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TITLE: Student Mean Income based on College Tiers and Household Income Hierarchy

DATE: 04/22/2022

Kwame Darko-Mensah

INTRODUCTION

The degree to which an individual's position in the income distribution continues or changes from one generation to the next is referred to as intergenerational income mobility (Stuhler, 2018). Policymakers are increasingly worried about intergenerational economic mobility since income inequality has risen in many nations in recent decades (Deutscher, et. al (2021). This study aims predict a child’s percentile using their parents’ income percentile and other factors. To do this analysis, a cross-sectional data obtained from the data repository https://opportunityinsights.org/data/ was used. The dataset contains information of 1515 and has 21 variables. Our most interesting variables are k_mean and par_pctile whereby we need to check if there exists any relationship between k_means and par_pctile. In the research, our dependent variable is child’s percentile income while our independent variable is parent’s percentile income. Other variables such as age and sex which are likely to have some impacts on our analysis will be included in the analysis.

Literature Review

Introduction

A variety of techniques are used in conceptualizing and assessing intergenerational mobility. This section focuses on illustrating several models for predicting children’s status based on their parents’ earnings and other related factors through case studies.

Case Studies

Intergenerational mobility, according to a new study by the National Bureau of Economic Research, is the relationship between parents' and children's socioeconomic level (Cholli & Durlauf, 2022). The study also utilized the term "socioeconomic status" to refer to a person's income. A variety of mechanisms have been proposed to explain the relationship between parental and child status, and they can be split into two categories, including family and social influences. According to Cholli and Durlauf (2022), wealth, education, and the composition of the family can all have a role in determining intergenerational mobility. Social models, on the other hand, are concerned with the social environment, specifically schools and neighborhoods.

Recent social science research has highlighted the importance of a broad set of cognitive skills and personality traits in determining labor market success. Parental attributes, as well as investments, have an impact on these abilities (Mogstad et al., 2021). Traditional family investment structures are used to enable for parental investment and education to be complimentary inputs, which means that each dollar of investment has a marginal impact. Parental education improves when parents invest in their children. When this is the case, parental education heterogeneity can increase intergenerational transmission. Persistence is important because parental education has an impact on the amount of money invested since parental education affects the amount of money invested and their efficacy (Torche, 2018). Studies on skills has also stressed the importance of investments made during childhood and adolescence, as well as the ways in which they are made.

Intergenerational mobility is defined as children's predicted wages conditional on parents' incomes in their study on the impact of neighborhoods on intergenerational mobility. Chetty et al. (2018) define intergenerational mobility as the correlation between a parent's and a child's income percentile ranks, characterizing the possibility of moving up the income distribution relative to parents as the correlation between a parent's and a child's income percentile ranks. Deutscher, 2020) used the rank definition to quantify intergenerational mobility in the Australian setting, and the results were consistent with Chetty's previous work. Another study on the decline of intergenerational mobility in the United States employs the Duncan socioeconomic index score, a ranking indicator for jobs, to assess the relative status of occupations through time (Mogstad et al., 2021). Duncan's SEI, on the other hand, has been criticized for its calculations, which are based on male census data and may not accurately reflect the female population. As a result, we have decided to employ the percentile rank definition of intergenerational mobility rather than the occupational definition. Many of these studies are limited when extrapolated to civilizations and cultures that emphasize attributes other than economic success because they were conducted in the United States as part of the Western world. Such research has been conducted in nations with market economy and nuclear families as the norm.

The parent's income and other characteristics are the predictor variables in most intergenerational mobility studies, which employ linear regression to predict the child's income (Torche, 2018). One of the numerous drawbacks of linear regression is that it cannot establish poverty or affluence traps, the idea that it is more difficult for a poor family to go up the social ladder than it is for a wealthy family to move down. This is compensated for using nonlinear models. Intergenerational mobility varies across geographical locations, demographics, and time, according to studies. The Great Gatsby curve was created by Krueger (2012), an economic adviser to the US President, to highlight an apparent direct relationship between income inequality and intergenerational mobility.

The causal effect of childhood neighborhood exposure on intergenerational mobility is evaluated by the difference between the mean rank outcome of a kid who moved to a new area and the mean rank outcome of a child who had always lived in the area moved to, according to Chetty et al. (2014). They also utilize linear regression to assess the effects of factors including parental marital status, displacement shocks, a change in parent income, natural disasters, and sibling comparisons. Feigenbaum (2018) utilized a fixed-effects regression model to find the characteristics of counties whose children have higher income than their parents, such as racial and income segregation, economic disparity, and educational quality.

Chetty et al. (2018) present two related models for their rank definition in their descriptive examination of the spatial aspects of intergenerational mobility in the United States. They rank children based on their incomes in comparison to other children in the same birth cohort, and parents based on their incomes in comparison to other parents with children in the same birth cohort. The authors calculate absolute mobility, the predicted rank of children from households at any given percentile, by adding the intercept and the product of the slope and parent's percentile after regressing the parents' and children's rank distributions (Corak, 2020). Relative mobility, on the other hand, is merely the regression model's slope, implying that mobility is aggregated rather than dependent on the parents of the child. This rank-rank method has also been used to quantify mobility in some other noteworthy research on mobility. A study of recent trends in intergenerational mobility (Chetty et al., 2018) and Deutscher's study on the impact of childhood exposure on mobility are two examples.

Chetty and Hendren's seminal study (2018) offered new evidence that where a child grows up affects their later life results. In this study, I look at when and why place matters, which are important considerations for anyone trying to address inequities caused by causal place effects. Place seems to matter the most throughout adolescence, with a strong role for local labor markets and evidence for peer effects on a smaller scale. The effects of exposure to location are greatest in adolescence, and they are often minor and non-statistically significant in early life. This is in line with age-atmigration studies, which show that the benefits of moving a year earlier on language acquisition are greatest in adolescence (Chetty et al., 2018) This finding does not rule out the importance of early infancy. Rather, factors such as family or more localized environmental influences may important in early life, where most variance is seen within rather than between the big communities studied here.

Conclusion

While apparent or structural mobility may differ between industrialized nations, circulatory mobility does not, according to the Featherman-Jones-Hauser theory. In essence, circulation mobility considers the independent relationship between an individual's status and that of their parents, and is unaffected by technological advancements, changes in the demand and supply of specific occupations, or family size. If this is correct, it could indicate that findings from US studies can be applied to the rest of the industrialized world.

METHODS

Participants

The study used a cross-sectional data obtained from the data repository https://opportunityinsights.org/data/ . The dataset contains information of 1515students and has 21 variables.

Materials

R-studio to run some analysis on the data to determine the best variables to be used in the model then proceed to perform the statistical analysis. According to Rachel et al. (2018), R-studio is among the best data analysis tools to obtain results from raw data collected for research.

Procedure

The mean, standard deviation, median, skewness, kurtosis, range, minimum, and maximum of the independent variables were calculated using the psych package, which displayed the mean, standard deviation, median, skewness, kurtosis, range, minimum, and maximum of the independent variables.

The data distribution for the parent's income and the child's income was shown using a histogram.

A correlation test was used to determine whether there is a significant correlation between our dependent and independent variables, as well as the sort of correlation that exists. Mishra et al. (2019) illustrated that correlation tests are essential in descriptive statistics and in normative tests for statistical data.

RESULTS

In the summary of our data there were no missing data. All entries had a value.

(a) Descriptive statistics

(b) Output of summary statistics

Output of summary statistics

The table of summary statistics shown above gave a summary of the average, maximum, minimum, standard deviation, skewness and kurtosis. It indicates that some of the independent variables were negatively skewed while all others were positively skewed. The table also shows some variables had a positive kurtosis indicating that their distribution had heavier tails (leptokurtic distribution) while other variables had light tails. They had a negative kurtosis thus a platykurtic distribution.

A histogram of Childs earning

The plot indicates that the distribution of child’s income is skewed to the right with most earnings ranging between 0 and 100000.

Scatter plot of Child’s earnings and parent’s earnings

The scatter plot indicates the trend in the data. As parent’s income increases , child’s income also increases.

(c) Scatter plot of child’s income and childs rank

The plot shows that as child’s rank increases, the child’s income also increases.

Correlation

A correlation test was run to evaluate if there was a significant correlation and the type of correlation that exists between the dependent variable and independent variables. Child’s earnings and parent’s earnings show a weak positive correlation. with a value of 0.1867327 and a p-value of 2.535e-13 which is less than 0.05 an indication that they had a significant correlation. The following variables were also significantly correlated to the dependent variable (child’s earnings) and might be considered in the regression model; k_rank, par_mean, k_median, k_top, tier and k_q. These variables were used as control variables in our study since they were significantly correlated to the dependent variable k_means.

Regression analysis

The regression summary show that the overall p-value of the model is < 2.2e-16 which is less than 0.05 implying the study is significant.

Also, also all the variables except par_pctile are significant with p-values less than 0.05. The variable par_pctile is not significant in the study of factors that affect mean child’s earning with a p-value of 0.4105 which is less than 0.05.

The adjusted r-squared is 0.9321 which means that 93.21% of the dependent variable is explained by the independent variables.

References

Chetty, R., & Hendren, N. (2018). The impacts of neighborhoods on intergenerational mobility II: County-level estimates. The Quarterly Journal of Economics, 133(3), 1163-1228. https://academic.oup.com/qje/article-abstract/133/3/1163/4850659

Chetty, R., & Hendren, N. (2018). The impacts of neighborhoods on intergenerational mobility I: Childhood exposure effects. The Quarterly Journal of Economics, 133(3), 1107-1162. https://academic.oup.com/qje/article-abstract/133/3/1107/4850660

Cholli, N. A., & Durlauf, S. N. (2022). Intergenerational Mobility. https://www.nber.org/papers/w29760

Corak, M. (2020). Intergenerational mobility: what do we care about? What should we care about?. Australian Economic Review, 53(2), 230-240. https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-8462.12372

Deutscher, N. (2020). Place, peers, and the teenage years: long-run neighborhood effects in Australia. American Economic Journal: Applied Economics, 12(2), 220-49. https://www.aeaweb.org/articles?id=10.1257/app.20180329

Deutscher, N., & Mazumder, B. (2021). Measuring Intergenerational Income Mobility: A Synthesis of Approaches.

Feigenbaum, J. J. (2018). Multiple measures of historical intergenerational mobility: Iowa 1915 to 1940. The Economic Journal, 128(612), F446-F481. https://academic.oup.com/ej/article-abstract/128/612/F446/5089529

Mishra, P., Pandey, C. M., Singh, U., Gupta, A., Sahu, C., & Keshri, A. (2019). Descriptive statistics and normality tests for statistical data. Annals of cardiac anaesthesia, 22(1), 67. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6350423/

Mogstad, M., & Torsvik, G. (2021). Family background, neighborhoods and intergenerational mobility. https://www.nber.org/papers/w28874

Rachel, V., Sudhamathy, G., & Parthasarathy, M. (2018). Analytics on moodle data using R package for enhanced learning management. International Journal of Applied Engineering Research, 13(22), 15580-15610. https://www.ripublication.com/ijaer18/ijaerv13n22_19.pdf

Stuhler, J. (2018). A review of intergenerational mobility and its drivers. Publications Office of the European Union, Luxembourg. https://core.ac.uk/download/pdf/162257020.pdf

Torche, F. (2018). Intergenerational mobility at the top of the educational distribution. Sociology of Education, 91(4), 266-289. https://journals.sagepub.com/doi/abs/10.1177/0038040718801812