ECO304_WEEK7_HW Answers
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Apr 3, 2024
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ECO304: Analytics for Economics
WEEK 7 Homework: Specification of Regression Model Submit STATA do file as a txt file with explanation you found (10 Points Total)
I. 2018 Current Population Data (6 points) Using the following CPS data, select only the first person from each family. . clear all . use https://bigblue.depaul.edu/jlee141/econdata/cps_data/cepr_march_2018.dta . keep if perno == 1 1)
Using dummy variables, perform a statistical test on the difference of means on total household income (rinch_all). a.
By race (wbhao) tab wbhao, gen(race) reg rinch_all race2-race5 Since the race2 to race5 variables are the dummy variables, the coefficients are the average of the real household income by race. Using F test, you can test if they have different means. The p-value from F statistics shows zero, which means p is less than 5% and 1%, thus are significatly different. b.
By family type (famtyp)
Since the family2 to family5 variables are the dummy variables, the coefficients are the average of the real household income by family type. Using F test, you can test if they have different means. The p-value from F statistics shows zero, which means p is less than 5% and 1%, thus are significatly different. 2)
Select only the first person for each family (keep if perno == 1), and estimate the following models. Carefully explain the meaning of the estimated coefficient ,
b
1
, for each model. Model1: ࠵?
!
= ࠵?0 + ࠵?1 ࠵?
!
+ ࠵?
!
Model2: ࠵?
!
= ࠵?0 + ࠵?1 ࠵?࠵?࠵?࠵?
!
+ ࠵?
!
Model3: ࠵?࠵?࠵?࠵?
!
= ࠵?0 + ࠵?1 ࠵?
!
+ ࠵?
!
Model4: ࠵?࠵?࠵?࠵?
!
= ࠵?0 + ࠵?1 ࠵?࠵?࠵?࠵?
!
+ ࠵?
!
where Xi = Total household income (rinch_all) Yi = Total child care spending (careval)
reg careval rinch_all eststo reg careval log_rinch_all eststo reg log_careval rinch_all eststo reg log_careval log_rinch_all eststo esttab Model1: ࠵?
!
= ࠵?0 + ࠵?1 ࠵?
!
+ ࠵?
!
If one dollar increase in the real household income, there are 0.02 dollar changes in the child care Model2: ࠵?
!
= ࠵?0 + ࠵?1 ࠵?࠵?࠵?࠵?
!
+ ࠵?
!
If one percent increases in the real household income, there is 2999/100 = 29.99 dollars increases in the child care spending. Model3: ࠵?࠵?࠵?࠵?
!
= ࠵?0 + ࠵?1 ࠵?
!
+ ࠵?
!
If one dollar increases in the real household income, there is 0.00000283*100 = 0.000283 percent changes in the child care spending. Model4: ࠵?࠵?࠵?࠵?
!
= ࠵?0 + ࠵?1 ࠵?࠵?࠵?࠵?
!
+ ࠵?
!
If one percent increases in the real household income, there is 0.512 percent changes in the child care spending. 3)
Find the best suitable model from 2) and estimate a regression model including race dummy variables (wbhao) as independent variables. Carefully explain the difference among the race groups. Suppose you chose the last model, and run a regression model with race variables:
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According to the model, the highest lowest race groups: Asian (2.417+0.06), Black(2.147+0.0396), White(2.417), Hispanic(2.417-0.102), and Others (2.417-0.521). 4)
Perform a restricted F test for the racial differences in the regression model in 3). Setup the hypothesis, perform the test and state your finding. The test shows that the F-statistic is 4.20 and its p-value is 0.0021, which is much lower than 1%, thus there are differences in the childcare spending by race. II. NBA Salary (4 points) Using the National Basketball Association (NBA) statistics, we obtain salary and career statistics for 269 players. You can get the data from: . use https://bigblue.depaul.edu/jlee141/econdata/eco304
/nba_stat
1)
Estimate a model relating points-per-game (points) to years in league (exper), age, and years played in college (coll). Include a quadratic in exper. Describe the model based on the output; R square, t test, F test and signs of the coefficients. Are they make sense?
The R-square shows that 14 percent of variations of the points can be explained by the included independent variables. The F-statistic of the model is 10.85 with p-value of 0, which means at least one of the variable is significant. According to the t-statistics, all included independent variables are significant at 1%. 2)
Holding college years and age fixed, at what value of experience does the next years of experience actually reduce points? Does this make sense? ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?
࠵? ࠵?࠵?࠵?࠵?࠵?
= 2.36 − 0.077 ∗ 2 ࠵?࠵?࠵?࠵?࠵? = 2.36 − 0.154 ࠵?࠵?࠵?࠵?࠵?
To find the turning point by the derivative rule. 2.36 − 0.154 ࠵?࠵?࠵?࠵?࠵? = 0
࠵?࠵?࠵?࠵?࠵? =
2.36
0.154
= 15.32
According to the model, after 15.32 year, the points scored by a player will be declined. 3)
Explain why years of played in college (coll) has a negative and statistically significant coefficient? One possible explanation might be the best players from high school might go to NBA directly without the college education. 4)
Add quadratic in age to the equation. Is it needed? What does appear to imply about the effects of age?
Agesq is not statistically significant., but the VIF indicates that agesq has a very high multicollinearity since VIF is much higher than 5. If the variable is not significant due to the multicollinearity, we might consider to include to the model. ࠵? ࠵?࠵?࠵?࠵?࠵?࠵?
࠵? ࠵?࠵?࠵?
= −3.984 + 2 ∗ .108 ࠵?࠵?࠵? = −3.984 + .108 ࠵?࠵?࠵?
To find the turning point by the derivative rule. −3.984 + 0.108 ࠵?࠵?࠵? = 0
࠵?࠵?࠵? =
3.984
0.108
= 36.89
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STATA CODE FOR THE EXAMPLE /* I. Income and Child Care Spending - CPS data */ clear all use https://bigblue.depaul.edu/jlee141/econdata/cps_data/cepr_march_2018
.dta /* We only choose one observation from a household */ keep if perno == 1 tab wbhao, gen(race) reg rinch_all race2-race5 tab famtyp, gen(family) reg rinch_all family2-family5 gen log_rinch_all = log(rinch_all) gen log_careval = log(careval) reg careval rinch_all eststo reg careval log_rinch_all eststo reg log_careval rinch_all eststo reg log_careval log_rinch_all eststo esttab esttab, r2 ar2 reg log_careval log_rinch_all race2-race5 test race2 race3 race4 race5 /* II. NBA Salary */ clear all use https://bigblue.depaul.edu/jlee141/econdata/eco304/nba_stat reg points exper expersq age coll reg points exper expersq coll age agesq vif