Economic Mobility

Why it matters, in detail. CDGPY's population estimates put the pooled rank-rank slope at 0.286 rising to 0.313 (age 27, 1978-92; +0.0022/yr) and at 0.320 rising to 0.355 (ages 29-30, 1980-86; +0.0034/yr over 1978-89). The chapter's source estimated -0.0006/yr with a 95% upper bound of +0.0008/yr ('at most 0.27 percent per year'). Substituting anchored measured changes for the AER P&P forecasts turns the 1971-1989/92 trend into +0.0020 to +0.0029/yr, with CIs excluding zero. Persistence therefore rose by roughly 0.03 (about 10% of its level), opposite in sign to the 'if anything increased' inference from college-attendance gradients. The rise is modest relative to geographic dispersion. Its exact size is uncertain because the AER P&P population series at age 26 fell over 1980-86.

Evidence. (1) The adjudicator recovered the plotted values of CDGPY Appendix Figure A.3 (p. 100) exactly from the PDF vector paths (scripts/extract_figA3_vector.py). The five navy SOI points match AER P&P App. Table 1 col. 5 to within 0.0004, which validates the calibration. Pooled rank-rank slopes: household income at 27, 0.286 (1978), 0.287 (1980), 0.303 (1986), 0.313 (1992); at ages 29-30, 0.326 (1978), 0.320 (1980), 0.355 (1986), 0.352 (1989). (2) OLS trends are +0.0022/yr (age 27, 1978-92) and +0.0034/yr (ages 29-30, 1978-89). The chapter's source reports a trend of -0.0006/yr with 95% upper bound 0.0008 (reproduced: -0.00057, CI [-0.00194, +0.00080]). (3) In the CDGPY public national Table 5 CSV, the pooled p75-p25 gap in child rank at 27 rises from 13.04 to 14.67 percentiles (+12.5%, 1978-92), and the mean rank of children from p25 families falls from 44.96 to 43.45 (scripts/cdgpy_national.py). (4) Replacing the AER P&P forecasts for 1983-89/92 with these measured changes, anchored to the 1980-82 SOI level, gives trends of +0.0020 to +0.0029/yr with 95% CIs excluding zero. The 1989 forecast (0.294) lies about 0.036 below the anchored measured value (0.330), and the 1992 forecast (0.281) about 0.05 below (scripts/trend_with_later_data.py). (5) Within-race bottom-to-top probabilities, 1978 to 1992 (CDGPY Tables A.9-A.11): white 13.7% to 11.9%, Hispanic 9.4% to 8.9%, Black 3.0% to 3.0%. (6) The college gradient behind the 1987-93 forecast fell (0.751 to 0.692; AER App. Table 1 col. 8). Over the same cohorts the measured income slope kept rising (0.305 to 0.313, 1987-92), and the white class gap in four-year graduation by 27 widened from 21.4 to 29.5 points (CDGPY Table A.3). (7) Caveat: the AER P&P's own measured population-sample slope at age 26 fell from 0.2735 to 0.2648 over 1980-86 (-0.0026/yr, SE 0.0008), whereas CDGPY's age-27 slope rose from 0.287 to 0.303. CDGPY do not reconcile the two. Their sample links children to parents from 1994 and measures parent income at ages 13-17; the AER P&P population sample links only from 1996 and covers 85.6% of the 1980 cohort versus 97.2% of the 1986 cohort.

Why this severity. Changes the chapter's headline trend from 'extremely stable / not declining / if anything improving' to a modest but precisely estimated rise in persistence (about +0.03, a trend 3-4 times the published upper bound). The qualitative claim is reversed in sign, though not by a large amount. Not critical: the rise is only about 0.4-0.6 of the cross-CZ SD of rank-rank slopes (0.056-0.065); it concerns only cohorts born after 1978; the conflict with the source's own measured age-26 series is unexplained; and the geography is untouched.

The authors' response. The lead author's later paper (CDGPY, Sec. II.C) acknowledges the upward trend and attributes its non-detection to SOI sampling error. It does not discuss the AER P&P population age-26 series. No statement by Hendren, Kline or Saez was located.

Why it matters, in detail. Eleven of the 23 trend points (1983-93) are proxies rescaled by constants fitted on the 1980-86 overlaps, and they enter the OLS as error-free observations. Only these points pin the CI down to 0.0008/yr. Measured age-29-30 data alone cannot exclude a rise of about 2.5% a year (upper bound +0.0075/yr), and dropping only the college-based points gives an upper bound of +0.0034/yr, four times the published one. The downward slope of the forecast segment comes from the college gradient's fall over the 1990-93 cohorts (0.732 to 0.692), a relation the authors themselves found had failed in an earlier period.

Evidence. Adjudicator reproduction from app_tables.xls (scripts/reproduce_pathways.py). (1) The consolidated series rebuilds from its components (max diff 6.9e-8; factors 1.117784 and 0.394790). Its trend is -0.000573/yr (SE 0.000658), 95% CI [-0.00194, +0.00080]. (2) Measured SOI ages 29-30 only, 1971-82: +0.00244/yr (SE 0.00227), 95% CI [-0.0026, +0.0075]. (3) Consolidated 1971-86 without the college-based points: +0.00061 (SE 0.00131), upper bound +0.0034. (4) Measured population age-26 slopes, 1980-86: -0.00263 (SE 0.00079). (5) Codex's illustrative scenarios raise the college conversion factor by 10% or 20% by 1993; the trend becomes +0.0004 or +0.0014. (6) Unquantified extra caveat: 1098-T forms miss some no-tuition low-income students. Only 87.1% of bottom-quintile college attendees appear in 1098-T records (Chetty, Friedman, Saez, Turner & Yagan 2020, Online Appendix fn. 7), so the gradient level is overstated, and any change in non-filing over 2003-12 would contaminate its trend.

Why this severity. Concerns the basis and precision of a core trend claim rather than an arithmetic error, and the assumption is disclosed in the figure note and the source. Its realised consequence (the forecasts missed a rise in persistence) is graded in F1, so this is kept at moderate to avoid double counting.

The authors' response. AER P&P p. 145 states the assumption. NBER WP 19844 fn. 9: 'The validity of this assumption should be evaluated as data for more cohorts become available.' The Figure 2 note labels the open circles as forecasts.

Why it matters, in detail. Unweighted CZ correlations are dominated by small, mostly rural CZs (331 of the 709 have fewer than 100,000 residents and together hold 5% of the population). Weighting by 2000 population, the estimand relevant to the typical child, roughly halves most associations. With state-clustered SEs, the following have |t| < 2: income segregation (t about 1.6), Gini (1.5), test scores (0.8), student-teacher ratio (+0.4, wrong sign), local tax rate (1.7) and fraction married (1.7). The correlates that remain robust are the single-parent share (-0.61), fraction Black (-0.62), dropout rate (-0.43), religiosity (0.41), the commute share (0.34), racial segregation (-0.31) and social capital (0.30).

Evidence. The adjudicator reproduced the unweighted and population-weighted point estimates exactly from ODT V and VIII (scripts/reproduce_pathways.py). State-clustered SEs are taken from QJE Online App. Table VIII. Unweighted to population-weighted (SE): income segregation -0.393 to -0.169 (0.105); racial segregation -0.361 to -0.311 (0.092); commute under 15 min 0.605 to 0.335 (0.115); Gini -0.578 to -0.236 (0.162); test scores 0.588 to 0.176 (0.220); dropout -0.574 to -0.433 (0.100); student-teacher ratio -0.328 to +0.062 (0.139); local tax rate 0.325 to 0.155 (0.092); social capital 0.641 to 0.299 (0.131); fraction married 0.571 to 0.221 (0.127); single-mother share -0.764 to -0.613 (0.129); fraction Black -0.580 to -0.616 (0.074). The community-level claims weaken in the same way. For mobility in >80%-white ZIP codes against fraction Black, the correlation goes from -0.408 to -0.138. For mobility of children of married parents against the single-mother share, it goes from -0.662 to -0.432 (scripts/community_level_checks.py).

Why this severity. Affects a secondary core finding. The signs of most associations survive, and family structure and race remain the strongest correlates. But for the places where most children live, the associations are about half as large. Three of the six correlates named in the key-findings box (income segregation, local tax rates, marriage rates) are not statistically distinguishable from zero under population weights, nor are two of the three school proxies (test scores, class size) or the Gini.

The authors' response. CHKS (2014a) report the weighted correlations in Online Appendix Table VIII and describe alternative specifications as 'very similar' (p. 1603). The chapter cautions that its correlations are not causal (p. 60) but does not mention weighting.

Why it matters, in detail. The cited PSID studies have about 50-60 children per cohort and estimate log-log IGEs for 1952-75 births. Davis & Mazumder's larger NLS samples show rank persistence rising by 0.11 (about two cross-CZ SDs of rank-rank slopes) between the 1948-53 and 1961-64 cohorts, concentrated in cohorts the PSID studies omit. Stability over 'the second half of the 20th century' is therefore not established, and the chapter's long-run framing ('the key issue is not that mobility is declining') rests on a contested premise.

Evidence. (1) Lee & Solon (2009, REStat 91(4), p. 771): 'Our estimates are still too imprecise to rule out modest trends in either direction'; cohorts 1952-75, about 58 sons per cohort for 1952-63. (2) Hertz (2007) abstract: 'no evidence of a linear trend in the intergenerational elasticity of family income' for those born 1952-1975. (3) Davis & Mazumder (Chicago Fed WP 2017-05 rev. Jan. 14, 2022, Sec. 4 p. 12; REStat 108(1):1-15, 2026): the rank-rank slope rises from 0.25 (born 1948-53) to 0.36 (born 1961-64). The difference is 0.11 (SE 0.03, 95% CI 0.05-0.16), and the IGE rises from 0.28 to 0.45. They attribute the PSID's stability to its omission of the 1948-51 cohorts and to samples 4-8 times smaller (pp. 24-25). Their 'easily reconciled' remark concerns only the 1971-82 tax-data window (p. 24). (4) Countervailing evidence: Davis & Mazumder (p. 24, fn. 39) report that Jacome, Kuziemko & Naidu (NBER WP 29289, 2021; JPE 133(1):306-354, 2025) find rank-rank trends that 'seem to stabilize beginning with the 1940s cohorts'.

Why this severity. A secondary synthesis sentence; the post-1971 window is unaffected by this issue. The later evidence is split: NLS data show +0.11 between the cohorts born around 1950 and the early 1960s, while occupation-imputed series are broadly stable from the 1940s. The claim is therefore unsettled rather than refuted.

The authors' response. NBER WP 19844 fn. 12 discusses Aaronson & Mazumder (2008) and Justman & Krush (2013) and argues that their methods are biased. No response to Davis & Mazumder was located.

Why it matters, in detail. Short windows produce two biases: life-cycle bias from measuring child income at about age 30, and attenuation from transitory variation in a five-year parent average. Together they bias persistence downward. The authors' own 15-year check (+2.8%), the age gradient in later data, and the PSID evidence (0.33 to 0.28 under tax windows; about 0.40 with long centred averages) bracket the bias at roughly 3-15% of the level. Because the bias raises persistence, it reinforces 'less mobility than appreciated'; the cross-CZ ranking is largely unaffected.

Evidence. (1) Mazumder (Chicago Fed WP 2015-04, pp. 31-33; Research in Labor Economics 43:83-129, 2016): 'the rank-rank slope may be around 0.4 or higher rather than the 0.34 reported by Chetty et al.' Imposing the tax-data windows on the PSID lowers the estimate from 0.33 to 0.28 (-15%). His abstract says rank estimates 'are also downward biased and modestly overstate mobility' but that geographic differences 'are unlikely to be affected'. (2) CHKS (2014a, p. 1582): with 15 years of parent income the slope is 0.350, 2.8% above 0.341. (3) In CDGPY's data the slope at ages 29-30 exceeds the slope at 27 by about 11-19% across cohorts (App. Fig. A.3), confirming that the level depends on age. (4) The adjudicator reproduced 0.3407 from the 100 public bins (R2 0.9956). (5) Mitnik et al. (2015, IGE about 0.50) concerns the IGE, which the chapter does not report.

Why this severity. Plausible understatement of a headline number by roughly 3-15% (about 0.35-0.40 against 0.34). That is a noticeable but not transformative change. It would strengthen, not weaken, the chapter's claim that US mobility is low, and it does not affect the geography or the trend.

The authors' response. CHKS (2014a, pp. 1580-1582 and Online Appendices C and E) show the rank slope stabilising around age 30 and changing little with 15 years of parent income (0.341 to 0.350). They attribute Mazumder's (2005) larger estimates to imputation of parent income. No reply to Mazumder (2016) was located.

Why it matters, in detail. Both endpoints are age-26 statistics. Bottom-to-top probabilities fall with age (12.2% at 26 vs 8.1% at 29-30 for the SOI 1980 cohort), so the mislabel also invites comparison with the 7.5% national figure (age about 30) and the CZ map (ages 26-32), which are on a different basis.

Evidence. AER P&P p. 145 ('Children's incomes are measured at age 26 ... 8.4 percent in 1971 and 9 percent in 1986') and the Figure 3 title ('... at Age 26 by Birth Cohort'). App. Table 4 cols. 1 and 6: 0.0840423 (SOI, 1971) and 0.090127 (population, 1986), reproduced. The level depends on age: SOI 1980 cohort 12.2% at 26 vs 8.1% at 29-30 (App. Table 4 cols. 1 and 11).

Why this severity. A labelling error in the summary box; the numbers are correct and the main text gives no age.

Why it matters, in detail. The claimed +0.6 pp is less than half the 1.33 pp level gap between the two samples in overlapping cohorts and is within about one sampling SE of the 1971 estimate. Like-for-like changes are 0.0 pp (SOI 1971-82) and -0.3 pp (population 1980-86).

Evidence. AER P&P App. Table 4 (scripts/reproduce_pathways.py). SOI at age 26: 8.40% (1971) and 8.39% (1982). Population at age 26: 9.33% (1980) and 9.01% (1986). SOI at ages 29-30: 5.95% (1971) and 8.79% (1982), a noisy series. In the overlapping 1980-82 cohorts the SOI level exceeds the population level by 1.33 pp. 1971 is the second-lowest of the 12 SOI values (mean 10.11%, SD 1.25 pp). With about 870 bottom-quintile children, the binomial SE is at least 0.94 pp. Later within-race data for 1978 to 1992 show the probability falling for white children (13.7% to 11.9%) and Hispanic children (9.4% to 8.9%) and flat for Black children (3.0%) (CDGPY Tables A.9-A.11).

Why this severity. The box's 'little change' reading is consistent with like-for-like data for these cohorts; what fails is the word 'increase' and the spliced comparison.

Why it matters, in detail. 'Not declining' holds only for the copula (relative mobility). Measures that combine the copula with the widening marginal distributions do decline over these cohorts: the expected-income gap between rich and poor children (source p. 142) and absolute mobility (61.2% to 50.3%, 1971-84). The pre-1980 absolute series holds the 1980-82 copula fixed, so its fall reflects slower, more unequal growth rather than rank mobility.

Evidence. Box (p. 55) vs p. 56 col. 1; AER P&P p. 142. Chetty, Grusky, Hell, Hendren, Manduca & Narang (2017), Science 356(6336):398-406: the share of children earning more than their parents is 61.2% for the 1971 cohort, 50.0% for 1980 and 50.3% for 1984 (archived absmob_fig1.csv, re-downloaded from the Wayback Machine).

Why this severity. A problem with the headline wording. The body defines mobility as rank-based and concedes the widening income gaps, so the content is disclosed. The substantive challenge to the rank-based claim itself is F1. Downgraded from Claude's 'moderate'.

The authors' response. The body text (p. 56) and Figure 3's ladder analogy state that the rungs have grown farther apart.

Why it matters, in detail. Pooling P(top | bottom) within a state needs weights N_c*q_c, not N_c. The difference matters only where the share of bottom-quintile parents varies strongly across a state's CZs, as with South Dakota's reservation CZs. It does not affect national or CZ-level estimates.

Evidence. Adjudicator (scripts/reproduce_pathways.py; identical to Codex). The published method reproduces all 51 bars and their order exactly. Re-weighting by 1980-85 children times P(parent in Q1) (ODT VI) gives: South Dakota 12.19% to 11.12%; North Dakota 18.91% to 19.14%; Wyoming 16.21% to 15.23%; Wisconsin 8.65% to 8.10%. The mean absolute change across the 51 bars is 0.16 pp and the maximum is 1.07 pp; Spearman rank correlation 0.995. Regions: West 9.95% to 9.68%, Northeast 9.19% to 9.27%, Midwest 7.61% to 7.36%, South 6.77% to 6.64%.

Why this severity. The weighting is disclosed, the changes are small (at most 1.1 pp), and no comparison in the text changes; the ND-SD contrast widens. Downgraded from Codex's 'moderate'.

Why it matters, in detail. A 13-country regression with SE 0.27 cannot distinguish 'no association' from an association as large as the Gini's. Cross-CZ correlations are silent on the time-series effect of rising top shares. The source's own Gatsby-style benchmark (+7.5%) is consistent with the later-measured rise and would have flagged that a modest increase in persistence was expected.

Evidence. CHKS (2014a) Table V (p. 1613), 13 countries: the standardized coefficient on the top-1% share is 0.17 (SE 0.27), 95% CI about -0.36 to 0.70, which includes the Gini coefficient's 0.62; with 2005 data (12 countries) it is -0.11 (SE 0.28). AER P&P p. 146 predicts persistence rising 'by only 7.5 percent (from 0.30 to 0.323)' over the 1971-93 cohorts. That is above its own 95% bound of about 5.9% over 22 years, and close to the 8-11% rise later measured (F1). Within the US, the CZ correlation of the top-1% share with upward mobility is -0.19 unweighted and +0.06 population-weighted (QJE Online App. Table VIII), so the metro-area part is supported. See also this project's adjudication of CHKS (2014a), F3, on the 'bottom-99% Gini' construct.

Why this severity. A secondary explanatory claim. Its within-US component is supported, and the chapter does not rest its trend finding on it. The part of Claude's I9 alleging a mis-citation is rejected (see rejected_claims).

Why it matters, in detail. The summary omits a correlate with |r| about 0.6 and includes one with r = 0.33 that the text describes as modest. Under population weights both shrink (Gini -0.24, local tax rate 0.16; see F5).

Evidence. Box (p. 55) vs pp. 59-60. Unweighted correlations with absolute upward mobility (709 CZs; reproduced): Gini -0.578, bottom-99% 'Gini' -0.647, middle-class share +0.679, local tax rate +0.325.

Why this severity. An inconsistency between the summary and the body; the body text is correct.

Why it matters, in detail. Pooling younger cohorts measured at 26-32 raises the national bottom-to-top rate by about 0.26 pp (3.5%) relative to the core sample. Readers are also not told that the trend rests on a small stratified SOI sample, which bears on F2.

Evidence. ODT V col. 7 is headed 'P(Child in Q5 | Parent in Q1), 80-85 Cohort', and the ODT VI notes say '1980-85 birth cohorts'; see also CHKS p. 1596. Aggregating the CZ matrices gives an implied national rate of 7.80% for the 1980-85 pool versus 7.54% for the 1980-82 core sample (reproduced). AER P&P App. Table 1 col. 4: coverage 85.6% (1980), 91.6% (1981), 93.7% (1982). SOI samples have 4,331-9,936 children per cohort (col. 1).

Why this severity. Undisclosed but small effects (about +0.26 pp on the national rate); the figure notes point to the source tables.

The authors' response. CHKS (2014a) disclose the 1980-85 pooling, which improves precision in small CZs.

Why it matters, in detail. The 34 vs 30 discrepancy (about 12%) mostly reflects one-year vs five-year parent income in the SOI vs population samples, i.e. attenuation. It is not a change over time.

Evidence. QJE population sample, five-year parent income: slope 0.341. SOI-based consolidated series: mean 0.296; SOI 1980-82 cohorts: 0.308 for the same cohorts (AER P&P App. Table 1 col. 5; reproduced). The page image of p. 56 shows a single-panel Figure 1. Crossref lists Piketty & Saez (2003), QJE 118(1), as pp. 1-41, as does the AER P&P reference list.

Why this severity. Presentation only; no conclusion depends on them.

Why it matters, in detail. A 55% majority, 10.6 pp above the rural baseline, becomes 'typically ... large metropolitan areas ... out of their state'. Neither metro size nor interstate moves is measured in the cited work.

Evidence. CHKS (2014a, p. 1595): 55.2% of rural-raised children who rose from the bottom to the top quintile live in urban CZs at 30, versus 44.6% of all rural-raised children. 'Urban' means any CZ intersecting an MSA. No statistic is given on large metros or on leaving the state of birth, and children are located by where they were claimed as dependents. CHKS's stayers check (Online Appendix robustness row 8; 62% of the sample) finds that high-mobility areas also raise mobility for children who stay. The authors' Vox column contains no such claim; Chetty (2015, Penn Press) was not available to check.

Why this severity. A descriptive overstatement of a side remark; the urban-rural comparison itself reproduces (child-weighted bottom-to-top probability 7.9% urban vs 9.7% rural).