# 7. The incidence question

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Everything to this point is partial equilibrium, and the assumption should be stated as an assumption. The correction takes observed prices — observed municipal yields, observed taxable yields, the observed gap — and reallocates measured burden at those prices. It makes no claim about what yields would be in a different tax system, and it needs none: the implicit tax is a burden current law imposes and current prices reveal. What the general-equilibrium question governs is not the measurement but its interpretation — who ultimately bears the burden, and who collects it.

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Who collects is the easy half. The implicit tax is real revenue: state and local issuers collect it as lower borrowing costs on roughly ${{N:z1_muni_total_bn:,}} billion of debt. The federal distribution table records neither side of the transaction — not the levy on the holder, not the receipt by the issuer. Galper, Rosenberg, Rueben, and Toder (2013) distributed the receipt side: under the traditional allocation the top 1 percent receive 57 percent of the exemption's benefit, and their capital-market simulation shifts part of it to issuers; this paper's correction is the levy side of the same transaction. Together they describe a tax system operating entirely off the federal books.

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The rent term connects the correction to the oldest efficiency critique of the exemption. Gordon and Slemrod (1983) modeled the exemption as subsidizing municipal borrowing through interest-rate adjustment; the inframarginal holder's rent is the leakage in that mechanism — the part of the federal revenue cost that reaches neither the issuer nor any public purpose. The decomposition prices that leakage at the household level: approximately zero at the short end, most of the statutory rate at the long end (Section 5). The efficiency critique, like the windfall critique, turns out to be a statement about maturity.

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The equilibrium behind the intuition has a name. Miller (1977) described the capital-market equilibrium in which pre-tax interest rates gross up until the marginal taxable investor is indifferent between taxable and tax-exempt returns (cited at claim level; the article is to be obtained). In that world, every fully taxed lender is compensated for her taxes through the grossed-up rate; the tax on interest is borne by borrowers; and tax-exempt lenders — endowments, pension funds, foreign official institutions — collect the gross-up as pure rent. The question at this project's origin — whether pre-tax interest rates are higher because of taxes, with the difference accruing to untaxed institutions while borrowers bear it — is the Miller equilibrium stated in one sentence.

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The strongest empirical statement in that direction is aggregate. Gordon and Slemrod (1988), on 1983 data, estimated that the United States collected approximately zero net revenue from taxing capital income once arbitrage across brackets and instruments is netted out: high-bracket taxpayers deduct interest at high rates while low-bracket and exempt lenders report it at low ones. Their counterfactuals raised revenue "mainly at the expense of those in the highest tax brackets." Revisiting the question on 1995 data, Gordon, Kalambokidis, and Slemrod (2004) found the net tax on capital income had turned positive — roughly $108 billion — so the near-zero result describes the 1980s tax system, not a constant of nature. To whatever extent capital income taxation shuffles rather than collects, distribution tables built on remittance misallocate who pays for it — the aggregate form of this paper's percentile-level point — and the shuffle was largest exactly when statutory rates were highest.

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The open-economy literature points the opposite way, and the two are not reconcilable by assumption. What world capital markets pin is the after-tax return investors require, not the domestic pre-tax rate (Gordon 1986; Razin and Sadka 1991). A source-based capital income tax therefore drives capital out until the domestic pre-tax marginal return has risen enough to restore that required return: the pre-tax rate moves, and the burden comes to rest on the immobile factors whose returns fall — which is why Gordon's own account has countries that tax capital more heavily paying higher real interest rates, and why Razin and Sadka find the optimal tax on perfectly mobile capital vanishing. The consequence for this paper is narrower than a fixed rate level would give. There is still no economy-wide transfer to tax-exempt lenders of the Miller kind, because the pre-tax rate here rises to compensate mobile capital rather than to compensate taxed domestic lenders; but the exemption's general-equilibrium footprint is not confined to relative prices either, and this stance does not by itself rule a gross-up out. Fullerton and Rogers (1991; 1993) remain the most serious attempt to trace tax burdens through factor prices in general equilibrium, over lifetimes rather than years, and their machinery would be needed to adjudicate; nothing lighter will.

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The direct evidence that would choose between the stories barely exists. The closest sustained attempt is the tax-adjusted Fisher-effect literature — Darby (1975) and Feldstein (1976) derived the gross-up that nominal rates should exhibit, and the empirical work that followed largely failed to find it (Summers 1983) — results whose negativity supports this section's agnosticism. Event studies of tax changes on equity prices exist in quantity; clean estimates of tax capitalization into the level of pre-tax interest rates do not. We searched for a credible design for identifying the interest-rate gross-up — both to cite and to propose — and found none; the central empirical question of this section is open.

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One implication of the Miller story has never been quantified by anyone, and this paper does not quantify it either. If pre-tax rates embed any gross-up, the tax-exempt sector collects it on its entire taxable fixed-income portfolio — every endowment, every pension fund, every foreign official holder of Treasuries and corporates. Measuring the transfer requires the sector's taxable holdings by class, an equilibrium gross-up per incidence stance, and a defended stance. Each piece is named in Section 8's design; none is delivered here.

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What each stance does to this paper's numbers can be stated exactly. Under open-economy pinning of the required after-tax return, the correction stands as measured — the yields in it are observed yields — and the ultimate burden lands on immobile domestic factors rather than on the holder. Under a full Miller gross-up, the correction stands as measured — prices are still observed prices — and a second, institution-side table is missing: the rent collected by tax-exempt lenders, which no framework records either. Under neither stance is the remittance convention's zero the right entry for the municipal holder. The incidence stances disagree about where the burden ultimately comes to rest, not about whether the holder's measured rate is wrong.

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The wedge between remitted and borne at observed prices is invariant to the incidence stance. What it ultimately means for the distribution of burdens awaits evidence that does not yet exist, and the paper leaves the question open rather than assuming it closed.
