代做Assignment # 3: Economics 312代写Web开发

日期：2024-08-03 05:56

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)

艹 一、一 艹

(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.