# 5. Results

;; 5.01
Table 3 and Figure 1 report the paper's central object: average effective federal income tax rates by income percentile group, measured and corrected, for tax year 2021 at the anchor rate of 38.0 percent. The corrections are +{{N:top1_delta_pp_headline:.2f}} percentage points for the 99th to 99.9th percentile (from {{N:etr_top1_baseline_pct}} to {{N:etr_top1_corrected_pct}} percent), +{{N:top01_delta_pp_headline:.2f}} for the top 0.1 percent, +{{N:p95_99_delta_pp:.2f}} for the 95th to 99th, and +{{N:p90_95_delta_pp:.2f}} for the 90th to 95th. Below the 90th percentile no group moves by more than a tenth of a point. For all tax units together, the measured rate rises from {{N:etr_all_baseline_pct}} to {{N:etr_all_corrected_pct}} percent.{{FN: Table entries are rounded from unrounded values and corrections are computed before rounding, so a displayed pair can differ from the displayed change by a hundredth. The marginal-rate column is a unit-weighted group mean; the text below reports dollar-weighted counterparts, which differ instructively.}}

@TABLE:percentiles| **Table 3. Effective federal income tax rates by income group, measured and corrected, tax year 2021.** Tax units ranked by expanded income. The correction applies τ* = 38.0 percent to reported tax-exempt interest; Table 4 reports the variants. Source: authors' calculations from the SCF, TAXSIM, and the sources described in Section 4.

@FIGURE:fig1_percentiles.png| **Figure 1. The correction is confined to the top of the distribution.** Left: measured and corrected average effective federal income tax rates by income group. Right: the correction in percentage points. Tax year 2021, τ* = 38.0 percent.

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Table 3's marginal-rate column reports the statutory side of the decomposition, and it rises exactly as the burden side requires: the average marginal rate on interest climbs from single digits in the bottom quintile to 27.5 percent in the 80th to 90th percentile group and just over 40 percent in the top percentile, where the 37 percent bracket and the net investment income tax bind together. The measured column shows two things. The top 0.1 percent's measured effective rate sits below the 99th to 99.9th percentile's — the familiar composition effect of preferentially taxed capital gains at the very top — and the municipal correction, similar in size for both groups, does not close that gap. And the corrected column preserves the schedule's shape everywhere: the correction changes levels at the top, not orderings.

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The geography of the correction follows the geography of the asset. Participation in tax-exempt interest runs from {{N:units_with_munis_pct:.1f}} percent of all tax units to {{N:p99_999_share_with_munis_pct}} percent of the 99th to 99.9th percentile and {{N:top01_share_with_munis_pct}} percent of the top 0.1 percent. Municipal income relative to total income peaks lower, in the 95th to 99th percentile group, which holds ${{N:p95_99_muni_income_bn:.0f}} billion of the ${{N:agg_taxexempt_interest_bn}} billion total; that is why the largest rate correction lands there rather than at the very top, where portfolios tilt toward equity and pass-through business income.

;; 5.03
Tax year 2021 is a low baseline year, and the worry is quantitative rather than structural. Pandemic-era refundable credits pushed measured rates in the bottom half of the distribution to unusual lows — the bottom quintile's measured rate is deeply negative. The correction is not algebraically independent of them: it equals I(Y − T)/[Y(Y + I)], which contains remitted tax T, and the credits move T. But it is numerically negligible wherever they bind, because I is negligible there: the largest movement below the 60th percentile is 0.02 points. The credits distort the baseline schedule the correction is applied to, not the correction.

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Figure 2 reports the aggregate under each construction, stated with its base. Grossing up the survey's reported tax-exempt interest at the identified rate gives ${{N:agg_implicit_tax_2021_bn:.0f}} billion of unrecorded burden for tax year 2021; scaling to the administrative income base gives ${{N:agg_implicit_tax_2021_soi_scaled_bn:.0f}} billion; the federal-component rate gives ${{N:fed_component_agg_2021_bn}} billion on the survey base. At current stocks and yields, applying the identified rate to the ten-year Treasury and the Financial Accounts household-channel stock gives ${{N:burden_current_anchored_bn}} billion a year, and the observed ten-year spread gives ${{N:burden_current_spread_bn}} billion. The anchored construction deliberately crosses the short-end rate with the ten-year yield — an upper-bound pairing, labeled as such. At 2021 market terms the market-value construction gives ${{N:burden_mv_2021_bn}} billion — a different estimand, not the low end of a bracket: the give-up on the 2021 stock at 2021 yields, against the coupon-flow measure's give-up on the income actually received (Section 4). For scale: calendar-2021 federal personal current taxes were ${{N:cy2021_personal_tax_receipts_bn:,}} billion, so the 2021 coupon-flow burden is {{N:burden_pct_of_cy2021_receipts}} percent of that, and roughly twice Treasury's ${{N:te_muni_bn:.0f}} billion scored expenditure for public-purpose municipal interest — a comparison of adjacent but not identical bases, since reported tax-exempt interest includes private-activity bonds whose expenditures Treasury scores separately.{{FN: The tax expenditure and the implicit tax measure different things: the expenditure scores forgone federal revenue given observed (depressed) yields, while the implicit tax measures the burden holders bear through those yields. They coincide only if the marginal and average holder's rates coincide.}}

@FIGURE:fig2_aggregate.png| **Figure 2. The aggregate unrecorded burden under each construction.** Sources and constructions as described in the text.

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The rent decomposition yields the paper's most unexpected finding, and it survived two corrections that each moved it toward the same answer. The holder's counterfactual rate matters as much as the market's: a unit with a large municipal position and modest ordinary income shows a low marginal rate precisely because the munis shelter its taxable income, so the local rate on a small increment understates what the taxable twin would face. We therefore compute each holding unit's counterfactual rate two ways — the local rate on a $1,000 increment, and the average rate on the full grossed-up block y/(1 − τ*), from a third TAXSIM run. The block-average federal rate, dollar-weighted, is {{N:blockavg_fed_dollarwtd_pct}} percent against the local rate's {{N:fed_mtr_dollarwtd_pct}}; the gap is the sheltering effect, concentrated exactly where the portfolios are largest (in the 95th to 99th percentile group the unit-weighted local mean is {{N:p95_99_mtr_unitwtd_pct}} percent but the dollar-weighted local rate is {{N:p95_99_mtr_dollarwtd_pct}}). Under the block-average rates and consistent tax-basis pairings, the aggregate 2021 rent at the anchor is approximately zero: plus ${{N:rent_blockavg_combined_bn:.1f}} billion on the expected-state pairing, minus ${{N:rent_blockavg_fedcap_bn_abs:.1f}} billion on the federal-component pairing, plus ${{N:rent_blockavg_hightax_bn:.0f}} billion only at the deliberately high maximum-state bound. Under the local rates the same three pairings run minus ${{N:rent_fedcap_pairing_bn_abs:.1f}}, minus ${{N:rent_combined_pairing_bn_abs:.1f}}, and plus ${{N:rent_hightax_pairing_bn:.1f}} billion, so the six consistent constructions together span minus ${{N:rent_fedcap_pairing_bn_abs:.1f}} to plus ${{N:rent_blockavg_hightax_bn:.1f}} billion. Set against ${{N:agg_implicit_tax_2021_bn:.0f}} billion of burden, every one of them is small, and the two block-average pairings — the paper's preferred construction, because the block average is the rate a holder switching her whole position would face — sit within a billion dollars of zero. Measured at the short-end rate, the exemption delivered its average 2021 holder little or no aggregate windfall: the market priced the average municipal bond dollar closely.

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The distribution behind the average carries more information than the average. {{N:holders_mtr_le0_wtd_pct}} percent of municipal-holding tax units, weighted, have a measured federal marginal rate on interest of zero or below: on the federal margin alone, the exemption is worth nothing to them. Strict dominance is a stronger claim than the data support — it would need a taxable alternative matched on maturity, credit, liquidity and call terms, and the holder's full tax treatment including the state component the public survey does not carry, any of which can reverse the comparison. What the measure does establish is heterogeneity in measured federal interest margins, and a sensitivity in the aggregate. This is the modern echo of what Feenberg and Poterba (1991) found in the first tax-return data on tax-exempt interest. Candidate explanations are the familiar ones — advisor defaults, state-tax motives a federal margin misses, liquidity preferences, inertia after income falls — and the SCF cannot distinguish them. These units hold {{N:dominated_interest_share_pct:.0f}} percent of the survey's tax-exempt interest, and excluding them entirely lowers the 2021 aggregate from ${{N:agg_implicit_tax_2021_bn:.0f}} billion to ${{N:agg_burden_excl_dominated_bn:.0f}} billion — a real sensitivity, because the burden construction charges the market rate to every municipal dollar whatever the holder's own bracket. What the fact establishes is that the exemption's incidence within the holder population is far from uniform.

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The anchor sits between the two state constructions. The dollar-weighted holder's combined local rate is {{N:combined_mtr_dollarwtd_pct}} percent at the expected state rate and {{N:combined_hightax_pct}} at the maximum-state assignment; the block-average counterparts run about six points higher. The published anchor of 38.0 falls between them — the identification's marginal investor and the survey's largest holders occupy the same neighborhood of combined rates, which is what near-zero aggregate rent requires. The claim is deliberately modest. Only the maximum-state figure is a bound in the literal sense, since no holder can face more than her own state's top rate; the population-weighted figure is an expectation under an assumption about where holders live, not a floor. What the pair establishes is consistency, not confirmation.

;; 5.08
Rent flips sign across the curve, and that reframes the oldest question about the exemption. At the ten-year implied rate the top groups' rent is roughly zero; at the twenty- and thirty-year rates it is large and positive (the arithmetic follows from Table 4's rates and Section 2's formulas). The maturity structure of the implied rate is the rent structure of the exemption: short-maturity holders bear nearly their full statutory rate as implicit tax, while long-maturity holders keep most of theirs as windfall. The household data contain no maturity composition, so the paper reports the rates side by side rather than choosing among them — and the spread between them is itself the answer to whether the exemption is a windfall to the rich: it depends on which maturities they hold, a fact no distribution table has ever recorded either way. The rows are not a range containing the truth; each is what the rent would be if holders faced that rate. [WRDS robustness to be added: holdings-weighted maturity composition from the MSRB transaction feed.]

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Figure 3's upper panel puts the naive implied rate against the top statutory rate on interest income from 1953 forward. The naive rate never approaches the statutory line: mid-century top rates of 70 to 91 percent coexisted with implied rates of 10 to 25 percent. That gap is the historical form of the windfall critique, and the figure is the case for taking the critique seriously — but the gap is not a measurement of historical rent. Rent is the distance between a holder's statutory rate and an identified market rate on a consistent basis, and the naive ratio is not one: it bundles credit, liquidity, call, maturity and benchmark effects with tax, which is the whole reason Section 3 rejects it for the modern period. No identified series exists before 2001, so the mid-century rent is unmeasured rather than large. The post-2008 sign flip described in Section 3 is visible at the right edge, and the spliced AA-curve segment from 2017 adds the March 2020 dislocation. The Longstaff correction, marked at the short end, is what an identified reading looks like against this backdrop.

@FIGURE:fig3_history.png| **Figure 3. Seven decades of the naive reading, and what identification changes.** Upper panel: the naive implied rate (Bond Buyer 20-Bond over 20-year Treasury; AA curve splice from 2017, dashed) against the top statutory rate on interest income, with Longstaff's short-end identification marked. Lower panel: the implied burden series — the naive spread times the household-channel stock (the pathological series the paper rejects), and the anchored construction, τ* = 38.0 percent times the ten-year Treasury times the stock, from 2001.

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The lower panel plots two burden series and does not compare them across eras. The naive-spread series repeats the upper panel's pathology in dollar form. The anchored series — the identified rate times the ten-year Treasury times the household-channel stock, the same construction as Figure 2 — runs from ${{N:burden_anchored_2001_bn}} billion in 2001 to ${{N:burden_current_anchored_bn}} billion today. What the data do support historically is a statement about the base: household-channel municipal holdings grew from {{N:stock_pct_gdp_1950s}} percent of GDP in the 1950s to a peak of {{N:stock_pct_gdp_peak}} percent in {{N:stock_pct_gdp_peak_year}}, so whatever the true implicit tax rate was in the high-statutory-rate decades, the stock it applied to was several times smaller relative to the economy.

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Table 4 collects the robustness grid. Across the τ* variants — 38.0 published anchor, 41.6 working-paper version, 35.6 at the 2021 ten-year, 35.0 federal-component, {{N:tau10_bval_pct}} at today's ten-year, 29.4 at Longstaff's forward rate, {{N:tau20_bval_pct}} at twenty years, and {{N:tau30_bval_pct}} at thirty — the top-percentile correction runs from {{N:grid_min_top1_delta_pp:.2f}} to {{N:wp_row_top1_delta_pp:.2f}} points and the 2021 aggregate from ${{N:grid_min_agg_2021_bn}} billion to ${{N:wp_row_agg_2021_bn}} billion; at the published anchor the pair is {{N:top1_delta_pp_headline:.2f}} points and ${{N:agg_implicit_tax_2021_bn:.0f}} billion. The table's second pair of columns restates both quantities on the administrative base, which divides each by the survey-to-SOI ratio of {{N:scf_soi_ratio}}: the correction at the published anchor becomes {{N:top1_delta_pp_soi_scaled:.2f}} points and the aggregate ${{N:agg_implicit_tax_2021_soi_scaled_bn:.0f}} billion, and across the grid the correction runs {{N:top1_delta_pp_grid_min_soi:.2f}} to {{N:top1_delta_pp_grid_max_soi:.2f}} points. Appendix A3 gives the rest of the corrected schedule on that base and the near-linearity that makes the rescaling pass through. The state add-on moves the rent decomposition, not the federal correction. What survives every row is the correction's sign and its concentration above the 90th percentile; what the rows move is its size, a maturity call the data cannot yet settle.

@TABLE:robustness| **Table 4. The correction under each τ* variant, on both income bases.** Correction to the 99th-to-99.9th percentile in percentage points and the 2021 aggregate, each reported on the survey base and on the administrative base — the survey rescaled so its tax-exempt interest aggregate matches IRS SOI. Ranks are the survey's on both bases (Appendix A3). Constructions as in Sections 2 and 4. Source: authors' calculations as in Table 3.

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The paper stops short of three claims. It computes no Kakwani or Suits index: the corrected schedule is the primitive, and any index built on it inherits the correction mechanically. It makes no welfare statement and no reform counterfactual: those need incidence, which is Section 7's subject. And it attaches only range-style uncertainty to the corrections, because the ranges show where the uncertainty lives: across the five SCF implicates the top-percentile correction runs {{N:top1_delta_imp_min:.2f}} to {{N:top1_delta_imp_max:.2f}} points, and moving τ* one standard deviation of Longstaff's estimate in either direction moves it {{N:top1_delta_tau_lo:.2f}} to {{N:top1_delta_tau_hi:.2f}} — both narrow next to the 0.09-to-0.39 span of the τ* grid itself. The rate choice dominates the sampling error; a full replicate-weight treatment belongs to the revision.
