Intergenerational Mobility: IGE, Rank-Rank Slope

Intergenerational mobility is the degree to which a person’s economic or social position differs from, or is tied to, the position of their parents. In quantitative work it is almost always summarised by one of two statistics: the intergenerational elasticity of income (IGE) or the rank-rank slope. This guide defines both, works through the arithmetic with numbers from a published study, and shows how to compute and report them.

Definition: what is intergenerational mobility?

Intergenerational mobility describes how strongly children’s outcomes, usually income, depend on their parents’ outcomes. If a child’s income is almost unrelated to parental income, mobility is high; if the two are tightly linked, mobility is low. Researchers separate two ideas. Relative mobility asks how much a child’s position in the distribution depends on the parents’ position, and is summarised by the IGE or the rank-rank slope (lower values mean more relative mobility). Absolute mobility asks what outcomes children from a given parental position actually reach. Chetty, Hendren, Kline and Saez (2014) define absolute upward mobility as the mean income rank of children whose parents are at the 25th percentile of the parent income distribution.

Measures and formulas

Intergenerational elasticity (IGE)

The IGE is the slope from regressing log child income on log parent income (Solon, 1999):

ln(Y_child) = α + β · ln(Y_parent) + ε

Y_child is the child’s adult income, Y_parent is parental income, α is the intercept, β is the IGE, and ε is the error term. Chetty et al. report that the log-log specification “yields very unstable estimates” in their tax data because it is sensitive to zero and very small incomes. Using parents between the 10th and 90th percentiles and excluding children with zero income, they estimate an IGE of 0.45, with alternative specifications ranging from 0.26 to 0.70.

Rank-rank slope

The rank-rank slope replaces incomes with percentile ranks. Children are ranked against other children in the same birth cohort and parents against other parents of those children:

R_child = a + b · P_parent + ε

R_child is the child’s income percentile rank (0 to 100), P_parent is the parent’s percentile rank, a is the intercept and b is the rank-rank slope, which equals the correlation of the two ranks. Chetty et al. find the relationship almost perfectly linear and report that a 10 percentile-point increase in parent rank is associated with a 3.41 percentile-point increase in the child’s rank on average, a slope of 0.341.

Worked example with the arithmetic shown

Take the rank-rank slope b = 0.341. Because both ranks have the same mean (50 on a 0 to 100 scale), the fitted line passes through (50, 50), so the intercept is a = 50 − 0.341 × 50 = 32.95.

Parent at the 25th percentile: expected child rank = 32.95 + 0.341 × 25 = 32.95 + 8.525 = 41.5.
Parent at the 75th percentile: expected child rank = 32.95 + 0.341 × 75 = 32.95 + 25.575 = 58.5.
Gap between the two: 58.5 − 41.5 = 17.0 ranks, which is 0.341 × 50 (the 50-point difference in parent rank).

The first line is an estimate of absolute upward mobility under a linear fit. For the IGE of 0.45, doubling parental income multiplies expected child income (in the geometric-mean sense) by 2^0.45 = e^{0.45 × 0.6931} = e^0.3119 ≈ 1.37, or about 37% higher.

Interpretation

Statistic	Value	Reading
Rank-rank slope	0	Child rank unrelated to parent rank (maximum relative mobility)
Rank-rank slope	0.341	Each 10-point rise in parent rank goes with a 3.41-point rise in child rank (Chetty et al., 2014)
Rank-rank slope	1	Child rank equals parent rank (no relative mobility)
IGE	0.45	A 1% difference in parent income goes with about a 0.45% difference in child income
Absolute upward mobility	35.8 to 46.2	Range of mean child rank at parent percentile 25 across the 50 largest US commuting zones, from Charlotte (35.8) to Salt Lake City (46.2)

Why published estimates differ

Estimates depend on the data and design. Chetty et al. used administrative tax records on more than 40 million children (1980 to 1982 birth cohorts), with child income measured as mean family income in 2011 to 2012 (around age 30) and parent income as mean family income in 1996 to 2000. Mazumder (2015), using the Panel Study of Income Dynamics, argues that the IGE in family income is likely greater than 0.6, meaning lower mobility than the tax-record IGE suggests, and that rank-based measures, while more robust to the limits of tax data, still modestly overstate mobility. He recommends using both IGE and rank measures, depending on which concept of mobility is of interest. Compare estimates only when age at measurement, income definition, and number of years averaged match.

Assumptions and common mistakes

Treating the IGE as a rank statistic. It is an elasticity in logs; it cannot handle zero incomes without exclusion or transformation.
Single-year income. Short income windows and measuring children too young bias estimates; multi-year averages near mid-career are preferred.
Assuming linearity. The rank-rank fit is linear in the Chetty et al. data, but check it in your own data with a scatter or binned means.
Mixing relative and absolute mobility. A low slope says nothing about whether children are better off than their parents.
Comparing across datasets with different income definitions or cohorts.

How to report intergenerational mobility (APA)

State the sample, the income definition, the ages at measurement, the exclusions, and the estimator. A format example: “The rank-rank slope was b = 0.34, 95% CI [lower, upper], N = sample size.” Replace the bracketed items with your own estimates. Reference list entry (APA 7th edition format):

Chetty, R., Hendren, N., Kline, P., & Saez, E. (2014). Where is the land of opportunity? The geography of intergenerational mobility in the United States. Quarterly Journal of Economics, 129(4), 1553–1624. https://doi.org/10.1093/qje/qju022

How to calculate it in Excel, R or Python

First convert incomes to percentile ranks within the cohort. Variable names below are placeholders for your data.

Excel

Parent rank (column C): =PERCENTRANK.INC($A$2:$A$1001, A2)*100
Child rank (column D):  =PERCENTRANK.INC($B$2:$B$1001, B2)*100
Rank-rank slope:        =SLOPE(D2:D1001, C2:C1001)
IGE (positive incomes): =SLOPE(LN(B2:B1001), LN(A2:A1001))   # array formula

R

d$pr <- rank(d$parent_inc) / nrow(d) * 100
d$cr <- rank(d$child_inc)  / nrow(d) * 100
coef(lm(cr ~ pr, data = d))["pr"]               # rank-rank slope
pos <- subset(d, parent_inc > 0 & child_inc > 0)
coef(lm(log(child_inc) ~ log(parent_inc), data = pos))[2]   # IGE

Python

import numpy as np, pandas as pd
d["pr"] = d["parent_inc"].rank(pct=True) * 100
d["cr"] = d["child_inc"].rank(pct=True) * 100
slope = np.polyfit(d["pr"], d["cr"], 1)[0]          # rank-rank slope
pos = d[(d.parent_inc > 0) & (d.child_inc > 0)]
ige = np.polyfit(np.log(pos.parent_inc), np.log(pos.child_inc), 1)[0]

Data sources and related CASRAI guides

US panel data commonly used for these estimates include the Panel Study of Income Dynamics (PSID) and the General Social Survey; neighbourhood-level mobility estimates built from the Chetty et al. work are covered in the Opportunity Atlas guide.

FAQ

What is the difference between relative and absolute mobility?

Relative mobility is how strongly child rank depends on parent rank (IGE or rank-rank slope). Absolute mobility is the outcome level reached by children from a given parental position, such as mean child rank at parent percentile 25.

Is a higher IGE good or bad?

A higher IGE or rank-rank slope means child outcomes are more tied to parental outcomes, so lower relative mobility. It is a descriptive measure, not a welfare judgement.

Why use rank-rank instead of the IGE?

Chetty et al. report the log-log IGE is unstable with zero and low incomes, while the rank-rank relationship is nearly linear. Mazumder (2015) recommends reporting both.

Sources

Chetty, R., Hendren, N., Kline, P., & Saez, E. (2014). Quarterly Journal of Economics, 129(4), 1553–1624. https://doi.org/10.1093/qje/qju022 (read 2026-11-08).
Mazumder, B. (2015). Federal Reserve Bank of Chicago Working Paper 2015-04 (intergenerational elasticity and rank association using PSID data). https://www.chicagofed.org/publications/working-papers/2015/wp2015-04 (read 2026-11-08).
Solon, G. (1999). Intergenerational mobility in the labor market. In Handbook of Labor Economics (Vol. 3), as cited by Chetty et al. (2014).

Intergenerational Mobility: Definition, IGE and Rank-Rank Slope