# 2. The remittance convention and the decomposition

;; 2.01
Every maintained distributional framework in the United States measures tax burdens by taxes remitted. Remittance and burden are different objects — the point is old and general (Slemrod 2008) (verify) — but for most income the difference is harmless in the respect that matters here: the wage earner's remitted liability is levied on income the tax system did not first depress, so recording it captures the direct burden even though incidence may shift it to others. (Withholding is a third object again — a provisional payment reconciled at filing — and it is the annual liability, not the withholding, that these frameworks and this paper use.) For income from an asset whose tax preference is capitalized into its price, remittance and burden come apart at the source: the price itself has moved. The preference changes the pre-tax income the asset generates, so a table that starts from observed income and remitted tax records a burden of zero on a holder who is in fact paying every year, in forgone yield, for the privilege of the exemption.

;; 2.02
Table 1 documents the convention across the six frameworks that produce the distribution tables policymakers use. The Congressional Budget Office includes tax-exempt interest in its capital income concept and records no tax against it (Congressional Budget Office 2024). Treasury's Office of Tax Analysis includes it in cash income on the same terms (Cronin 2022). The Joint Committee on Taxation includes it in expanded income (Joint Committee on Taxation 2013) (verify). Auten and Splinter (2024) include it in pre-tax income, as do Piketty, Saez, and Zucman (2018) in distributional national accounts; Splinter (2020) carries the same convention into progressivity indices, and the Tax Policy Center's microsimulation does the same in expanded cash income. None makes a capitalization adjustment. The uniformity is the finding: this is a shared convention, not an oversight by one agency.

@TABLE:frameworks| **Table 1. How the maintained distributional frameworks treat tax-exempt interest.** Sources: the methodology documents cited in the text, reviewed for this paper.

;; 2.03
The correction rests on one definition and one identity. For municipal and taxable bonds of comparable maturity and risk, define the market-implied tax rate τ* = 1 − r_m/r_t, where r_m and r_t are the tax-exempt and taxable yields. A holder whose statutory marginal rate on interest is τi and who could hold either bond earns the same after-tax return from the municipal bond as from a taxable bond taxed at rate τ*. Against a risk- and maturity-matched taxable twin, a voluntary holder must satisfy τi ≥ τ*, and her statutory rate splits into two parts:

@DISPLAY:| τi = τ* + (τi − τ*).

;; 2.03 (continued — same contract paragraph)
The first part is a burden: every holder gives up τ* of the taxable yield, whoever she is. The second part is an inframarginal rent: a holder whose own rate exceeds the market-clearing rate keeps the difference, a windfall priced by some other investor's lower bracket. The inequality's conditions matter for what follows. Real holders do not face matched twins: their bonds differ from Treasuries in maturity and risk, their tax rates include state components a federal calculation misses, and some hold munis for reasons other than tax. Measured violations of τi ≥ τ* are therefore diagnostic rather than paradoxical, and Section 5 reads them that way. One further objection belongs here: a holder whose rate sits below the market's could avoid the wedge by selling, so is an avoidable wedge a tax borne? It differs from an ordinary dominated portfolio choice in the respect that matters for burden accounting: the wedge is created by the tax law, and it is collected by a government — the issuer's lower borrowing cost is revenue, whoever remits it. Section 7 returns to who collects.

;; 2.04
The operational form works from observed income. A holder who reports tax-exempt interest y would have needed pre-tax income y/(1 − τ*) to net the same amount from a taxable bond taxed at the market rate. The implicit tax is the difference, y·τ*/(1 − τ*), and the corrected effective rate adds it to both sides of the ratio:

@DISPLAY:| ETR corrected = (T + y·τ*/(1 − τ*)) / (Y + y·τ*/(1 − τ*)),

;; 2.04 (continued)
where T is remitted federal income tax and Y is the household's expanded income with tax-exempt interest counted at the observed yield. After-tax income is unchanged by the correction: the household keeps Y − T under either convention, because the implicit tax added to the numerator is exactly the pre-tax income added to the denominator: the entire measurement error sits in the rate, not the level.{{FN: The algebra is in Appendix A1.}}

;; 2.04b
A worked example fixes magnitudes, with the rates it pairs stated each time. A household reporting $100,000 of municipal interest, corrected at the federal-component rate of 35 percent, has a pre-tax-equivalent income of $153,846 and an implicit tax of $53,846; at the 2021 federal top rate on interest of 40.8 percent, its rent is $8,923. The same income at today's thirty-year implied rate of 14.5 percent carries an implicit tax of $16,959 and a rent of $30,760. And against the full combined anchor of 38.0 percent, a holder whose combined rate matches the dollar-weighted average of 32.4 percent pays more through the yield than the statute would have charged: rent of minus $9,032 — the diagnostic case Section 5 measures in the population, where it turns on how the counterfactual rate is computed. The same contrast runs through everything that follows: at the short end the exemption is all burden and no windfall; at the long end it is mostly windfall.

;; 2.04c
What counts as burden needs one more sentence, because the municipal market since 2008 makes it easy to get wrong. The burden is the tax component of the yield give-up. In stretches where municipal bonds out-yield Treasuries, the extra yield compensates credit and liquidity risk that the holder actually bears; compensation for risk is not taxable-equivalent income, and a negative naive spread is not a negative burden. It is contamination, and stripping it out is precisely what the identification in Section 3 is for.

;; 2.05
Rates are what progressivity is measured on: average-rate schedules directly, and any index or top-share claim built on such a schedule inherits the convention with it.

;; 2.06
The convention errs in both directions at once, which is why the decomposition matters. Recording zero tax understates the burden at the top: the system is more progressive on the municipal margin than the tables say. Recording nothing about the rent understates what the exemption gives away to holders whose brackets exceed the market rate. A paper that reported only the first would read as a brief for the proposition that the rich pay more than you think; one that reported only the second, as a brief against the exemption. Reporting both, by percentile, is measurement. Which part dominates is an empirical question about τ*, and Section 5 shows the answer depends on maturity.

;; 2.07
The idea has a lineage that makes its absence from the tables harder to explain. Galper and Toder (1984) built a "full effective tax rate" against the return available absent the preference and computed illustrative households. Fullerton (1984) cataloged the competing effective-tax-rate concepts and insisted the choice follow the question being asked. Scholes and Wolfson (1992) systematized implicit taxes at the level of firms and asset classes, and Williams (2002) models the multi-clientele equilibrium that keeps the market-clearing implicit rate below the top statutory rate — the theoretical face of this paper's rent term. What never happened, on the evidence of the methodology documents in Table 1 and the searches behind this paper, is the carry-through to an economy-wide distribution table.

;; 2.08
Saez and Zucman (2024) give the convention its best defense, and the disagreement is narrower than it looks. Their argument: distributional analysis should allocate taxes actually paid at observed incomes, because counterfactual gross-ups import incidence assumptions and blur what a reform would collect. For scoring reforms, we agree. But progressivity statements are burden statements about current law, and their own municipal litmus test concedes the point on which this paper rests: current-tax analysis, they write, "captures that the pre-tax incomes of the owners of munis are depressed, although it does not single out taxes as the culprit." Measurement of who bears burdens needs the culprit. The implicit tax is a burden the current law imposes and current prices reveal; assigning it requires no counterfactual behavior, only the market's own rate.

;; 2.09
The correction accordingly needs three observables and nothing else: holdings or income from the asset, statutory rates household by household, and τ*. The first two are routine. The third is where casual treatments fail, and the next section is about getting it right.

;; 2.10
One scope note belongs before the identification. The schedule this paper corrects is the federal individual income tax schedule. The market rate τ* that the correction applies, however, is what the market charges, and Section 3 argues that rate is best read as embedding state as well as federal tax. The two constructions that follow from that tension — correcting the federal schedule with the full market rate, or with its federal component only — are both computed, both reported, and named wherever they appear.
