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Assignment # 3: Economics 312
1. An important policy question often asked by firms is what determines workers’ participation in retirement savings scheme. The following regression is estimated based on the survey of 1,534 firms in the Unites States, with a focus on 401K retirement scheme participation.
prate = 97.32 + 5.02 mrate + 0.314 old − 2.66 log(totemp)
(0.51) (0.044) (0.28)
R 2 = 0.144, ESS = 61579.7017
(Standard errors are underneath each coefficient in parenthesis)
where prate = percent of total employees participating: (percentage)
mrate = proportion of employer’s matching contribution: (proportion) old =how long the 401K scheme has been operative in the firm, (year) totemp = total number of employees in the firm: (number)
a. (5-Points) Comment on the sign of each coefficient. Are the signs intuitive?
b. (5-Points) Interpret carefully the coefficient associated with log (totemp).
c. (5-Points) Find the adjusted R2 ( R 2 ) for the above problem.
d. (10-Points) Complete the following ANOVA table:
|
Source |
DF |
SS |
MS |
F |
P-value |
|
Regression |
-- |
-- |
-- |
-- |
-- |
|
Error |
-- |
-- |
-- |
-- |
-- |
|
Total |
-- |
-- |
|
|
|
e. (5-Points) Using the ANOVA results above, test if the three variables taken together are jointly significant in determining employees’ participation rate. Write the null hypothesis, alternative hypothesis, F-value, p-value, decision, and conclusion.
2. Consider the following model population model for a long-run average cost function:
ac = β1 + β2 q + β3 q 2 + β4 tech + β5 largecap + β6 tech*largecap + u ,
where ac: long-run average cost of a firm
q: output per year
tech: = 1 if the firm is in the tech sector; and = 0 if otherwise
largecap: = 1 if the firm’s market capitalization is $50 billion or more; and = 0 if in the small cap with less than $50 billion market cap.
tech*largecap: interaction variable.
a. (10-Points) Suppose the estimated coefficients for β2 and β3 are b2 = −6.06; b3 = 0.505 . Find the estimate of the slope of the average cost function at
(i) q = 3 (ii) q = 6 (iii) q = 9
b. (5-Points) All else remaining the same, when q increases from 3 to 9, what kind of shape of the average cost function do you observe from the data: Straight line, U- shaped, or inverted U- shaped? Discuss in a few sentences with your reasoning.
c. (10-Points) Using the population parameters ( βs), write down the average cost for a firm with q = 0, if the firm belongs to
(i) a largecap group and in the tech sector,
(ii) a large cap group and NOT in the tech sector,
(iii) a smallcap group and in the tech sector,
(iv) a small cap group and NOT in the tech sector.
d. (5-Points) Clearly identify the group that is in the reference category in the population model.
3. A data set on baseball players (named bballdata) is provided to you in the iLearn site. In this data set we need to investigate how the salaries of the major league baseball players are determined. The variable definitions in the data set are as follows. The last six variables are dummy variables signifying positions of the player in the field.
salary: 1993 season salary
years: years in major leagues
gamesyr: games per year in league
bavg: career batting average
hrunsyr: home runs per year
rbisyr: career runs batted in per year
runsyr: runs scored per year
fldperc: career fielding percentage
allstar: percentage of years an all-star
frstbase: =1 if first base
scndbase: =1 if second base
thrdbase: =1 if third base
shrtstop: =1 if shortstop
outfield: =1 if outfield
catcher: =1 if catcher
a. (5-Points) Run an OLS using the following population model and report the estimated equation with standard errors in parenthesis and R2. Population model:
log(salary) = β1 + β2 years + β3 gamesyr + β4 bavg + β5 hrunsyr +
β6 rbisyr + β7 runsyr + β8 fldperc + β9 allstar + β10 frstbase + β11scbdbase +
β12 thrdbase + β13 shrtstop + β14 catcher + u
b. (5-Points) State clearly, which position you had to use in (a) as the reference category.
c. (5-Points) Interpret the coefficients associated with bavg and shrtstop.
d. (5-Points) Test using the p-value approach, the null hypothesis that catchers and outfielders earn, on average, the same amount, all else equal. Show all your work.
e. (10-Points) Test at 5 percent level, that there is no difference in average salary across positions. (Hint: this is a subset test).
f. (5-Points) Find the correlation matrix of the explanatory variables and comment on the possible multicollinearity problem in the data. Use VIF command in STATA to check if multicollinearity is an issue.