Tax Form 2555 filers' income at stacked rates (26 U.S.C. 911(f))

[MaxGhenis]

Summary

A filer who excludes foreign earned income under section 911 pays tax on the rest of their income at the rates it would face on top of the excluded amount. The model did not do this: nothing in the income tax read foreign_earned_income_exclusion, so the included income was taxed from the bottom bracket. This PR applies 26 U.S.C. 911(f) to the regular tax, the capital gains rates and the alternative minimum tax, following the IRS worksheets line by line.

Example (2025, head of household, $60,000 of included wages, $40,000 excluded): tax before credits was $4,025. The Foreign Earned Income Tax Worksheet gives tax on $76,375 ($9,978 by the Tax Table) less tax on $40,000 ($4,463) = $5,515. The model now gives $5,517.50: the Tax Table taxes the middle of each $50 row, the model the exact amounts.

The law

26 U.S.C. 911(f)(1) (read at https://www.law.cornell.edu/uscode/text/26/911#f on 2026-10-02): if any amount is excluded under section 911(a), then, notwithstanding sections 1 and 55,

(A) if such taxpayer has taxable income for such taxable year, the tax imposed by section 1 for such taxable year shall be equal to the excess (if any) of— (i) the tax which would be imposed by section 1 for such taxable year if the taxpayer's taxable income were increased by the amount excluded under subsection (a) for such taxable year, over (ii) the tax which would be imposed by section 1 for such taxable year if the taxpayer's taxable income were equal to the amount excluded under subsection (a) for such taxable year, and

(B) if such taxpayer has a taxable excess (as defined in section 55(b)(1)(B)) for such taxable year, the amount determined under the first sentence of section 55(b)(1)(A) for such taxable year shall be equal to the excess (if any) of— (i) the amount which would be determined under such sentence for such taxable year (subject to the limitation of section 55(b)(3)) if the taxpayer's taxable excess (as so defined) were increased by the amount excluded under subsection (a) for such taxable year, over (ii) the amount which would be determined under such sentence for such taxable year if the taxpayer's taxable excess (as so defined) were equal to the amount excluded under subsection (a) for such taxable year.

For purposes of this paragraph, the amount excluded under subsection (a) shall be reduced by the aggregate amount of any deductions or exclusions disallowed under subsection (d)(6) with respect to such excluded amount.

911(f)(2)(A) handles a filer whose net capital gain exceeds taxable income (the "capital gain excess"): in figuring the tax under (1)(A)(i), "(i) the taxpayer's net capital gain (determined without regard to section 1(h)(11)) shall be reduced (but not below zero) by such capital gain excess, (ii) the taxpayer's qualified dividend income shall be reduced by so much of such capital gain excess as exceeds the taxpayer's net capital gain (determined without regard to section 1(h)(11) and the reduction under clause (i)), and (iii) adjusted net capital gain, unrecaptured section 1250 gain, and 28-percent rate gain shall each be determined after increasing the amount described in section 1(h)(4)(B) by such capital gain excess." 911(f)(2)(B) applies the same rules to the AMT with the taxable excess in place of taxable income, and keeps the regular tax's 0% and 15% bracket room for Form 6251 Part III.

Effective dates. Pub. L. 109-222 (TIPRA) §515(c) added 911(f); §515(d): "shall apply to taxable years beginning after December 31, 2005." Pub. L. 110-172 §4(c) rewrote it in its current form (the capital gain excess rules and "if such taxpayer has taxable income"); §4(d)(3): "The amendment made by subsection (c) shall apply to taxable years beginning after December 31, 2006." Pub. L. 113-295 §215(a) restored the (d)(6) sentence and §202(b) widened (2)(B)(ii), both as technical corrections. The earliest year the model computes the federal income tax is 2015 (2014 raises ParameterNotFoundError), so no date gate is needed.

The IRS worksheets (2025, https://www.irs.gov/pub/irs-pdf/i1040gi.pdf#page=37): Foreign Earned Income Tax Worksheet—Line 16. "If Form 1040 or 1040-SR, line 15, is zero, don't complete this worksheet." Line 1 is taxable income; line 2a the Form 2555 lines 45 and 50 amounts; line 2b "the total amount of any itemized deductions or exclusions you couldn't claim because they are related to excluded income"; line 2c = 2a − 2b, not below zero; line 3 = 1 + 2c; line 4 = tax on line 3 (the Qualified Dividends and Capital Gain Tax Worksheet or Schedule D Tax Worksheet with line 3 as its line 1); line 5 = tax on line 2c (Tax Table or Tax Computation Worksheet); line 6 = 4 − 5, not below zero. Its footnote defines the capital gain excess as "line 4 of your Qualified Dividends and Capital Gain Tax Worksheet (line 10 of your Schedule D Tax Worksheet)" less Form 1040 line 15, and makes four modifications to a second worksheet: reduce line 3 (Schedule D Tax Worksheet line 9) by the excess; reduce line 2 (line 6) by the excess not used; reduce Schedule D line 18 by the excess; enter the excess as a loss on line 16 of the Unrecaptured Section 1250 Gain Worksheet. The 2025 Form 6251 instructions (https://www.irs.gov/pub/irs-pdf/i6251.pdf#page=10) have the same worksheet for line 7, figured at the 26%/28% rates or through Part III, and (page 13) the same four modifications for an "AMT capital gain excess" (gains less Form 6251 line 6). Lines 20 and 27 of Part III "take into account your regular tax capital gain excess".

What changed

New variables (variables/gov/irs/tax/federal_income/foreign_earned_income_exclusion/), each equal to the existing amount for a filer without an exclusion:

Variable	Law	Worksheet
taxable_income_plus_section_911_exclusion	911(f)(1)(A)(i)	line 3
section_911_capital_gain_excess	911(f)(2)(A)	footnote
section_911_net_capital_gain, section_911_qualified_dividend_income	911(f)(2)(A)(i)-(ii)	modifications 1 and 2
section_911_28_percent_rate_gain, section_911_unrecaptured_section_1250_gain, section_911_adjusted_net_capital_gain	911(f)(2)(A)(iii), 1(h)(3)-(6)	modifications 3 and 4
amt_income_less_exemptions_plus_section_911_exclusion	911(f)(1)(B)(i)	Form 6251 worksheet line 3
amt_section_911_capital_gain_excess	911(f)(2)(B)(i)	Form 6251 Part III, Form 2555 (line 10 of the Schedule D Tax Worksheet less line 6)

Formulas changed:

• income_tax_main_rates: tax on line 3 less capital gains, less the tax on the excluded amount (lines 4 to 6). A shared helper, tax_at_main_rates, now runs the bracket loop for it, regular_tax_before_credits and the additional_tax_bracket reform, and keeps the income_tax_main_rates returns large negative values (−$81.7k on $8.2k taxable income) under TCJA-expiration parameters; NE/CO/OR conformity imports it into state tax #9084 clamp.
• capital_gains_excluded_from_taxable_income, capital_gains_tax: section 1(h) on line 3 with the reduced gains.
• dwks14, dwks19, regular_tax_before_credits (the Schedule D Tax Worksheet copy used as the AMT comparator): line 1 is line 3 and lines 9, 10, 13 and Schedule D line 19 are refigured for the excess (helper schedule_d_tax_worksheet_after_capital_gain_excess). The worksheet path measures the excess from worksheet line 10, as the footnote does; the section 1(h) path measures it from net capital gain, as the statute does. On a return the two are the same amount. In the model dwks10 and net_capital_gain are separate formulas that can disagree: net_capital_gain subtracts the Form 4952 election and the worksheet lines do not apply it as lines 3 to 9 do. That predates this PR and is filed as a follow-up; two YAML cases set the two amounts apart by direct input, labelled synthetic, to pin which one each path reads.
• The reduced non-dividend gain used for unrecaptured section 1250 gain is computed in place (section_911_net_capital_gain_other_than_dividends) rather than stored: a stored amount is rounded to single precision, and an earlier revision that stored it moved capital_gains_tax by up to $0.004 for 3 tax units with nothing excluded (caught by the microsimulation below; test_nothing_excluded_changes_nothing now has households with cent amounts and compares the helper with main's expression bit for bit, so it would catch that).
• amt_lower_base_tax, amt_higher_base_tax, amt_tax_including_cg: Form 6251 on line 3, Part III lines 13 to 15 after the AMT capital gain excess, lines 20 and 27 from the regular tax.
• alternative_minimum_tax: subtracts the AMT on the excluded amount (Form 6251 worksheet lines 5 and 6).
• Reform copies kept consistent: additional_tax_bracket (both variables, with the reform's own schedule for line 5), the Biden and Harris capital_gains_tax copies, and the CRFB highest_tax_rate. In the Biden reform the rates stack but the $1 million threshold is tested on taxable income without the excluded amount: the proposal tests the filer's income, which leaves out amounts excluded under section 911.
• foreign_earned_income_exclusion is relabelled "Foreign earned income exclusion" (it was "Foreign earned income ALD"; it is not subtracted in AGI).

The child tax credit's tax limit reads income_tax_before_credits on its no_salt branch (ctc_limiting_tax_liability), so it sees the stacked tax with no change; the itemization branches likewise compare stacked liabilities.

Invariants (stated and executed)

policyengine_us/tests/test_section_911_tax_stacking.py, run on a 700-household grid (four filing statuses × wages, gains and exclusions) and on Hypothesis-generated households (some itemizing), for 2018, 2022, 2025 and 2026:

1. With nothing excluded, every amount section 911(f) replaces equals the amount it replaces, bit for bit: the stacked bases, the reduced gains, and the refigured Schedule D Tax Worksheet lines 9, 10, 13 and Schedule D line 19 (test_nothing_excluded_changes_nothing, on households with 28-percent rate gain, unrecaptured section 1250 gain and itemized deductions, 2018, 2025, 2026). A household without an exclusion also gets the same results whatever other households in the batch exclude.
2. Worksheet line 3 is line 1 plus line 2c.
3. The stacked tax is never below the unstacked tax (regular tax and tax before credits).
4. The tax never falls as the excluded amount rises.
5. Zero taxable income gives zero regular tax, whatever is excluded.
6. The regular tax is at most 37% of taxable income.
7. The capital gain excess is non-negative and only a filer with an exclusion has one.

Differential test. The same file transcribes the 2025 Foreign Earned Income Tax Worksheet, Qualified Dividends and Capital Gain Tax Worksheet, Form 6251 worksheet and Part III line by line, and compares them with the model household by household. The model reaches the tax by a different route (the section 1(h) formulas), so this checks one against the other. The transcribed rate schedule matches all 8,240 cells of the 2025 Tax Table (rounded at each row's midpoint) and the Tax Computation Worksheet exactly; the full check ran outside the repo, and test_transcribed_schedule_matches_the_2025_tax_table keeps 12 Tax Table rows and 8 Tax Computation Worksheet rows in the repo. The differential and property tests leave out 28-percent rate gain and unrecaptured section 1250 gain because of the pre-existing capital_gains_tax gaps listed under "Not covered"; YAML cases cover the excess reductions of those gains.

Regression against main (run outside the repo). A 4,000-household random grid per year (2018, 2022, 2025, 2026; wages, self-employment income, long- and short-term gains, collectibles, unrecaptured section 1250 gain, dividends, interest, itemized deductions; all four filing statuses), plus the additional bracket, Biden and Harris capital gains reforms in 2025 and 2026, with no exclusion: all 234 output arrays are bitwise identical on main and this branch. (In the additional bracket reform, 16 arrays are NaN for every household on both, at the same positions; that predates this PR.) Scripts: grid.py / grid_diff.py in the evidence folder.

Tests

• YAML unit tests for each new variable and for income_tax_main_rates, capital_gains_excluded_from_taxable_income, capital_gains_tax, dwks14, dwks19, regular_tax_before_credits, the AMT base taxes, amt_tax_including_cg and alternative_minimum_tax, with worksheet line comments.
• Household cases (foreign_earned_income_exclusion/integration.yaml): head of household in the 12% bracket where the Tax Table is exact (line 4 $6,869, line 5 $3,263, line 6 $3,606, against $3,266 unstacked), the review example, joint filers on the Tax Computation Worksheet, gains with and without a capital gain excess, an excess that reaches qualified dividends, zero taxable income, and an AMT case with an AMT capital gain excess.
• credits/ctc/integration.yaml: a 2025 head of household with two children, $60,000 of wages and $40,000 excluded (positive taxable income). The CTC limit sees the stacked tax ($5,517.50), which covers the whole $4,400 credit, so income tax is $1,117.50 and nothing is refundable with or without the section 24(d)(3) bar of Deny the refundable CTC and the EITC to section 911 filers (26 U.S.C. 24(d)(3), 32(c)(1)(C), 6012(c)) #9750. Deny the refundable CTC and the EITC to section 911 filers (26 U.S.C. 24(d)(3), 32(c)(1)(C), 6012(c)) #9750's own household case uses zero taxable income, where stacking cannot matter; the new case sits at the top of the file so the two PRs do not conflict (checked with git merge-tree).

Microsimulation

Default dataset (populace_us_2024.h5@populace-us-2024-spm-20260909), 2026, main (615a0f2) against this branch, one run each, compared per tax unit (79,729 tax units, 165.4 million weighted). The dataset has no foreign_earned_income_exclusion column (no tax unit has a positive value), so the expected impact is $0, and it is: all 18 outputs compared are bitwise identical on every tax unit (taxable_income, capital_gains_excluded_from_taxable_income, income_tax_main_rates, capital_gains_tax, dwks14, dwks19, regular_tax_before_credits, amt_income_less_exemptions, amt_base_tax, amt_tax_including_cg, alternative_minimum_tax, income_tax_before_credits, non_refundable_ctc, refundable_ctc, income_tax_capped_non_refundable_credits, income_tax, state_income_tax, and the exclusion itself). Weighted federal income tax: $2,571.09bn on both. Peak memory 13.8 GB (main) and 15.5 GB (branch) on policyengine-core 3.32.12. The change takes effect for Form 2555 filers once a dataset carries the exclusion.

Other readers of the changed amounts

• Arizona property tax credit. az_property_tax_credit_income adds capital_gains_excluded_from_taxable_income, which for a Form 2555 filer is now figured on the stacked base. For a filer whose gains exceed taxable income this lowers that amount. Run on both: a single 2025 Arizona filer with $10,000 of long-term gains and $40,000 excluded has capital_gains_excluded_from_taxable_income $10,000 on main and $0 here, so az_property_tax_credit_income falls from $20,000 to $10,000 (on main the gains were counted twice, once in AGI). Arizona's use of this variable was already wrong: ARS 43-1072 counts "capital gains excluded from adjusted gross income", while the variable is gains taxed at the capital gains rates, which are already in AGI. That is filed as a follow-up rather than patched here.
• Form 6251 line 18 for separate filers (the existing bug below) now applies to more filers: line 17 includes the excluded amount, so a separate filer with gains and a large exclusion reaches the misapplied breakpoint more often. Run here: a 2025 separate filer with $100,000 of qualified dividends and $200,000 excluded has Form 6251 line 12 of $231,500 and line 17 of $200,000. The model's line 38 is $56,725 where the form gives $58,334 (line 18 at the separate filer's breakpoint, $53,609 rather than $52,000), so worksheet line 6 is $3,116 rather than $4,725. The regular tax ($12,637.50) is higher either way, so the AMT is $0 in both.

Not covered

• Line 2b (itemized deductions disallowed because they relate to excluded income) and the Form 2555 line 50 housing deduction have no separate inputs; foreign_earned_income_exclusion stands for line 2c.
• Schedule J and Form 8615 are not modeled, so there is no interaction to handle.
• Three gaps in the model's capital gains and AMT computations that predate this PR and are not about section 911 showed up in the differential test: capital_gains_tax taxes 28-percent rate gain in full even beyond taxable income (1(h)(1)(F)), uses the zero-rate amount where 1(h)(1)(A)(ii)(I) says "taxed at a rate below 25 percent", and omits the 1(h)(1) cap at the ordinary-rate tax (worksheet line 25); and Form 6251 Part III line 18 ignores the separate-filer breakpoint. Each is filed as a follow-up. The tests here stay out of those cases and say so. Related and also predating this PR: Form 6251 line 27 reads dwks14 where the form asks for Schedule D Tax Worksheet line 21, which differs for filers with 25% or 28% gains above the 24% bracket (covered by the capital gains follow-up).

axiom: TheAxiomFoundation/rulespec-us#1478 queued (us:statutes/26/911/f; rulespec-us has no 911(f) module, and its §55 module fails closed for any section 911 exclusion)

🤖 Generated with Claude Code

[MaxGhenis]

Merged by the US + core hub at head 8f283a5aa3ff4bd923514a805e856204a5973e37 (squash, --admin --match-head-commit). The only block was the required approving review, which no one else can give on Max's PRs.

Gates:

• Model review: delta round 5 (GPT-6.1 Sol) approved e962c91f5a with no findings.
• Main merge: the branch was 51 commits behind main, so the hub merged main into it with update-branch, giving 8f283a5aa3. The PR's own diff, uv.lock included, is byte-identical before and after. An independent Opus 5.5 review of the merge approved 8f283a5aa3. It checked that the delta is only main's changes, that pyproject and uv.lock are consistent, and that none of the 11 IRS commits on main since 615a0f2d97 affects the PR. It also checked the PR together with Order the residential clean energy credit after the CTC, following Schedule 8812 Credit Limit Worksheets A and B #9742 (merged just before this): 112 + 11 YAML cases pass.
• CI: gh pr checks exits 0. All 35 check runs on 8f283a5aa3 succeeded, including the Hypothesis property tests in the Rest job.
• State: MERGEABLE, not a draft, no CHANGES_REQUESTED review.
• Impact: the PR body has the real-microsimulation result, $0 on the default dataset, which has no foreign earned income exclusion.
• Judgment: a bug fix to 26 U.S.C. 911(f) stacking, with nothing needing Max's judgment.

Follow-up noted by the reviewer, not in this PR's scope: niit_magi does not add back the section 911 exclusion.