[SOLVED] R Midterm Coursework

Midterm Coursework
Introduction to Quantitative Research Methods PUBL0055
Instructions
The coursework will be posted on Moodle on 1st November 2019 at 6pm, and is due on 6th November 2019 at 2pm. Please follow all designated SPP submission guidelines for online submission as detailed on the PUBL0055 Moodle page. Standard late submission penalties apply.
This is an assessed piece of coursework worth 25 of your final module mark for the PUBL0055 module; collaboration andor discussion of the coursework with anyone is strictly prohibited. The rules for plagiarism apply and any cases of suspected plagiarism of published work or the work of classmates will be taken seriously.
As this is an assessed piece of work, you may not emailask the course tutors or teaching fellows questions about the coursework.
Along with the coursework itself, the datasets for the coursework can be found in the PUBL0055 page on Moodle.
Coursework should be submitted via the Turnitin Submission: PUBL0055 Essay 1 link on the course Moodle page. You will need to click the Submit Paper link at the bottom of the page. When presented with the Submit Paper box, the Submission Title should be your candidate number, and you should upload your document into the box provided.
Please remember to state ONLY your candidate number on your coursework your candidate number is made up of four letters and one number e.g. ABCD5. Your name andor student number MUST NOT appear on your coursework.
The coursework consists of five questions; you must complete each part of each question to achieve full marks. Each question is worth 20 marks in total.
Unless otherwise stated, answers should be written in complete sentences. Be sure to answer all parts of the questions posed and interpret the results.
The word count for this assessment is 1000 words. This does not include the appendix, or any words or numbers contained within tables.
Please submit your typewritten numbered answers in a single document. Create an appendix section at the end which contains all the R code needed to reproduce your results you do not need to include the code that failed to run, but just the cleanedup version. Your code has to work when we run it. Failure to include the R code means that the coursework will be marked incomplete.
You may assume the methods you have used e.g. difference in means, linear regression, etc are understood by the reader and do not need definitions, but you do need to explain how they apply to answering the question.
Round all numbers to two digits after the decimal point.
Do not copy and paste any brute R output e.g. lmyx into your answers. Create a formatted table that is easy to read.
Assign every table and figure a title and a number and refer to the number in the text when discussing a specific figure or table.
All variable names in the coursework are written in thisfont.
1

The Motherhood Wage Penalty
Does having children cause women to earn less? It is a wellknown empirical phenomenon that women without children are paid more on average than women who have children. In this assignment, you will use survey data to investigate the size of the wage penalty that mothers face in the USA; ask whether these differences represent the causal effect of motherhood; and consider the degree to which these differences have changed over time.
This exercise is loosely based on a paper by Weihsin Yu and Janet ChenLan Kuo entitled The Motherhood Wage Penalty by Work Conditions: How Do Occupational Characteristics Hinder or Empower Mothers?, American Sociological Review 824: 744769. The authors of this paper use data from the National Longitudinal Survey of Youth to estimate the effects of having children on the wages of young women. The data file you will use, which can be downloaded on the PUBL0055 webpage, is titled motherhood.csv and contains information from two waves 2004 and 2009 of this survey.
Each observation in this data N2479 represents a woman all aged between 19 and 30, and the names and descriptions of the variables included in the data are:
Name
PUBID
wage
numChildren
age
educ
experience
tenure
marstat
fullTime
y2009
Question 1 20 marks
Description
ID of woman
Hourly wage, in dollars
Number of children that the woman has
Age, in years
Level of education categorical: 1.Less than HS; 2.High school; 3.Some college; 4.College
Relevant work experience, in months
Current job tenure, in years
Marital status categorical: Cohabiting; Married; No romantic union Employment status binary: fulltimeTRUE, parttimeFALSE
The year of observation binary: 20091, 20040
a numChildren records the number of children a woman has at the time of observation. Provide a table that shows the proportion of women in the data set with each different number of children. Provide a brief substantive interpretation of the results.
b Using the code below, create a new variableisMotherthat takes a value of 1 if the woman has at least one child and a value of 0 otherwise.
motherhoodisMotherifelsemotherhoodnumChildren0, 1, 0
You will use this variable throughout the rest of the assignment.
Tabulate the new variable. What proportion of women have at least one child?
c What proportion of women with children work full time? What proportion of women without children work full time?
d Report the mean and standard deviation for the wage variable and for the experience variable. e Create the following plots:
1. A scatter plot with experience on the xaxis and wage on the yaxis
2. A boxplot which compares the wages of women with and without children
Provide a single sentence interpretation for each of these plots. 2

Question 2 20 marks
a Calculate the difference in mean wages between women with children and women without children. Interpret this difference in substantive terms.
b Does the difference in means calculated above represent the causal effect of motherhood on wages? Why, or why not? You may use evidence from other variables to support your argument if you wish.
c Imagine that the researcher conducting this study is not confident that the difference in means represents the causal effect of motherhood. Describe one alternative approach that the researcher might adopt to estimate the desired effect. How does your proposed approach improve on the difference in means comparison?
d Explain why a a randomized experiment would provide clear evidence in favour ofagainst a causal relationship between having children and womens wages and b why it is impossible to run such an experiment here.
Question 3 20 marks
It is clearly not the case that whether or not a woman has children completely determines her hourly wage level. For instance, another presumably relevant determinant is the amount of work experience that a woman has in the relevant area. In this question, you will investigate the relationship between experience and wages using linear regression.
a Estimate a simple linear regression model with wage as the outcome, and experience as the explanatory variable. Present your results in a table.
b Interpret the coefficients of the model.
c Interpret the R2 of the model.
d Using the model you estimated above, calculate the fitted values for an individual at the 25th and 75th percentiles of the experience variable. Compare the difference in these fitted values to the difference in means that you calculated in question 2a and describe whether you think the effect of experience is large or not.
Question 4 20 marks
a Estimate two multiple linear regression models. For the first model, you should use wage as your dependent variable, and experience and isMother as your independent variables. For the second model, add educ as an additional explanatory variable. Present the results of these models in a table.
b Interpret the coefficients associated with the isMother variable in model 1 and model 2. c Interpret the coefficients associated with the educ variable in model 2.
d Which model provides a better fit to this data?
Question 5 20 marks
Has the motherhood wage penalty changed over time? The data we have been using in this question includes information from two surveys: one in 2004 and one in 2009. Table 2 presents the results of two regression models, one of which includes an interaction term between the isMother variable and the y2009 variable.
The formula for model 1 is:
wagei 1 isMotheri 2 y2009i 3 experiencei i
3

The formula for model 2 is:
wagei1isMotheri2y2009i3isMotheriy2009i4experienceii
You will use the results presented in the table to assess the degree to which the wage penalty for mothers has
changed over time.
a Interpret the effects of motherhood on wages using the coefficients from models 1 and 2.
b Based on model 2, what is the predicted wage level for a woman with the following characteristics?
1. A woman without children, interviewed in 2004, with 10 months of relevant job experience 2. A woman with children, interviewed in 2004, with 10 months of relevant job experience
3. A woman without children, interviewed in 2009, with 10 months of relevant job experience 4. A woman with children, interviewed in 2009, with 10 months of relevant job experience
c Based on your answers to the questions above, do you conclude that the size of the motherhood wage penalty has changed over time?
Table 2: Interaction model
Dependent variable:
wage
2 0.200
3.707 2.311 0.374 6.405
2,284 0.226
isMother
y2009
isMothery2009 experience Constant
Observations R2
1 1.403
2.727
0.376 6.785
2,284 0.218
4