Problem 4. Opportunity Insights is a research initiative based at Harvard University and led by Raj Chetty, John Friedman, and Nathaniel Hendren, with the goal of improving upward mobility in the United States by studying barriers to economic opportunity and translating findings into pol- icy change.3 As part of a 2017 study to understand the effect of the higher education system on upward mobility, Chetty et al. constructed an anonymized dataset covering all college students in the United States from 1999 - 2013 (30 million students) that includes parental income distribu- tions and student earnings outcomes by college. Monetary values are measured in 2015 dollars; i.e. adjusted for inflation to 2015 dollars. Parental income distributions were based on average pre-tax household income during the five- year period when a child is aged 15-19 years. Parents were ranked relative to other parents with children in the same birth cohort. Children's individual earnings were measured in their mid-30s and compared to others in the same birth cohort. Chetty et al. were particularly interested in characterizing colleges' mobility rates?at which col- leges do the largest number of children come from poor families and end up in the upper middle class? They defined a college's mobility rate as the percentage of students with parents in the bottom income quintile who ended up in the top x% (in their mid-30s). The variables mr_kq5_pq1 and mr_ktop1_pq1 refer to the percentage of students with parents in the bottom income quintile who ended up in the top 20% and top 1%, respectively. In this problem, you will examine a subset of data from the study; the data are in the file colleges.Rdata. The following table provides a list of the variables in the dataset and their descriptions.

data

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pset_01_summer2021_solution x pset_01_summer2021_solution x * pset_01_summer2021_solution x R RStudio Cloud X R Problem Set 1 X C A 6c25beaee378419698493eb94e4f4d3d.app.rstudio.cloud/file_show?path=%2Fcloud%2Fproject%2Fpset_01_summer2022.pdf Update : E Problem Set 1 6 / 9 1 - 100% + Variable Description name name of college region region, 1 for Northeast, 2 for Midwest, 3 for South, and 4 for West state state tier_name tier defined by selectivity and type 3 type coded 1 for public, 2 for private non-profit, 3 for for-profit exp_instr_pc_2013 instructional expenditures per student in 2013 ipeds_enrollment_2013 |total undergraduate enrollment in Fall 2013 sticker_price_2013 average annual cost of attendance in 2013 grad_rate_150_p_2013 percentage of students graduating within 150% of normal time in 2013 avgfacsal_2013 average faculty salary in 2013 sat_avg_2013 average SAT scores (scaled to 1600) in 2013 endowment_pc_2000 endowment assets per student in 200 mr_kq5_pq1 mobility rate, top 20% of the income distribution mr_ktop1_pq1 mobility rate, top 1% of the income distribution par_median median parent household income par_q1 fraction of parents in first (bottom) income quintile par_q2 fraction of parents in second income quintile par_q3 fraction of parents in third income quintile par_q4 fraction of parents in fourth income quintile par_q5 fraction of parents in fifth (top) income quintile par_top5pc fraction of parents in top 5% of income distribution par_top1pc fraction of parents in top 1% of income distribution k_median median child individual earnings in 2014 (at age 34) k_top5pc fraction of children in top 5% of income distribution k_top1pc | fraction of children in top 1% of income distribution 5 Use these data to answer the following questions. a) Investigate the distribution of median parent household income. i. Describe the distribution of median parent household income among all colleges in the dataset. Reference appropriate numerical and graphical summaries as needed. Be sure to frame your description in the context of the data, rather than simply listing statistics and their numerical values. ii. The colleges in this dataset are classified by tiers defined by selectivity and type. The most selective tier, labeled as Ivy Plus, consists of the Ivy League colleges plus Stan- 6 ford, Chicago, Duke, and MIT. prob0.pdf Show All X