04 Jun Question Econ 122B Problem Set 3
Question
Econ 122B Problem Set 3
1. In class, we have talked about the following simple wage equation wage female u =+ + a b , where female is a dummy that is equal to 1 if female, and 0 otherwise. Given the OLS estimates ˆ aˆ and b for the above model, what are the OLS estimates for a model with a male dummy instead of a female dummy, i.e., what are aˆ and ˆ b for wage a bmale u =+ + ? (Hint: female = 1? male)
2. Consider the following model: 11 2 2 log( ) Y X D Du =+ + + + a bd d , 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 b , 1 d and 2 d ? (2) How would you interpret 1 d and 2 d (hint: what is the base group here; note that earnings are in the log form)? (3) If 1 2 d > d , what conclusion would you draw?
2. 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 D D D u =+ + + + a bb b , 2 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) 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? Write down the null hypothesis and decide whether you would use a t test or an F test.
(4) How would you test that sales do not have seasonality, i.e., there is no significant difference in sales across seasons? Write down the null hypothesis and decide if you would use a t test or an F test.
3. Suppose you are interested in learning how recession could change people’s charitable donation behavior. Suppose you have data on individual’s dollar amount donated to some good cause (Donate) and individual’s income (Inc), in dollars, for the United States for the period 1979?1985. In 1982 the United States suffered a very bad recession, an event that might disturb the relationship between Donate and Inc. To see if this happened, you estimate a simple savings function that relates Donate to Inc. 1 23 log( ) log( ) log( ) * , Donate Inc T Inc T u =+ + + + a b bb where T=1 for 1979?1981, and 0 for 1982?1985. (1) What is the impact of the recession (T) on donations? Write down the expression for it.
(2)How would you test the null hypothesis that the donation?income relationship did not change before and after the 1982 recession? Write down the null hypothesis and determine if you need to perform a t test or an F test.
5. You are curious about how many words people speak per day, so you estimate the following model, 12 3 + * , words female married female married u =+ + + a bb b Below is what you get, 2 1,000 1,000 500 1,000 * , ˆ (300) (350) (200) (400) n=526, R .308 words female married female married =+ – + = where words is the number of words one speaks per day; female is a dummy equal to 1 if female and 0 otherwise; and married is a dummy indicating one is married or not, and married is 1 if married and 0 otherwise. (1) How would you interpret the coefficient of female? (2) How would you interpret the coefficient of married? (3) How would you test the hypothesis that marital status does not hav
ANY significant impact on words spoke per day? That is, for both males and females, being married does not have significant impacts on words spoke per day. Write down the null hypothesis, determine if you need a t or an F test.
(4) How would you determine whether the gender difference in talkativeness depends significantly on marital status. Write down the null hypothesis, determine if you need a t or an F test, and what is your conclusion (using a 5% significance level)?
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