her high school diploma, she got a job and started working instead of getting a higher education. Now she has a five-year of experience in the industry and is working full time (40 hours a week). Using the benchmark model, predict her hourly wage. Be careful: the left-hand side variable is ln(wage), but you should predict Keoka's wage.
4. It may be more useful to estimate the effect on earnings of education by using the highest diploma/degree rather than years of schooling. Define four dummy variables to indicate educational achievements; ? lt hs = 1 if educ
(a) (6 points) Create the dummy variables (lt hs, hs, col, some col) as defined above (3 points) and compute the sample means of hourly wage for each of the four education categories (3 points).
(b) (9 points) Regress wage on the four dummies (lt hs, hs, col, some col). You will face a problem. What is the problem here? Under what circumstances would you face the problem (4 points). To avoid it, you now regress wage on three dummies (lt hs, col, some col) excluding hs. Interpret the estimated coefficients and compare the estimation results with the findings in (a)
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