POLS6481-Assignment 2 Solved

Is it generally true that height confers unfair advantages? Conventional wisdom holds that taller candidates win presidential elections, and taller executives tend to earn higher salaries.

Download the dataset HeightWage_MenWomenUS_HW.csv or HeightWage_MenWomenUS_HW.dta. These data are drawn from the National Longitudinal Study of Youth, 1979 cohort (age 14 to 22 years old in 1979). Our dependent variable is the wages earned in 1996 (wage96). Here is a codebook:

Variable name
Description
male
Male (1 = yes, 0 = no)
white
White (1 = yes, 0 = no)
black
Black (1 = yes, 0 = no)
hispanic
Hispanic (1 = yes, 0 = no)
wage96
Adult hourly wages (dollars) reported in 1996 (salary and wages in past calendar year divided by hours worked in past calendar year)
height85
Adult height (inches), self-reported in 1985
height81
Adolescent height (inches), self-reported in 1981
athlets
Participation in high school athletics (1 = yes, 0 = no)
clubnum
Number of club memberships in high school, excluding athletics, academic/honor society clubs, and vocational clubs
momed79
Mother’s years of education
daded79
Father’s years of education
mompro2
Mother in a professional/managerial occupation (1 = yes, 0 = no)
poppro2
Father in a professional/managerial occupation (1 = yes, 0 = no)
siblings 
Number of siblings
age
Age (years) in 1996
esteem80
Score on Rosenberg Self-Esteem Scale as an adolescent in 1980 (higher values indicate higher self-esteem)
hgc96
Highest grade of education completed in 1996
Also download the R script titled “HW2q1-4prep.R” and run the script to (a) eliminate cases with missing observations – but only for the variables you care about – and (b) eliminate variables you won’t care about and (c) limit the sample to male subjects, using the male variable.

Estimate the following bivariate regression model using ordinary least squares:
What does this regression suggest about the relationships between height and wages?
Can the slope coefficient, , be statistically distinguished from zero?
Estimate the following multivariate regression model using ordinary least squares, which controls for the individual’s height as an adolescent:
How does the estimated slope coefficient from the multivariate model compare with the estimated slope coefficient  from the simple regression model?
How does the standard error of from the multivariate model compare to the bivariate regression model?
Is from the multivariate model statistically significant, i.e., distinguishable from zero?
Use the equations from lecture to solve for the standard errors for the simple and multiple regression coefficients for height85. Explain how the numerator changed, then explain how and specifically why the denominator changed, relative to the simple regression model.
What is the correlation between height85 and height81?
How much of an effect did multicollinearity have on  and/or its standard error?
The researchers were interested in whether the effect of adolescent height on wages is partly due to height encouraging participation in sports and belonging to clubs. Adding two variables to the analysis will allow you to evaluate whether taller adolescents simply had more opportunities to develop leadership and other skills (i.e., social capital).

Estimate the following regression models using ordinary least squares:
What do these regressions suggest about how height and social capital (belonging to clubs and/or participating in athletics) affect wages?
In the last regression above, which slope coefficients are “statistically significant”?
In the last regression above, how does the estimated slope coefficient 2 compare with the estimated slope coefficients from the earlier regression models?
How does the standard error of the estimated slope coefficient 2 from the multivariate model compare to standard errors from the earlier regression models?
What is the correlation between clubnum and athlets?
What is the correlation between each of these variables and height81?
Maybe there’s more to life than just making money. Perhaps taller people get greater social capital, which increases self-esteem. The dataset includes scores on the Rosenberg Self-Esteem Scale, taken as an adolescent in 1980; higher values indicate more self-esteem.

Estimate the following regression models using ordinary least squares:
What do these regressions suggest about the relationship between height and self-esteem?
What does the second regression suggest about the relationship between social capital (belonging to clubs and/or participating in athletics) and self-esteem?
Which slope coefficients are “statistically significant”?
Is multicollinearity a potential problem here? Use the casual methods described in lecture 8 to describe why it is or isn’t a problem?
 

Does raising education levels tend to improve economic growth? For their article, “Do Better Schools Lead to More Growth? Cognitive Skills, Economic Outcomes, and Causation,” Hanushek and Woessmann (2012) collected a dataset on economic growth of 50 countries from 1960 to 2000. Here is a codebook:

 

Variable name
Description
code
Country code
name
Country name
open
Openness of the economy scale
ed60
Average years of schooling in 1960
ypc60
GDP per capita in 1960
ypcgr
Average annual growth rate (GDP per capita), 1960–2000
testavg
Average combined math and science standardized test scores, 1964–2003
proprts
Security of property rights scale
edavg
Average years of schooling, 1960–2000
region
Region
 

Download the dataset globaled.csv or globaled.dta and use it to answer questions 5–8:

Estimate a regression in which ypcgr is the dependent variable and edavg is the independent variable.
Examine the coefficient for edavg; what effect does education have on growth?
Examine the t statistic and p value; is the estimated coefficient statistically significant (p < .05)?
How much of the variation in average economic growth is explained by average education?
5½. Optional question: estimate a regression in which ypcgr is the dependent variable and ypc60 is the independent variable.

Examine the coefficient for ypc60; what effect did GDP per capita in 1960 have on subsequent growth?
Examine the t statistic and p value; is the estimated coefficient statistically significant (p < .05)?
Add the ypc60 variable to the regression estimated in 5. The stated purpose of doing this is to control for GDP per capita, given the phenomenon that countries that are wealthier have slower growth rates, since poorer countries simply have more capacity to grow. You’ll also see that countries that are wealthier tend to have higher average years of education.
Create a scatterplot with GDP per capita in 1960 on the horizontal axis and average years of education since 1960 on the vertical axis. How, and how strongly, are these variables related?
Examine the coefficients; how did edavg and ypc60 impact average growth since 1960?
Examine the standard errors and t statistics for edavg and ypc60; is either of the estimated coefficients statistically significant (p < .05)?
Examine the variance-covariance and/or correlation matrix. Why did the coefficient on edavg change so much between the simple regression and multiple regression?
Once you control for GDP, how much does each additional year of schooling contribute to average economic growth?
How much of the variation in average economic growth is explained by the combination of average education and GDP per capita in 1960?
Add another variable, testavg, to the regression estimated in 6. This variable average standardized test scores in math and science. Hanushek and Woessmann believed that quality of education would matter more than quantity of education.
Create a scatterplot with average years of education on the horizontal axis and average standardized test scores on the vertical axis. How, and how strongly, are these variables related?
Explain how omitting average standardized test scores (testavg) could have created omitted variable bias. Identify which cell of Wooldridge’s Table 3.2 this example would be classified in, treating the edavg variable as x1 and the testavg variable as x2?
Examine the coefficients for edavg and ypc60 and testavg; what effect does each variable have on average economic growth?
How has the coefficient on edavg changed from the regression you ran in 6.? How has the coefficient on ypc60 changed from the regression you ran in 6.?
Examine the standard errors of the coefficients and t statistics for edavg and ypc60 and testavg; which estimated coefficients are statistically significant (p < .05)?
Examine both the residual standard error (sigma-hat) and the standard errors of the regression coefficients for the edavg and ypc60 variables; how did they change when you added testavg to the equation?
Does adding the testavg variable introduce a problem of multicollinearity? Use two of the “casual” methods for detecting multicollinearity and calculate Variance Inflation Factors.
 
 
 
 
 
 
 
Drop the edavg variable, leaving only the ypc60 and testavg variables in the regression.
Have you created an omitted variable bias problem by dropping the edavg variable? Provide appropriate support for your conclusion (consult Lab 3 for ideas).
What happens to the coefficient, standard error, and t statistic for testavg when the edavg variable is dropped?
How much of the variation in average economic growth is explained by all three variables (edavg and ypc60 and testavg), and how much of the variation is explained by just the last two variables (ypc60 and testavg)?Is it generally true that height confers unfair advantages? Conventional wisdom holds that taller candidates win presidential elections, and taller executives tend to earn higher salaries.Download the dataset HeightWage_MenWomenUS_HW.csv or HeightWage_MenWomenUS_HW.dta. These data are drawn from the National Longitudinal Study of Youth, 1979 cohort (age 14 to 22 years old in 1979). Our dependent variable is the wages earned in 1996 (wage96). Here is a codebook:

Variable name
Description
male
Male (1 = yes, 0 = no)
white
White (1 = yes, 0 = no)
black
Black (1 = yes, 0 = no)
hispanic
Hispanic (1 = yes, 0 = no)
wage96
Adult hourly wages (dollars) reported in 1996 (salary and wages in past calendar year divided by hours worked in past calendar year)
height85
Adult height (inches), self-reported in 1985
height81
Adolescent height (inches), self-reported in 1981
athlets
Participation in high school athletics (1 = yes, 0 = no)
clubnum
Number of club memberships in high school, excluding athletics, academic/honor society clubs, and vocational clubs
momed79
Mother’s years of education
daded79
Father’s years of education
mompro2
Mother in a professional/managerial occupation (1 = yes, 0 = no)
poppro2
Father in a professional/managerial occupation (1 = yes, 0 = no)
siblings 
Number of siblings
age
Age (years) in 1996
esteem80
Score on Rosenberg Self-Esteem Scale as an adolescent in 1980 (higher values indicate higher self-esteem)
hgc96
Highest grade of education completed in 1996
Also download the R script titled “HW2q1-4prep.R” and run the script to (a) eliminate cases with missing observations – but only for the variables you care about – and (b) eliminate variables you won’t care about and (c) limit the sample to male subjects, using the male variable.

Estimate the following bivariate regression model using ordinary least squares:
What does this regression suggest about the relationships between height and wages?
Can the slope coefficient, , be statistically distinguished from zero?
Estimate the following multivariate regression model using ordinary least squares, which controls for the individual’s height as an adolescent:
How does the estimated slope coefficient from the multivariate model compare with the estimated slope coefficient  from the simple regression model?
How does the standard error of from the multivariate model compare to the bivariate regression model?
Is from the multivariate model statistically significant, i.e., distinguishable from zero?
Use the equations from lecture to solve for the standard errors for the simple and multiple regression coefficients for height85. Explain how the numerator changed, then explain how and specifically why the denominator changed, relative to the simple regression model.
What is the correlation between height85 and height81?
How much of an effect did multicollinearity have on  and/or its standard error?
The researchers were interested in whether the effect of adolescent height on wages is partly due to height encouraging participation in sports and belonging to clubs. Adding two variables to the analysis will allow you to evaluate whether taller adolescents simply had more opportunities to develop leadership and other skills (i.e., social capital).

Estimate the following regression models using ordinary least squares:
What do these regressions suggest about how height and social capital (belonging to clubs and/or participating in athletics) affect wages?
In the last regression above, which slope coefficients are “statistically significant”?
In the last regression above, how does the estimated slope coefficient 2 compare with the estimated slope coefficients from the earlier regression models?
How does the standard error of the estimated slope coefficient 2 from the multivariate model compare to standard errors from the earlier regression models?
What is the correlation between clubnum and athlets?
What is the correlation between each of these variables and height81?
Maybe there’s more to life than just making money. Perhaps taller people get greater social capital, which increases self-esteem. The dataset includes scores on the Rosenberg Self-Esteem Scale, taken as an adolescent in 1980; higher values indicate more self-esteem.

Estimate the following regression models using ordinary least squares:
What do these regressions suggest about the relationship between height and self-esteem?
What does the second regression suggest about the relationship between social capital (belonging to clubs and/or participating in athletics) and self-esteem?
Which slope coefficients are “statistically significant”?
Is multicollinearity a potential problem here? Use the casual methods described in lecture 8 to describe why it is or isn’t a problem?
 

Does raising education levels tend to improve economic growth? For their article, “Do Better Schools Lead to More Growth? Cognitive Skills, Economic Outcomes, and Causation,” Hanushek and Woessmann (2012) collected a dataset on economic growth of 50 countries from 1960 to 2000. Here is a codebook:

 

Variable name
Description
code
Country code
name
Country name
open
Openness of the economy scale
ed60
Average years of schooling in 1960
ypc60
GDP per capita in 1960
ypcgr
Average annual growth rate (GDP per capita), 1960–2000
testavg
Average combined math and science standardized test scores, 1964–2003
proprts
Security of property rights scale
edavg
Average years of schooling, 1960–2000
region
Region
 

Download the dataset globaled.csv or globaled.dta and use it to answer questions 5–8:

Estimate a regression in which ypcgr is the dependent variable and edavg is the independent variable.
Examine the coefficient for edavg; what effect does education have on growth?
Examine the t statistic and p value; is the estimated coefficient statistically significant (p < .05)?
How much of the variation in average economic growth is explained by average education?
5½. Optional question: estimate a regression in which ypcgr is the dependent variable and ypc60 is the independent variable.

Examine the coefficient for ypc60; what effect did GDP per capita in 1960 have on subsequent growth?
Examine the t statistic and p value; is the estimated coefficient statistically significant (p < .05)?
Add the ypc60 variable to the regression estimated in 5. The stated purpose of doing this is to control for GDP per capita, given the phenomenon that countries that are wealthier have slower growth rates, since poorer countries simply have more capacity to grow. You’ll also see that countries that are wealthier tend to have higher average years of education.
Create a scatterplot with GDP per capita in 1960 on the horizontal axis and average years of education since 1960 on the vertical axis. How, and how strongly, are these variables related?
Examine the coefficients; how did edavg and ypc60 impact average growth since 1960?
Examine the standard errors and t statistics for edavg and ypc60; is either of the estimated coefficients statistically significant (p < .05)?
Examine the variance-covariance and/or correlation matrix. Why did the coefficient on edavg change so much between the simple regression and multiple regression?
Once you control for GDP, how much does each additional year of schooling contribute to average economic growth?
How much of the variation in average economic growth is explained by the combination of average education and GDP per capita in 1960?
Add another variable, testavg, to the regression estimated in 6. This variable average standardized test scores in math and science. Hanushek and Woessmann believed that quality of education would matter more than quantity of education.
Create a scatterplot with average years of education on the horizontal axis and average standardized test scores on the vertical axis. How, and how strongly, are these variables related?
Explain how omitting average standardized test scores (testavg) could have created omitted variable bias. Identify which cell of Wooldridge’s Table 3.2 this example would be classified in, treating the edavg variable as x1 and the testavg variable as x2?
Examine the coefficients for edavg and ypc60 and testavg; what effect does each variable have on average economic growth?
How has the coefficient on edavg changed from the regression you ran in 6.? How has the coefficient on ypc60 changed from the regression you ran in 6.?
Examine the standard errors of the coefficients and t statistics for edavg and ypc60 and testavg; which estimated coefficients are statistically significant (p < .05)?
Examine both the residual standard error (sigma-hat) and the standard errors of the regression coefficients for the edavg and ypc60 variables; how did they change when you added testavg to the equation?
Does adding the testavg variable introduce a problem of multicollinearity? Use two of the “casual” methods for detecting multicollinearity and calculate Variance Inflation Factors.
 
 
 
 
 
 
 
Drop the edavg variable, leaving only the ypc60 and testavg variables in the regression.
Have you created an omitted variable bias problem by dropping the edavg variable? Provide appropriate support for your conclusion (consult Lab 3 for ideas).
What happens to the coefficient, standard error, and t statistic for testavg when the edavg variable is dropped?
How much of the variation in average economic growth is explained by all three variables (edavg and ypc60 and testavg), and how much of the variation is explained by just the last two variables (ypc60 and testavg)?