Question

For the following exercises you can use the 'Wooldridge' package in R to load the data 9. (7 marks) (using dataset: "k401k") The data in 401K are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account; this is the variable we would like to explain. The dummy variable sole represents whether a firm has more pension plan options. Hence, sole-1 if 40lk is a firm's sole plan and sole-0 if a firm has other pension plan(s) i Find the average participation rate and the percentage of firms that only provide the 401k pension plan in the sample of plans. ii Now, estimate the simple regression equation prate Bo B1 sole, and report the results along with the sample size and R-squared. iii Interpret the intercept in your equation. Interpret the coefficient on sole. iv How much of the variation in prate is explained by sole? Is this a lot in your opinion? Hint: you can load the data into R and run a simple regression model using the following code: library(wooldridge) data(k401k, package-'wooldridge') ml <- lm(prate- sole, data-k401k) summary(ml)

Answer 1

code in R

library(wooldridge)
data(k401k,package='woolridge')
m1 <- lm(prate~sole,data=k401k)
summary(m1)

sum(k401k$sole)/nrow(k401k)
mean(k401k[k401k$sole==1 ,'prate' ])

summary(m1)

Call:
lm(formula = prate ~ sole, data = k401k)

Residuals:
    Min      1Q  Median      3Q     Max 
-81.782  -8.282   8.872   9.925  15.218 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  84.7821     0.5889 143.959  < 2e-16 ***
sole          5.2928     0.8434   6.276 4.52e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16.51 on 1532 degrees of freedom
Multiple R-squared:  0.02506,   Adjusted R-squared:  0.02443 
F-statistic: 39.38 on 1 and 1532 DF,  p-value: 4.522e-10

> 
> 
> 
> sum(k401k$sole)/nrow(k401k)
[1] 0.4876141
> mean(k401k[k401k$sole==1 ,'prate' ])
[1] 90.07487

i)
mean participation rate = 90.07487 that only provide the 401k pension plan
% of firm = 48.76 % only provide the 401k pension plan

ii)

y^= 84.7821 + 5.2928 * sole
iii)
intercept = 84.7821
% of eligible worker with an active account for firm who have other pension plan = 84.7821

slope = 5.2928

percentage of eligible worker with an active account when 401k is firm's sole plan is 5.2928 more than firm who have other pension plan.

iv)
R^2 = 0.02506
hence 2.5 % of variation is explained by sole.

This is very low