How do Pew, DHS, and CMS methods for estimating undocumented populations differ in detail?

1. A shared skeleton — the residual method and its common inputs

All three groups build from the same basic arithmetic: start with Census Bureau survey counts (principally the ACS or historically the CPS), subtract the legally resident foreign‑born estimated from administrative admission records, and treat the remainder as undocumented after adjusting for mortality, emigration, and survey coverage error; uncertainty in those adjustments drives most inter‑agency differences ^{[1] [3] [4]}.

2. Emigration: where methods most visibly split

DHS and the Congressional Budget Office adopt emigration rates tied to empirical re‑analyses of the 1980 and 1990 censuses (Ahmed and Robinson), a choice that underpins their outflows assumptions ^[2]. By contrast, Pew has not published a comparable, transparent emigration model in its public documentation according to academic reviewers, leaving outside analysts to infer differences from final totals ^{[2] [1]}. CMS’s revision sidesteps explicit year‑by‑year emigration modeling by anchoring to a 2010 residual benchmark and then propagating country‑specific ratios forward, which the CMS team argues reduces sensitivity to uncertain emigration parameters ^{[2] [3]}.

3. Data sources, sample frames, and timing differences

All three rely heavily on large federal surveys, especially the ACS; some work also references CPS or administrative datasets for cross‑checks ^{[3] [5]}. Pew’s published methodology indicates it calculates initial estimates separately for age‑gender groups in six large states and the balance of the country and further subdivides by country of origin and entry period—an explicit geographic and cohort granularity that shapes how it apports national totals regionally ^[6]. CMS produced annual series from 2010 onward using its 2010 base, while DHS issues periodic benchmarks tied to January reference dates—timing mismatches and ACS sampling variability explain part of the small numeric divergence among their point estimates ^{[3] [7]}.

4. Undercount, mortality and sensitivity reporting

Residual estimates require adjustments for survey undercount and differential mortality; DHS has at times published ranges showing how totals move under alternative assumptions (the GAO praised DHS for publishing some sensitivity ranges), while many other analysts note that organizations often do not provide full plausibility bands even though assumptions materially affect results ^{[4] [1]}. Pew and CMS apply their own coverage‑error assumptions; academic reviews find the resulting point estimates cluster closely but vary by a few hundred thousand—differences traceable to undercount, emigration, and timing choices ^{[3] [8]}.

5. Why the small numeric differences matter politically and analytically

Although recent point estimates (DHS ~10.99M, Pew ~11.0M, CMS ~10.94M for 2022) are similar, choice of emigration model, benchmark year, state‑level apportionment, and whether to publish sensitivity ranges create both substantive and rhetorical differences that fuel competing narratives about migration trends; CMS explicitly warns against equating enforcement “encounters” with population growth, a misreading that has circulated in media treatment of DHS data ^{[3] [9]}.

6. Limits of the reporting and open questions

Public documentation makes clear the common structure but leaves gaps: Pew’s emigration assumptions are not transparently published for independent replication, DHS and CBO rely on older census‑based emigration estimates that some scholars question, and CMS’s post‑2010 anchoring trades one uncertain input (emigration rates) for another (stability of country‑specific ratios)—each approach is defensible and each carries tradeoffs that analysts must weigh ^{[2] [1] [3]}.