Econ 122a Problem Set 6
Econ 122A Problem Set 6 Name(Print)______________________ Due in class on March 14 UCI ID_____________________________ 1. In class, we have talked about the following simple wage equation
wage = α + β female + u , where female is a dummy that is equal to 1 if female, and 0 otherwise. ˆ ˆ Given the OLS estimates α and β for the above model, what are the OLS estimates ˆ ˆ for a model with a male dummy instead of a female dummy, i.e., what are a and b for wage = a + bmale + u ? (Hint: female = 1‐ male)
2. Consider the following model:
log(Y ) = α + β X + δ1 D1 + δ 2 D2 + u , where Y = annual earnings of MBA graduates, X = years of experience, D1=1 if Harvard MBA; =0 otherwise, D2=1 if Wharton MBA; =0 otherwise.
(1) What are the expected signs of β , δ1 and δ 2 ? note that earnings are in the log form)? (3) If δ1 > δ 2 , what conclusion would you draw?
(2) How would you interpret δ1 and δ 2 (hint: what is the base group here;
3. Suppose you are interested in learning if there are seasonal patterns in party supply sales in OC, that is, you would like to know if sales in a particular season are significantly different from other seasons. Suppose the following model is estimated:
sales = α + β1 D1 + β 2 D2 + β3 D3 + u , where sales is the quarterly party supply sales in thousands of dollars in OC; D1, D2, and D3 are dummies indicating the first, the second, and the third quarter respectively. 1
(1) How would you interpret the estimated intercept and slopes? (2) How would you test if sales in the third quarter are significantly different from those in the fourth quarter? Write down the null hypothesis and decide whether you need to do a t or an F test. (3) How would you test if sales in the first quarter are significantly different from those in the second quarter?
wage = α + β female + u , where female is a dummy that is equal to 1 if female, and 0 otherwise. ˆ ˆ Given the OLS estimates α and β for the above model, what are the OLS estimates ˆ ˆ for a model with a male dummy instead of a female dummy, i.e., what are a and b for wage = a + bmale + u ? (Hint: female = 1‐ male)
2. Consider the following model:
log(Y ) = α + β X + δ1 D1 + δ 2 D2 + u , where Y = annual earnings of MBA graduates, X = years of experience, D1=1 if Harvard MBA; =0 otherwise, D2=1 if Wharton MBA; =0 otherwise.
(1) What are the expected signs of β , δ1 and δ 2 ? note that earnings are in the log form)? (3) If δ1 > δ 2 , what conclusion would you draw?
(2) How would you interpret δ1 and δ 2 (hint: what is the base group here;
3. Suppose you are interested in learning if there are seasonal patterns in party supply sales in OC, that is, you would like to know if sales in a particular season are significantly different from other seasons. Suppose the following model is estimated:
sales = α + β1 D1 + β 2 D2 + β3 D3 + u , where sales is the quarterly party supply sales in thousands of dollars in OC; D1, D2, and D3 are dummies indicating the first, the second, and the third quarter respectively. 1
(1) How would you interpret the estimated intercept and slopes? (2) How would you test if sales in the third quarter are significantly different from those in the fourth quarter? Write down the null hypothesis and decide whether you need to do a t or an F test. (3) How would you test if sales in the first quarter are significantly different from those in the second quarter?