Problem set 3 - SP2024

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Feb 20, 2024

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Economics 5850: Labor Economics Spring 2024, Professor Brown Problem set 3 Name(s):__________________________________ Problem Set 3 is due by midnight on Thursday, February 22 nd . You may work with up to four group members on this problem set. Problem sets will be submitted via the class Carmen page. Look for “Problem Set 3” under “Assignments” and follow instructions for submitting your problem set file. We will (again) work on solving the following data analysis questions together as a class. Please attend class or view the recorded class meetings for guidance. Problem Set 3 will be graded out of 10 points. Question 1. Race and Ethnicity Wage Gaps – OLS estimation Return to our ECON5850SP24 Rstudio cloud computing/collaboration space on site rstudio.cloud. Use the same dataset that you used for Problem Set 1. (a) Load dataset PS1_data.Rdata as before. This dataset (still) contains more than 20 distinct variables describing the work and demographic characteristics of 31-35 year-old U.S. workers in 2014, as recorded by the National Longitudinal Study of Youth’s 1997 cohort (our nation’s leading panel data resource on young workers, which is developed and maintained by OSU’s own CHRR.) [1 point] Create subsamples based on the self-reported race and ethnicity groups of the workers. Create a sample containing only Asian workers, only Black workers, only Hispanic workers (based on the NLSY97 variable name), and only White workers. Use the KEY!ETHNICITY and KEY!RACE variables and the codebook for our PS1_data to create your subgroups. Calculate and report the mean wage and the count of workers in each race and ethnicity subsample. (Note that all sample members in PS1_data work positive hours and have positive wages.) (b) Using Ordinary Least Squares, estimate the following Human Capital regression, with indicators for your subgroups: 𝑌𝑌 𝑖𝑖 = 𝛽𝛽 0 + 𝛽𝛽 1 𝐵𝐵 𝑖𝑖 + 𝛽𝛽 2 𝐴𝐴 𝑖𝑖 + 𝛽𝛽 3 𝐻𝐻 𝑖𝑖 + 𝛽𝛽 4 𝑂𝑂 𝑖𝑖 + 𝛽𝛽 5 𝑆𝑆 𝑖𝑖 + 𝛽𝛽 6 𝐸𝐸 𝑖𝑖 + 𝛽𝛽 7 𝐸𝐸 𝑖𝑖 2 + 𝜀𝜀 𝑖𝑖 , (1) where outcome i Y represents the ln(wage)) of worker i , 𝐵𝐵 𝑖𝑖 is an indicator taking the value 1 if worker i ‘s self-reported race is Black and 0 if not, 𝐴𝐴 𝑖𝑖 is an indicator taking the value 1 if worker

i ‘s self-reported race is Asian and 0 if not, 𝐻𝐻 𝑖𝑖 is an indicator taking the value 1 if worker i ‘s self- reported ethnicity is Hispanic and 0 if not, 𝑂𝑂 𝑖𝑖 is an indicator taking the value 1 if worker i ‘s self- reported race is a category other than Black, Asian, or White and worker i reports that their ethnicity is non-Hispanic and 0 if not, i S represents the years of schooling of worker i , and i E represents the years of work experience of worker i . The final term in (1) is an idiosyncratic error. Subscript i = 1,…, n represents the n members of the NLSY97 estimation sample. (This is the Mincer Regression, and has been used to describe the wage returns to schooling and experience by labor economists since Jacob Mincer published this method in the JPE in 1958. But we have modified our Mincer regression to include indicators for race and ethnicity.) [1 point] Which coefficients in (1) describe the wage gaps by race, controlling for human capital characteristics? (c) [1 point] Which race is the omitted race category? Why would we omit this category in particular? (d) [1 point] What are your estimates of these coefficients? Is each coefficient significant or insignificant? Does your estimate of the human capital-controlled wage gap by race favor any particular groups? By how much? (e) [1 point] What do you think is the most informative set of estimates of the wage gaps among race and ethnicity groups – the difference in mean wages by race and ethnicity, as in 1(a)? Or the wage gaps among race and ethnicity groups controlling for human capital as in 1(b)? Why is this your preferred measure? [Note: Scholars disagree about the preferred measure. Choose one and argue your case.] Question 2. Intergenerational Economic Mobility Return to our ECON5850SP24 shared project space at Rstudio.cloud. I have loaded a NEW NLSY97 data extract called ps3_data in a NEW project I’ve started called “Problem Set 3 Together”, which is set for all members to access. The data should be available to you as an R dataset already loaded in our shared project space. I have posted a codebook for this newly uploaded dataset, ps3_data.cdb, to our class CarmenCanvas page. Load dataset ps3_data.Rdata. This dataset contains eight variables describing the demographic characteristics and family income of U.S. children ages 12-16 in 1997, and their income at ages 34-39 in 2019, as recorded by the National Longitudinal Study of Youth’s 1997 cohort. “Subset” ps3_data to remove all observations with negative values of CV_INCOME_GROSS_YR (parents’ household income in 1997) or CV_INCOME_FAMILY (child’s household income in 2019). (a) [1 point for all four items] Create a variable representing the centile of the parents’ income among all sample parents in 1997.

Create a variable representing the centile of the child’s income among all sample children in 2019. Create a variable representing the income quintile of the parents’ income among all sample parents in 1997. Create a variable representing the income quintile of the child’s income among all sample children in 2019. Generate and submit output representing the sample mean of each of these four income rank measures. (b) [1 point] Generate, output, and submit a Transition Matrix for parent income to child income: Create a crosstab of parent income quintile (row) by child income quintile (column). Each entry should be the row percentage. For example: The first row shows the percent of children whose parents’ income was in the first quintile whose adult incomes are in: the first quintile, the second quintile, the third quintile, the fourth quintile, and the fifth quintile, respectively. (c) [1 point] What percent of children of parents in the first income quintile reach adult incomes in the fifth quintile? (d) [1 point] What percent of children of parents in the fifth income quintile fall to adult incomes in the first quintile? (e) [1 point] What does this exercise tell you about intergenerational economic mobility in the U.S. for the current cohort of middle aged (now 39-43 years old) U.S. adults?

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