knitr::opts_chunk$set(fig.path='figures/')

Introduction

One out of five women in the United States of America is a victim of either completed or attempted rape in their lifetime[1]. This paper explores the question if online dating applications increased rates of violence against women through the instrumental variable approach. Dating apps can facilitate as platforms of access among all genders and allow individuals to know and meet each other and to see what effect this has on sexual violence incidents. However, previous studies on this have been exclusively qualitative and hypothesized an increase in sexual violence because of dating apps. 

Due to the novel nature of this problem and the limited availability of data, this paper aims to understand if the presence of a dating application such as Tinder has caused a change in reported cases of sexual violence, codified as reported rape from 1986-2022.  The population are all the women in the United States of America. The sample in the data are however only the women that have reported that they were victims of rape[2]. 

Data

The unit of analysis in this study is the United States. 

The dependent variable in this study is the incidence of rape. This data is collected from the FBI UCR dataset and includes the percentage of reported rape incidences per 100,000 people- adjusting it for any change in population. 

Our independent variable is tinder users. The data for Tinder was users per year from several reports on Statista from 2013 until 2022 in millions[3]. 

The instrument variables are Population and Gender Ratio. Data on population is collected from the Federal Reserve at St. Louis through the database: Federal Reserve Economic Data (FRED). Gender ratio information is calculated as number of females relative to the population and is collected from the Bureau of Labor Statistics (BLS) website.   

We have a total of 38 observations. We further explain the relationship between these variables with the help of a directed acyclic graph (Figure 1). 

Figure 1. Directed Acyclic Graph (DAG) relationship between the variables

The DAG visually represents the relationship between the variables. Population (U1) influences Tinder (D), which when interpreted mean that populous areas have more Tinder users. Gender Ratio (U2) also influences Tinder (D), given that the gender ratio composition will have an effect on the number of users of dating applications. Tinder (D) directly affects Rape (Y), assuming that increased usage of Tinder could lead to more incidents of rape, as hypothesized above in the study. The DAG gives a clearer interpretation of how the variables influence each other, directly or indirectly. 

Is the sample representative?

No,  our data reports only subscribers of Tinder as users when there are several users of the unpaid version of the application, as well as other easily accessible dating applications that emerged shortly thereafter.  

Additionally, the dependent variable, codified as reported rape per 100,000 individuals limits the scope of the definition of sexual violence in this paper.  

Research Design

We use population and gender ratio as instrument variables (IV) to test the effect of Tinder on the number of rape incidents. The treatment group is population of women exposed to tinder after 2012 while the control group comprise of women who were not exposed to tinder between the years 1985-2012. 

The control group is not an ideal comparison of the treatment group due to the limited number of observations. It fails to account for other web-based dating sites that existed but were not as freely available. Due to the geographically dependent nature of dating apps and the unavailability of information on a more micro-level, the impact of Tinder, either positively or negatively, cannot be determined. 

The Identification Strategy

The identification strategy of an instrument variable analysis entails two assumptions, the exclusion restriction, and the ignitability assumption. The exclusion restriction necessitates that the instrument is related to the outcome variable only through the treatment status- i.e. it is uncorrelated with the error term. In the context of this paper that would mean that our instruments gender ratio and population are related to the dependent variable, rape incidents only through the treatment status of if they were exposed to Tinder or not. 

Scatter Plot of GR vs. Rape

# Load necessary libraries
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(readxl)

# Conditionally install and load the 'ivreg' package if it's not already installed
if (!requireNamespace("ivreg", quietly = TRUE)) {
    install.packages("ivreg")
}
library(ivreg)

# Read the dataset
df <- read_excel("df.xlsx")

# Check column names of df
names(df)
##  [1] "Year"             "Rape"             "Rape Revised"     "Tinder"          
##  [5] "GDP"              "PR"               "GR"               "Pop"             
##  [9] "predicted_rape"   "lagged_pop"       "lagged_pr"        "treatment_binary"
# Create the scatter plot using ggplot
ggplot(data = df, aes(x = GR, y = Rape)) +
  geom_point() +
  labs(title = "Scatter Plot of GR vs. Rape")
## Warning: Removed 1 row containing missing values or values outside the scale range
## (`geom_point()`).

Scatter Plot of Population vs. Rape (1986 onwards)

library(ggplot2)
library(dplyr)

# Assuming the year column is named 'Year' and your dataset is named 'df'
df_filtered <- df %>%
  filter(Year >= 1986)  # Filter the data for years 1986 onwards

# Create the scatter plot using ggplot
ggplot(data = df_filtered, aes(x = Pop, y = Rape)) +
  geom_point() +  # Add points
  labs(title = "Scatter Plot of Population vs. Rape (1986 onwards)",
       x = "Population",
       y = "Rape") +
  theme_minimal()  # Use a minimal theme

Figure 2 and Figure 3 show the trends overtime of gender ratio and population in the context of rape. We can observe how there is a deviation in the trends close to the right end of the plots, which would mark the cut-off of the year 2012, which is when Tinder was launched. 

The second assumption is the ignorability assumption which suggests that the potential outcomes are independent of the treatment status: people do not use tinder expecting to be assaulted. Therefore, the potential outcomes Y1 (becoming the victim of rape) and YO (not being a victim of rape) is independent of the treatment status which is D1 (women who used tinder after 2012) and D0 (women who did not use tinder). 

Clean data, include lagged variables

# Load necessary library
library(readxl)

# Read the dataset
df <- read_excel("df.xlsx")

# Check column names of df
names(df)
##  [1] "Year"             "Rape"             "Rape Revised"     "Tinder"          
##  [5] "GDP"              "PR"               "GR"               "Pop"             
##  [9] "predicted_rape"   "lagged_pop"       "lagged_pr"        "treatment_binary"
# Add lagged variables
df <- df %>%
  mutate(lagged_pop = lag(Pop, 1),
         lagged_pr = lag(PR, 1))

# Filter data based on the Year
data_filtered <- df %>%
  filter(Year >= 1985 & Year <= 2012)

# Create a linear model using the filtered data
model_lagged <- lm(Rape ~ lagged_pr + lagged_pop + lagged_pr * lagged_pop, data = data_filtered)

summary(model_lagged)
## 
## Call:
## lm(formula = Rape ~ lagged_pr + lagged_pop + lagged_pr * lagged_pop, 
##     data = data_filtered)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.43148 -0.55141  0.01971  0.51775  1.53471 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)  
## (Intercept)          -1.045e+01  4.169e+01  -0.251   0.8054  
## lagged_pr             7.415e+00  3.005e+00   2.468   0.0261 *
## lagged_pop            1.375e-07  1.440e-07   0.954   0.3551  
## lagged_pr:lagged_pop -2.495e-08  1.035e-08  -2.411   0.0292 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8498 on 15 degrees of freedom
##   (9 observations deleted due to missingness)
## Multiple R-squared:  0.9579, Adjusted R-squared:  0.9495 
## F-statistic: 113.9 on 3 and 15 DF,  p-value: 1.519e-10
# Run the linear model (later in FS also)
model <- lm(Tinder ~ Pop + GR, data = df)

summary(model)
## 
## Call:
## lm(formula = Tinder ~ Pop + GR, data = df)
## 
## Residuals:
##       31       32       33       34       35       36       37       38 
##  0.74683 -0.31808 -1.03247 -0.68055  1.44445 -0.41169  0.21315  0.03836 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -8.537e+02  6.648e+02  -1.284 0.255367    
## Pop          9.621e-07  1.176e-07   8.184 0.000443 ***
## GR           1.077e+01  1.260e+01   0.855 0.431478    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9477 on 5 degrees of freedom
##   (31 observations deleted due to missingness)
## Multiple R-squared:  0.9617, Adjusted R-squared:  0.9464 
## F-statistic: 62.75 on 2 and 5 DF,  p-value: 0.0002873

IV Analysis

# Load the necessary library
library(AER)
## Loading required package: car
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:dplyr':
## 
##     recode
## Loading required package: lmtest
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: survival
## Registered S3 methods overwritten by 'AER':
##   method              from 
##   print.ivreg         ivreg
##   print.summary.ivreg ivreg
##   summary.ivreg       ivreg
##   vcov.ivreg          ivreg
##   bread.ivreg         ivreg
##   estfun.ivreg        ivreg
##   hatvalues.ivreg     ivreg
##   predict.ivreg       ivreg
##   anova.ivreg         ivreg
##   terms.ivreg         ivreg
##   model.matrix.ivreg  ivreg
##   update.ivreg        ivreg
## 
## Attaching package: 'AER'
## The following objects are masked from 'package:ivreg':
## 
##     ivreg, ivreg.fit
# 'Pop' and 'GR' are being used as instruments
a <- ivreg(Rape ~ Tinder | Pop + GR, data = df)

summary(a)
## 
## Call:
## ivreg(formula = Rape ~ Tinder | Pop + GR, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0715 -1.0093  0.1232  1.0582  1.7755 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  30.0633     0.9493  31.668 6.59e-08 ***
## Tinder       -0.0429     0.1453  -0.295    0.778    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.542 on 6 degrees of freedom
## Multiple R-Squared: 0.01108, Adjusted R-squared: -0.1537 
## Wald test: 0.08725 on 1 and 6 DF,  p-value: 0.7777

The results of the IV regression show that when Tinder is considered as a predictor of Rape with Pop (population) and GR (growth rate) serving as instruments for Tinder, the coefficient for Tinder is 0.0429. This means that for each increase in the Tinder variable by one unit, the Rape variable decreases by 0.0429 units. However this relationship is not statistically significant (p = 0.778) suggesting that in this models context changes in the Tinder variable do not significantly affect the Rape variable. The intercept is calculated at 30.0633. Is highly significant (p < 0.0001) indicating a baseline level for the Rape variable when Tinder is zero and all other variables are constant, in the model.

First Stage

# Run the linear model using the df data frame which contains the 'Tinder' column
FS <- lm(Tinder ~ Pop + GR, data = df)
summary(FS)  # Display the summary of the regression model
## 
## Call:
## lm(formula = Tinder ~ Pop + GR, data = df)
## 
## Residuals:
##       31       32       33       34       35       36       37       38 
##  0.74683 -0.31808 -1.03247 -0.68055  1.44445 -0.41169  0.21315  0.03836 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -8.537e+02  6.648e+02  -1.284 0.255367    
## Pop          9.621e-07  1.176e-07   8.184 0.000443 ***
## GR           1.077e+01  1.260e+01   0.855 0.431478    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9477 on 5 degrees of freedom
##   (31 observations deleted due to missingness)
## Multiple R-squared:  0.9617, Adjusted R-squared:  0.9464 
## F-statistic: 62.75 on 2 and 5 DF,  p-value: 0.0002873
# Adding predicted values column to the df data frame
df$predicted_tinder <- predict(FS, newdata = df)

Interpretation: As we can observe that the first stage is when population and gender ratio are regressed on Tinder users. The F-statistic of the model is 62.75[4].  This is an indication of the validity of the instrument used (as F>10). the `ivreg` command also displays strong evidence through the “weak instruments test” that the instruments used are valid. The coefficient for Pop is approximately 0.0000009621. This means that for each one-unit increase in population, the Tinder variable increases by about 0.0000009621 units. This coefficient is highly significant (p = 0.000443), suggesting a strong positive relationship between population size and the Tinder variable. The intercept (-853.7) is not statistically significant (p = 0.255), implying that when both Pop and GR are zero, the baseline level of the Tinder variable is not significantly different from zero at conventional significance levels. The model has a residual standard error of 0.9477 on 5 degrees of freedom, suggesting that the model predictions are reasonably close to the actual data points. The first stage and reduced form equations used are as follows:  

\[Tinder = \beta_0 + \beta_1 \cdot \text{Pop} + \beta_2 \cdot \text{GR} + e\] \[{Rape} = \beta_0 + \text{predicted tinder} + v\]

The estimand in our paper is the LATE (Local Average Treatment Effect). This is the effect that is calculated based on the compliers group. The compliers in this study are women who used tinder because of the increase in population and the balance of gender ratio and were therefore the victims of rape.

Limitations and Future Research

The small number of observations (38 total) due to the aggregated data pose a limited statistical power. Additionally, the effects of time would suggest SCQE as a better research design. However, the unavailability of data for state wise tinder users, makes it difficult to get around this limitation. Furthermore, Statista provides data only on subscribers of tinder, which potentially overlooks all other users of tinder that do not use the paid subscription of the app, especially increasing the confounders of socio-economic status related variables. 

The narrow scope of this paper, with limiting sexual violence to rape incidents, and rape incidents only on women instead of all genders is a serious limitation. We also only look at one dating application while there are plenty applications that are being used. Beyond this, we also only account for the cases that were reported. It is hard to believe that all rape incidents get reported. 

This project could further use the shift share design where we would use population for the shift and gender ratio for the share. This will help provide a regional understanding of the incidence of crime as facilitated by dating apps related to geographic density.  

This project could further use the shift share design where we would use population for the shift and gender ratio for the share. This will help provide a regional understanding of the incidence of crime as facilitated by dating apps related to geographic density.  

References:
[1] https://www.nsvrc.org/statistics

[2] The definition rape changes in 2013 to account for all genders. We ensure to create revised rape rates to account for the incidents that involve women only. https://ucr.fbi.gov/crime-in-the-u.s/2018/crime-in-the-u.s.-2018/topic-pages/rape

[3] Note that Tinder was launched in 2012, the data thus ranges from 2013-2022.

[4] The F-statistic of above 10 is usually the standard for a good model.