Where is the Land of Opportunity? The Geography of Intergenerational Mobility in the United States

Why it matters, in detail. Weighting and magnitudes: - The CZ-level analysis is unweighted, so very small rural CZs carry as much weight as the large metros. - Population weighting (the estimand that matters for the typical child) cuts the five headline correlations by 20-53% (median 50% across 20 correlates) and the unstandardised slopes by 33-64% (median 66%). - Covariate dispersion barely changes, so this is heterogeneity, not range restriction. - 8 of 20 correlates become insignificant. Multivariate results: - The five-factor R2 falls from 0.76 to 0.45, and only dropout and the single-parent share stay significant. - In the relative-mobility regressions social capital is significantly wrong-signed: +0.154 unweighted, +0.396 weighted. - The univariate signs are preserved, but the magnitudes and the claim that the multivariate predictors are robust are overstated for the population.

Evidence. (a) Univariate associations (Online App. Table VIII cols 1-3, 6; adjudicator reproduced every cell exactly with scripts/verify_core.py). - Across the 20 correlates in the six highlighted categories, population-weighted correlations are a median 0.50x the unweighted ones, and 8 of 20 lose significance. - Examples: income segregation -0.393 -> -0.169 (SE 0.105); Gini -0.578 -> -0.236 (0.162); test scores 0.588 -> 0.176 (0.220). - The others losing significance: segregation of affluence, top-1% share, class size, violent crime, share married. - The five chosen proxies fall by 20-53%: commute 0.605 -> 0.335, Gini99 -0.647 -> -0.416, dropout -0.574 -> -0.433, social capital 0.641 -> 0.299, single mothers -0.764 -> -0.613. - With state fixed effects the median ratio is 0.67 and 18 of 20 stay significant, so that claim holds. (b) Adjudicator test of the range-restriction defence. - Unstandardised slopes (rank points per unweighted SD of the covariate) under population weights are a median 0.34x the unweighted slopes. - For the five proxies: commute 0.47x, Gini99 0.39x, dropout 0.63x, social capital 0.36x, single mothers 0.67x. - Covariate SDs barely change under weighting (median 0.86x), so the weaker weighted associations are not a range-restriction artefact (scripts/unstandardized_slopes.py). - Among the 50 largest CZs (55% of the population), correlations with r25 are: single mothers -0.52, Gini99 -0.36, dropout -0.36, commute +0.06, social capital -0.01 (each SE about 0.14). - 193 CZs with fewer than 2,000 sample children hold 1.7% of the population but have an r25 SD of 6.6, against 4.6 elsewhere. (c) Multivariate results (Table VI, confirmed in the authors' own log replicate/tables.smcl). - The bottom-99% Gini is insignificant in every five-factor column. - With state fixed effects, social capital is also insignificant: 0.065 (0.050). - Urban CZs only: the Gini (+0.060) and dropout rate (-0.109, SE 0.085) are insignificant. - Relative mobility (col 4): only commute and single mothers are significant with the expected sign. Social capital enters at +0.154 (0.060), i.e. more social capital goes with a steeper rank-rank slope, opposite to its univariate correlation (-0.327). The text says the other factors 'are not statistically significant'. - Col 5 repeats +0.154 (0.070), which the text calls one of 'all four ... strong predictors' without mentioning the sign. - Population-weighting the QJE specification (adjudicator; matches Auditor A): commute 0.106 (0.109), Gini99 0.060 (0.091), dropout -0.234 (0.102), social capital 0.075 (0.087), single mothers -0.543 (0.125). R2 falls from 0.757 to 0.445. The weighted relative-mobility version gives social capital +0.396 (0.090). (d) Version history: NBER WP 19843. - Jan. 2014, Sec. V.K (printed pp.45-46) and Table IX (PDF p.72) included a population-weighted column: racial segregation -0.042 (0.091), Gini99 0.069 (0.093), social capital 0.120 (0.086), R2 0.441. The text called it 'roughly similar'. - The QJE dropped that column and adopted the commute share as the 'strongest and most robust' segregation proxy (p.1617). - The commute share correlates -0.80 with log CZ population. Its partial correlation with r25 net of log population is still 0.46.

Why this severity. The direction survives: each factor keeps at least one significant proxy under population weights (racial segregation -0.31, Gini99 -0.42, dropout -0.43, social capital 0.30, single mothers -0.61). But for the population-weighted estimand the paper itself claims is 'very similar', the associations are 20-53% weaker in correlation terms and 33-64% weaker per unit of covariate. Several highlighted proxies become insignificant: the overall Gini, test scores and income segregation. The 'five robust multivariate predictors' result holds only in the unweighted absolute-mobility specification. That is a change of more than a quarter in the magnitude of a core finding (C3) under a defensible alternative.

The authors' response. No direct response located. The paper reports the population-weighted univariate results (Online App. Table VIII col. 3) and warns that the multivariate coefficients 'should be interpreted with caution' (p.1619). The NBER version described its weighted multivariate column as 'roughly similar'.

Why it matters, in detail. Because G - S is approximately (1-S)G_B - 0.01, conditioning on G - S while varying S induces co-movement in G_B. The conditional top-1% coefficient is therefore a function of the construct. It ranges from -0.41 to +0.17 for absolute mobility (and -0.19 to +0.18 for relative mobility) across normalised, reconstructed and published measures, and several of these values are significant. The cross-country coefficient (N=13, SE 0.27) cannot distinguish zero from the Gini's own coefficient. Cross-sectional associations with top shares say nothing about the time-series rise in top shares.

Evidence. The identity was checked algebraically by both auditors and the adjudicator. With the normalised G_B in place of G - S (G_T set to 0, 0.5 or 1; results insensitive), the top-1% coefficient moves as follows (scripts/verify_core.py; identical to both auditors): - all CZs: -0.123 (0.035) -> +0.088 (0.046); - urban CZs: +0.029 (0.039) -> +0.172 (0.048); - relative mobility: -0.032 (0.032) -> -0.192 (0.039). With other bottom-inequality constructs (adjudicator): - reconstructed local bottom-99% Gini: -0.414 (0.073) all CZs, -0.108 (0.050) urban, +0.182 (0.069) relative; - national-rank-corrected measure: -0.190, +0.129, +0.019. So the conditional association of top shares with mobility ranges from significantly negative to significantly positive. Cross-country evidence: - Table V col 7 (N=13): 0.17 (0.27), 95% CI about [-0.36, 0.70], which includes the Gini coefficient (0.62). - Col 8 (N=12): -0.11 (0.28). Other points: - The CZ top-1% share comes from parents of 1980-82 births in each CZ, so in a CZ with 250 children it rests on 2-3 families. - Unconditional correlations of the top-1% share with mobility: -0.190 (0.072) unweighted, +0.059 (0.094) population-weighted, -0.144 (0.069) urban, +0.019 (0.063) with relative mobility.

Why this severity. The descriptive statement that bottom-99% inequality tracks mobility far more closely than top shares survives in unconditional terms, and nothing suggests that top-end inequality reduces mobility. What is not supported: the Table V decomposition, the 'uncorrelated' conditional claims, the extrapolation to the rise of top shares over time, and the cross-country test. These are a secondary result (C4), not the geography.

Why it matters, in detail. The like-for-like comparator for a person-level parental effect (0.341 SD per SD) is the child-weighted dispersion of CZ effects. That gives 0.12 SD per SD (34-36% of the parental effect), not 0.20 (58-60%). The unweighted figure is driven by very small CZs: 193 CZs with fewer than 2,000 sample children (1.7% of the population) have an SD of 6.6.

Evidence. Recomputed from DT5 (scripts/verify_core.py): - unweighted SD 5.68 -> 0.197 SD of child rank -> 58% of 0.341; - population-weighted SD 3.34 -> 0.116 -> 34%; - weighted by core-sample children, SD 3.51 -> 0.122 -> 36%. The correlation between cohorts (1980-82 vs 1983-85) is 0.97 (Online App. Table VII row 5), so sampling noise does not explain the gap.

Why this severity. The existence of substantial geographic variation is unaffected: for the typical child a 1 SD better CZ is still worth about 3.3-3.5 rank points. But the paper's headline measure of how much place matters relative to family income is overstated by about 70% (60% vs about 35%).

Why it matters, in detail. Price deflation shifts both generations' national ranks in high-price CZs. Absolute upward mobility (the fitted child rank at parent rank 25) therefore falls by roughly (1 - slope)*D, while the slope is nearly invariant (correlation 0.99). The overall correlation (0.98 unweighted) is dominated by many rural CZs with similar price indexes. Weighted, and among large metros, the ranking changes substantially: correlation 0.82 among the 50 largest, and the San Jose-Charlotte gap falls 56%.

Evidence. The authors' own 'AM, Cost of Living Adjusted' series (Online Data Table 5; scripts/verify_core.py). Among the 50 largest CZs: - correlation with the nominal series 0.82; - San Jose 44.7 -> 40.3 (rank 3 -> 27); - San Francisco 5 -> 28; Los Angeles 11 -> 36; - San Antonio 24 -> 6; Fort Worth 18 -> 5; Austin 26 -> 13; - the San Jose-Charlotte gap falls from 8.9 to 4.0 rank points (-56%). Across all CZs: - correlation 0.98 unweighted, 0.87 weighted; SD ratio 1.06; - for relative mobility the correlation is 0.99. No cost-of-living-adjusted Q1->Q5 probability is published.

Why this severity. The national pattern and the dispersion survive. But the ranking of expensive coastal metros by absolute upward mobility is not robust to the paper's own real-income adjustment, and that includes San Jose, the abstract's high-mobility example. The paper's stated reason for robustness does not apply to the absolute measure.

The authors' response. Online App. F (pp.11-12) argues that the adjustment cancels because parents and children mostly live in areas with similar prices. That reasoning applies to rank differences and to the rank-rank slope, not to the absolute measure r25.

Why it matters, in detail. If P_ic is the national rank, the statistic is 2Cov(X, F_nat(X))/mean_c, a concentration index on national ranks. It is not scale-invariant and depends on the CZ's location and its dispersion relative to the nation (an inverted U in location). The published values match the reconstructed national-rank index in level (0.410 vs 0.413) and in the location gradient (-0.063 vs -0.060 per 0.2 national-rank shift of the median). Correcting for the distortion leaves the bottom-99% correlation with r25 about unchanged (-0.63 vs -0.65). It weakens the overall-Gini correlation modestly (-0.50 to -0.58 vs -0.578) and the already insignificant weighted one more (-0.13/-0.17 vs -0.24). Auditor A's 40-100% overstatement figure is not robust to the reconstruction.

Evidence. Auditor A's scale-invariance test. - Conditional on scale-free shape measures, location in the national distribution strongly predicts the published Gini. For the 111 CZs with at least 20,000 children: F=201, p=2e-35. - The same holds for the county Ginis in Online Data Table 3: F=737, against F=666 for a simulated national-rank version, with near-identical coefficients. Adjudicator's independent reconstruction (scripts/gini_national_rank_test_v2.py). - Method: each CZ's parent distribution is rebuilt from the DT7 quantiles P10-P99, the mean and the DT8 top-1% share (body interpolated in logit space, Pareto tail, bottom segment matched to the mean). - Validation on the national distribution: true Gini 0.501, reconstructed 0.493. - Large CZs (n>=20,000): the published Gini tracks the national-rank formula (RMSE 0.018, corr 0.975) better than a true Gini (RMSE 0.032, corr 0.944). - All 709 CZs: average level 0.410 published, 0.413 national-rank, 0.433 local. - Regressing (published - local) on (national-rank - local) gives a slope of 0.78; 0 would indicate a true Gini, 1 a national-rank Gini. - A cruder first-pass reconstruction gives corr 0.997 vs 0.911 and a slope of 1.03. - Holding shape fixed, moving the CZ median from national rank 0.5 to 0.7 lowers the published Gini by 0.063. A simulated national-rank Gini falls by 0.060; a simulated local Gini by about 0. - The Lorenz bound G >= S - 0.01 is never violated, so no published value is impossible for a true Gini. Impact (adjudicator; published Gini purged of the reconstructed national-rank distortion). - Overall Gini correlation with r25: -0.578 becomes -0.50 (-0.58 with reconstructed local Ginis). - Population-weighted: -0.236 becomes -0.13 to -0.17. - Bottom-99% Gini: -0.647 becomes -0.63 (weighted -0.416 becomes -0.43). - Table VI col 6 Gini99 coefficient: -0.287 becomes -0.25 (-0.19).

Why this severity. The measure behind 'less income inequality' and the within-US 'Great Gatsby' curve is labelled a Gini but partly reflects where the CZ sits in the national income distribution. This undisclosed property matters when the paper compares it with true Ginis across countries. But the demonstrated effect on the headline correlations is modest: at most about 15% for the unweighted overall Gini and about zero for the bottom-99% measure under the adjudicator's correction. The qualitative inequality-mobility association survives.

Why it matters, in detail. Measuring child income at about 30 and averaging parent income over five years attenuates persistence through life-cycle and transitory error, and the population data only reach age 32. Later estimates from the same administrative source (SOI-M panel, ages 35-38, 9-year parent average) put the expected-income IGE near 0.50 against 0.335. PSID evidence suggests the rank-rank slope could be 0.36-0.40 against 0.341, although like-for-like PSID windows give 0.28. The rank-rank level is therefore modestly uncertain, and the IGE level substantially so.

Evidence. Mitnik, Bryant, Weber & Grusky (2015, IRS SOI WP; Table 8, p.94; pp.44-45): - The expected-income IGE is 0.50 (nonparametric, children aged 35-38, 9 years of parent income) and 0.46 under constant elasticity. - Re-imposing ages 29-32 and a 5-year parent average brings it to 0.37, against 0.34 in CHKS (dollar-weighted 0.335). About one fifth of the gap remains. - Their Appendix A results are 'inconsistent with Chetty et al.'s ... claim ... that the IGE e of income stabilizes around age 30' (pp.35-36). Mazumder (Chicago Fed WP 2015-04; RLE 43, 2016): - The family-income IGE is likely above 0.6 in the PSID. - Rank-rank row-weighted averages are 0.31-0.36, and the slope 'may be around 0.4 or higher' (Table 4; p.32). - Imposing tax-data windows lowers the PSID rank estimate from 0.33 to 0.28. - He concludes the tax data 'modestly overstate mobility' and that the geographic differences are 'unlikely to be affected'. Evidence in the authors' favour for ranks: Corak (2018), cited by Connolly, Corak & Haeck (2019, fn 16), reports a Canadian rank-rank slope of 0.242 at ages 35-48 and 0.240 at ages 31-32. Indicative check: Auditor A's calibrated Opportunity Atlas calculation (ages 31-37) implies about 0.36-0.37 nationally.

Why this severity. For the headline rank-rank slope (0.341) the likely understatement is small (about 0-15%), below the threshold for a major issue. The geography is unaffected: correlation 0.95 with the Atlas re-estimate at ages 31-37. For the IGE the understatement is about 30-45%, but the paper already treats the IGE as unstable and secondary. The blanket assurance in footnote 1 is too strong.

The authors' response. Online App. C, partly written in response to an earlier Mitnik et al. draft (Mitnik et al. fn 79), and App. E argue that attenuation largely disappears with five years of parent income. App. E attributes Mazumder's (2005) larger IGEs to imputation. Footnote 22 notes: 'A useful direction for further work would be to understand why the two samples yield different IGE estimates.' No reply to Mazumder (2016) or to the final Mitnik et al. (2015) located.

Why it matters, in detail. Like-for-like administrative estimates put the foreign family-income rank-rank slopes at 0.20-0.23. The US slope is therefore 1.5-1.7 times theirs, not about 2 times. The 'nearly half' gap is overstated by roughly 25-50%. Against these benchmarks, 26-50 US CZs (1.2-4.4 million people) have slopes at or below 0.203-0.229, and Los Angeles, San Diego and San Jose are at 0.231-0.237. The paper's claim that some CZs are 'comparable' therefore stands.

Evidence. - The paper's own US slope with children's individual income is 0.287 (Table I row 7). - Helsø (2021, Scandinavian Journal of Economics 123(2):508-531, Table 1), using CHKS's sample definitions: the Danish family-income rank-rank slope is 0.203, i.e. 60% of the US 0.341. For individual earnings: 0.223 vs 0.282 (79%). Helsø writes that the differences are 'smaller than previously reported'. - Connolly, Corak & Haeck (2019, Journal of Labor Economics 37(S2):S595-S641, Tables 2-3), Canadian 1980/1982 cohorts, family income: 0.212-0.229 vs 0.341 (62-67%). The Canadian Q1->Q5 is 11.2%, against the 13.4% cited. - The cited Canadian 0.174 does reproduce from Corak-Heisz (1998/1999) Table 6B (both auditors).

Why this severity. The direction (the US is substantially less mobile) is robust, and fn 25 discloses that the benchmarks are not fully comparable. Like-for-like, the US-Nordic/Canadian ratio is about 0.60-0.67 rather than about 0.5. This is a contextual comparison outside the paper's within-US core.

The authors' response. Footnote 25 discloses the definitional differences and calls the Canadian sample 'less comparable'.

Why it matters, in detail. The school-quality proxies are contemporaneous with, or later than, the outcomes for later cohorts. Their population-weighted association (test scores) is insignificant. Education-mediated channels account for a small share of cross-CZ differences in transmission (Rothstein 2019). The college/teen-birth correlations cannot separate childhood-environment channels from anticipated labour-market returns.

Evidence. - Test scores are grade 3-8 scores averaged over 2004, 2005 and 2007 (App. G p.14). The 1980-82 cohort was in grades 3-8 around 1988-95. - Dropout rates are for 2000-01 (a high-school measure). Expenditure and class size are for 1996-97. App. G acknowledges the timing only for spending. - Test scores are insignificant with population weights: 0.176 (SE 0.220). - College attendance at p25 correlates 0.71 unweighted and 0.53 weighted with r25 (Online App. Table VII row 22). - Context: Rothstein (2019, JOLE 37(S1):S85-S123) finds that differences in the human-capital gradient explain only one-ninth of the CZ variation in income transmission, while 40% reflects marriage patterns. - In the authors' favour: the later quasi-experimental exposure designs of Chetty & Hendren (2018, QJE 133(3)) support childhood-exposure effects.

Why this severity. The problem is in labels and interpretation. The correlational results themselves are unaffected, and the childhood interpretation is hedged elsewhere in the paper and supported by later causal work.

The authors' response. Sec. V.E (p.1602) mentions 'anticipatory behavioral responses'. App. G argues that school spending is persistent (correlation 0.86 across states between 1982 and 1992).

Why it matters, in detail. The labelling and definition slips concern variables that are otherwise reproducible from the released data. The alternatives that could be computed (male-householder families, Hispanic Black residents, restoring Newark's school spending) leave the correlations essentially unchanged.

Evidence. Covariate definitions: - (1) Footnote 50 (p.1617) says dropout data are missing for 126 CZs. Table VI notes and the data say 116 (verified: 116 missing among the 709 CZs). The NBER Table IX note said 128. - (2) Table VI notes and DT9 say test scores and dropout/graduation rates are residualised on 'mean household income in 2000'. The published variables reproduce only with mean parent family income for 1996-2000 (dropout: corr 1.000000, max diff 5e-8; corr 0.994 with census income), as Sec. VI.D and App. G state. - (3) The single-mother share is described as the fraction of children with single mothers (p.1616; Table VI). It is actually female-householder households with own children divided by all households with own children, from SF1 P018 by ZCTA (clean_public_data.do lines 775-783). App. G cites SF3 P018 and DT9 cites SF3 P015. Adding male-householder families changes the correlation from -0.764 to -0.769 (Auditor B). - (4) The black share is described as 'black alone' but uses NHGIS FMS002, which is non-Hispanic Black alone (codebook line 85). The effect is negligible (Auditor B). - (5) The Online App. Table VIII row 'Teacher-Student Ratio' is in fact the student-teacher ratio. - (6) Local tax rate: App. G says 1990 nominal income per household and DT9 says 2000 income per working-age adult. The data equal 1992 taxes per capita divided by 1990 income per working-age adult in 2007 dollars (Auditor A). - (7) School spending: App. G says the 8 CZs in the top 1% are dropped. In fact 9 are dropped, including Newark NJ: 5.8m people, $12.30k per pupil against a raw 99th percentile of $12.54k (adjudicator confirmed from covariates.dta). The effect is negligible. Labels and cross-references: - (8) Table III reads 'Kansas City, MI'; App. Fig. IV reads 'Minneapolis, IN'. - Table III notes cite Online Data Table VII for Q1->Q5; Fig. VIII notes cite App. Table VII instead of VIII; the DT8/DT9 notes cite 'Section V' and 'Appendix D' (NBER numbering). - The App. Fig. XIII note lists the violent-crime arrest rate, while the legend and App. I use the religious share. - p.1580 describes five-year parent-income windows starting in 1996-2010, whereas the App. Fig. II-B notes describe single years. A five-year window starting in 2010 is impossible with data ending in 2012. Replication package: - (9) The readme uses pre-QJE table numbering. - Residualisation, the 25%-missing rule and the outlier drops are absent from the published code. - clean_public_data.do line 687 assigns the origin CZ conditional on dest_county==8014; it should be orig_county. This is negligible. Other definitions: - (10) State tax progressivity is defined two ways (App. G vs App. H). EITC exposure years are given as 1980-2001 (App. G) and 1981-2001 (App. H).

Why this severity. None of these items changes a correlation materially. They do hinder exact reproduction and correct interpretation of the covariates.

Why it matters, in detail. The slips are immaterial: the intended ratio is 5.68/28.9 = 0.20, and the dollar values are off by one centile.

Evidence. - (1) p.1593 prints '5.68/2.89 = 0.20'. The denominator should be 28.9 (checked on the page image). - (2) '$28,800—the 25th percentile of the national parent family income distribution' (p.1590) and the child 37th/52nd percentiles of '$22,900/$35,500' (p.1592) equal the means of centiles 24/36/51 in Online Data Table 2, whose bins are numbered from 1. The centile 25/37/52 means are $29,900/$23,700/$36,500. - (3) Decile cut-offs: the top-decile relative-mobility gap is 'less than 23.5' against 24.0 in the data, the bottom decile is 'more than 40.2' against 40.3, and the teen-birth bottom decile is '<15.4%' against 15.19%. - (4) The column 4 percentages in Online App. Table I imply 9.81m core children, against the 9,867,736 reported (-0.55%).

Why this severity. These are transcription and arithmetic slips of about $1,100-1,600 or 0.2-0.6 rank points, with no effect on any conclusion.

Why it matters, in detail. There is an undocumented revision of the CZ transition probabilities: mean absolute change 0.04 pp, maximum 0.68 pp, mostly in small CZs. Rank-based statistics are unaffected.

Evidence. Checked by the adjudicator (scripts/misc_verifications.py): - AM and RM: 0 of 709 values differ. - Q1->Q5 (DT5 col G): about 578 of 729 CZs differ beyond storage precision, by up to 0.68 pp (Gunnison). - June DT6 equals the January DT5 exactly. - Published Table III follows the January/DT6 values: St. Louis 5.052% rounds to 5.1, whereas the June DT5 value of 5.049% rounds to 5.0. - The headline cities are unchanged at displayed precision: Charlotte 4.379%/4.373%, San Jose 12.933%/12.938%. - Auditor A's count of 724 uses a tolerance of about 1e-9, which includes storage noise. - Appendix Table VIII also changes slightly between the NBER and QJE versions (e.g. crime -0.346 -> -0.380).

Why this severity. The changes are small and go in both directions, and the headline numbers are unchanged.