inequality

Generational Mobility Overview

• The discussion centers around the generational mobility of children born in different decades, specifically comparing those born in 1940 and 1980.

  • Key Observation:

  • There has been a decline in absolute mobility.

  • Impact:

  • The majority of children are no longer earning more than their parents.

Absolute Mobility Decline

• Definition of Absolute Mobility:

  • Absolute mobility refers to the likelihood of children achieving a higher income than their parents.

  • The data indicates that absolute mobility has decreased between the cohorts under consideration (1940 vs. 1980).

Equal Opportunity Hypothesis

• Concept Introduction:

  • The discussion introduces a hypothetical scenario where parental income does not influence children's income, characterized as a situation of equal opportunity.

  • Implication of Equal Opportunity:

  • If there is no effect from parents' income positions on children’s outcomes, then each child has an equal chance of ending up in any income category.

• Probabilities of Staying in Place:

  • Under zero mobility (where a child's economic position mirrors that of their parents):

  • Probability of a child remaining in the same income category as their parents = 100%.

  • With perfect equal opportunity:

  • Probability of remaining in the same income category = 20% for each of five categories (1 in 5 chance for random assignment).

  • Calculation Example:

    • For zero mobility, if the parent’s income is the 90th percentile, the child would also be at the 90th percentile.

    • For equal opportunity with a random scenario across categories, the chance is distributed uniformly among categories.

Statistical Analysis

• Raj Chetty's Research:

  • Raj Chetty is referenced as a significant researcher on the mobility study, focusing on the relationship between parents' and children's income positions.

  • The relationship can be modeled using a slope coefficient of 0.35.

Income Percentiles - Calculation Example

• Specific Examples Analyzed:

  • Parents in the 90th Percentile:

  • If the parents are at the 90th percentile income:

    • Using the model, a child’s income is calculated as:

    • $ext{child's position} = 20 + 0.5 imes ext{parents' position}$

    • So if parents are at the 90th percentile:

      • $ext{child's position} = 20 + 0.5 imes 90 = 20 + 45 = 65$

      • Therefore, the child would be at the 65th percentile.

  • Parents in the 10th Percentile:

  • If the parents are at the 10th percentile:

    • The model suggests:

    • $ext{child's position} = 20 + 0.5 imes 10$

    • This simplifies to:

      • $ext{child's position} = 20 + 5 = 25$

Generational Transitions

• Progression to Grandchildren:

  • Extends analysis to future generations (grandchildren):

  • For grandchildren of parents in a lower income percentile:

  • Example calculation from previous positions:

    • $ext{grandchild's position} = ext{last generation's position} imes 0.5$. This indicates that the income position continues to fluctuate across generations.

  • Trends Observed:

  • Over generations:

    • There is evidence that some children fall into lower percentiles (e.g., a child from the 90th percentile may fall to the 65th).

    • A child from the 10th percentile may rise to the 25th and then to the 35th.

  • Conclusion on Trends:

    • The outcomes across generations reveal a convergence over time as the income positions of children begin to stabilize and reflect more equality.

    • The concept of mobility is reinforced through the slope coefficient of 0.5, indicating that there is some level of economic mobility at play.

Additional Notes for Future Discussion

• This topic will be revisited in a follow-up session, emphasizing the implications and deeper analysis of generational mobility and its trends.