Upward Intergenerational Social Mobility
Leon Luo, Mark Fu, Tony Pappas
Project Overview
This project uses statistics and model building to predict the Intergenerational Social Mobility
Rate, as defined in Chetty et al. 2020. This project, an intersection of data science and social
science, consists of data collection, statistical analysis, data revision and merging, and model build-
ing. The project first generates correlation matrices to observe correlations between mobility rate
and independent variables, such as parent median income, kid median income, college tiers, median
income differences, and percent of parents earning in 1st quintile, and the dependent variable, social
mobility rate. Through the investigation in correlation with additional exploratory analysis with
graphs and plots, unnecessary variables are filtered out and more accurate multivariable regression
models are built.
Related Work
Our data and analysis drew from an Opportunity Insights paper examining intergenerational
mobility by Chetty, Friedman, Saez, Turner, and Yagan.
During the planning of this project, we acquired a more precise understanding of social mobility
on Lumen Learning, a teaching website where key social-related terms are defined. This website
provides a clear explanation of the important factors that influence social mobility, including financial and material resources, job markets, and educational opportunities.
In addition to getting an idea of how social mobility is characterized and analyzed, we studied
a research paper on social mobility: “How do we characteristically measure and analyze intergenerational mobility?”, written by Florencia Torche. From there, we further developed our knowledge
of different types of mobility and the approaches to measuring mobility rate.
Lastly, we used Opportunity Insights, a database established by Harvard professors, which
utilizes data from publicly available federal government records. We compared different datasets
related to social mobility and scrutinized all the presented variables and descriptions of different studies.
Initial Questions
Our research question is: What socioeconomic factors influence the social mobility rate in
the United States? As we moved into exploratory analysis after obtaining necessary variables,
we wanted to know the extent of each feature’s influence on the dependent variable: social mobility
rate. After generating correlation matrices and multiple linear regression analysis, we sought to test
the influence of variables such as parent median income, kid median income, and college tier. For
future study, we would like to consider more independent variables, such as location, race, gender,
and measure the indication of variance in social mobility rate on the wealth gap, and the impact of
policy on mobility rate within society.
Data
Once we decided to research social mobility, we looked for datasets that yielded enough features
to make a multiple linear regression model, where the dependent variable would be social mobility.
Social mobility would be either portrayed as parent income subtracted from kid income or as a rate,
such as the probability of a kid having an income in the top quintile of income distributions while
having parents earning in the bottom quintile. Some key features we hoped to use as independent
variables were education level, race, and housing. Many datasets only had one of the factors we
were looking for but we eventually found several datasets that matched our needs. Opportunity
Insights, a research institute focused on finding solutions for economic disparities, had several
datasets that had features such as mean incomes, median incomes, and social mobility rates to
make our dependent variable. They also collect government data on location, education level, race,
birth year, and the number of people in each family. All financial data was normalized to the 2014 US
dollar value.
Unfortunately, We were able to merge datasets with only education level and parent income,
and child income as dependent variables. The merge took place on both features state and par q1
(fraction of parents in the bottom quintile for income distribution). Before the merge we cleaned
up the datasets by eliminating extraneous variables, which were almost all string data types. The
only string features we kept were state and tier (rank for level of college/university). The tier
column was converted to integers from 1 (most prestigious schools) to 14 (not attending college
between the ages 19-22) by creating a library pointing each level description to a number. This was
a key step because now we could use tier as a variable in correlation matrices and our multi-linear
regression model. Another pre-merge change was multiplying the second dataset par q1 column
by 100 and then rounding both par q1 columns to the fourth decimal point. This was because
the first dataset measured par q1 as a percent and the second dataset presented it as a decimal.
To finalize the merged dataset we divided the parent and kid median incomes by 1000 so that our
visualizations would be easier to interpret.
Exploratory Analysis
Following the merge of our two main datasets, we graphed correlation matrices to determine
which variables we would want to use for our multi-linear regression model. Collinearity was
discovered after running a correlation matrix for the merged data frame (fig 1). Both parent median
income and kid median income had a high correlation and indicated collinearity. As a result, parent
median income and kid median income could not be used as independent variables in the same multi-
linear regression model. The matrix revealed positive correlations between normed mr kq5 pq1
(mobility rate) and k median, as well as a negative correlation between parent median income and
college tier or kid median income. This means that as the college tier decreases to 1, the highest
school level, median income increases.
collinearity.
Figure 1: Correlation matrix. Note strong correlation between k median and par median, indicating
collinearity.
After creating the correlation matrices, we looked at other descriptive statistics for our variables.
This process involved compiling averages, standard deviations, and counts for our independent and
dependent variables. We were able to verify our distribution graphs (histogram plots) based on
this information. The most important distribution graphs were for the difference between kid and
parent median incomes and the difference between kid and parent mean incomes. The median
income difference histogram plot revealed that most of our data was negative or that most kids had
lower income than their parents (fig 2). The mean income difference revealed outlier points such as
a mean parents income of 1.6 million dollars with a mean kid income of 16 thousand dollars. We
determined that the parent income features were in fact representations of household income and
could consist of more than one earner. Due to this discovery, we made the parent and kid median
income features independent variables and made the social mobility rate our dependent variable.
because parent income is defined by household, while child income is defined by the individual.
Predictive Analyses
We chose to use multiple linear regression to build our predictive model. This choice was
made due to the numerous advantages multiple regression provided over other modeling techniques;
namely, we were interested in examining the strength and importance of the relationships between
each predictor and mobility. By using multiple regression, we were able to gain these insights from
the generated coefficients.
We chose k median, par median, and tier as predictors and normed mr kq5 pq1 as the
response variable. k median represents average child income, par median average child income,
tier college tier, and normed mr kq5 pq1 is the mobility rate, defined as the joint probability
of an individual earning in the top quintile and their parents earning in the bottom quintile.
As noted in the Exploratory Analysis section, our k median and par median predictors
clearly exhibited collinearity. We chose to resolve this issue by producing two separate regression
models, each incorporating one of the collinear predictors.
Our chosen method of regression was OLS (Ordinary Least Squares) regression. The results are
shown below.
0.118, the low p-values all indicate significant results
The first regression included the predictors k median and tier. The R2 value was 0.118,
indicating a fairly low accuracy score, but we suspect this can be attributed to high variance in
the data. Indeed, all P values were all less than the standard 0.05 threshold, indicating a significant
correlation for all predictors.
0.063, the low p-values all indicate significant results.
The second regression included the predictor’s par median and tier. The R2 value was 0.063,
indicating an even lower accuracy score than the first model, but we again attribute this to high
variance in the data. Indeed, all P values were all less than the standard 0.05 threshold, indicating
a significant correlation for all predictors.
Conclusion
We conclude that child income is positively correlated with mobility. This makes intuitive sense;
if the child has a higher income, then there will be a higher chance for them to earn more than their
parents. Furthermore, parent income is negatively correlated with mobility. This also agrees with
intuition; if parent income is high, then it will be more difficult for the child to earn more than their
parents. Finally, school tier is both positively and negatively correlated with mobility, depending
on the regression model. This interesting result is not actually contradictory and can be explained
by examining const in the models. In the first model, with tier showing positive correlation, const
= -0.64, while in the second model, with tier showing negative correlation, const = 4.2. Thus, the
two regressions fit different intercepts but still move in the same direction.
Our research is not perfect; it is likely that we failed to account for several predictors. In fact,
there are several additional questions yet to be answered:
• How would social mobility be affected by location, race, and gender?
• What should parents do to set the next generation up for positive social mobility?
• What does a wealth gap look like in terms of social mobility?
• How can social mobility solve a wealth gap?
• How does public policy affect social mobility?
We hope future research may answer these questions.
Cited Works
Boundless. (2021). Boundless sociology. Lumen. https://courses.lumenlearning.com/boundlesssociology/chapter/social-mobility/.
Chetty, R., Friedman, J. N., Saez, E., Turner, N., & Yagan, D. (2021, January 15). Income
segregation and intergenerational mobility Across colleges in the United States. Opportunity
Insights. https://opportunityinsights.org/paper/undermatching/.
Policy solutions to the American Dream. Opportunity Insights. (2021, July). https://opportunityinsights.org/.
Torche, F. (2013). How do we characteristically measure and analyze intergenerational mobility?
Stanford Center on Poverty and Inequality. http://cpi.stanford.edu/ media/working papers/torche how
-do-we-measure.pdf.