The Effect of the Proportion of Female Economics Freshmen on the Academic Rnaking of Universities in the U.S.
Justa Lukoshius
2023-08-09
Set Up
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# Prepare needed libraries
packages <- c("psych", # quick summary stats for data exploration,
"stargazer", # summary stats for sharing,
"tidyverse", # data manipulation like selecting variables,
"corrplot", # correlation plots
"ggplot2", # graphing
"data.table", # reshape for graphing
"car", # vif
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"readxl", # read and open xl files
"visdat"
)
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# IMPORT DATA #
# Load required package
library(readxl)
# Read excel file
Data_Gender_composition_at_ranked_universities <- read_excel("Downloads/Take-home assignment #1-5/Data - Gender composition at ranked universities.xlsx")
# View(Data_Gender_composition_at_ranked_universities)
# Store file in df called df_data
df_data <- as.data.frame(Data_Gender_composition_at_ranked_universities)
# 98 obs of 27varIntroduction
The following paper seeks to measure and understand the causal effect of the percentage of female Economics freshmen on the academic ranking of an institution. By examining this relationship, we can further determine whether there is a significant connection between the representation of women in Economics programs and the academic ranking of a College or University. Additionally, we can uncover insights into potential barriers that may affect women's success in the field of Economics.
Methodology
Data
The data used in the following analysis comes from the Integrated Postsecondary Education Data System (IPEDS) which is provided by the National Center for Education Statistics (NCES). The cross-sectional data set describes the gender composition of students and faculty across several top-ranked medium to large Universities within the United States for the year 2015.
The raw data set only had less than 0.1% of its values missing, which I replaced with their corresponding medians.
Sample
To ensure an accurate analysis of the relationship between the percentage of female Economics freshmen and the academic ranking of an institution, I enhanced the data set by including four additional variables that aimed to provide a more comprehensive and meaningful assessment of gender representation within the Economics program of the institutions. To achieve this, I calculated the following percentages:
EconFacultyFemale_Percentage:This variable measures the percentage of female Economics faculty by dividing the number of female Economics faculty members by the total number of Economics faculty members (EconFaculty_Female / EconFaculty_Total). By including this variable, I aimed to account for the gender composition within the faculty which plays an important role on the overall dynamics of the Economics program.
EconFreshmenFemale_Percentage: Similar to the previous variable, this measure calculates the percentage of female Economics freshmen by dividing the number of female Economics freshmen by the total number of Economics freshmen. Employing the same formula as above, this variable serves as the main independent variable in the regression analysis, allowing us to examine its impact on the academic ranking of each institution.
FreshmenFemale_Percentage: In addition, I introduced this variable to capture the overall representation of female freshmen across all fields of study. By considering the percentage of female freshmen in relation to the total number of freshmen, we gain a broader perspective on gender diversity within the student body.
FacultyFemale_Percentage: Similarly, this variable accounts for the proportion of female faculty members in all academic disciplines. It provides a broader view of gender representation across the entire faculty.
The inclusion of these percentages in the data set enables a more comprehensive analysis, considering both the size and composition of the student and faculty populations. This facilitates better and more meaningful comparisons between the different institutions, as it accounts for the relative representation of female students and faculty members within each university.
After the adjustments and the inclusion of the four percentage variables, the data set includes 98 observations of 31 variables. The following table comprises of a few summary statistics (mean, standard deviation, minimum and maximum) of the variables in the data frame.
# SUMMARY STATISTICS #
# Load required packages
require(stargazer)
# Create label for table
labels <- c(
'Academic Ranking',
'Faculty Total',
'Faculty Female',
'Faculty Male',
'Econ Faculty Total',
'Econ Faculty Female',
'Econ Faculty Male',
'Freshmen Total',
'Freshmen Male',
'Freshmen Female',
'Freshmen Econ Total',
'Freshmen Econ Male',
'Freshmen Econ Female',
'Econ Degrees Granted Total',
'Econ Degrees Granted Male',
'Econ Degrees Granted Female',
'Stem Degrees Granted Total',
'Stem Degrees Granted Male',
'Stem Degrees Granted Female',
'Student Faculty Ratio',
'SATMath75 Freshmen Average',
'Acceptance Rate (%)',
'Student Yield Total (%)',
'Student Yield Male (%)',
'Student Yield Female (%)',
'Prof Salary Average',
'Econ Faculty Female %',
'Econ Freshmen Female %',
'Freshmen Female %',
'Faculty Female %'
)
# summary statistic table
stargazer(df_data,
type = "text",
title = "Summary Statistics of Data",
summary.stat = c("mean", "sd", "median", "min", "max"),
covariate.labels = labels
)##
## Summary Statistics of Data
## ===========================================================================
## Statistic Mean St. Dev. Median Min Max
## ---------------------------------------------------------------------------
## Academic Ranking 47.806 27.827 48.5 1 98
## Faculty Total 1,902.857 1,045.557 1,685 341 6,344
## Faculty Female 747.082 426.217 655 155 2,457
## Faculty Male 1,155.776 629.306 1,039.5 178 3,887
## Econ Faculty Total 33.439 14.237 30.5 9 99
## Econ Faculty Female 7.235 3.481 7 1 19
## Econ Faculty Male 26.204 12.307 22 6 82
## Freshmen Total 4,407.378 2,339.158 4,337 957 10,187
## Freshmen Male 2,109.857 1,149.279 1,969.5 385 5,245
## Freshmen Female 2,297.520 1,221.374 2,192 486 5,190
## Freshmen Econ Total 187.071 128.961 167 7 623
## Freshmen Econ Male 127.082 83.303 115.5 4 326
## Freshmen Econ Female 59.990 53.432 51 0 331
## Econ Degrees Granted Total 157.918 109.744 138 10 544
## Econ Degrees Granted Male 110.020 73.747 98 8 349
## Econ Degrees Granted Female 47.898 41.788 36 2 252
## Stem Degrees Granted Total 834.918 594.971 659.5 59 2,329
## Stem Degrees Granted Male 519.867 389.799 409 20 1,491
## Stem Degrees Granted Female 315.051 220.785 249 38 1,070
## Student Faculty Ratio 15.245 5.026 16 5 27
## SATMath75 Freshmen Average 696.643 58.580 690 570 800
## Acceptance Rate (%) 48.378 23.658 51 6 93
## Student Yield Total (%) 36.214 13.516 35 10 84
## Student Yield Male (%) 37.398 13.486 36 12 83
## Student Yield Female (%) 35.163 14.161 34 1 84
## Prof Salary Average 137,104.200 25,784.600 131,251.5 85,824 202,464
## Econ Faculty Female % 29.972 9.658 30.553 0.000 56.537
## Econ Freshmen Female % 52.166 4.301 52.239 40.237 68.493
## Freshmen Female % 22.588 8.658 21.807 4.255 41.176
## Faculty Female % 39.271 4.449 39.443 25.450 50.960
## ---------------------------------------------------------------------------The academic ranking of the universities in the dataset ranges from 1 to 98, where a lower number indicates a higher ranking. The variable representing the rankings appears to follow a normal distribution, as the mean and median are very close in value. The dataset includes universities of varying sizes, as indicated by the total faculty variable, which ranges from 341 to 6,344.
When examining the number of male Economics freshmen, the range is from 4 to 326 students, with a median value of approximately 116. In contrast, the number of female Economics freshmen ranges from 0 to 331 students, with a median value of 51. This indicates that, overall, there are more male freshmen enrolled in the Economics program of universities compared to female freshmen.
Similarly, the median number of Economics degrees granted to male students is nearly three times higher (98) than the median number granted to female students (36). This highlights a disparity in the number of degrees awarded and the composition between male and female students in Economics across universities.
Moreover, the percentage of female Economics faculty ranges from 4.3% to 41.2%, with a mean and median around 22%. These figures suggest that the representation of female faculty members in the Economics department is consistently lower than that of male faculty members.
Lastly, the percentage of female Economics freshmen ranges from 0% to 56.5%. This variable also follows a normal distribution, with the mean and median approximately at 30%. This indicates that, on average, around 30% of the Economics freshmen are female across the universities in the dataset.
In summary, the descriptive statistics illustrate the distribution and characteristics of various variables, including academic rankings, institution sizes, gender composition of freshmen and faculty within the institutions and within the Economics departments. These statistics provide an overview of the gender disparities and enrollment patterns within the Economics discipline.
Methods
A multivariate regression model was used to explore the relationship between the percentage of female freshmen within the Economics department of an institution on the academic ranking of a university in 2015, controlling for student and faculty composition demographics, and student's prior knowledge.
The equation for my model is:
\[ \text{Academic Ranking}_i = \beta_0 + \beta_1 \cdot \text{Percentage of Female Econ Freshmen}_i + \beta_2 \cdot \alpha_i + \beta_3 \cdot \gamma_i + \beta_4 \cdot \delta_i + \epsilon_i \]
where
Academic Ranking, the dependent variable, represents the academic ranking for the i(th) institution;
Percentage of Female Econ Freshmen, the main independent variable, represents the percentage of female freshmen in Economics for the i(th) institution;
\(\alpha\) represents student demographics in the i(th) institution. I included the percentage of female students and the percentage of female freshmen as controls for student demographics since the gender composition of the university as a whole may impact the gender representation in specific programs like economics;
\(\gamma\) represents faculty demographics in the i(th) institution. I included the percentage of female faculty and female faculty in Economics as controls since the gender composition of the faculty may also impact the gender representation in specific programs like economics;
\(\delta\) represents the controls for students’ knowledge prior to getting into the program. I included the variable representing mathematics SAT scores as a control since the SAT scores may be related with the gender composition of the freshmen class;
\(\beta_0\) represents the intercept/constant term
\(\beta_1\) represents the coefficient for the percentage of female economics freshmen variable, which quantifies the expected change in academic ranking for institutions depending on the percentage of female freshmen in economics.
Results
Four OLS models were conducted to measure this causal relationship, gradually including different controls.
In model 1, simple OLS is used to get a raw estimate of the effect of the percentage of female Economics freshmen on the academic ranking of an institution without controlling for any observable differences across the institutions. Based on the OLS model, a 1 percent increase in the percentage of female Economics freshmen, decreases the institution's academic ranking by 1.143 percentage points, holding all other variables constant. This is significant at the 1% level. However, the model has omitted variable bias (OVB) since there are variables that are related with y and correlated with x, which produce unreliable estimates of the relationships between the variables. Additionally, the relatively small R2 and large residual standard error for this model suggests that the model’s ability to explain the variations in the dependent variable is limited, and there may be unaccounted factors that are influencing the outcome.
In model 2, a multivariate regression is used to account for differences in the composition of students in institutions. Interestingly, when controlling for student composition differences, a 1 percent increase in the percentage of female Economics freshmen, decreases the institution's academic ranking by 1.254 percentage points, holding all variables constant. This is statistically significant at the 1% level. The R2 has increased a bit while the residual standard error has decreased a bit, meaning an improved model fit. However, there are still omitted variables that need to be controlled for.
In model 3, a multivariate regression is used to account for both differences in the composition of students and faculty in institutions. In adding these variables to the model, a 1 percent increase in the percentage of female Economics freshmen, decreases the institution's academic ranking by 1.090 percentage points, holding all variables constant. This is statistically significant at the 1% level. When adding the controls for the composition differences in the faculty, the coefficient got closer to 0. Additionally, the R2 is continuing to increase a bit while the residual standard error is decreasing slowly, which all together, is telling us the bias is slowly getting smaller and the model is becoming a better fit.
Lastly, in model 4, a multivariate regression is used to account for both differences in the composition of students and faculty in institutions, and students' prior knowledge that affects who is admitted to Economics. Based on this model, a 1 percent increase in the percentage of female Economics freshmen, decreases the institution's academic ranking by 0.578 percentage points, holding other variables constant. Although, this is statistically significant at the 5% level, the R2 and residual standard error have significantly improved, indicating an even better model fit. Additionally, the coefficient makes a lot more theoretical sense. Based on the descriptive statistics from the dataset, on average, less economics and stem degrees were granted to women than men, which could explain why an increase in the female composition of freshmen in economics decreases an institutions academic ranking.
##
## Summary Statistics Table of Models
## ====================================================================================================================
## Dependent variable:
## -------------------------------------------------------------------------------------------
## Academic_ranking
## No Controls +Student Demographics +Faculty Demographic +Intelligence Controls
## (1) (2) (3) (4)
## --------------------------------------------------------------------------------------------------------------------
## Freshmen Econ Female % -1.143*** -1.254*** -1.090*** -0.578**
## (0.270) (0.251) (0.259) (0.223)
##
## Student Yield Female -0.732*** -0.642*** -0.278*
## (0.169) (0.170) (0.148)
##
## Freshmen Female % 1.090* 0.032 -0.112
## (0.580) (0.789) (0.642)
##
## Econ Faculty Female % 0.408 0.370*
## (0.271) (0.220)
##
## Faculty Female % 1.248* 0.285
## (0.746) (0.623)
##
## SAT Math Freshmen Scores -0.272***
## (0.039)
##
## Constant 82.053*** 54.294* 43.106 250.843***
## (8.497) (30.896) (30.757) (39.089)
##
## --------------------------------------------------------------------------------------------------------------------
## Observations 98 98 98 98
## R2 0.157 0.352 0.388 0.599
## Adjusted R2 0.148 0.332 0.355 0.573
## Residual Std. Error 25.678 (df = 96) 22.750 (df = 94) 22.349 (df = 92) 18.190 (df = 91)
## F Statistic 17.914*** (df = 1; 96) 17.041*** (df = 3; 94) 11.675*** (df = 5; 92) 22.666*** (df = 6; 91)
## ====================================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Finally, to ensure that there was low multicollinearity in my final model, I conducted a multicollinearity test on the variables in model 4. From the table below, the Variance Inflation Factor (VIF), a measure of multicollinearity, for each variable is below 5, which indicated low levels of multicollinearity.
Conclusion
Overall, we find that an increase in the percentage of female Economics freshmen negatively affects the academic ranking of an institution using a multivariate OLS regression.